From 41557a15096e0dcee45de23842f468dadc389242 Mon Sep 17 00:00:00 2001 From: Simon Cruanes Date: Tue, 16 Aug 2016 17:20:48 +0200 Subject: [PATCH 01/25] wip: make SMT great again --- .merlin | 6 +- META | 23 ++ Makefile | 36 +- _tags | 6 +- src/example/cc.ml | 99 ------ src/example/cc.mli | 18 - src/example/sig.mli | 13 - src/main.ml | 9 +- src/msat.mlpack | 13 +- src/msat.odocl | 8 +- src/msat_sat.mlpack | 2 + src/msat_sat.odocl | 3 + src/msat_smt.mlpack | 12 + src/msat_smt.odocl | 17 + src/{example => sat}/sat.ml | 2 + src/{example => sat}/sat.mli | 2 + src/smt/ID.ml | 39 +++ src/smt/ID.mli | 25 ++ src/smt/cc.ml | 517 +++++++++++++++++++++++++++++ src/smt/cc.mli | 37 +++ src/{example => smt}/cnf.ml | 2 + src/{example => smt}/cnf.mli | 2 + src/smt/explanation.ml | 68 ++++ src/smt/explanation.mli | 39 +++ src/{example => smt}/expr.ml | 57 ++-- src/{example => smt}/expr.mli | 29 +- src/smt/literal.ml | 184 ++++++++++ src/smt/literal.mli | 62 ++++ src/{example => smt}/mcsat.ml | 2 + src/{example => smt}/smt.ml | 0 src/{example => smt}/smt.mli | 0 src/smt/symbols.ml | 62 ++++ src/smt/symbols.mli | 33 ++ src/smt/term.ml | 100 ++++++ src/smt/term.mli | 45 +++ src/smt/ty.ml | 60 ++++ src/smt/ty.mli | 29 ++ src/smt/uf.ml | 381 +++++++++++++++++++++ src/smt/uf.mli | 78 +++++ src/{example => smt}/unionfind.ml | 11 +- src/{example => smt}/unionfind.mli | 7 +- src/util/hashcons.ml | 28 ++ 42 files changed, 1968 insertions(+), 198 deletions(-) delete mode 100644 src/example/cc.ml delete mode 100644 src/example/cc.mli delete mode 100644 src/example/sig.mli create mode 100644 src/msat_sat.mlpack create mode 100644 src/msat_sat.odocl create mode 100644 src/msat_smt.mlpack create mode 100644 src/msat_smt.odocl rename src/{example => sat}/sat.ml (99%) rename src/{example => sat}/sat.mli (99%) create mode 100644 src/smt/ID.ml create mode 100644 src/smt/ID.mli create mode 100644 src/smt/cc.ml create mode 100644 src/smt/cc.mli rename src/{example => smt}/cnf.ml (93%) rename src/{example => smt}/cnf.mli (94%) create mode 100644 src/smt/explanation.ml create mode 100644 src/smt/explanation.mli rename src/{example => smt}/expr.ml (50%) rename src/{example => smt}/expr.mli (54%) create mode 100644 src/smt/literal.ml create mode 100644 src/smt/literal.mli rename src/{example => smt}/mcsat.ml (99%) rename src/{example => smt}/smt.ml (100%) rename src/{example => smt}/smt.mli (100%) create mode 100644 src/smt/symbols.ml create mode 100644 src/smt/symbols.mli create mode 100644 src/smt/term.ml create mode 100644 src/smt/term.mli create mode 100644 src/smt/ty.ml create mode 100644 src/smt/ty.mli create mode 100644 src/smt/uf.ml create mode 100644 src/smt/uf.mli rename src/{example => smt}/unionfind.ml (88%) rename src/{example => smt}/unionfind.mli (72%) create mode 100644 src/util/hashcons.ml diff --git a/.merlin b/.merlin index beb445b8..d7ed7f73 100644 --- a/.merlin +++ b/.merlin @@ -1,6 +1,7 @@ S src/core S src/solver -S src/example +S src/sat +S src/smt S src/backend S src/util S src/util/smtlib @@ -9,7 +10,8 @@ S tests B _build/src/ B _build/src/core B _build/src/solver -B _build/src/example +B _build/src/sat +B _build/src/smt B _build/src/util B _build/src/util/smtlib B _build/src/backend diff --git a/META b/META index f2ed910c..993b7f01 100644 --- a/META +++ b/META @@ -1,3 +1,4 @@ +# meta name="msat" version="dev" description="MSAT is a modular SAT solver, plus extensions" @@ -6,3 +7,25 @@ archive(byte) = "msat.cma" archive(byte, plugin) = "msat.cma" archive(native) = "msat.cmxa" archive(native, plugin) = "msat.cmxs" + +package "sat" ( + version = "dev" + description = "SAT solver instance" + requires = "msat" + archive(byte) = "msat_sat.cma" + archive(byte, plugin) = "msat_sat.cma" + archive(native) = "msat_sat.cmxa" + archive(native, plugin) = "msat_sat.cmxs" + exists_if = "msat_sat.cma" +) + +package "smt" ( + version = "dev" + description = "SMT solver instance" + requires = "msat" + archive(byte) = "msat_smt.cma" + archive(byte, plugin) = "msat_smt.cma" + archive(native) = "msat_smt.cmxa" + archive(native, plugin) = "msat_smt.cmxs" + exists_if = "msat_smt.cma" +) diff --git a/Makefile b/Makefile index 406b5b38..92f4bc5e 100644 --- a/Makefile +++ b/Makefile @@ -3,12 +3,20 @@ LOG=build.log COMP=ocamlbuild -log $(LOG) -use-ocamlfind FLAGS= -DOC=msat.docdir/index.html +DOC=msat.docdir/index.html msat_smt.docdir/index.html BIN=main.native TEST_BIN=tests/test_api.native -NAME=msat -LIB=$(addprefix $(NAME), .cma .cmxa .cmxs) +NAME_OCAMLFIND=msat +NAME_BIN=msat +NAME_CORE=msat +NAME_SAT=msat_sat +NAME_SMT=msat_smt + +LIB_CORE=$(addprefix $(NAME_CORE), .cma .cmxa .cmxs) +LIB_SAT=$(addprefix $(NAME_SAT), .cma .cmxa .cmxs) +LIB_SMT=$(addprefix $(NAME_SMT), .cma .cmxa .cmxs) +LIB=$(LIB_CORE) $(LIB_SAT) $(LIB_SMT) all: lib test @@ -20,7 +28,7 @@ doc: bin: $(COMP) $(FLAGS) $(BIN) - cp $(BIN) $(NAME) && rm $(BIN) + cp $(BIN) $(NAME_BIN) && rm $(BIN) test_bin: $(COMP) $(FLAGS) $(TEST_BIN) @@ -44,16 +52,26 @@ log: clean: $(COMP) -clean -TO_INSTALL=META $(addprefix _build/src/,$(LIB) $(NAME).a $(NAME).cmi) +ALL_NAMES = $(NAME_CORE) $(NAME_SAT) $(NAME_SMT) +TO_INSTALL_LIB=$(addsuffix .a, $(ALL_NAMES)) \ + $(addsuffix .cmi, $(ALL_NAMES)) +TO_INSTALL=META $(addprefix _build/src/,$(LIB) $(TO_INSTALL_LIB)) install: lib - ocamlfind install msat $(TO_INSTALL) + ocamlfind install $(NAME_OCAMLFIND) $(TO_INSTALL) uninstall: - ocamlfind remove msat + ocamlfind remove $(NAME_OCAMLFIND) reinstall: all - ocamlfind remove msat || true - ocamlfind install msat $(TO_INSTALL) + ocamlfind remove $(NAME_OCAMLFIND) || true + ocamlfind install $(NAME_OCAMLFIND) $(TO_INSTALL) + +watch: + while find src/ -print0 | xargs -0 inotifywait -e delete_self -e modify ; do \ + echo "============ at `date` ==========" ; \ + sleep 0.1; \ + make all; \ + done .PHONY: clean doc all bench install uninstall reinstall enable_log disable_log bin test diff --git a/_tags b/_tags index c918133e..6511633d 100644 --- a/_tags +++ b/_tags @@ -9,7 +9,8 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : include : include : include -: include +: include +: include : include : include @@ -18,7 +19,8 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : for-pack(Msat) : for-pack(Msat) : for-pack(Msat) -: for-pack(Msat) +: for-pack(Msat_sat) +: for-pack(Msat_smt) # more warnings : warn_K, warn_Y, warn_X diff --git a/src/example/cc.ml b/src/example/cc.ml deleted file mode 100644 index cbfa7d97..00000000 --- a/src/example/cc.ml +++ /dev/null @@ -1,99 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -module Make(T : Sig.OrderedType) = struct - - module M = Map.Make(T) - module U = Unionfind.Make(T) - - exception Unsat of (T.t * T.t * (T.t list)) - - type t = { - repr : U.t; - expl : T.t M.t; - size : int M.t; - } - - let empty = { - repr = U.empty; - expl = M.empty; - size = M.empty; - } - - let repr t a = U.find t.repr a - - let map_find m v default = try M.find v m with Not_found -> default - let find_parent v m = map_find m v v - - let rev_root m root = - let rec aux m curr next = - if T.compare curr next = 0 then - m, curr - else - let parent = find_parent next m in - let m' = M.add next curr (M.remove curr m) in - aux m' next parent - in - aux m root (find_parent root m) - - let rec root m acc curr = - let parent = find_parent curr m in - if T.compare curr parent = 0 then - curr :: acc - else - root m (curr :: acc) parent - - let expl t a b = - let rec aux last = function - | x :: r, y :: r' when T.compare x y = 0 -> - aux (Some x) (r, r') - | l, l' -> begin match last with - | Some z -> List.rev_append (z :: l) l' - | None -> List.rev_append l l' - end - in - aux None (root t.expl [] a, root t.expl [] b) - - let add_eq_aux t i j = - if T.compare (U.find t.repr i) (U.find t.repr j) = 0 then - t - else - let m, old_root_i = rev_root t.expl i in - let m, old_root_j = rev_root m j in - let nb_i = map_find t.size old_root_i 0 in - let nb_j = map_find t.size old_root_j 0 in - if nb_i < nb_j then { - repr = t.repr; - expl = M.add i j m; - size = M.add j (nb_i + nb_j + 1) t.size; } - else { - repr = t.repr; - expl = M.add j i m; - size = M.add i (nb_i + nb_j + 1) t.size; } - - let add_eq t i j = - let t' = add_eq_aux t i j in - try - let u' = U.union t.repr i j in - { t' with repr = u' } - with U.Unsat (a, b) -> - raise (Unsat (a, b, expl t' a b)) - - let add_neq t i j = - try - let u' = U.forbid t.repr i j in - { t with repr = u' } - with U.Unsat (a, b) -> - raise (Unsat (a, b, expl t a b)) - - let are_neq t a b = - try - ignore (U.union t.repr a b); - false - with U.Unsat _ -> - true - -end diff --git a/src/example/cc.mli b/src/example/cc.mli deleted file mode 100644 index 005264d8..00000000 --- a/src/example/cc.mli +++ /dev/null @@ -1,18 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -module Make(T : Sig.OrderedType) : sig - type t - - exception Unsat of (T.t * T.t * (T.t list)) - - val empty : t - val add_eq : t -> T.t -> T.t -> t - val add_neq : t -> T.t -> T.t -> t - - val repr : t -> T.t -> T.t - val are_neq : t -> T.t -> T.t -> bool -end diff --git a/src/example/sig.mli b/src/example/sig.mli deleted file mode 100644 index 1441de22..00000000 --- a/src/example/sig.mli +++ /dev/null @@ -1,13 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - - -module type OrderedType = sig - (** Signature for ordered types (mainly for use in Map.Make) *) - - type t - val compare : t -> t -> int -end diff --git a/src/main.ml b/src/main.ml index 866c29c0..16a0ed8d 100644 --- a/src/main.ml +++ b/src/main.ml @@ -5,9 +5,10 @@ Copyright 2014 Simon Cruanes *) module F = Expr -module T = Cnf.S -module Smt = Smt.Make(struct end) -module Mcsat = Mcsat.Make(struct end) +module T = Msat_smt.Cnf.S +module Sat = Msat_sat.Sat.Make(struct end) +module Smt = Msat_smt.Smt.Make(struct end) +module Mcsat = Msat_smt.Mcsat.Make(struct end) exception Incorrect_model exception Out_of_time @@ -26,6 +27,7 @@ type sat_output = | Dot type solver = + | Sat | Smt | Mcsat @@ -43,6 +45,7 @@ let output_list = [ "dk", Dedukti; ] let solver_list = [ + "sat", Sat; "smt", Smt; "mcsat", Mcsat; ] diff --git a/src/msat.mlpack b/src/msat.mlpack index bf7c053c..b07295d9 100644 --- a/src/msat.mlpack +++ b/src/msat.mlpack @@ -19,20 +19,11 @@ Mcsolver Solver_types # Backends +Backend_intf Dot Dedukti # Auxiliary modules Res Tseitin - -# Sat/Smt modules -Expr -Cnf -Sat -Mcsat -Cc -Sig -Smt -Unionfind - +Hashcons diff --git a/src/msat.odocl b/src/msat.odocl index 09f5e4ce..ff4f7d94 100644 --- a/src/msat.odocl +++ b/src/msat.odocl @@ -13,6 +13,7 @@ solver/Tseitin_intf # Main modules core/Res +core/Res_intf core/Internal core/External core/Solver_types @@ -20,13 +21,12 @@ core/Solver_types solver/Solver solver/Mcsolver solver/Tseitin +solver/Tseitin_intf # Backends backend/Dot backend/Dedukti backend/Backend_intf -# Examples -example/Sat -example/Smt - +# Auxiliary +util/Hashcons diff --git a/src/msat_sat.mlpack b/src/msat_sat.mlpack new file mode 100644 index 00000000..492570c2 --- /dev/null +++ b/src/msat_sat.mlpack @@ -0,0 +1,2 @@ +Sat + diff --git a/src/msat_sat.odocl b/src/msat_sat.odocl new file mode 100644 index 00000000..1fb3c3bf --- /dev/null +++ b/src/msat_sat.odocl @@ -0,0 +1,3 @@ + +smt/Sat + diff --git a/src/msat_smt.mlpack b/src/msat_smt.mlpack new file mode 100644 index 00000000..cfd8b1ba --- /dev/null +++ b/src/msat_smt.mlpack @@ -0,0 +1,12 @@ +Cc +Cnf +Explanation +Expr +ID +Literal +Mcsat +Smt +Symbols +Term +Ty +Unionfind diff --git a/src/msat_smt.odocl b/src/msat_smt.odocl new file mode 100644 index 00000000..ab9aa609 --- /dev/null +++ b/src/msat_smt.odocl @@ -0,0 +1,17 @@ + +smt/Smt + +# support +smt/Cc +smt/Cnf +smt/Explanation +smt/Expr +smt/ID +smt/Sat +smt/Literal +smt/Mcsat +smt/Symbols +smt/Term +smt/Ty +smt/Unionfind + diff --git a/src/example/sat.ml b/src/sat/sat.ml similarity index 99% rename from src/example/sat.ml rename to src/sat/sat.ml index fcf4ed34..448cecb4 100644 --- a/src/example/sat.ml +++ b/src/sat/sat.ml @@ -4,6 +4,8 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + module FI = Formula_intf module Fsat = struct diff --git a/src/example/sat.mli b/src/sat/sat.mli similarity index 99% rename from src/example/sat.mli rename to src/sat/sat.mli index bcc87f68..06e4185b 100644 --- a/src/example/sat.mli +++ b/src/sat/sat.mli @@ -4,6 +4,8 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + module Fsat : sig include Formula_intf.S with type t = private int diff --git a/src/smt/ID.ml b/src/smt/ID.ml new file mode 100644 index 00000000..fb0f64d4 --- /dev/null +++ b/src/smt/ID.ml @@ -0,0 +1,39 @@ +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2016 Guillaume Bury +Copyright 2016 Simon Cruanes +*) + +type t = { + id: int; + name: string; +} + +let make = + let n = ref 0 in + fun name -> + let x = { id= !n; name; } in + incr n; + x + +let copy {name;_} = make name + +let to_string id = id.name + +let equal a b = a.id=b.id +let compare a b = Pervasives.compare a.id b.id +let hash a = a.id land max_int +let pp out a = Format.fprintf out "%s/%d" a.name a.id +let pp_name out a = Format.pp_print_string out a.name + +module AsKey = struct + type t_ = t + type t = t_ + let equal = equal + let compare = compare + let hash = hash +end + +module Map = Map.Make(AsKey) +module Set = Set.Make(AsKey) +module Tbl = Hashtbl.Make(AsKey) diff --git a/src/smt/ID.mli b/src/smt/ID.mli new file mode 100644 index 00000000..f0ac869d --- /dev/null +++ b/src/smt/ID.mli @@ -0,0 +1,25 @@ + +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2016 Guillaume Bury +Copyright 2016 Simon Cruanes +*) + +(** {1 Unique Identifiers} *) + +type t + +val make : string -> t +val copy : t -> t + +val to_string : t -> string + +val equal : t -> t -> bool +val compare : t -> t -> int +val hash : t -> int + +val pp_name : Format.formatter -> t -> unit + +module Map : Map.S with type key = t +module Set : Set.S with type elt = t +module Tbl : Hashtbl.S with type key = t diff --git a/src/smt/cc.ml b/src/smt/cc.ml new file mode 100644 index 00000000..a4114398 --- /dev/null +++ b/src/smt/cc.ml @@ -0,0 +1,517 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon, Evelyne Contejean *) +(* Francois Bobot, Mohamed Iguernelala, Alain Mebsout *) +(* CNRS, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +let max_split = 1000000 + +let cc_active = ref true + +type answer = Yes of Explanation.t | No + +module type S = sig + type t + + val empty : unit -> t + val assume : cs:bool -> + Literal.LT.t -> Explanation.t -> t -> t * Term.Set.t * int + val query : Literal.LT.t -> t -> answer + val class_of : t -> Term.t -> Term.t list +end + +module Make (Dummy : sig end) = struct + + module Ex = Explanation + module Uf = Uf.Make(Term) + module T = Term + module A = Literal + module LR = A.Make(struct type t = X.r include X end) + module SetT = Term.Set + module S = Symbols + + module SetX = Set.Make(struct type t = X.r let compare = X.compare end) + + (* module Uf = Pptarjan.Uf *) + + type env = { + uf : Uf.t ; + relation : X.Rel.t + } + + type choice_sign = + | CPos of int (* The explication of this choice *) + | CNeg (* The choice has been already negated *) + + type t = { + gamma : env; + gamma_finite : env ; + choices : (X.r A.view * Num.num * choice_sign * Ex.t) list; + (** the choice, the size, choice_sign, the explication set, + the explication for this choice. *) + } + + module Print = struct + + let begin_case_split () = () + + let end_case_split () = () + + let cc r1 r2 = () + + let make_cst t ctx = () + + let add_to_use t = () + + let lrepr fmt = List.iter (Format.fprintf fmt "%a " X.print) + + let leaves t lvs = () + + let contra_congruence a ex = () + + let split_size sz = () + + let split_backtrack neg_c ex_c = () + + let split_assume c ex_c = () + + let split_backjump c dep = () + + let assume_literal sa = () + + let congruent a ex = () + + let query a = () + + end + + let bottom = Hstring.make "@bottom" + let one, _ = X.make (Term.make (S.name bottom) [] Ty.Tint) + + let concat_leaves uf l = + let rec concat_rec acc t = + match X.leaves (fst (Uf.find uf t)) , acc with + [] , _ -> one::acc + | res, [] -> res + | res , _ -> List.rev_append res acc + in + match List.fold_left concat_rec [] l with + [] -> [one] + | res -> res + + let are_equal env ex t1 t2 = + if T.equal t1 t2 then ex + else match Uf.are_equal env.uf t1 t2 with + | Yes dep -> Ex.union ex dep + | No -> raise Exit + + let equal_only_by_congruence env ex t1 t2 acc = + if T.equal t1 t2 then acc + else + let {T.f=f1; xs=xs1; ty=ty1} = T.view t1 in + if X.fully_interpreted f1 then acc + else + let {T.f=f2; xs=xs2; ty=ty2} = T.view t2 in + if Symbols.equal f1 f2 && Ty.equal ty1 ty2 then + try + let ex = List.fold_left2 (are_equal env) ex xs1 xs2 in + let a = A.LT.make (A.Eq(t1, t2)) in + Print.congruent a ex; + (LTerm a, ex) :: acc + with Exit -> acc + else acc + + let congruents env t1 s acc ex = + SetT.fold (equal_only_by_congruence env ex t1) s acc + + let fold_find_with_explanation find ex l = + List.fold_left + (fun (lr, ex) t -> let r, ex_r = find t in r::lr, Ex.union ex_r ex) + ([], ex) l + + let view find va ex_a = + match va with + | A.Eq (t1, t2) -> + let r1, ex1 = find t1 in + let r2, ex2 = find t2 in + let ex = Ex.union (Ex.union ex1 ex2) ex_a in + A.Eq(r1, r2), ex + | A.Distinct (b, lt) -> + let lr, ex = fold_find_with_explanation find ex_a lt in + A.Distinct (b, lr), ex + | A.Builtin(b, s, l) -> + let lr, ex = fold_find_with_explanation find ex_a l in + A.Builtin(b, s, List.rev lr), ex + + let term_canonical_view env a ex_a = + view (Uf.find env.uf) (A.LT.view a) ex_a + + let canonical_view env a ex_a = view (Uf.find_r env.uf) a ex_a + + let new_facts_by_contra_congruence env r bol ex = + match X.term_extract r with + | None -> [] + | Some t1 -> + match T.view t1 with + | {T.f=f1 ; xs=[x]} -> + List.fold_left + (fun acc t2 -> + match T.view t2 with + | {T.f=f2 ; xs=[y]} when S.equal f1 f2 -> + let a = A.LT.make (A.Distinct (false, [x; y])) in + let dist = LTerm a in + begin match Uf.are_distinct env.uf t1 t2 with + | Yes ex' -> + let ex_r = Ex.union ex ex' in + Print.contra_congruence a ex_r; + (dist, ex_r) :: acc + | No -> assert false + end + | _ -> acc + ) [] (Uf.class_of env.uf bol) + | _ -> [] + + let contra_congruence = + let true_,_ = X.make T.true_ in + let false_, _ = X.make T.false_ in + fun env r ex -> + if X.equal (fst (Uf.find_r env.uf r)) true_ then + new_facts_by_contra_congruence env r T.false_ ex + else if X.equal (fst (Uf.find_r env.uf r)) false_ then + new_facts_by_contra_congruence env r T.true_ ex + else [] + + let clean_use = + List.fold_left + (fun env (a, ex) -> + match a with + | LSem _ -> assert false + | LTerm t -> + begin + match A.LT.view t with + | A.Distinct (_, lt) + | A.Builtin (_, _, lt) -> + let lvs = concat_leaves env.uf lt in + List.fold_left + (fun env rx -> + let st, sa = Use.find rx env.use in + let sa = SetA.remove (t, ex) sa in + { env with use = Use.add rx (st,sa) env.use } + ) env lvs + | _ -> assert false + end) + + let rec congruence_closure env r1 r2 ex = + Print.cc r1 r2; + let uf, res = Uf.union env.uf r1 r2 ex in + List.fold_left + (fun (env, l) (p, touched, v) -> + (* we look for use(p) *) + let p_t, p_a = Use.find p env.use in + + (* we compute terms and atoms to consider for congruence *) + let repr_touched = List.map (fun (_,a,_) -> a) touched in + let st_others, sa_others = Use.congr_close_up env.use p repr_touched in + + (* we update use *) + let nuse = Use.up_close_up env.use p v in + Use.print nuse; + + (* we check the congruence of the terms. *) + let env = {env with use=nuse} in + let new_eqs = + SetT.fold (fun t l -> congruents env t st_others l ex) p_t l in + let touched_atoms = + List.map (fun (x,y,e)-> (LSem(A.Eq(x, y)), e)) touched + in + let touched_atoms = SetA.fold (fun (a, ex) acc -> + (LTerm a, ex)::acc) p_a touched_atoms in + let touched_atoms = SetA.fold (fun (a, ex) acc -> + (LTerm a, ex)::acc) sa_others touched_atoms in + env, new_eqs @ touched_atoms + + ) ({env with uf=uf}, []) res + + let replay_atom env sa = + let relation, result = X.Rel.assume env.relation sa in + let env = { env with relation = relation } in + let env = clean_use env result.remove in + env, result.assume + + let rec add_term env choices t ex = + (* nothing to do if the term already exists *) + if Uf.mem env.uf t then env, choices + else begin + Print.add_to_use t; + (* we add t's arguments in env *) + let {T.f = f; xs = xs} = T.view t in + let env, choices = + List.fold_left (fun (env, ch) t -> add_term env ch t ex) + (env, choices) xs + in + (* we update uf and use *) + let nuf, ctx = Uf.add env.uf t in + Print.make_cst t ctx; + let rt, _ = Uf.find nuf t in (* XXX : ctx only in terms *) + + if !cc_active then + let lvs = concat_leaves nuf xs in + let nuse = Use.up_add env.use t rt lvs in + + (* If finitetest is used we add the term to the relation *) + let rel = X.Rel.add env.relation rt in + Use.print nuse; + + (* we compute terms to consider for congruence *) + (* we do this only for non-atomic terms with uninterpreted head-symbol *) + let st_uset = Use.congr_add nuse lvs in + + (* we check the congruence of each term *) + let env = {uf = nuf; use = nuse; relation = rel} in + let ct = congruents env t st_uset [] ex in + let ct = (List.map (fun lt -> LTerm lt, ex) ctx) @ ct in + assume_literal env choices ct + else + let rel = X.Rel.add env.relation rt in + let env = {env with uf = nuf; relation = rel} in + env, choices + end + + and add env choices a ex = + match A.LT.view a with + | A.Eq (t1, t2) -> + let env, choices = add_term env choices t1 ex in + add_term env choices t2 ex + | A.Distinct (_, lt) + | A.Builtin (_, _, lt) -> + let env, choices = List.fold_left + (fun (env, ch) t-> add_term env ch t ex) (env, choices) lt in + let lvs = concat_leaves env.uf lt in (* A verifier *) + let env = List.fold_left + (fun env rx -> + let st, sa = Use.find rx env.use in + { env with + use = Use.add rx (st,SetA.add (a, ex) sa) env.use } + ) env lvs + in + env, choices + + and semantic_view env choices la = + List.fold_left + (fun (env, choices, lsa) (a, ex) -> + match a with + | LTerm a -> + let env, choices = add env choices a ex in + let sa, ex = term_canonical_view env a ex in + env, choices, (sa, Some a, ex)::lsa + + (* XXX si on fait canonical_view pour + A.Distinct, la theorie des tableaux + part dans les choux *) + | LSem (A.Builtin _ (*| A.Distinct _*) as sa) -> + let sa, ex = canonical_view env sa ex in + env, choices, (sa, None, ex)::lsa + | LSem sa -> + env, choices, (sa, None, ex)::lsa) + (env, choices, []) la + + and assume_literal env choices la = + if la = [] then env, choices + else + let env, choices, lsa = semantic_view env choices la in + let env, choices = + List.fold_left + (fun (env, choices) (sa, _, ex) -> + Print.assume_literal sa; + match sa with + | A.Eq(r1, r2) -> + if !cc_active then + let env, l = congruence_closure env r1 r2 ex in + let env, choices = assume_literal env choices l in + let env, choices = + assume_literal env choices (contra_congruence env r1 ex) + in + assume_literal env choices (contra_congruence env r2 ex) + else + {env with uf = fst(Uf.union env.uf r1 r2 ex)}, choices + | A.Distinct (false, lr) -> + if Uf.already_distinct env.uf lr then env, choices + else + {env with uf = Uf.distinct env.uf lr ex}, choices + | A.Distinct (true, _) -> assert false + | A.Builtin _ -> env, choices) + (env, choices) lsa + in + let env, l = replay_atom env lsa in + assume_literal env (choices@l) l + + let look_for_sat ?(bad_last=No) ch t base_env l = + let rec aux ch bad_last dl base_env li = + match li, bad_last with + | [], _ -> + begin + match X.Rel.case_split base_env.relation with + | [] -> + { t with gamma_finite = base_env; choices = List.rev dl }, ch + | l -> + let l = + List.map + (fun (c, ex_c, size) -> + let exp = Ex.fresh_exp () in + let ex_c_exp = Ex.add_fresh exp ex_c in + (* A new explanation in order to track the choice *) + (c, size, CPos exp, ex_c_exp)) l in + let sz = + List.fold_left + (fun acc (a,s,_,_) -> + Num.mult_num acc s) (Num.Int 1) (l@dl) in + Print.split_size sz; + if Num.le_num sz max_split then aux ch No dl base_env l + else + { t with gamma_finite = base_env; choices = List.rev dl }, ch + end + | ((c, size, CNeg, ex_c) as a)::l, _ -> + let base_env, ch = assume_literal base_env ch [LSem c, ex_c] in + aux ch bad_last (a::dl) base_env l + + (** This optimisation is not correct with the current explanation *) + (* | [(c, size, CPos exp, ex_c)], Yes dep -> *) + (* let neg_c = LR.neg (LR.make c) in *) + (* let ex_c = Ex.union ex_c dep in *) + (* Print.split_backtrack neg_c ex_c; *) + (* aux ch No dl base_env [LR.view neg_c, Num.Int 1, CNeg, ex_c] *) + + | ((c, size, CPos exp, ex_c_exp) as a)::l, _ -> + try + Print.split_assume (LR.make c) ex_c_exp; + let base_env, ch = assume_literal base_env ch [LSem c, ex_c_exp] in + aux ch bad_last (a::dl) base_env l + with Exception.Inconsistent dep -> + match Ex.remove_fresh exp dep with + | None -> + (* The choice doesn't participate to the inconsistency *) + Print.split_backjump (LR.make c) dep; + raise (Exception.Inconsistent dep) + | Some dep -> + (* The choice participates to the inconsistency *) + let neg_c = LR.neg (LR.make c) in + Print.split_backtrack neg_c dep; + aux ch No dl base_env [LR.view neg_c, Num.Int 1, CNeg, dep] + in + aux ch bad_last (List.rev t.choices) base_env l + + let try_it f t = + Print.begin_case_split (); + let r = + try + if t.choices = [] then look_for_sat [] t t.gamma [] + else + try + let env, lt = f t.gamma_finite in + look_for_sat lt t env [] + with Exception.Inconsistent dep -> + look_for_sat ~bad_last:(Yes dep) + [] { t with choices = []} t.gamma t.choices + with Exception.Inconsistent d -> + Print.end_case_split (); + raise (Exception.Inconsistent d) + in + Print.end_case_split (); r + + let extract_from_semvalues = + List.fold_left + (fun acc r -> + match X.term_extract r with Some t -> SetT.add t acc | _ -> acc) + + let extract_terms_from_choices = + List.fold_left + (fun acc (a, _, _, _) -> + match a with + | A.Eq(r1, r2) -> extract_from_semvalues acc [r1; r2] + | A.Distinct (_, l) -> extract_from_semvalues acc l + | _ -> acc) + + let extract_terms_from_assumed = + List.fold_left + (fun acc (a, _) -> + match a with + | LTerm r -> begin + match Literal.LT.view r with + | Literal.Eq (t1, t2) -> + SetT.add t1 (SetT.add t2 acc) + | Literal.Distinct (_, l) | Literal.Builtin (_, _, l) -> + List.fold_right SetT.add l acc + end + | _ -> acc) + + let assume ~cs a ex t = + let a = LTerm a in + let gamma, ch = assume_literal t.gamma [] [a, ex] in + let t = { t with gamma = gamma } in + let t, ch = + if cs then try_it (fun env -> assume_literal env ch [a, ex] ) t + else t, ch + in + let choices = extract_terms_from_choices SetT.empty t.choices in + let all_terms = extract_terms_from_assumed choices ch in + t, all_terms, 1 + + let class_of t term = Uf.class_of t.gamma.uf term + + let add_and_process a t = + let aux a ex env = + let gamma, l = add env [] a ex in assume_literal gamma [] l + in + let gamma, _ = aux a Ex.empty t.gamma in + let t = { t with gamma = gamma } in + let t, _ = try_it (aux a Ex.empty) t in + Use.print t.gamma.use; t + + let query a t = + Print.query a; + try + match A.LT.view a with + | A.Eq (t1, t2) -> + let t = add_and_process a t in + Uf.are_equal t.gamma.uf t1 t2 + + | A.Distinct (false, [t1; t2]) -> + let na = A.LT.neg a in + let t = add_and_process na t in (* na ? *) + Uf.are_distinct t.gamma.uf t1 t2 + + | A.Distinct _ -> + assert false (* devrait etre capture par une analyse statique *) + + | _ -> + let na = A.LT.neg a in + let t = add_and_process na t in + let env = t.gamma in + let rna, ex_rna = term_canonical_view env na Ex.empty in + X.Rel.query env.relation (rna, Some na, ex_rna) + with Exception.Inconsistent d -> Yes d + + let empty () = + let env = { + use = Use.empty ; + uf = Uf.empty ; + relation = X.Rel.empty (); + } + in + let t = { gamma = env; gamma_finite = env; choices = [] } in + let t, _, _ = + assume ~cs:false + (A.LT.make (A.Distinct (false, [T.true_; T.false_]))) Ex.empty t + in t + +end diff --git a/src/smt/cc.mli b/src/smt/cc.mli new file mode 100644 index 00000000..935ed2ea --- /dev/null +++ b/src/smt/cc.mli @@ -0,0 +1,37 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon, Evelyne Contejean *) +(* Francois Bobot, Mohamed Iguernelala, Alain Mebsout *) +(* CNRS, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +val cc_active : bool ref + +type answer = Yes of Explanation.t | No + +module type S = sig + type t + + val empty : unit -> t + + val assume : + cs:bool -> + Literal.LT.t -> + Explanation.t -> + t -> t * Term.Set.t * int + + val query : Literal.LT.t -> t -> answer + + val class_of : t -> Term.t -> Term.t list +end + +module Make (Dummy : sig end) : S diff --git a/src/example/cnf.ml b/src/smt/cnf.ml similarity index 93% rename from src/example/cnf.ml rename to src/smt/cnf.ml index f778231a..999271ac 100644 --- a/src/example/cnf.ml +++ b/src/smt/cnf.ml @@ -4,4 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + module S = Tseitin.Make(Expr) diff --git a/src/example/cnf.mli b/src/smt/cnf.mli similarity index 94% rename from src/example/cnf.mli rename to src/smt/cnf.mli index b0eae539..6eb68976 100644 --- a/src/example/cnf.mli +++ b/src/smt/cnf.mli @@ -4,4 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + module S : Tseitin.S with type atom = Expr.Formula.t diff --git a/src/smt/explanation.ml b/src/smt/explanation.ml new file mode 100644 index 00000000..3646c112 --- /dev/null +++ b/src/smt/explanation.ml @@ -0,0 +1,68 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Stephane Lescuyer *) +(* INRIA, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type atom = Literal.LT.t + +type exp = Atom of atom | Fresh of int + +module S = + Set.Make + (struct + type t = exp + let compare a b = match a,b with + | Atom _, Fresh _ -> -1 + | Fresh _, Atom _ -> 1 + | Fresh i1, Fresh i2 -> i1 - i2 + | Atom a, Atom b -> a.aid - b.aid + end) + +type t = S.t + +let singleton e = S.singleton (Atom e) + +let empty = S.empty + +let union s1 s2 = S.union s1 s2 + +let iter_atoms f s = + S.iter (fun e -> match e with + | Fresh _ -> () + | Atom a -> f a) s + +let fold_atoms f s acc = + S.fold (fun e acc -> match e with + | Fresh _ -> acc + | Atom a -> f a acc) s acc + +let merge e1 e2 = e1 + + +let fresh_exp = + let r = ref (-1) in + fun () -> incr r; !r + +let remove_fresh i s = + let fi = Fresh i in + if S.mem fi s then Some (S.remove fi s) + else None + +let add_fresh i = S.add (Fresh i) + + +let print fmt ex = + fprintf fmt "{"; + S.iter (function + | Atom a -> fprintf fmt "%a, " Debug.atom a + | Fresh i -> fprintf fmt "Fresh%d " i) ex; + fprintf fmt "}" diff --git a/src/smt/explanation.mli b/src/smt/explanation.mli new file mode 100644 index 00000000..b362b0c3 --- /dev/null +++ b/src/smt/explanation.mli @@ -0,0 +1,39 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Stephane Lescuyer *) +(* INRIA, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type t + +type exp + +type atom = Literal.LT.t + +val empty : t + +val singleton : atom-> t + +val union : t -> t -> t + +val merge : t -> t -> t + +val iter_atoms : (atom -> unit) -> t -> unit + +val fold_atoms : (atom -> 'a -> 'a ) -> t -> 'a -> 'a + +val fresh_exp : unit -> int + +val remove_fresh : int -> t -> t option + +val add_fresh : int -> t -> t + +val print : Format.formatter -> t -> unit diff --git a/src/example/expr.ml b/src/smt/expr.ml similarity index 50% rename from src/example/expr.ml rename to src/smt/expr.ml index 72eef2e1..dda3d7fc 100644 --- a/src/example/expr.ml +++ b/src/smt/expr.ml @@ -3,36 +3,56 @@ MSAT is free software, using the Apache license, see file LICENSE Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat module I = Formula_intf +module Term = Term -exception Invalid_var +exception Invalid_prop -type var = string +type term = Term.t + +(* atomic formula + + Prop: + - sign of int determines sign of formula + - odd numbers --> fresh atoms (for Tseitin CNF) + - even numbers --> used for regular int-mapping +*) type formula = | Prop of int - | Equal of var * var - | Distinct of var * var + | Equal of term * term + | Distinct of term * term + type t = formula type proof = unit let dummy = Prop 0 let max_fresh = ref 0 + let fresh () = incr max_fresh; Prop (2 * !max_fresh + 1) let mk_prop i = if i <> 0 && i < max_int / 2 then Prop (2 * i) - else raise Invalid_var + else raise Invalid_prop -let mk_var i = - if i <> "" then i - else raise Invalid_var +let order_ t1 t2 = if Term.compare t1 t2 > 0 then t2,t1 else t1,t2 -let mk_eq i j = Equal (mk_var (min i j), mk_var (max i j)) -let mk_neq i j = Distinct (mk_var (min i j), mk_var (max i j)) +let mk_eq a b = + let a, b = order_ a b in + Equal (a, b) + +let mk_neq a b = + let a, b = order_ a b in + Distinct (a, b) + +let mk_true = mk_eq Term.true_ Term.true_ +let mk_false = mk_eq Term.true_ Term.false_ +let mk_atom = mk_eq Term.true_ +let mk_atom_neg = mk_eq Term.false_ let neg = function | Prop i -> Prop (-i) @@ -50,17 +70,12 @@ let equal = (=) let compare = Pervasives.compare let print fmt = function - | Prop i -> Format.fprintf fmt "%s%s%d" (if i < 0 then "¬ " else "") (if i mod 2 = 0 then "v" else "f") ((abs i) / 2) - | Equal (a, b) -> Format.fprintf fmt "%s = %s" a b - | Distinct (a, b) -> Format.fprintf fmt "%s ≠ %s" a b - -module Term = struct - type t = var - let hash = Hashtbl.hash - let equal = (=) - let compare = Pervasives.compare - let print fmt t = Format.fprintf fmt "%s" t -end + | Prop i -> + Format.fprintf fmt "%s%s%d" + (if i < 0 then "¬ " else "") + (if i mod 2 = 0 then "v" else "f") ((abs i) / 2) + | Equal (a, b) -> Format.fprintf fmt "(@[=@ %a@ %a@])" Term.print a Term.print b + | Distinct (a, b) -> Format.fprintf fmt "(@[!=@ %a@ %a@])" Term.print a Term.print b module Formula = struct type t = formula diff --git a/src/example/expr.mli b/src/smt/expr.mli similarity index 54% rename from src/example/expr.mli rename to src/smt/expr.mli index 8a9f7591..0f01ae83 100644 --- a/src/example/expr.mli +++ b/src/smt/expr.mli @@ -3,12 +3,14 @@ MSAT is free software, using the Apache license, see file LICENSE Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + +type term = Term.t -type var = string type formula = private - | Prop of int - | Equal of var * var - | Distinct of var * var + | Prop of int (* prop or tseitin atom *) + | Equal of term * term + | Distinct of term * term type t = formula type proof = unit @@ -20,16 +22,17 @@ val dummy : t val fresh : unit -> t val mk_prop : int -> t -val mk_eq : var -> var -> t -val mk_neq : var -> var -> t +(** [mk_prop i] makes a prop literal from [i], whose sign matters. + @raise Invalid_prop if [i=0] or if [i] is too large *) -module Term : sig - type t = var - val hash : t -> int - val equal : t -> t -> bool - val compare : t -> t -> int - val print : Format.formatter -> t -> unit -end +val mk_true : t +val mk_false : t +val mk_atom : term -> t +val mk_atom_neg : term -> t +val mk_eq : term -> term -> t +val mk_neq : term -> term -> t + +module Term = Term module Formula : sig type t = formula val hash : t -> int diff --git a/src/smt/literal.ml b/src/smt/literal.ml new file mode 100644 index 00000000..0d939be7 --- /dev/null +++ b/src/smt/literal.ml @@ -0,0 +1,184 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +type 'a view = + | Eq of 'a * 'a + | Distinct of bool * 'a list + | Builtin of bool * ID.t * 'a list + +module type OrderedType = sig + type t + val compare : t -> t -> int + val hash : t -> int + val print : Format.formatter -> t -> unit +end + +module type S = sig + type elt + type t + + val make : elt view -> t + val view : t -> elt view + + val neg : t -> t + + val print : Format.formatter -> t -> unit + + val compare : t -> t -> int + val equal : t -> t -> bool + val hash : t -> int + + module Map : Map.S with type key = t + module Set : Set.S with type elt = t + +end + +module Make (X : OrderedType) : S with type elt = X.t = struct + + type elt = X.t + type t = { + view: X.t view; + mutable tag: int; + } + + module V = struct + type t_ = t + type t = t_ + + let equal a1 a2 = + match a1.view, a2.view with + | Eq(t1, t2), Eq(u1, u2) -> + (X.compare t1 u1 = 0 && X.compare t2 u2 = 0) || + (X.compare t1 u2 = 0 && X.compare t2 u1 = 0) + | Distinct (b1,lt1), Distinct (b2,lt2) -> + (try + b1 = b2 && + List.for_all2 (fun x y -> X.compare x y = 0) lt1 lt2 + with Invalid_argument _ -> false) + | Builtin(b1, n1, l1), Builtin(b2, n2, l2) -> + (try + b1 = b2 && ID.equal n1 n2 + && + List.for_all2 (fun x y -> X.compare x y = 0) l1 l2 + with Invalid_argument _ -> false) + | _ -> false + + let hash a = match a.view with + | Eq(t1, t2) -> abs (19 * (X.hash t1 + X.hash t2)) + | Distinct (b,lt) -> + let x = if b then 7 else 23 in + abs (17 * List.fold_left (fun acc t -> (X.hash t) + acc ) x lt) + | Builtin(b, n, l) -> + let x = if b then 7 else 23 in + abs + (List.fold_left + (fun acc t-> acc*13 + X.hash t) (ID.hash n+x) l) + + let set_id t tag = t.tag <- tag + end + + module H = Hashcons.Make(V) + + let compare a1 a2 = Pervasives.compare a1.tag a2.tag + let equal a1 a2 = a1 == a2 + let hash a1 = a1.tag + + module T = struct + type t_ = t + type t = t_ + let compare=compare + end + + let make t = H.hashcons {view=t; tag= -1} + let view a = a.view + + let neg a = match view a with + | Eq(x, y) -> make (Distinct (false,[x; y])) + | Distinct (false, [x; y]) -> make (Eq (x, y)) + | Distinct (true, [x; y]) -> make (Distinct (false,[x; y])) + | Distinct (false, l) -> make (Distinct (true,l)) + | Distinct _ -> assert false + | Builtin(b, n, l) -> make (Builtin (not b, n, l)) + + let print_list fmt = function + | [] -> () + | z :: l -> + Format.fprintf fmt "%a" X.print z; + List.iter (Format.fprintf fmt ", %a" X.print) l + + let print fmt a = match view a with + | Eq (z1, z2) -> + if equal z1 z2 then Format.fprintf fmt "True" + else Format.fprintf fmt "%a=%a" X.print z1 X.print z2 + | Distinct (b,(z::l)) -> + let b = if b then "~" else "" in + Format.fprintf fmt "%s%a" b X.print z; + List.iter (fun x -> Format.fprintf fmt "<>%a" X.print x) l + | Builtin (b, n, l) -> + let b = if b then "" else "~" in + Format.fprintf fmt "%s%s(%a)" b (ID.to_string n) print_list l + | _ -> assert false + + module Set = Set.Make(T) + module Map = Map.Make(T) + +end + +module type S_Term = sig + + include S with type elt = Term.t + + val mk_pred : Term.t -> t + + val true_ : t + val false_ : t + + (* val terms_of : t -> Term.Set.t + val vars_of : t -> Symbols.Set.t + *) + (* module SetEq : Set.S with type elt = t * Term.t * Term.t*) +end + +module LT : S_Term = struct + + module L = Make(Term) + include L + + let mk_pred t = make (Eq (t, Term.true_) ) + + let true_ = mk_pred Term.true_ + let false_ = mk_pred Term.false_ + + let neg a = match view a with + | Eq(t1, t2) when Term.equal t2 Term.false_ -> + make (Eq (t1, Term.true_)) + | Eq(t1, t2) when Term.equal t2 Term.true_ -> + make (Eq (t1, Term.false_)) + | _ -> L.neg a + + (* let terms_of a = + let l = match view a with + | Eq (t1, t2) -> [t1; t2] + | Distinct (_, l) | Builtin (_, _, l) -> l + in + List.fold_left Term.subterms Term.Set.empty l + *) + + module SS = Symbols.Set + (* let vars_of a = + Term.Set.fold (fun t -> SS.union (Term.vars_of t)) (terms_of a) SS.empty + *) +end + diff --git a/src/smt/literal.mli b/src/smt/literal.mli new file mode 100644 index 00000000..f38963ab --- /dev/null +++ b/src/smt/literal.mli @@ -0,0 +1,62 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +module type OrderedType = sig + type t + val compare : t -> t -> int + val hash : t -> int + val print : Format.formatter -> t -> unit +end + +type 'a view = + | Eq of 'a * 'a + | Distinct of bool * 'a list + | Builtin of bool * ID.t * 'a list + +module type S = sig + type elt + type t + + val make : elt view -> t + val view : t -> elt view + + val neg : t -> t + + val print : Format.formatter -> t -> unit + + val compare : t -> t -> int + val equal : t -> t -> bool + val hash : t -> int + + module Map : Map.S with type key = t + module Set : Set.S with type elt = t + +end + +module Make ( X : OrderedType ) : S with type elt = X.t + +module type S_Term = sig + + include S with type elt = Term.t + + val mk_pred : Term.t -> t + val true_ : t + val false_ : t + +end + +module LT : S_Term + + diff --git a/src/example/mcsat.ml b/src/smt/mcsat.ml similarity index 99% rename from src/example/mcsat.ml rename to src/smt/mcsat.ml index 9be8e7bc..9a5b67fc 100644 --- a/src/example/mcsat.ml +++ b/src/smt/mcsat.ml @@ -4,6 +4,8 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +open Msat + module Fsmt = Expr module Tsmt = struct diff --git a/src/example/smt.ml b/src/smt/smt.ml similarity index 100% rename from src/example/smt.ml rename to src/smt/smt.ml diff --git a/src/example/smt.mli b/src/smt/smt.mli similarity index 100% rename from src/example/smt.mli rename to src/smt/smt.mli diff --git a/src/smt/symbols.ml b/src/smt/symbols.ml new file mode 100644 index 00000000..c39e60ab --- /dev/null +++ b/src/smt/symbols.ml @@ -0,0 +1,62 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type name_kind = Constructor | Other + +type t = + | True + | False + | Name of ID.t * name_kind + | Var of ID.t + +let name ?(kind=Other) s = Name (s, kind) +let var s = Var s + +let compare_kind k1 k2 = match k1, k2 with + | Other, Other -> 0 + | Other, _ -> 1 + | _ , Other -> -1 + | Constructor, Constructor -> 0 + +let compare s1 s2 = match s1, s2 with + | Name (n1,k1), Name (n2,k2) -> + let c = compare_kind k1 k2 in + if c = 0 then ID.compare n1 n2 else c + | Name _, _ -> -1 + | _, Name _ -> 1 + | Var n1, Var n2 -> ID.compare n1 n2 + | Var _, _ -> -1 + | _ ,Var _ -> 1 + | _ -> Pervasives.compare s1 s2 + +let equal s1 s2 = compare s1 s2 = 0 + +let hash = function + | Name (n,_) -> ID.hash n * 19 + | Var n (*| Int n*) -> ID.hash n * 19 + 1 + | s -> Hashtbl.hash s + +let to_string = function + | Name (n,_) -> ID.to_string n + | Var x -> "*var* "^(ID.to_string x) + | True -> "true" + | False -> "false" + +let print fmt s = Format.fprintf fmt "%s" (to_string s) + +module Map = + Map.Make(struct type t' = t type t=t' let compare=compare end) + +module Set = + Set.Make(struct type t' = t type t=t' let compare=compare end) + diff --git a/src/smt/symbols.mli b/src/smt/symbols.mli new file mode 100644 index 00000000..17dd3e0b --- /dev/null +++ b/src/smt/symbols.mli @@ -0,0 +1,33 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type name_kind = Constructor | Other + +type t = + | True + | False + | Name of ID.t * name_kind + | Var of ID.t + +val name : ?kind:name_kind -> ID.t -> t +val var : ID.t -> t + +val equal : t -> t -> bool +val compare : t -> t -> int +val hash : t -> int + +val print : Format.formatter -> t -> unit + +module Map : Map.S with type key = t +module Set : Set.S with type elt = t + diff --git a/src/smt/term.ml b/src/smt/term.ml new file mode 100644 index 00000000..4d0db744 --- /dev/null +++ b/src/smt/term.ml @@ -0,0 +1,100 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +module Sy = Symbols + +type view = { + head: head; + ty: Ty.t; + mutable tag: int; +} + +and head = + | App of Symbols.t * t list + | Ite of t * t * t + +and t = view + +module H = struct + type t = view + let equal t1 t2 = match t1.head, t2.head with + | App (f1,l1), App (f2,l2) -> + begin try + Sy.equal f1 f2 + && List.for_all2 (==) l1 l2 + && Ty.equal t1.ty t2.ty + with Invalid_argument _ -> + false + end + | Ite (a1,b1,c1), Ite (a2,b2,c2) -> + a1==a2 && b1==b2 && c1==c2 + | App _, Ite _ + | Ite _, App _ -> false + + let hash t = match t.head with + | Ite (a,b,c) -> + abs + (List.fold_left + (fun acc x-> acc*19 +x.tag) 17 [a;b;c]) + | App (f,l) -> + abs + (List.fold_left + (fun acc x-> acc*19 +x.tag) (Sy.hash f + Ty.hash t.ty) + l) + let set_id x tag = x.tag <- tag +end + +module T = Hashcons.Make(H) + +let view t = t + +let rec print fmt t = match t.head with + | Ite (a,b,c) -> + Format.fprintf fmt "(@[<2>ite@ %a@ %a@ %a@])" print a print b print c + | App (x, l) -> + match x, l with + | _, [] -> Format.fprintf fmt "%a" Sy.print x + | _, _ -> Format.fprintf fmt "%a(%a)" Sy.print x print_list l + +and print_list fmt = function + | [] -> () + | [t] -> print fmt t + | t::l -> Format.fprintf fmt "%a,%a" print t print_list l + +let compare t1 t2 = + let c = Pervasives.compare t2.tag t1.tag in + if c = 0 then c + else match t1.head, t2.head with + | App ((Sy.True | Sy.False), _), App ((Sy.True | Sy.False), _) -> c + | App ((Sy.True | Sy.False), _), _ -> -1 + | _, App ((Sy.True | Sy.False), _) -> 1 + | _,_ -> c + +let app s l ty = T.hashcons {head=App(s,l); ty=ty; tag= -1; } +let const s ty = app s [] ty +let ite a b c = T.hashcons {head=Ite (a,b,c); ty=b.ty; tag= -1; } + +let true_ = app (Sy.True) [] Ty.Tbool +let false_ = app (Sy.False) [] Ty.Tbool + +let equal t1 t2 = t1 == t2 + +let hash t = t.tag + +module Set = + Set.Make(struct type t' = t type t=t' let compare=compare end) + +module Map = + Map.Make(struct type t' = t type t=t' let compare=compare end) diff --git a/src/smt/term.mli b/src/smt/term.mli new file mode 100644 index 00000000..c9542d3d --- /dev/null +++ b/src/smt/term.mli @@ -0,0 +1,45 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +type t + +type view = private { + head: head; + ty: Ty.t; + mutable tag: int; +} + +and head = + | App of Symbols.t * t list + | Ite of t * t * t + +val view : t -> view + +val app : Symbols.t -> t list -> Ty.t -> t +val const : Symbols.t -> Ty.t -> t +val ite : t -> t -> t -> t + +val true_ : t +val false_ : t + +val compare : t -> t -> int +val equal : t -> t -> bool +val hash : t -> int + +val print : Format.formatter -> t -> unit + +module Map : Map.S with type key = t +module Set : Set.S with type elt = t + diff --git a/src/smt/ty.ml b/src/smt/ty.ml new file mode 100644 index 00000000..a3af5bd7 --- /dev/null +++ b/src/smt/ty.ml @@ -0,0 +1,60 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +open Msat + +type symbol = Symbols.t + +type t = + | Tbool + | Tabstract of ID.t + | Tsum of ID.t * symbol list + +let bool = Tbool +let abstract i = Tabstract i +let sum i l = Tsum (i, l) + +let hash t = + match t with + | Tabstract s -> ID.hash s + | Tsum (s, l) -> + let h = + List.fold_left + (fun h x -> 13 * h + Symbols.hash x) (ID.hash s) l + in + abs h + | _ -> Hashtbl.hash t + +let equal t1 t2 = + match t1, t2 with + | Tabstract s1, Tabstract s2 + | Tsum (s1, _), Tsum (s2, _) -> + ID.equal s1 s2 + | Tbool, Tbool -> true + | _ -> false + +let compare t1 t2 = + match t1, t2 with + | Tabstract s1, Tabstract s2 -> + ID.compare s1 s2 + | Tabstract _, _ -> -1 | _ , Tabstract _ -> 1 + | Tsum (s1, _), Tsum(s2, _) -> + ID.compare s1 s2 + | Tsum _, _ -> -1 | _ , Tsum _ -> 1 + | t1, t2 -> Pervasives.compare t1 t2 + +let print fmt ty = + match ty with + | Tbool -> Format.fprintf fmt "bool" + | Tabstract s -> Format.fprintf fmt "%s" (ID.to_string s) + | Tsum (s, _) -> Format.fprintf fmt "%s" (ID.to_string s) diff --git a/src/smt/ty.mli b/src/smt/ty.mli new file mode 100644 index 00000000..0c94cf71 --- /dev/null +++ b/src/smt/ty.mli @@ -0,0 +1,29 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon and Alain Mebsout *) +(* Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) +open Msat + +type symbol = Symbols.t + +type t = + | Tbool + | Tabstract of ID.t + | Tsum of ID.t * symbol list + +val bool : t +val abstract : ID.t -> t +val sum : ID.t -> symbol list -> t + +val hash : t -> int +val equal : t -> t -> bool +val compare : t -> t -> int +val print : Format.formatter -> t -> unit diff --git a/src/smt/uf.ml b/src/smt/uf.ml new file mode 100644 index 00000000..573189c6 --- /dev/null +++ b/src/smt/uf.ml @@ -0,0 +1,381 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon, Evelyne Contejean *) +(* Francois Bobot, Mohamed Iguernelala, Alain Mebsout *) +(* CNRS, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type answer = Yes of Explanation.t | No + +type 'a literal = + | LSem of 'a Literal.view + | LTerm of Literal.LT.t + +exception Inconsistent of Explanation.t +exception Unsolvable + +module type ELT = sig + type r + + val make : Term.t -> r * Literal.LT.t list + + val compare : r -> r -> int + + val equal : r -> r -> bool + + val hash : r -> int + + val leaves : r -> r list + + val subst : r -> r -> r -> r + + val can_be_equal : r -> r -> bool + + val term_embed : Term.t -> r + + val term_extract : r -> Term.t option + + val unsolvable : r -> bool + + val fully_interpreted : Symbols.t -> bool + + val print : Format.formatter -> r -> unit +end + +module type S = sig + type t + + module R : ELT + + val empty : t + val add : t -> Term.t -> t * Literal.LT.t list + + val mem : t -> Term.t -> bool + + val find : t -> Term.t -> R.r * Explanation.t + + val find_r : t -> R.r -> R.r * Explanation.t + + val union : + t -> R.r -> R.r -> Explanation.t -> + t * (R.r * (R.r * R.r * Explanation.t) list * R.r) list + + val distinct : t -> R.r list -> Explanation.t -> t + + val are_equal : t -> Term.t -> Term.t -> Sig.answer + val are_distinct : t -> Term.t -> Term.t -> Sig.answer + val already_distinct : t -> R.r list -> bool + + val class_of : t -> Term.t -> Term.t list +end + +module Make ( R : ELT ) = struct + + module Ex = Explanation + module R = R + module Sy = Symbols + module T = Term + module MapT = Term.Map + module SetT = Term.Set + + module Lit = Literal.Make(struct type t = R.r include R end) + module MapL = Lit.Map + + module MapR = Map.Make(struct type t = R.r let compare = R.compare end) + + module SetR = Set.Make(struct type t = R.r let compare = R.compare end) + + module SetRR = Set.Make(struct + type t = R.r * R.r + let compare (r1, r1') (r2, r2') = + let c = R.compare r1 r2 in + if c <> 0 then c + else R.compare r1' r2' + end) + + + type t = { + + (* term -> [t] *) + make : R.r MapT.t; + + (* representative table *) + repr : (R.r * Ex.t) MapR.t; + + (* r -> class (of terms) *) + classes : SetT.t MapR.t; + + (*associates each value r with the set of semantical values whose + representatives contains r *) + gamma : SetR.t MapR.t; + + (* the disequations map *) + neqs: Ex.t MapL.t MapR.t; + + } + + let empty = { + make = MapT.empty; + repr = MapR.empty; + classes = MapR.empty; + gamma = MapR.empty; + neqs = MapR.empty; + } + + module Env = struct + + let mem env t = MapT.mem t env.make + + let lookup_by_t t env = + try MapR.find (MapT.find t env.make) env.repr + with Not_found -> + assert false (*R.make t, Ex.empty*) (* XXXX *) + + let lookup_by_r r env = + try MapR.find r env.repr with Not_found -> r, Ex.empty + + let lookup_for_neqs env r = + try MapR.find r env.neqs with Not_found -> MapL.empty + + let add_to_classes t r classes = + MapR.add r + (SetT.add t (try MapR.find r classes with Not_found -> SetT.empty)) + classes + + let update_classes c nc classes = + let s1 = try MapR.find c classes with Not_found -> SetT.empty in + let s2 = try MapR.find nc classes with Not_found -> SetT.empty in + MapR.remove c (MapR.add nc (SetT.union s1 s2) classes) + + let add_to_gamma r c gamma = + List.fold_left + (fun gamma x -> + let s = try MapR.find x gamma with Not_found -> SetR.empty in + MapR.add x (SetR.add r s) gamma) + gamma (R.leaves c) + + (* r1 = r2 => neqs(r1) \uplus neqs(r2) *) + let update_neqs r1 r2 dep env = + let nq_r1 = lookup_for_neqs env r1 in + let nq_r2 = lookup_for_neqs env r2 in + let mapl = + MapL.fold + (fun l1 ex1 mapl -> + try + let ex2 = MapL.find l1 mapl in + let ex = Ex.union (Ex.union ex1 ex2) dep in (* VERIF *) + raise (Inconsistent ex) + with Not_found -> + MapL.add l1 (Ex.union ex1 dep) mapl) + nq_r1 nq_r2 + in + MapR.add r2 mapl (MapR.add r1 mapl env.neqs) + + let filter_leaves r = + List.fold_left (fun p r -> SetR.add r p) SetR.empty (R.leaves r) + + let canon_empty st env = + SetR.fold + (fun p ((z, ex) as acc) -> + let q, ex_q = lookup_by_r p env in + if R.equal p q then acc else (p,q)::z, Ex.union ex_q ex) + st ([], Ex.empty) + + let canon_aux rx = List.fold_left (fun r (p,v) -> R.subst p v r) rx + + let rec canon env r ex_r = + let se = filter_leaves r in + let subst, ex_subst = canon_empty se env in + let r2 = canon_aux r subst in + let ex_r2 = Ex.union ex_r ex_subst in + if R.equal r r2 then r2, ex_r2 else canon env r2 ex_r2 + + let normal_form env r = canon env r Ex.empty + + let find_or_normal_form env r = + try MapR.find r env.repr with Not_found -> normal_form env r + + let init_leaf env p = + let in_repr = MapR.mem p env.repr in + let in_neqs = MapR.mem p env.neqs in + { env with + repr = + if in_repr then env.repr + else MapR.add p (p, Ex.empty) env.repr; + classes = + if in_repr then env.classes + else update_classes p p env.classes; + gamma = + if in_repr then env.gamma + else add_to_gamma p p env.gamma ; + neqs = + if in_neqs then env.neqs + else update_neqs p p Ex.empty env } + + let init_term env t = + let mkr, ctx = R.make t in + let rp, ex = normal_form env mkr in + { make = MapT.add t mkr env.make; + repr = MapR.add mkr (rp,ex) env.repr; + classes = add_to_classes t rp env.classes; + gamma = add_to_gamma mkr rp env.gamma; + neqs = + if MapR.mem rp env.neqs then env.neqs (* pourquoi ce test *) + else MapR.add rp MapL.empty env.neqs}, ctx + + + let update_aux dep set env= + SetRR.fold + (fun (rr, nrr) env -> + { env with + neqs = update_neqs rr nrr dep env ; + classes = update_classes rr nrr env.classes}) + set env + + let apply_sigma_uf env (p, v, dep) = + assert (MapR.mem p env.gamma); + let use_p = MapR.find p env.gamma in + try + let env, tch, neqs_to_up = SetR.fold + (fun r (env, touched, neqs_to_up) -> + let rr, ex = MapR.find r env.repr in + let nrr = R.subst p v rr in + if R.equal rr nrr then env, touched, neqs_to_up + else + let ex = Ex.union ex dep in + let env = + {env with + repr = MapR.add r (nrr, ex) env.repr; + gamma = add_to_gamma r nrr env.gamma } + in + env, (r, nrr, ex)::touched, SetRR.add (rr, nrr) neqs_to_up + ) use_p (env, [], SetRR.empty) in + (* Correction : Do not update neqs twice for the same r *) + update_aux dep neqs_to_up env, tch + + with Not_found -> assert false + + let apply_sigma eqs env tch ((p, v, dep) as sigma) = + let env = init_leaf env p in + let env, touched = apply_sigma_uf env sigma in + env, ((p, touched, v) :: tch) + + end + + let add env t = + if MapT.mem t env.make then env, [] else Env.init_term env t + + let ac_solve eqs dep (env, tch) (p, v) = + (* pourquoi recuperer le representant de rv? r = rv d'apres testopt *) + (* assert ( let rp, _ = Env.find_or_normal_form env p in R.equal p rp); *) + let rv, ex_rv = Env.find_or_normal_form env v in + (* let rv = v in *) + (* assert ( let rv, _ = Env.find_or_normal_form env v in R.equal v rv); *) + let dep = Ex.union ex_rv dep in + Env.apply_sigma eqs env tch (p, rv, dep) + + let check_consistent env r1 r2 dep : unit = + let rr1, ex_r1 = Env.find_or_normal_form env r1 in + let rr2, ex_r2 = Env.find_or_normal_form env r2 in + if R.equal rr1 rr2 + then () (* Remove rule *) + else + let dep = Ex.union dep (Ex.union ex_r1 ex_r2) in + begin + ignore (Env.update_neqs rr1 rr2 dep env); + if R.can_be_equal rr1 rr2 + then () + else raise (Inconsistent dep) + end + + let union env r1 r2 dep = + check_consistent env r1 r2 dep; + () + + let rec distinct env rl dep = + let d = Lit.make (Literal.Distinct (false,rl)) in + let env, _, newds = + List.fold_left + (fun (env, mapr, newds) r -> + let rr, ex = Env.find_or_normal_form env r in + try + let exr = MapR.find rr mapr in + raise (Inconsistent (Ex.union ex exr)) + with Not_found -> + let uex = Ex.union ex dep in + let mdis = + try MapR.find rr env.neqs with Not_found -> MapL.empty in + let mdis = + try + MapL.add d (Ex.merge uex (MapL.find d mdis)) mdis + with Not_found -> + MapL.add d uex mdis + in + let env = Env.init_leaf env rr in + let env = {env with neqs = MapR.add rr mdis env.neqs} in + env, MapR.add rr uex mapr, (rr, ex, mapr)::newds + ) + (env, MapR.empty, []) + rl + in + List.fold_left + (fun env (r1, ex1, mapr) -> + MapR.fold (fun r2 ex2 env -> + let ex = Ex.union ex1 (Ex.union ex2 dep) in + try match R.solve r1 r2 with + | [a, b] -> + if (R.equal a r1 && R.equal b r2) || + (R.equal a r2 && R.equal b r1) then env + else + distinct env [a; b] ex + | [] -> + raise (Inconsistent ex) + | _ -> env + with Unsolvable -> env) mapr env) + env newds + + let are_equal env t1 t2 = + let r1, ex_r1 = Env.lookup_by_t t1 env in + let r2, ex_r2 = Env.lookup_by_t t2 env in + if R.equal r1 r2 then Yes(Ex.union ex_r1 ex_r2) else No + + let are_distinct env t1 t2 = + let r1, ex_r1 = Env.lookup_by_t t1 env in + let r2, ex_r2 = Env.lookup_by_t t2 env in + try + ignore (union env r1 r2 (Ex.union ex_r1 ex_r2)); + No + with Inconsistent ex -> Yes(ex) + + let already_distinct env lr = + let d = Lit.make (Literal.Distinct (false,lr)) in + try + List.iter (fun r -> + let mdis = MapR.find r env.neqs in + ignore (MapL.find d mdis) + ) lr; + true + with Not_found -> false + + let find env t = + Env.lookup_by_t t env + + let find_r = Env.find_or_normal_form + + let mem = Env.mem + + let class_of env t = + try + let rt, _ = MapR.find (MapT.find t env.make) env.repr in + SetT.elements (MapR.find rt env.classes) + with Not_found -> [t] + + +end diff --git a/src/smt/uf.mli b/src/smt/uf.mli new file mode 100644 index 00000000..3b30e261 --- /dev/null +++ b/src/smt/uf.mli @@ -0,0 +1,78 @@ +(**************************************************************************) +(* *) +(* Cubicle *) +(* Combining model checking algorithms and SMT solvers *) +(* *) +(* Sylvain Conchon, Evelyne Contejean *) +(* Francois Bobot, Mohamed Iguernelala, Alain Mebsout *) +(* CNRS, Universite Paris-Sud 11 *) +(* *) +(* Copyright 2011. This file is distributed under the terms of the *) +(* Apache Software License version 2.0 *) +(* *) +(**************************************************************************) + +type answer = Yes of Explanation.t | No + +type 'a literal = + | LSem of 'a Literal.view + | LTerm of Literal.LT.t + +module type ELT = sig + type r + + val make : Term.t -> r * Literal.LT.t list + + val type_info : r -> Ty.t + + val compare : r -> r -> int + + val equal : r -> r -> bool + + val hash : r -> int + + val leaves : r -> r list + + val subst : r -> r -> r -> r + + val solve : r -> r -> (r * r) list + + val term_embed : Term.t -> r + + val term_extract : r -> Term.t option + + val unsolvable : r -> bool + + val fully_interpreted : Symbols.t -> bool + + val print : Format.formatter -> r -> unit +end + +module type S = sig + type t + + module R : ELT + + val empty : t + val add : t -> Term.t -> t * Literal.LT.t list + + val mem : t -> Term.t -> bool + + val find : t -> Term.t -> R.r * Explanation.t + + val find_r : t -> R.r -> R.r * Explanation.t + + val union : + t -> R.r -> R.r -> Explanation.t -> + t * (R.r * (R.r * R.r * Explanation.t) list * R.r) list + + val distinct : t -> R.r list -> Explanation.t -> t + + val are_equal : t -> Term.t -> Term.t -> Sig.answer + val are_distinct : t -> Term.t -> Term.t -> Sig.answer + val already_distinct : t -> R.r list -> bool + + val class_of : t -> Term.t -> Term.t list +end + +module Make ( X : ELT ) : S with module R = X diff --git a/src/example/unionfind.ml b/src/smt/unionfind.ml similarity index 88% rename from src/example/unionfind.ml rename to src/smt/unionfind.ml index 7211fbe0..ab81a1ad 100644 --- a/src/example/unionfind.ml +++ b/src/smt/unionfind.ml @@ -4,13 +4,20 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) +module type OrderedType = sig + type t + val compare : t -> t -> int +end + (* Union-find Module *) -module Make(T : Sig.OrderedType) = struct +module Make(T : OrderedType) = struct exception Unsat of T.t * T.t type var = T.t module M = Map.Make(T) + (* TODO: better treatment of inequalities *) + type t = { rank : int M.t; forbid : ((var * var) list); @@ -43,7 +50,7 @@ module Make(T : Sig.OrderedType) = struct h.parent <- f; cx - (* Highly ineficient treatment of inequalities *) + (* Highly inefficient treatment of inequalities *) let possible h = let aux (a, b) = let ca = find h a in diff --git a/src/example/unionfind.mli b/src/smt/unionfind.mli similarity index 72% rename from src/example/unionfind.mli rename to src/smt/unionfind.mli index 4d559ced..adf2cd25 100644 --- a/src/example/unionfind.mli +++ b/src/smt/unionfind.mli @@ -4,7 +4,12 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Make(T : Sig.OrderedType) : sig +module type OrderedType = sig + type t + val compare : t -> t -> int +end + +module Make(T : OrderedType) : sig type t exception Unsat of T.t * T.t val empty : t diff --git a/src/util/hashcons.ml b/src/util/hashcons.ml new file mode 100644 index 00000000..2f2fa7e7 --- /dev/null +++ b/src/util/hashcons.ml @@ -0,0 +1,28 @@ + +module type ARG = sig + type t + val equal : t -> t -> bool + val hash : t -> int + val set_id : t -> int -> unit +end + +module Make(A : ARG): sig + val hashcons : A.t -> A.t + val iter : (A.t -> unit) -> unit +end = struct + module W = Weak.Make(A) + + let tbl_ = W.create 1024 + let n_ = ref 0 + + (* hashcons terms *) + let hashcons t = + let t' = W.merge tbl_ t in + if t == t' then ( + incr n_; + A.set_id t' !n_; + ); + t' + + let iter yield = W.iter yield tbl_ +end From bb2c931d6826515a37392513fc6389a3fb59e690 Mon Sep 17 00:00:00 2001 From: Simon Cruanes Date: Wed, 24 Aug 2016 18:23:01 +0200 Subject: [PATCH 02/25] wip --- src/smt/literal.ml | 184 --------------- src/smt/literal.mli | 62 ----- src/smt/term.ml | 1 + src/smt/term.mli | 1 + src/smt/uf.ml | 547 +++++++++++++++++++------------------------- src/smt/uf.mli | 65 ++---- 6 files changed, 256 insertions(+), 604 deletions(-) delete mode 100644 src/smt/literal.ml delete mode 100644 src/smt/literal.mli diff --git a/src/smt/literal.ml b/src/smt/literal.ml deleted file mode 100644 index 0d939be7..00000000 --- a/src/smt/literal.ml +++ /dev/null @@ -1,184 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -open Msat - -type 'a view = - | Eq of 'a * 'a - | Distinct of bool * 'a list - | Builtin of bool * ID.t * 'a list - -module type OrderedType = sig - type t - val compare : t -> t -> int - val hash : t -> int - val print : Format.formatter -> t -> unit -end - -module type S = sig - type elt - type t - - val make : elt view -> t - val view : t -> elt view - - val neg : t -> t - - val print : Format.formatter -> t -> unit - - val compare : t -> t -> int - val equal : t -> t -> bool - val hash : t -> int - - module Map : Map.S with type key = t - module Set : Set.S with type elt = t - -end - -module Make (X : OrderedType) : S with type elt = X.t = struct - - type elt = X.t - type t = { - view: X.t view; - mutable tag: int; - } - - module V = struct - type t_ = t - type t = t_ - - let equal a1 a2 = - match a1.view, a2.view with - | Eq(t1, t2), Eq(u1, u2) -> - (X.compare t1 u1 = 0 && X.compare t2 u2 = 0) || - (X.compare t1 u2 = 0 && X.compare t2 u1 = 0) - | Distinct (b1,lt1), Distinct (b2,lt2) -> - (try - b1 = b2 && - List.for_all2 (fun x y -> X.compare x y = 0) lt1 lt2 - with Invalid_argument _ -> false) - | Builtin(b1, n1, l1), Builtin(b2, n2, l2) -> - (try - b1 = b2 && ID.equal n1 n2 - && - List.for_all2 (fun x y -> X.compare x y = 0) l1 l2 - with Invalid_argument _ -> false) - | _ -> false - - let hash a = match a.view with - | Eq(t1, t2) -> abs (19 * (X.hash t1 + X.hash t2)) - | Distinct (b,lt) -> - let x = if b then 7 else 23 in - abs (17 * List.fold_left (fun acc t -> (X.hash t) + acc ) x lt) - | Builtin(b, n, l) -> - let x = if b then 7 else 23 in - abs - (List.fold_left - (fun acc t-> acc*13 + X.hash t) (ID.hash n+x) l) - - let set_id t tag = t.tag <- tag - end - - module H = Hashcons.Make(V) - - let compare a1 a2 = Pervasives.compare a1.tag a2.tag - let equal a1 a2 = a1 == a2 - let hash a1 = a1.tag - - module T = struct - type t_ = t - type t = t_ - let compare=compare - end - - let make t = H.hashcons {view=t; tag= -1} - let view a = a.view - - let neg a = match view a with - | Eq(x, y) -> make (Distinct (false,[x; y])) - | Distinct (false, [x; y]) -> make (Eq (x, y)) - | Distinct (true, [x; y]) -> make (Distinct (false,[x; y])) - | Distinct (false, l) -> make (Distinct (true,l)) - | Distinct _ -> assert false - | Builtin(b, n, l) -> make (Builtin (not b, n, l)) - - let print_list fmt = function - | [] -> () - | z :: l -> - Format.fprintf fmt "%a" X.print z; - List.iter (Format.fprintf fmt ", %a" X.print) l - - let print fmt a = match view a with - | Eq (z1, z2) -> - if equal z1 z2 then Format.fprintf fmt "True" - else Format.fprintf fmt "%a=%a" X.print z1 X.print z2 - | Distinct (b,(z::l)) -> - let b = if b then "~" else "" in - Format.fprintf fmt "%s%a" b X.print z; - List.iter (fun x -> Format.fprintf fmt "<>%a" X.print x) l - | Builtin (b, n, l) -> - let b = if b then "" else "~" in - Format.fprintf fmt "%s%s(%a)" b (ID.to_string n) print_list l - | _ -> assert false - - module Set = Set.Make(T) - module Map = Map.Make(T) - -end - -module type S_Term = sig - - include S with type elt = Term.t - - val mk_pred : Term.t -> t - - val true_ : t - val false_ : t - - (* val terms_of : t -> Term.Set.t - val vars_of : t -> Symbols.Set.t - *) - (* module SetEq : Set.S with type elt = t * Term.t * Term.t*) -end - -module LT : S_Term = struct - - module L = Make(Term) - include L - - let mk_pred t = make (Eq (t, Term.true_) ) - - let true_ = mk_pred Term.true_ - let false_ = mk_pred Term.false_ - - let neg a = match view a with - | Eq(t1, t2) when Term.equal t2 Term.false_ -> - make (Eq (t1, Term.true_)) - | Eq(t1, t2) when Term.equal t2 Term.true_ -> - make (Eq (t1, Term.false_)) - | _ -> L.neg a - - (* let terms_of a = - let l = match view a with - | Eq (t1, t2) -> [t1; t2] - | Distinct (_, l) | Builtin (_, _, l) -> l - in - List.fold_left Term.subterms Term.Set.empty l - *) - - module SS = Symbols.Set - (* let vars_of a = - Term.Set.fold (fun t -> SS.union (Term.vars_of t)) (terms_of a) SS.empty - *) -end - diff --git a/src/smt/literal.mli b/src/smt/literal.mli deleted file mode 100644 index f38963ab..00000000 --- a/src/smt/literal.mli +++ /dev/null @@ -1,62 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -open Msat - -module type OrderedType = sig - type t - val compare : t -> t -> int - val hash : t -> int - val print : Format.formatter -> t -> unit -end - -type 'a view = - | Eq of 'a * 'a - | Distinct of bool * 'a list - | Builtin of bool * ID.t * 'a list - -module type S = sig - type elt - type t - - val make : elt view -> t - val view : t -> elt view - - val neg : t -> t - - val print : Format.formatter -> t -> unit - - val compare : t -> t -> int - val equal : t -> t -> bool - val hash : t -> int - - module Map : Map.S with type key = t - module Set : Set.S with type elt = t - -end - -module Make ( X : OrderedType ) : S with type elt = X.t - -module type S_Term = sig - - include S with type elt = Term.t - - val mk_pred : Term.t -> t - val true_ : t - val false_ : t - -end - -module LT : S_Term - - diff --git a/src/smt/term.ml b/src/smt/term.ml index 4d0db744..8a670468 100644 --- a/src/smt/term.ml +++ b/src/smt/term.ml @@ -59,6 +59,7 @@ end module T = Hashcons.Make(H) let view t = t +let head t = t.head let rec print fmt t = match t.head with | Ite (a,b,c) -> diff --git a/src/smt/term.mli b/src/smt/term.mli index c9542d3d..92defc96 100644 --- a/src/smt/term.mli +++ b/src/smt/term.mli @@ -26,6 +26,7 @@ and head = | Ite of t * t * t val view : t -> view +val head : t -> head val app : Symbols.t -> t list -> Ty.t -> t val const : Symbols.t -> Ty.t -> t diff --git a/src/smt/uf.ml b/src/smt/uf.ml index 573189c6..9ee4e98f 100644 --- a/src/smt/uf.ml +++ b/src/smt/uf.ml @@ -21,191 +21,124 @@ type 'a literal = exception Inconsistent of Explanation.t exception Unsolvable -module type ELT = sig - type r +module Ex = Explanation +module Sy = Symbols +module T = Term +module MapT = Term.Map +module SetT = Term.Set - val make : Term.t -> r * Literal.LT.t list +module Lit = Literal.Make(T) +module MapL = Lit.Map - val compare : r -> r -> int +module MapR = MapT +module SetR = SetT - val equal : r -> r -> bool +module R = struct + include T + type r = t - val hash : r -> int - - val leaves : r -> r list - - val subst : r -> r -> r -> r - - val can_be_equal : r -> r -> bool - - val term_embed : Term.t -> r - - val term_extract : r -> Term.t option - - val unsolvable : r -> bool - - val fully_interpreted : Symbols.t -> bool - - val print : Format.formatter -> r -> unit + let leaves t : r list = match T.head t with + | T.Ite (a, _, _) -> [a] + | T.App (_, l) -> l end -module type S = sig - type t +type r = R.r - module R : ELT - - val empty : t - val add : t -> Term.t -> t * Literal.LT.t list - - val mem : t -> Term.t -> bool - - val find : t -> Term.t -> R.r * Explanation.t - - val find_r : t -> R.r -> R.r * Explanation.t - - val union : - t -> R.r -> R.r -> Explanation.t -> - t * (R.r * (R.r * R.r * Explanation.t) list * R.r) list - - val distinct : t -> R.r list -> Explanation.t -> t - - val are_equal : t -> Term.t -> Term.t -> Sig.answer - val are_distinct : t -> Term.t -> Term.t -> Sig.answer - val already_distinct : t -> R.r list -> bool - - val class_of : t -> Term.t -> Term.t list -end - -module Make ( R : ELT ) = struct - - module Ex = Explanation - module R = R - module Sy = Symbols - module T = Term - module MapT = Term.Map - module SetT = Term.Set - - module Lit = Literal.Make(struct type t = R.r include R end) - module MapL = Lit.Map - - module MapR = Map.Make(struct type t = R.r let compare = R.compare end) - - module SetR = Set.Make(struct type t = R.r let compare = R.compare end) - - module SetRR = Set.Make(struct - type t = R.r * R.r - let compare (r1, r1') (r2, r2') = - let c = R.compare r1 r2 in - if c <> 0 then c - else R.compare r1' r2' - end) +module SetRR = Set.Make(struct + type t = r * r + let compare (r1, r1') (r2, r2') = + let c = T.compare r1 r2 in + if c <> 0 then c + else T.compare r1' r2' + end) - type t = { +type t = { + (* term -> [t] *) + make : r MapT.t; - (* term -> [t] *) - make : R.r MapT.t; + (* representative table *) + repr : (r * Ex.t) MapR.t; - (* representative table *) - repr : (R.r * Ex.t) MapR.t; + (* r -> class (of terms) *) + classes : SetT.t MapR.t; - (* r -> class (of terms) *) - classes : SetT.t MapR.t; + (*associates each value r with the set of semantical values whose + representatives contains r *) + gamma : SetR.t MapR.t; - (*associates each value r with the set of semantical values whose - representatives contains r *) - gamma : SetR.t MapR.t; + (* the disequations map *) + neqs: Ex.t MapL.t MapR.t; - (* the disequations map *) - neqs: Ex.t MapL.t MapR.t; +} - } +let empty = { + make = MapT.empty; + repr = MapR.empty; + classes = MapR.empty; + gamma = MapR.empty; + neqs = MapR.empty; +} - let empty = { - make = MapT.empty; - repr = MapR.empty; - classes = MapR.empty; - gamma = MapR.empty; - neqs = MapR.empty; - } +module Env = struct + let mem env t = MapT.mem t env.make - module Env = struct + let lookup_by_t t env = + try MapR.find (MapT.find t env.make) env.repr + with Not_found -> + assert false (*R.make t, Ex.empty*) (* XXXX *) - let mem env t = MapT.mem t env.make + let lookup_by_r r env = + try MapR.find r env.repr with Not_found -> r, Ex.empty - let lookup_by_t t env = - try MapR.find (MapT.find t env.make) env.repr - with Not_found -> - assert false (*R.make t, Ex.empty*) (* XXXX *) + let lookup_for_neqs env r = + try MapR.find r env.neqs with Not_found -> MapL.empty - let lookup_by_r r env = - try MapR.find r env.repr with Not_found -> r, Ex.empty + let add_to_classes t r classes = + MapR.add r + (SetT.add t (try MapR.find r classes with Not_found -> SetT.empty)) + classes - let lookup_for_neqs env r = - try MapR.find r env.neqs with Not_found -> MapL.empty + let update_classes c nc classes = + let s1 = try MapR.find c classes with Not_found -> SetT.empty in + let s2 = try MapR.find nc classes with Not_found -> SetT.empty in + MapR.remove c (MapR.add nc (SetT.union s1 s2) classes) - let add_to_classes t r classes = - MapR.add r - (SetT.add t (try MapR.find r classes with Not_found -> SetT.empty)) - classes + let add_to_gamma r c gamma = + List.fold_left + (fun gamma x -> + let s = try MapR.find x gamma with Not_found -> SetR.empty in + MapR.add x (SetR.add r s) gamma) + gamma + (R.leaves c) - let update_classes c nc classes = - let s1 = try MapR.find c classes with Not_found -> SetT.empty in - let s2 = try MapR.find nc classes with Not_found -> SetT.empty in - MapR.remove c (MapR.add nc (SetT.union s1 s2) classes) + (* r1 = r2 => neqs(r1) \uplus neqs(r2) *) + let update_neqs r1 r2 dep env = + let nq_r1 = lookup_for_neqs env r1 in + let nq_r2 = lookup_for_neqs env r2 in + let mapl = + MapL.fold + (fun l1 ex1 mapl -> + try + let ex2 = MapL.find l1 mapl in + let ex = Ex.union (Ex.union ex1 ex2) dep in (* VERIF *) + raise (Inconsistent ex) + with Not_found -> + MapL.add l1 (Ex.union ex1 dep) mapl) + nq_r1 nq_r2 + in + MapR.add r2 mapl (MapR.add r1 mapl env.neqs) - let add_to_gamma r c gamma = - List.fold_left - (fun gamma x -> - let s = try MapR.find x gamma with Not_found -> SetR.empty in - MapR.add x (SetR.add r s) gamma) - gamma (R.leaves c) + let filter_leaves r = + List.fold_left (fun p r -> SetR.add r p) SetR.empty (R.leaves r) - (* r1 = r2 => neqs(r1) \uplus neqs(r2) *) - let update_neqs r1 r2 dep env = - let nq_r1 = lookup_for_neqs env r1 in - let nq_r2 = lookup_for_neqs env r2 in - let mapl = - MapL.fold - (fun l1 ex1 mapl -> - try - let ex2 = MapL.find l1 mapl in - let ex = Ex.union (Ex.union ex1 ex2) dep in (* VERIF *) - raise (Inconsistent ex) - with Not_found -> - MapL.add l1 (Ex.union ex1 dep) mapl) - nq_r1 nq_r2 - in - MapR.add r2 mapl (MapR.add r1 mapl env.neqs) + let find_or_normal_form env r = + try MapR.find r env.repr with Not_found -> r, Ex.empty - let filter_leaves r = - List.fold_left (fun p r -> SetR.add r p) SetR.empty (R.leaves r) - - let canon_empty st env = - SetR.fold - (fun p ((z, ex) as acc) -> - let q, ex_q = lookup_by_r p env in - if R.equal p q then acc else (p,q)::z, Ex.union ex_q ex) - st ([], Ex.empty) - - let canon_aux rx = List.fold_left (fun r (p,v) -> R.subst p v r) rx - - let rec canon env r ex_r = - let se = filter_leaves r in - let subst, ex_subst = canon_empty se env in - let r2 = canon_aux r subst in - let ex_r2 = Ex.union ex_r ex_subst in - if R.equal r r2 then r2, ex_r2 else canon env r2 ex_r2 - - let normal_form env r = canon env r Ex.empty - - let find_or_normal_form env r = - try MapR.find r env.repr with Not_found -> normal_form env r - - let init_leaf env p = - let in_repr = MapR.mem p env.repr in - let in_neqs = MapR.mem p env.neqs in - { env with + let init_leaf env p = + let in_repr = MapR.mem p env.repr in + let in_neqs = MapR.mem p env.neqs in + { env with repr = if in_repr then env.repr else MapR.add p (p, Ex.empty) env.repr; @@ -219,163 +152,159 @@ module Make ( R : ELT ) = struct if in_neqs then env.neqs else update_neqs p p Ex.empty env } - let init_term env t = - let mkr, ctx = R.make t in - let rp, ex = normal_form env mkr in - { make = MapT.add t mkr env.make; - repr = MapR.add mkr (rp,ex) env.repr; - classes = add_to_classes t rp env.classes; - gamma = add_to_gamma mkr rp env.gamma; - neqs = - if MapR.mem rp env.neqs then env.neqs (* pourquoi ce test *) - else MapR.add rp MapL.empty env.neqs}, ctx + let init_term env t = + let mkr, ctx = R.make t in + let rp, ex = normal_form env mkr in + { make = MapT.add t mkr env.make; + repr = MapR.add mkr (rp,ex) env.repr; + classes = add_to_classes t rp env.classes; + gamma = add_to_gamma mkr rp env.gamma; + neqs = + if MapR.mem rp env.neqs then env.neqs (* pourquoi ce test *) + else MapR.add rp MapL.empty env.neqs}, ctx - let update_aux dep set env= - SetRR.fold - (fun (rr, nrr) env -> - { env with + let update_aux dep set env= + SetRR.fold + (fun (rr, nrr) env -> + { env with neqs = update_neqs rr nrr dep env ; classes = update_classes rr nrr env.classes}) - set env + set env - let apply_sigma_uf env (p, v, dep) = - assert (MapR.mem p env.gamma); - let use_p = MapR.find p env.gamma in - try - let env, tch, neqs_to_up = SetR.fold - (fun r (env, touched, neqs_to_up) -> - let rr, ex = MapR.find r env.repr in - let nrr = R.subst p v rr in - if R.equal rr nrr then env, touched, neqs_to_up - else - let ex = Ex.union ex dep in - let env = - {env with + let apply_sigma_uf env (p, v, dep) = + assert (MapR.mem p env.gamma); + let use_p = MapR.find p env.gamma in + try + let env, tch, neqs_to_up = SetR.fold + (fun r (env, touched, neqs_to_up) -> + let rr, ex = MapR.find r env.repr in + let nrr = R.subst p v rr in + if R.equal rr nrr then env, touched, neqs_to_up + else + let ex = Ex.union ex dep in + let env = + {env with repr = MapR.add r (nrr, ex) env.repr; gamma = add_to_gamma r nrr env.gamma } - in - env, (r, nrr, ex)::touched, SetRR.add (rr, nrr) neqs_to_up - ) use_p (env, [], SetRR.empty) in - (* Correction : Do not update neqs twice for the same r *) - update_aux dep neqs_to_up env, tch - - with Not_found -> assert false - - let apply_sigma eqs env tch ((p, v, dep) as sigma) = - let env = init_leaf env p in - let env, touched = apply_sigma_uf env sigma in - env, ((p, touched, v) :: tch) - - end - - let add env t = - if MapT.mem t env.make then env, [] else Env.init_term env t - - let ac_solve eqs dep (env, tch) (p, v) = - (* pourquoi recuperer le representant de rv? r = rv d'apres testopt *) - (* assert ( let rp, _ = Env.find_or_normal_form env p in R.equal p rp); *) - let rv, ex_rv = Env.find_or_normal_form env v in - (* let rv = v in *) - (* assert ( let rv, _ = Env.find_or_normal_form env v in R.equal v rv); *) - let dep = Ex.union ex_rv dep in - Env.apply_sigma eqs env tch (p, rv, dep) - - let check_consistent env r1 r2 dep : unit = - let rr1, ex_r1 = Env.find_or_normal_form env r1 in - let rr2, ex_r2 = Env.find_or_normal_form env r2 in - if R.equal rr1 rr2 - then () (* Remove rule *) - else - let dep = Ex.union dep (Ex.union ex_r1 ex_r2) in - begin - ignore (Env.update_neqs rr1 rr2 dep env); - if R.can_be_equal rr1 rr2 - then () - else raise (Inconsistent dep) - end - - let union env r1 r2 dep = - check_consistent env r1 r2 dep; - () - - let rec distinct env rl dep = - let d = Lit.make (Literal.Distinct (false,rl)) in - let env, _, newds = - List.fold_left - (fun (env, mapr, newds) r -> - let rr, ex = Env.find_or_normal_form env r in - try - let exr = MapR.find rr mapr in - raise (Inconsistent (Ex.union ex exr)) - with Not_found -> - let uex = Ex.union ex dep in - let mdis = - try MapR.find rr env.neqs with Not_found -> MapL.empty in - let mdis = - try - MapL.add d (Ex.merge uex (MapL.find d mdis)) mdis - with Not_found -> - MapL.add d uex mdis - in - let env = Env.init_leaf env rr in - let env = {env with neqs = MapR.add rr mdis env.neqs} in - env, MapR.add rr uex mapr, (rr, ex, mapr)::newds - ) - (env, MapR.empty, []) - rl - in - List.fold_left - (fun env (r1, ex1, mapr) -> - MapR.fold (fun r2 ex2 env -> - let ex = Ex.union ex1 (Ex.union ex2 dep) in - try match R.solve r1 r2 with - | [a, b] -> - if (R.equal a r1 && R.equal b r2) || - (R.equal a r2 && R.equal b r1) then env - else - distinct env [a; b] ex - | [] -> - raise (Inconsistent ex) - | _ -> env - with Unsolvable -> env) mapr env) - env newds - - let are_equal env t1 t2 = - let r1, ex_r1 = Env.lookup_by_t t1 env in - let r2, ex_r2 = Env.lookup_by_t t2 env in - if R.equal r1 r2 then Yes(Ex.union ex_r1 ex_r2) else No - - let are_distinct env t1 t2 = - let r1, ex_r1 = Env.lookup_by_t t1 env in - let r2, ex_r2 = Env.lookup_by_t t2 env in - try - ignore (union env r1 r2 (Ex.union ex_r1 ex_r2)); - No - with Inconsistent ex -> Yes(ex) - - let already_distinct env lr = - let d = Lit.make (Literal.Distinct (false,lr)) in - try - List.iter (fun r -> - let mdis = MapR.find r env.neqs in - ignore (MapL.find d mdis) - ) lr; - true - with Not_found -> false - - let find env t = - Env.lookup_by_t t env - - let find_r = Env.find_or_normal_form - - let mem = Env.mem - - let class_of env t = - try - let rt, _ = MapR.find (MapT.find t env.make) env.repr in - SetT.elements (MapR.find rt env.classes) - with Not_found -> [t] + in + env, (r, nrr, ex)::touched, SetRR.add (rr, nrr) neqs_to_up + ) use_p (env, [], SetRR.empty) in + (* Correction : Do not update neqs twice for the same r *) + update_aux dep neqs_to_up env, tch + with Not_found -> assert false + let apply_sigma eqs env tch ((p, v, dep) as sigma) = + let env = init_leaf env p in + let env, touched = apply_sigma_uf env sigma in + env, ((p, touched, v) :: tch) end + +let add env t = + if MapT.mem t env.make then env, [] else Env.init_term env t + +let ac_solve eqs dep (env, tch) (p, v) = + (* pourquoi recuperer le representant de rv? r = rv d'apres testopt *) + (* assert ( let rp, _ = Env.find_or_normal_form env p in R.equal p rp); *) + let rv, ex_rv = Env.find_or_normal_form env v in + (* let rv = v in *) + (* assert ( let rv, _ = Env.find_or_normal_form env v in R.equal v rv); *) + let dep = Ex.union ex_rv dep in + Env.apply_sigma eqs env tch (p, rv, dep) + +let check_consistent env r1 r2 dep : unit = + let rr1, ex_r1 = Env.find_or_normal_form env r1 in + let rr2, ex_r2 = Env.find_or_normal_form env r2 in + if R.equal rr1 rr2 + then () (* Remove rule *) + else + let dep = Ex.union dep (Ex.union ex_r1 ex_r2) in + begin + ignore (Env.update_neqs rr1 rr2 dep env); + if R.can_be_equal rr1 rr2 + then () + else raise (Inconsistent dep) + end + +let union env r1 r2 dep = + check_consistent env r1 r2 dep; + () + +let rec distinct env rl dep = + let d = Lit.make (Literal.Distinct (false,rl)) in + let env, _, newds = + List.fold_left + (fun (env, mapr, newds) r -> + let rr, ex = Env.find_or_normal_form env r in + try + let exr = MapR.find rr mapr in + raise (Inconsistent (Ex.union ex exr)) + with Not_found -> + let uex = Ex.union ex dep in + let mdis = + try MapR.find rr env.neqs with Not_found -> MapL.empty in + let mdis = + try + MapL.add d (Ex.merge uex (MapL.find d mdis)) mdis + with Not_found -> + MapL.add d uex mdis + in + let env = Env.init_leaf env rr in + let env = {env with neqs = MapR.add rr mdis env.neqs} in + env, MapR.add rr uex mapr, (rr, ex, mapr)::newds + ) + (env, MapR.empty, []) + rl + in + List.fold_left + (fun env (r1, ex1, mapr) -> + MapR.fold (fun r2 ex2 env -> + let ex = Ex.union ex1 (Ex.union ex2 dep) in + try match R.solve r1 r2 with + | [a, b] -> + if (R.equal a r1 && R.equal b r2) || + (R.equal a r2 && R.equal b r1) then env + else + distinct env [a; b] ex + | [] -> + raise (Inconsistent ex) + | _ -> env + with Unsolvable -> env) mapr env) + env newds + +let are_equal env t1 t2 = + let r1, ex_r1 = Env.lookup_by_t t1 env in + let r2, ex_r2 = Env.lookup_by_t t2 env in + if R.equal r1 r2 then Yes(Ex.union ex_r1 ex_r2) else No + +let are_distinct env t1 t2 = + let r1, ex_r1 = Env.lookup_by_t t1 env in + let r2, ex_r2 = Env.lookup_by_t t2 env in + try + ignore (union env r1 r2 (Ex.union ex_r1 ex_r2)); + No + with Inconsistent ex -> Yes(ex) + +let already_distinct env lr = + let d = Lit.make (Literal.Distinct (false,lr)) in + try + List.iter (fun r -> + let mdis = MapR.find r env.neqs in + ignore (MapL.find d mdis) + ) lr; + true + with Not_found -> false + +let find env t = + Env.lookup_by_t t env + +let find_r = Env.find_or_normal_form + +let mem = Env.mem + +let class_of env t = + try + let rt, _ = MapR.find (MapT.find t env.make) env.repr in + SetT.elements (MapR.find rt env.classes) + with Not_found -> [t] diff --git a/src/smt/uf.mli b/src/smt/uf.mli index 3b30e261..8205e3ee 100644 --- a/src/smt/uf.mli +++ b/src/smt/uf.mli @@ -18,61 +18,28 @@ type 'a literal = | LSem of 'a Literal.view | LTerm of Literal.LT.t -module type ELT = sig - type r +type t - val make : Term.t -> r * Literal.LT.t list +type r +(** representative *) - val type_info : r -> Ty.t +val empty : t +val add : t -> Term.t -> t * Literal.LT.t list - val compare : r -> r -> int +val mem : t -> Term.t -> bool - val equal : r -> r -> bool +val find : t -> Term.t -> r * Explanation.t - val hash : r -> int +val find_r : t -> r -> r * Explanation.t - val leaves : r -> r list +val union : + t -> r -> r -> Explanation.t -> + t * (r * (r * r * Explanation.t) list * r) list - val subst : r -> r -> r -> r +val distinct : t -> r list -> Explanation.t -> t - val solve : r -> r -> (r * r) list +val are_equal : t -> Term.t -> Term.t -> Sig.answer +val are_distinct : t -> Term.t -> Term.t -> Sig.answer +val already_distinct : t -> r list -> bool - val term_embed : Term.t -> r - - val term_extract : r -> Term.t option - - val unsolvable : r -> bool - - val fully_interpreted : Symbols.t -> bool - - val print : Format.formatter -> r -> unit -end - -module type S = sig - type t - - module R : ELT - - val empty : t - val add : t -> Term.t -> t * Literal.LT.t list - - val mem : t -> Term.t -> bool - - val find : t -> Term.t -> R.r * Explanation.t - - val find_r : t -> R.r -> R.r * Explanation.t - - val union : - t -> R.r -> R.r -> Explanation.t -> - t * (R.r * (R.r * R.r * Explanation.t) list * R.r) list - - val distinct : t -> R.r list -> Explanation.t -> t - - val are_equal : t -> Term.t -> Term.t -> Sig.answer - val are_distinct : t -> Term.t -> Term.t -> Sig.answer - val already_distinct : t -> R.r list -> bool - - val class_of : t -> Term.t -> Term.t list -end - -module Make ( X : ELT ) : S with module R = X +val class_of : t -> Term.t -> Term.t list From 742f8c469d94113b703e60fa84e02d0d1a316065 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Wed, 7 Sep 2016 17:58:07 +0200 Subject: [PATCH 03/25] Added Expr and typing module from ArchSat --- .merlin | 4 +- _tags | 7 +- src/main.ml | 137 +------ src/smt/cnf.ml | 9 - src/smt/cnf.mli | 9 - src/smt/expr.ml | 87 ----- src/smt/expr.mli | 42 -- src/util/.merlin | 11 - src/util/expr.ml | 522 +++++++++++++++++++++++++ src/util/expr.mli | 319 +++++++++++++++ src/util/parsedimacs.ml | 75 ---- src/util/parsedimacs.mli | 9 - src/util/smtlib/.merlin | 9 - src/util/smtlib/lexsmtlib.mli | 3 - src/util/smtlib/lexsmtlib.mll | 48 --- src/util/smtlib/parsesmtlib.mly | 330 ---------------- src/util/smtlib/smtlib.ml | 112 ------ src/util/smtlib/smtlib.mli | 7 - src/util/smtlib/smtlib_syntax.ml | 229 ----------- src/util/smtlib/smtlib_syntax.mli | 123 ------ src/util/smtlib/smtlib_util.ml | 12 - src/util/smtlib/smtlib_util.mli | 14 - src/util/type.ml | 619 ++++++++++++++++++++++++++++++ src/util/type.mli | 15 + 24 files changed, 1503 insertions(+), 1249 deletions(-) delete mode 100644 src/smt/cnf.ml delete mode 100644 src/smt/cnf.mli delete mode 100644 src/smt/expr.ml delete mode 100644 src/smt/expr.mli delete mode 100644 src/util/.merlin create mode 100644 src/util/expr.ml create mode 100644 src/util/expr.mli delete mode 100644 src/util/parsedimacs.ml delete mode 100644 src/util/parsedimacs.mli delete mode 100644 src/util/smtlib/.merlin delete mode 100644 src/util/smtlib/lexsmtlib.mli delete mode 100644 src/util/smtlib/lexsmtlib.mll delete mode 100644 src/util/smtlib/parsesmtlib.mly delete mode 100644 src/util/smtlib/smtlib.ml delete mode 100644 src/util/smtlib/smtlib.mli delete mode 100644 src/util/smtlib/smtlib_syntax.ml delete mode 100644 src/util/smtlib/smtlib_syntax.mli delete mode 100644 src/util/smtlib/smtlib_util.ml delete mode 100644 src/util/smtlib/smtlib_util.mli create mode 100644 src/util/type.ml create mode 100644 src/util/type.mli diff --git a/.merlin b/.merlin index d7ed7f73..6457aa65 100644 --- a/.merlin +++ b/.merlin @@ -4,7 +4,6 @@ S src/sat S src/smt S src/backend S src/util -S src/util/smtlib S tests B _build/src/ @@ -13,6 +12,7 @@ B _build/src/solver B _build/src/sat B _build/src/smt B _build/src/util -B _build/src/util/smtlib B _build/src/backend B _build/tests + +PKG dolmen diff --git a/_tags b/_tags index 6511633d..47e25776 100644 --- a/_tags +++ b/_tags @@ -9,10 +9,9 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : include : include : include -: include : include +: include : include -: include # Pack options : for-pack(Msat) @@ -22,6 +21,10 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : for-pack(Msat_sat) : for-pack(Msat_smt) +# Bin options +: package(dolmen) +: package(dolmen) + # more warnings : warn_K, warn_Y, warn_X : short_paths, safe_string, strict_sequence diff --git a/src/main.ml b/src/main.ml index 16a0ed8d..0a8676db 100644 --- a/src/main.ml +++ b/src/main.ml @@ -5,45 +5,27 @@ Copyright 2014 Simon Cruanes *) module F = Expr + (* module T = Msat_smt.Cnf.S module Sat = Msat_sat.Sat.Make(struct end) module Smt = Msat_smt.Smt.Make(struct end) module Mcsat = Msat_smt.Mcsat.Make(struct end) + *) + +module P = + Dolmen.Logic.Make(Dolmen.ParseLocation) + (Dolmen.Id)(Dolmen.Term)(Dolmen.Statement) exception Incorrect_model exception Out_of_time exception Out_of_space -(* IO wrappers *) -(* Types for input/output languages *) -type sat_input = - | Auto - | Dimacs - | Smtlib - -type sat_output = - | Standard (* Only output problem status *) - | Dedukti - | Dot - type solver = | Sat | Smt | Mcsat -let input = ref Auto -let output = ref Standard let solver = ref Smt - -let input_list = [ - "auto", Auto; - "dimacs", Dimacs; - "smtlib", Smtlib; -] -let output_list = [ - "dot", Dot; - "dk", Dedukti; -] let solver_list = [ "sat", Sat; "smt", Smt; @@ -61,86 +43,8 @@ let set_flag opt arg flag l = with Not_found -> invalid_arg (error_msg opt arg l) -let set_input s = set_flag "Input" s input input_list -let set_output s = set_flag "Output" s output output_list let set_solver s = set_flag "Solver" s solver solver_list -(* Input Parsing *) -let rec rev_flat_map f acc = function - | [] -> acc - | a :: r -> rev_flat_map f (List.rev_append (f a) acc) r - -let format_of_filename s = - let last n = - try String.sub s (String.length s - n) n - with Invalid_argument _ -> "" - in - if last 4 = ".cnf" then - Dimacs - else if last 5 = ".smt2" then - Smtlib - else (* Default choice *) - Dimacs - -let parse_with_input file = function - | Auto -> assert false - | Dimacs -> List.rev_map (List.rev_map F.mk_prop) (Parsedimacs.parse file) - | Smtlib -> rev_flat_map T.make_cnf [] (Smtlib.parse file) - -let parse_input file = - parse_with_input file (match !input with - | Auto -> format_of_filename file - | f -> f) - -(* Printing wrappers *) -let std = Format.std_formatter - -let print format = match !output with - | Standard -> - Format.kfprintf (fun fmt -> Format.fprintf fmt "@.") std format - | Dot -> - Format.fprintf std "/* "; - Format.kfprintf (fun fmt -> Format.fprintf fmt " */@.") std format - | Dedukti -> - Format.fprintf std "(; "; - Format.kfprintf (fun fmt -> Format.fprintf fmt " ;)@.") std format - -let print_proof proof = match !output with - | Standard -> () - | Dot -> Smt.print_dot std proof - | Dedukti -> Smt.print_dedukti std proof - -let print_mcproof proof = match !output with - | Standard -> () - | Dot -> Mcsat.print_dot std proof - | Dedukti -> Mcsat.print_dedukti std proof - -let rec print_cl fmt = function - | [] -> Format.fprintf fmt "[]" - | [a] -> F.print fmt a - | a :: ((_ :: _) as r) -> Format.fprintf fmt "%a ∨ %a" F.print a print_cl r - -let print_lcl l = - List.iter (fun c -> Format.fprintf std "%a@\n" print_cl c) l - -let print_lclause l = - List.iter (fun c -> Format.fprintf std "%a@\n" Smt.print_clause c) l - -let print_mclause l = - List.iter (fun c -> Format.fprintf std "%a@\n" Mcsat.print_clause c) l - -let print_cnf cnf = match !output with - | Standard -> print_lcl cnf - | Dot | Dedukti -> () - -let print_unsat_core u = match !output with - | Standard -> print_lclause u - | Dot | Dedukti -> () - -let print_mc_unsat_core u = match !output with - | Standard -> print_mclause u - | Dot | Dedukti -> () - (* Arguments parsing *) let file = ref "" let p_cnf = ref false @@ -170,7 +74,7 @@ let int_arg r arg = | 'd' -> multiplier 86400. | '0'..'9' -> r := float_of_string arg | _ -> raise (Arg.Bad "bad numeric argument") - with Failure "float_of_string" -> raise (Arg.Bad "bad numeric argument") + with Failure _ -> raise (Arg.Bad "bad numeric argument") let setup_gc_stat () = at_exit (fun () -> @@ -189,12 +93,8 @@ let argspec = Arg.align [ " Build, check and print the proof (if output is set), if unsat"; "-gc", Arg.Unit setup_gc_stat, " Outputs statistics about the GC"; - "-i", Arg.String set_input, - " Sets the input format (default auto)"; - "-o", Arg.String set_output, - " Sets the output format (default none)"; "-s", Arg.String set_solver, - "{smt,mcsat} Sets the solver to use (default smt)"; + "{sat,smt,mcsat} Sets the solver to use (default smt)"; "-size", Arg.String (int_arg size_limit), "[kMGT] Sets the size limit for the sat solver"; "-time", Arg.String (int_arg time_limit), @@ -215,9 +115,6 @@ let check () = else if s > !size_limit then raise Out_of_space -(* Entry file parsing *) -let get_cnf () = parse_input !file - let main () = (* Administrative duties *) Arg.parse argspec input_file usage; @@ -228,6 +125,12 @@ let main () = let al = Gc.create_alarm check in (* Interesting stuff happening *) + let _, _input = P.parse_file !file in + Gc.delete_alarm al; + () + + (* Old code ... + let cnf = get_cnf () in if !p_cnf then print_cnf cnf; @@ -257,7 +160,6 @@ let main () = | Mcsat -> Mcsat.assume cnf; let res = Mcsat.solve () in - Gc.delete_alarm al; begin match res with | Mcsat.Sat sat -> let t = Sys.time () in @@ -275,18 +177,21 @@ let main () = print_mc_unsat_core (Mcsat.unsat_core p) end; print "Unsat (%f/%f)" t (Sys.time () -. t) - end + end + +*) let () = try main () with | Incorrect_model -> - print "Internal error : incorrect *sat* model"; + Format.printf "Internal error : incorrect *sat* model@."; exit 4 | Out_of_time -> - print "Timeout"; + Format.printf "Timeout@."; exit 2 | Out_of_space -> - print "Spaceout"; + Format.printf "Spaceout@."; exit 3 + diff --git a/src/smt/cnf.ml b/src/smt/cnf.ml deleted file mode 100644 index 999271ac..00000000 --- a/src/smt/cnf.ml +++ /dev/null @@ -1,9 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -open Msat - -module S = Tseitin.Make(Expr) diff --git a/src/smt/cnf.mli b/src/smt/cnf.mli deleted file mode 100644 index 6eb68976..00000000 --- a/src/smt/cnf.mli +++ /dev/null @@ -1,9 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -open Msat - -module S : Tseitin.S with type atom = Expr.Formula.t diff --git a/src/smt/expr.ml b/src/smt/expr.ml deleted file mode 100644 index dda3d7fc..00000000 --- a/src/smt/expr.ml +++ /dev/null @@ -1,87 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) -open Msat - -module I = Formula_intf -module Term = Term - -exception Invalid_prop - -type term = Term.t - -(* atomic formula - - Prop: - - sign of int determines sign of formula - - odd numbers --> fresh atoms (for Tseitin CNF) - - even numbers --> used for regular int-mapping -*) -type formula = - | Prop of int - | Equal of term * term - | Distinct of term * term - -type t = formula -type proof = unit - -let dummy = Prop 0 - -let max_fresh = ref 0 - -let fresh () = - incr max_fresh; - Prop (2 * !max_fresh + 1) - -let mk_prop i = - if i <> 0 && i < max_int / 2 then Prop (2 * i) - else raise Invalid_prop - -let order_ t1 t2 = if Term.compare t1 t2 > 0 then t2,t1 else t1,t2 - -let mk_eq a b = - let a, b = order_ a b in - Equal (a, b) - -let mk_neq a b = - let a, b = order_ a b in - Distinct (a, b) - -let mk_true = mk_eq Term.true_ Term.true_ -let mk_false = mk_eq Term.true_ Term.false_ -let mk_atom = mk_eq Term.true_ -let mk_atom_neg = mk_eq Term.false_ - -let neg = function - | Prop i -> Prop (-i) - | Equal (a, b) -> Distinct (a, b) - | Distinct (a, b) -> Equal (a, b) - -let norm = function - | Prop i -> Prop (abs i), if i < 0 then I.Negated else I.Same_sign - | Equal (a, b) -> Equal (a, b), I.Same_sign - | Distinct (a, b) -> Equal (a, b), I.Negated - -(* Only used after normalisation, so usual functions should work *) -let hash = Hashtbl.hash -let equal = (=) -let compare = Pervasives.compare - -let print fmt = function - | Prop i -> - Format.fprintf fmt "%s%s%d" - (if i < 0 then "¬ " else "") - (if i mod 2 = 0 then "v" else "f") ((abs i) / 2) - | Equal (a, b) -> Format.fprintf fmt "(@[=@ %a@ %a@])" Term.print a Term.print b - | Distinct (a, b) -> Format.fprintf fmt "(@[!=@ %a@ %a@])" Term.print a Term.print b - -module Formula = struct - type t = formula - let hash = Hashtbl.hash - let equal = (=) - let compare = Pervasives.compare - let print = print -end - diff --git a/src/smt/expr.mli b/src/smt/expr.mli deleted file mode 100644 index 0f01ae83..00000000 --- a/src/smt/expr.mli +++ /dev/null @@ -1,42 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) -open Msat - -type term = Term.t - -type formula = private - | Prop of int (* prop or tseitin atom *) - | Equal of term * term - | Distinct of term * term - -type t = formula -type proof = unit - -include Formula_intf.S with type t := formula and type proof := proof - -val dummy : t - -val fresh : unit -> t - -val mk_prop : int -> t -(** [mk_prop i] makes a prop literal from [i], whose sign matters. - @raise Invalid_prop if [i=0] or if [i] is too large *) - -val mk_true : t -val mk_false : t -val mk_atom : term -> t -val mk_atom_neg : term -> t -val mk_eq : term -> term -> t -val mk_neq : term -> term -> t - -module Term = Term -module Formula : sig - type t = formula - val hash : t -> int - val equal : t -> t -> bool - val compare : t -> t -> int - val print : Format.formatter -> t -> unit -end diff --git a/src/util/.merlin b/src/util/.merlin deleted file mode 100644 index 962d669c..00000000 --- a/src/util/.merlin +++ /dev/null @@ -1,11 +0,0 @@ -S ./ -S ./smtlib/ -S ../sat/ -S ../common/ - -B ../_build/ -B ../_build/util/ -B ../_build/util/smtlib/ -B ../_build/sat/ -B ../_build/smt/ -B ../_build/common/ diff --git a/src/util/expr.ml b/src/util/expr.ml new file mode 100644 index 00000000..752b55e7 --- /dev/null +++ b/src/util/expr.ml @@ -0,0 +1,522 @@ +(* + Base modules that defines the terms used in the prover. +*) + +(* Type definitions *) +(* ************************************************************************ *) + +(* Private aliases *) +type hash = int +type index = int + +(* Identifiers, parametrized by the kind of the type of the variable *) +type 'ty id = { + id_type : 'ty; + id_name : string; + index : index; (** unique *) +} + +(* Type for first order types *) +type ttype = Type + +(* The type of functions *) +type 'ty function_descr = { + fun_vars : ttype id list; (* prenex forall *) + fun_args : 'ty list; + fun_ret : 'ty; +} + +(* Types *) +type ty_descr = + | TyVar of ttype id (** Bound variables *) + | TyApp of ttype function_descr id * ty list + +and ty = { + ty : ty_descr; + mutable ty_hash : hash; (** lazy hash *) +} + +(* Terms & formulas *) +type term_descr = + | Var of ty id + | App of ty function_descr id * ty list * term list + +and term = { + term : term_descr; + t_type : ty; + mutable t_hash : hash; (* lazy hash *) +} + +type atom_descr = + | Pred of term + | Equal of term * term + +and atom = { + sign : bool; + atom : atom_descr; + mutable f_hash : hash; (* lazy hash *) +} + +(* Utilities *) +(* ************************************************************************ *) + +let rec list_cmp ord l1 l2 = + match l1, l2 with + | [], [] -> 0 + | [], _ -> -1 + | _, [] -> 1 + | x1::l1', x2::l2' -> + let c = ord x1 x2 in + if c = 0 + then list_cmp ord l1' l2' + else c + +(* Exceptions *) +(* ************************************************************************ *) + +exception Type_mismatch of term * ty * ty +exception Bad_arity of ty function_descr id * ty list * term list +exception Bad_ty_arity of ttype function_descr id * ty list + +(* Printing functions *) +(* ************************************************************************ *) + +module Print = struct + let rec list f sep fmt = function + | [] -> () + | [x] -> f fmt x + | x :: ((y :: _) as r) -> + Format.fprintf fmt "%a%s" f x sep; + list f sep fmt r + + let id fmt v = Format.fprintf fmt "%s" v.id_name + let ttype fmt = function Type -> Format.fprintf fmt "Type" + + let rec ty fmt t = match t.ty with + | TyVar v -> id fmt v + | TyApp (f, []) -> + Format.fprintf fmt "%a" id f + | TyApp (f, l) -> + Format.fprintf fmt "%a(%a)" id f (list ty ", ") l + + let params fmt = function + | [] -> () + | l -> Format.fprintf fmt "∀ %a. " (list id ", ") l + + let signature print fmt f = + match f.fun_args with + | [] -> Format.fprintf fmt "%a%a" params f.fun_vars print f.fun_ret + | l -> Format.fprintf fmt "%a%a -> %a" params f.fun_vars + (list print " -> ") l print f.fun_ret + + let fun_ty = signature ty + let fun_ttype = signature ttype + + let id_type print fmt v = Format.fprintf fmt "%a : %a" id v print v.id_type + + let id_ty = id_type ty + let id_ttype = id_type ttype + let const_ty = id_type fun_ty + let const_ttype = id_type fun_ttype + + let rec term fmt t = match t.term with + | Var v -> id fmt v + | App (f, [], []) -> + Format.fprintf fmt "%a" id f + | App (f, [], args) -> + Format.fprintf fmt "%a(%a)" id f + (list term ", ") args + | App (f, tys, args) -> + Format.fprintf fmt "%a(%a; %a)" id f + (list ty ", ") tys + (list term ", ") args + + let atom_aux fmt f = + match f.atom with + | Equal (a, b) -> Format.fprintf fmt "%a = %a" term a term b + | Pred t -> Format.fprintf fmt "%a" term t + + let atom fmt f = Format.fprintf fmt "⟦%a⟧" atom_aux f + +end + +(* Substitutions *) +(* ************************************************************************ *) + +module Subst = struct + module Mi = Map.Make(struct + type t = int * int + let compare (a, b) (c, d) = match compare a c with 0 -> compare b d | x -> x + end) + + type ('a, 'b) t = ('a * 'b) Mi.t + + (* Usual functions *) + let empty = Mi.empty + + let is_empty = Mi.is_empty + + let iter f = Mi.iter (fun _ (key, value) -> f key value) + + let fold f = Mi.fold (fun _ (key, value) acc -> f key value acc) + + let bindings s = Mi.fold (fun _ (key, value) acc -> (key, value) :: acc) s [] + + (* Comparisons *) + let equal f = Mi.equal (fun (_, value1) (_, value2) -> f value1 value2) + let compare f = Mi.compare (fun (_, value1) (_, value2) -> f value1 value2) + let hash h s = Mi.fold (fun i (_, value) acc -> Hashtbl.hash (acc, i, h value)) s 1 + + let choose m = snd (Mi.choose m) + + (* Iterators *) + let exists pred s = + try + iter (fun m s -> if pred m s then raise Exit) s; + false + with Exit -> + true + + let for_all pred s = + try + iter (fun m s -> if not (pred m s) then raise Exit) s; + true + with Exit -> + false + + let print print_key print_value fmt map = + let aux _ (key, value) = + Format.fprintf fmt "%a -> %a@ " print_key key print_value value + in + Format.fprintf fmt "@[%a@]" (fun _ -> Mi.iter aux) map + + module type S = sig + type 'a key + val get : 'a key -> ('a key, 'b) t -> 'b + val mem : 'a key -> ('a key, 'b) t -> bool + val bind : 'a key -> 'b -> ('a key, 'b) t -> ('a key, 'b) t + val remove : 'a key -> ('a key, 'b) t -> ('a key, 'b) t + end + + (* Variable substitutions *) + module Id = struct + type 'a key = 'a id + let tok v = (v.index, 0) + let get v s = snd (Mi.find (tok v) s) + let mem v s = Mi.mem (tok v) s + let bind v t s = Mi.add (tok v) (v, t) s + let remove v s = Mi.remove (tok v) s + end + +end + +(* Dummies *) +(* ************************************************************************ *) + +module Dummy = struct + + let id_ttype = + { index = -1; id_name = ""; id_type = Type; } + + let ty = + { ty = TyVar id_ttype; ty_hash = -1; } + + let id = + { index = -2; id_name = ""; id_type = ty; } + + let term = + { term = Var id; t_type = ty; t_hash = -1; } + + let atom = + { atom = Pred term; sign = true; f_hash = -1; } + +end + +(* Variables *) +(* ************************************************************************ *) + +module Id = struct + type 'a t = 'a id + + (* Hash & comparisons *) + let hash v = v.index + + let compare: 'a. 'a id -> 'a id -> int = + fun v1 v2 -> compare v1.index v2.index + + let equal v1 v2 = compare v1 v2 = 0 + + (* Printing functions *) + let print = Print.id + + (* Id count *) + let _count = ref 0 + + (* Constructors *) + let mk_new id_name id_type = + incr _count; + let index = !_count in + { index; id_name; id_type } + + let ttype name = mk_new name Type + let ty name ty = mk_new name ty + + let const name fun_vars fun_args fun_ret = + mk_new name { fun_vars; fun_args; fun_ret; } + + let ty_fun name n = + let rec replicate acc n = + if n <= 0 then acc + else replicate (Type :: acc) (n - 1) + in + const name [] (replicate [] n) Type + + let term_fun = const + + (* Builtin Types *) + let prop = ty_fun "Prop" 0 + let base = ty_fun "$i" 0 + +end + +(* Types *) +(* ************************************************************************ *) + +module Ty = struct + type t = ty + type subst = (ttype id, ty) Subst.t + + (* Hash & Comparisons *) + let rec hash_aux t = match t.ty with + | TyVar v -> Id.hash v + | TyApp (f, args) -> + Hashtbl.hash (Id.hash f, List.map hash args) + + and hash t = + if t.ty_hash = -1 then + t.ty_hash <- hash_aux t; + t.ty_hash + + let discr ty = match ty.ty with + | TyVar _ -> 1 + | TyApp _ -> 2 + + let rec compare u v = + let hu = hash u and hv = hash v in + if hu <> hv then Pervasives.compare hu hv + else match u.ty, v.ty with + | TyVar v1, TyVar v2 -> Id.compare v1 v2 + | TyApp (f1, args1), TyApp (f2, args2) -> + begin match Id.compare f1 f2 with + | 0 -> list_cmp compare args1 args2 + | x -> x + end + | _, _ -> Pervasives.compare (discr u) (discr v) + + let equal u v = + u == v || (hash u = hash v && compare u v = 0) + + (* Printing functions *) + let print = Print.ty + + (* Constructors *) + let mk_ty ty = { ty; ty_hash = -1; } + + let of_id v = mk_ty (TyVar v) + + let apply f args = + assert (f.id_type.fun_vars = []); + if List.length args <> List.length f.id_type.fun_args then + raise (Bad_ty_arity (f, args)) + else + mk_ty (TyApp (f, args)) + + (* Builtin types *) + let prop = apply Id.prop [] + let base = apply Id.base [] + + (* Substitutions *) + let rec subst_aux map t = match t.ty with + | TyVar v -> begin try Subst.Id.get v map with Not_found -> t end + | TyApp (f, args) -> + let new_args = List.map (subst_aux map) args in + if List.for_all2 (==) args new_args then t + else apply f new_args + + let subst map t = if Subst.is_empty map then t else subst_aux map t + + (* Typechecking *) + let instantiate f tys args = + if List.length f.id_type.fun_vars <> List.length tys || + List.length f.id_type.fun_args <> List.length args then + raise (Bad_arity (f, tys, args)) + else + let map = List.fold_left2 (fun acc v ty -> Subst.Id.bind v ty acc) Subst.empty f.id_type.fun_vars tys in + let fun_args = List.map (subst map) f.id_type.fun_args in + List.iter2 (fun t ty -> + if not (equal t.t_type ty) then raise (Type_mismatch (t, t.t_type, ty))) + args fun_args; + subst map f.id_type.fun_ret + +end + +(* Terms *) +(* ************************************************************************ *) + +module Term = struct + type t = term + type subst = (ty id, term) Subst.t + + (* Hash & Comparisons *) + let rec hash_aux t = match t.term with + | Var v -> Id.hash v + | App (f, tys, args) -> + let l = List.map Ty.hash tys in + let l' = List.map hash args in + Hashtbl.hash (Id.hash f, l, l') + + and hash t = + if t.t_hash = -1 then + t.t_hash <- hash_aux t; + t.t_hash + + let discr t = match t.term with + | Var _ -> 1 + | App _ -> 2 + + let rec compare u v = + let hu = hash u and hv = hash v in + if hu <> hv then Pervasives.compare hu hv + else match u.term, v.term with + | Var v1, Var v2 -> Id.compare v1 v2 + | App (f1, tys1, args1), App (f2, tys2, args2) -> + begin match Id.compare f1 f2 with + | 0 -> + begin match list_cmp Ty.compare tys1 tys2 with + | 0 -> list_cmp compare args1 args2 + | x -> x + end + | x -> x + end + | _, _ -> Pervasives.compare (discr u) (discr v) + + let equal u v = + u == v || (hash u = hash v && compare u v = 0) + + (* Printing functions *) + let print = Print.term + + (* Constructors *) + let mk_term term t_type = + { term; t_type; t_hash = -1; } + + let of_id v = + mk_term (Var v) v.id_type + + let apply f ty_args t_args = + mk_term (App (f, ty_args, t_args)) (Ty.instantiate f ty_args t_args) + + (* Substitutions *) + let rec subst_aux ty_map t_map t = match t.term with + | Var v -> begin try Subst.Id.get v t_map with Not_found -> t end + | App (f, tys, args) -> + let new_tys = List.map (Ty.subst ty_map) tys in + let new_args = List.map (subst_aux ty_map t_map) args in + if List.for_all2 (==) new_tys tys && List.for_all2 (==) new_args args then t + else apply f new_tys new_args + + let subst ty_map t_map t = + if Subst.is_empty ty_map && Subst.is_empty t_map then + t + else + subst_aux ty_map t_map t + + let rec replace (t, t') t'' = match t''.term with + | _ when equal t t'' -> t' + | App (f, ty_args, t_args) -> + apply f ty_args (List.map (replace (t, t')) t_args) + | _ -> t'' + +end + +(* Formulas *) +(* ************************************************************************ *) + +module Atom = struct + type t = atom + + type proof = unit + + (* Hash & Comparisons *) + let h_eq = 2 + let h_pred = 3 + + let rec hash_aux f = match f.atom with + | Equal (t1, t2) -> + Hashtbl.hash (h_eq, Term.hash t1, Term.hash t2) + | Pred t -> + Hashtbl.hash (h_pred, Term.hash t) + + and hash f = + if f.f_hash = -1 then + f.f_hash <- hash_aux f; + f.f_hash + + let discr f = match f.atom with + | Equal _ -> 1 + | Pred _ -> 2 + + let compare f g = + let hf = hash f and hg = hash g in + if hf <> hg then Pervasives.compare hf hg + else match f.atom, g.atom with + | Equal (u1, v1), Equal(u2, v2) -> + list_cmp Term.compare [u1; v1] [u2; v2] + | Pred t1, Pred t2 -> Term.compare t1 t2 + | _, _ -> Pervasives.compare (discr f) (discr g) + + let equal u v = + u == v || (hash u = hash v && compare u v = 0) + + (* Printing functions *) + let print = Print.atom + + (* Constructors *) + let mk_formula f = { + sign = true; + atom = f; + f_hash = -1; + } + + let dummy = Dummy.atom + + let pred t = + if not (Ty.equal Ty.prop t.t_type) then + raise (Type_mismatch (t, t.t_type, Ty.prop)) + else + mk_formula (Pred t) + + let fresh () = + let id = Id.ty "fresh" Ty.prop in + pred (Term.of_id id) + + let neg f = + { f with sign = not f.sign } + + let eq a b = + if not (Ty.equal a.t_type b.t_type) then + raise (Type_mismatch (b, b.t_type, a.t_type)) + else if Term.compare a b < 0 then + mk_formula (Equal (a, b)) + else + mk_formula (Equal (b, a)) + + let norm f = + { f with sign = true }, + if f.sign then Msat.Formula_intf.Same_sign + else Msat.Formula_intf.Negated + +end + +module Formula = Msat.Tseitin.Make(Atom) + diff --git a/src/util/expr.mli b/src/util/expr.mli new file mode 100644 index 00000000..1f819b2c --- /dev/null +++ b/src/util/expr.mli @@ -0,0 +1,319 @@ + +(** Expressions for TabSat *) + +(** {2 Type definitions} *) + +(** These are custom types used in functions later. *) + +(** {3 Identifiers} *) + +(** Identifiers are the basic building blocks used to build types terms and expressions. *) + +type hash +type index = private int + +(** Private aliases to provide access. You should not have any need + to use these, instead use the functions provided by this module. *) + +type 'ty id = private { + id_type : 'ty; + id_name : string; + index : index; (** unique *) +} + +(** The type of identifiers. An ['a id] is an identifier whose solver-type + is represented by an inhabitant of type ['a]. + All identifier have an unique [index] which is used for comparison, + so that the name of a variable is only there for tracability + and/or pretty-printing. *) + +(** {3 Types} *) + +type ttype = Type + +(** The caml type of solver-types. *) + +type 'ty function_descr = private { + fun_vars : ttype id list; (* prenex forall *) + fun_args : 'ty list; + fun_ret : 'ty; +} + +(** This represents the solver-type of a function. + Functions can be polymorphic in the variables described in the + [fun_vars] field. *) + +type ty_descr = private + | TyVar of ttype id + (** bound variables (i.e should only appear under a quantifier) *) + | TyApp of ttype function_descr id * ty list + (** application of a constant to some arguments *) + +and ty = private { + ty : ty_descr; + mutable ty_hash : hash; (** Use Ty.hash instead *) +} + +(** These types defines solver-types, i.e the representation of the types + of terms in the solver. Record definition for [type ty] is shown in order + to be able to use the [ty.ty] field in patter matches. Other fields shoud not + be accessed directly, but throught the functions provided by the [Ty] module. *) + +(** {3 Terms} *) + +type term_descr = private + | Var of ty id + (** bound variables (i.e should only appear under a quantifier) *) + | App of ty function_descr id * ty list * term list + (** application of a constant to some arguments *) + +and term = private { + term : term_descr; + t_type : ty; + mutable t_hash : hash; (** Do not use this filed, call Term.hash instead *) +} + +(** Types defining terms in the solver. The definition is vary similar to that + of solver-types, except for type arguments of polymorphic functions which + are explicit. This has the advantage that there is a clear and typed distinction + between solver-types and terms, but may lead to some duplication of code + in some places. *) + +(** {3 Formulas} *) + +type atom_descr = private + (** Atoms *) + | Pred of term + | Equal of term * term + +and atom = private { + sign : bool; + atom : atom_descr; + mutable f_hash : hash; (** Use Formula.hash instead *) +} + +(** The type of atoms in the solver. The list of free arguments in quantifiers + is a bit tricky, so you should not touch it (see full doc for further + explanations). *) + +(** {3 Exceptions} *) + +exception Type_mismatch of term * ty * ty +(* Raised when as Type_mismatch(term, actual_type, expected_type) *) + +exception Bad_arity of ty function_descr id * ty list * term list +exception Bad_ty_arity of ttype function_descr id * ty list +(** Raised when trying to build an application with wrong arity *) + +(** {2 Printing} *) + +module Print : sig + (** Pretty printing functions *) + + val id : Format.formatter -> 'a id -> unit + val id_ty : Format.formatter -> ty id -> unit + val id_ttype : Format.formatter -> ttype id -> unit + + val const_ty : Format.formatter -> ty function_descr id -> unit + val const_ttype : Format.formatter -> ttype function_descr id -> unit + + val ty : Format.formatter -> ty -> unit + val fun_ty : Format.formatter -> ty function_descr -> unit + + val ttype : Format.formatter -> ttype -> unit + val fun_ttype : Format.formatter -> ttype function_descr -> unit + + val term : Format.formatter -> term -> unit + val atom : Format.formatter -> atom -> unit +end + +(** {2 Identifiers & Metas} *) + +module Id : sig + type 'a t = 'a id + (* Type alias *) + + val hash : 'a t -> int + val equal : 'a t -> 'a t -> bool + val compare : 'a t -> 'a t -> int + (** Usual functions for hash/comparison *) + + val print : Format.formatter -> 'a t -> unit + (** Printing for variables *) + + val prop : ttype function_descr id + val base : ttype function_descr id + (** Constants representing the type for propositions and a default type + for term, respectively. *) + + val ttype : string -> ttype id + (** Create a fresh type variable with the given name. *) + + val ty : string -> ty -> ty id + (** Create a fresh variable with given name and type *) + + val ty_fun : string -> int -> ttype function_descr id + (** Create a fresh type constructor with given name and arity *) + + val term_fun : string -> ttype id list -> ty list -> ty -> ty function_descr id + (** [ty_fun name type_vars arg_types return_type] returns a fresh constant symbol, + possibly polymorphic with respect to the variables in [type_vars] (which may appear in the + types in [arg_types] and in [return_type]). *) + +end + +(** {2 Substitutions} *) + +module Subst : sig + (** Module to handle substitutions *) + + type ('a, 'b) t + (** The type of substitutions from values of type ['a] to values of type ['b]. *) + + val empty : ('a, 'b) t + (** The empty substitution *) + + val is_empty : ('a, 'b) t -> bool + (** Test wether a substitution is empty *) + + val iter : ('a -> 'b -> unit) -> ('a, 'b) t -> unit + (** Iterates over the bindings of the substitution. *) + + val fold : ('a -> 'b -> 'c -> 'c) -> ('a, 'b) t -> 'c -> 'c + (** Fold over the elements *) + + val bindings : ('a, 'b) t -> ('a * 'b) list + (** Returns the list of bindings ofa substitution. *) + + val exists : ('a -> 'b -> bool) -> ('a, 'b) t -> bool + (** Tests wether the predicate holds for at least one binding. *) + + val for_all : ('a -> 'b -> bool) -> ('a, 'b) t -> bool + (** Tests wether the predicate holds for all bindings. *) + + val hash : ('b -> int) -> ('a, 'b) t -> int + val compare : ('b -> 'b -> int) -> ('a, 'b) t -> ('a, 'b) t -> int + val equal : ('b -> 'b -> bool) -> ('a, 'b) t -> ('a, 'b) t -> bool + (** Comparison and hash functions, with a comparison/hash function on values as parameter *) + + val print : + (Format.formatter -> 'a -> unit) -> + (Format.formatter -> 'b -> unit) -> + Format.formatter -> ('a, 'b) t -> unit + (** Prints the substitution, using the given functions to print keys and values. *) + + val choose : ('a, 'b) t -> 'a * 'b + (** Return one binding of the given substitution, or raise Not_found if the substitution is empty.*) + + (** {5 Concrete subtitutions } *) + module type S = sig + type 'a key + val get : 'a key -> ('a key, 'b) t -> 'b + (** [get v subst] returns the value associated with [v] in [subst], if it exists. + @raise Not_found if there is no binding for [v]. *) + val mem : 'a key -> ('a key, 'b) t -> bool + (** [get v subst] returns wether there is a value associated with [v] in [subst]. *) + val bind : 'a key -> 'b -> ('a key, 'b) t -> ('a key, 'b) t + (** [bind v t subst] returns the same substitution as [subst] with the additional binding from [v] to [t]. + Erases the previous binding of [v] if it exists. *) + val remove : 'a key -> ('a key, 'b) t -> ('a key, 'b) t + (** [remove v subst] returns the same substitution as [subst] except for [v] which is unbound in the returned substitution. *) + end + + module Id : S with type 'a key = 'a id +end + +(** {2 Types} *) + +module Ty : sig + type t = ty + (** Type alias *) + + type subst = (ttype id, ty) Subst.t + (** The type of substitutions over types. *) + + val hash : t -> int + val equal : t -> t -> bool + val compare : t -> t -> int + (** Usual hash/compare functions *) + + val print : Format.formatter -> t -> unit + + val prop : ty + val base : ty + (** The type of propositions and individuals *) + + val of_id : ttype id -> ty + (** Creates a type from a variable *) + + val apply : ttype function_descr id -> ty list -> ty + (** Applies a constant to a list of types *) + + val subst : subst -> ty -> ty + (** Substitution over types. *) + +end + +(** {2 Terms} *) + +module Term : sig + type t = term + (** Type alias *) + + type subst = (ty id, term) Subst.t + (** The type of substitutions in types. *) + + val hash : t -> int + val equal : t -> t -> bool + val compare : t -> t -> int + (** Usual hash/compare functions *) + + val print : Format.formatter -> t -> unit + (** Printing functions *) + + val of_id : ty id -> term + (** Create a term from a variable *) + + val apply : ty function_descr id -> ty list -> term list -> term + (** Applies a constant function to type arguments, then term arguments *) + + val subst : Ty.subst -> subst -> term -> term + (** Substitution over types. *) + + val replace : term * term -> term -> term + (** [replace (t, t') t''] returns the term [t''] where every occurence of [t] + has been replace by [t']. *) + +end + +(** {2 Formulas} *) + +module Atom : sig + type t = atom + (** Type alias *) + + val hash : t -> int + val equal : t -> t -> bool + val compare : t -> t -> int + (** Usual hash/compare functions *) + + val print : Format.formatter -> t -> unit + (** Printing functions *) + + val eq : term -> term -> atom + (** Create an equality over two terms. The two given terms + must have the same type [t], which must be different from {!Ty.prop} *) + + val pred : term -> atom + (** Create a atom from a term. The given term must have type {!Ty.prop} *) + + val neg : atom -> atom + (** Returns the negation of the given atom *) + + val norm : atom -> atom * Msat.Formula_intf.negated + (** Normalization functions as required by msat. *) + +end + +module Formula : Msat.Tseitin.S with type atom = atom + diff --git a/src/util/parsedimacs.ml b/src/util/parsedimacs.ml deleted file mode 100644 index df5c3c8c..00000000 --- a/src/util/parsedimacs.ml +++ /dev/null @@ -1,75 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -exception Syntax_error of int - -type line = - | Empty - | Comment - | Pcnf of int * int - | Clause of int list - -let rec _read_word s acc i len = - assert (len>0); - if i+len=String.length s - then String.sub s i len :: acc - else match s.[i+len] with - | ' ' | '\t' -> - let acc = String.sub s i len :: acc in - _skip_space s acc (i+len+1) - | _ -> _read_word s acc i (len+1) - -and _skip_space s acc i = - if i=String.length s - then acc - else match s.[i] with - | ' ' | '\t' -> _skip_space s acc (i+1) - | _ -> _read_word s acc i 1 - -let ssplit s = List.rev (_skip_space s [] 0) - -let of_input f = - match ssplit (input_line f) with - | [] -> Empty - | "c" :: _ -> Comment - | "p" :: "cnf" :: i :: j :: [] -> - begin try - Pcnf (int_of_string i, int_of_string j) - with Failure _ -> - raise (Syntax_error (-1)) - end - | l -> - begin try - begin match List.rev_map int_of_string l with - | 0 :: r -> Clause r - | _ -> raise (Syntax_error (-1)) - end - with Failure _ -> raise (Syntax_error (-1)) - end - -let parse_with todo file = - let f = open_in file in - let line = ref 0 in - try - while true do - incr line; - todo (of_input f) - done - with - | Syntax_error _ -> - raise (Syntax_error !line) - | End_of_file -> - close_in f - -let cnf = ref [] -let parse_line = function - | Empty | Comment | Pcnf _ -> () - | Clause l -> cnf := l :: !cnf - -let parse f = - cnf := []; - parse_with parse_line f; - !cnf diff --git a/src/util/parsedimacs.mli b/src/util/parsedimacs.mli deleted file mode 100644 index 84a7b222..00000000 --- a/src/util/parsedimacs.mli +++ /dev/null @@ -1,9 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -exception Syntax_error of int - -val parse : string -> int list list diff --git a/src/util/smtlib/.merlin b/src/util/smtlib/.merlin deleted file mode 100644 index 23ddf6ef..00000000 --- a/src/util/smtlib/.merlin +++ /dev/null @@ -1,9 +0,0 @@ -S ./ -S ../ -S ../../sat/ - -B ../../_build/ -B ../../_build/util/ -B ../../_build/util/smtlib/ -B ../../_build/sat/ -B ../../_build/smt/ diff --git a/src/util/smtlib/lexsmtlib.mli b/src/util/smtlib/lexsmtlib.mli deleted file mode 100644 index a53450a7..00000000 --- a/src/util/smtlib/lexsmtlib.mli +++ /dev/null @@ -1,3 +0,0 @@ -(* Copyright 2014 INIA *) - -val token : Lexing.lexbuf -> Parsesmtlib.token diff --git a/src/util/smtlib/lexsmtlib.mll b/src/util/smtlib/lexsmtlib.mll deleted file mode 100644 index b192c3f3..00000000 --- a/src/util/smtlib/lexsmtlib.mll +++ /dev/null @@ -1,48 +0,0 @@ -{ - (* auto-generated by gt *) - -open Parsesmtlib;; -} - -rule token = parse -| ['\t' ' ' ]+ { token lexbuf } -| ';' (_ # '\n')* { token lexbuf } -| ['\n']+ as str { Smtlib_util.line := (!Smtlib_util.line + (String.length str)); token lexbuf } -| "_" { UNDERSCORE } -| "(" { LPAREN } -| ")" { RPAREN } -| "as" { AS } -| "let" { LET } -| "forall" { FORALL } -| "exists" { EXISTS } -| "!" { EXCLIMATIONPT } -| "set-logic" { SETLOGIC } -| "set-option" { SETOPTION } -| "set-info" { SETINFO } -| "declare-sort" { DECLARESORT } -| "define-sort" { DEFINESORT } -| "declare-fun" { DECLAREFUN } -| "define-fun" { DEFINEFUN } -| "push" { PUSH } -| "pop" { POP } -| "assert" { ASSERT } -| "check-sat" { CHECKSAT } -| "get-assertions" { GETASSERT } -| "get-proof" { GETPROOF } -| "get-unsat-core" { GETUNSATCORE } -| "get-value" { GETVALUE } -| "get-assignment" { GETASSIGN } -| "get-option" { GETOPTION } -| "get-info" { GETINFO } -| "exit" { EXIT } -| '#' 'x' ['0'-'9' 'A'-'F' 'a'-'f']+ as str { HEXADECIMAL(str) } -| '#' 'b' ['0'-'1']+ as str { BINARY(str) } -| '|' ([ '!'-'~' ' ' '\n' '\t' '\r'] # ['\\' '|'])* '|' as str { ASCIIWOR(str) } -| ':' ['a'-'z' 'A'-'Z' '0'-'9' '+' '-' '/' '*' '=' '%' '?' '!' '.' '$' '_' '~' '&' '^' '<' '>' '@']+ as str { KEYWORD(str) } -| ['a'-'z' 'A'-'Z' '+' '-' '/' '*' '=''%' '?' '!' '.' '$' '_' '~' '&' '^' '<' '>' '@'] ['a'-'z' 'A'-'Z' '0'-'9' '+' '-' '/' '*' '=''%' '?' '!' '.' '$' '_' '~' '&' '^' '<' '>' '@']* as str { SYMBOL(str) } -| '"' (([ '!'-'~' ' ' '\n' '\t' '\r' ] # ['\\' '"']) | ('\\' ['!'-'~' ' ' '\n' '\t' '\r'] ))* '"' as str { STRINGLIT(str) } -| ( '0' | ['1'-'9'] ['0'-'9']* ) as str { NUMERAL(str) } -| ( '0' | ['1'-'9'] ['0'-'9']* ) '.' ['0'-'9']+ as str { DECIMAL(str) } -| eof { EOF } -| _ {failwith((Lexing.lexeme lexbuf) ^ - ": lexing error on line "^(string_of_int !Smtlib_util.line))}{} diff --git a/src/util/smtlib/parsesmtlib.mly b/src/util/smtlib/parsesmtlib.mly deleted file mode 100644 index 65a14660..00000000 --- a/src/util/smtlib/parsesmtlib.mly +++ /dev/null @@ -1,330 +0,0 @@ -%{ - (* auto-generated by gt *) - -open Smtlib_syntax;; -let parse_error s = - print_string s; - print_string " on line "; - print_int !Smtlib_util.line; - print_string "\n";; - -%} - -%start main - -%token EOF AS ASSERT CHECKSAT DECLAREFUN DECLARESORT DEFINEFUN DEFINESORT EXCLIMATIONPT EXISTS EXIT FORALL GETASSERT GETASSIGN GETINFO GETOPTION GETPROOF GETUNSATCORE GETVALUE LET LPAREN POP PUSH RPAREN SETINFO SETLOGIC SETOPTION UNDERSCORE -%token ASCIIWOR BINARY DECIMAL HEXADECIMAL KEYWORD NUMERAL STRINGLIT SYMBOL - - %type main - - %type an_option - - %type attribute - - %type attributevalsexpr_attributevalue_sexpr5 - - %type attributevalue - - %type command - - %type commanddeclarefun_command_sort13 - - %type commanddefinefun_command_sortedvar15 - - %type commanddefinesort_command_symbol11 - - %type commandgetvalue_command_term24 - - %type commands - - %type commands_commands_command30 - - %type identifier - - %type idunderscoresymnum_identifier_numeral33 - - %type infoflag - - %type qualidentifier - - %type sexpr - - %type sexprinparen_sexpr_sexpr41 - - %type sort - - %type sortedvar - - %type sortidsortmulti_sort_sort44 - - %type specconstant - - %type symbol - - %type term - - %type termexclimationpt_term_attribute64 - - %type termexiststerm_term_sortedvar62 - - %type termforallterm_term_sortedvar60 - - %type termletterm_term_varbinding58 - - %type termqualidterm_term_term56 - - %type varbinding - - %type cur_position - - %% - - main: - | commands { Some($1) } - | EOF { None } - - cur_position: - | { Smtlib_util.cur_pd() } - - an_option: - | attribute { AnOptionAttribute(pd_attribute $1, $1) } - - attribute: - | cur_position KEYWORD { AttributeKeyword($1, $2) } - - attribute: - | cur_position KEYWORD attributevalue { AttributeKeywordValue($1, $2, $3) } - - attributevalue: - | specconstant { AttributeValSpecConst(pd_specconstant $1, $1) } - - attributevalue: - | symbol { AttributeValSymbol(pd_symbol $1, $1) } - - attributevalue: - | cur_position LPAREN attributevalsexpr_attributevalue_sexpr5 RPAREN { AttributeValSexpr($1, $3) } - - command: - | cur_position LPAREN SETLOGIC symbol RPAREN { CommandSetLogic($1, $4) } - - command: - | cur_position LPAREN SETOPTION an_option RPAREN { CommandSetOption($1, $4) } - - command: - | cur_position LPAREN SETINFO attribute RPAREN { CommandSetInfo($1, $4) } - - command: - | cur_position LPAREN DECLARESORT symbol NUMERAL RPAREN { CommandDeclareSort($1, $4, $5) } - - command: - | cur_position LPAREN DEFINESORT symbol LPAREN commanddefinesort_command_symbol11 RPAREN sort RPAREN { CommandDefineSort($1, $4, $6, $8) } - - command: - | cur_position LPAREN DECLAREFUN symbol LPAREN commanddeclarefun_command_sort13 RPAREN sort RPAREN { CommandDeclareFun($1, $4, $6, $8) } - - command: - | cur_position LPAREN DEFINEFUN symbol LPAREN commanddefinefun_command_sortedvar15 RPAREN sort term RPAREN { CommandDefineFun($1, $4, $6, $8, $9) } - - command: - | cur_position LPAREN PUSH NUMERAL RPAREN { CommandPush($1, $4) } - - command: - | cur_position LPAREN POP NUMERAL RPAREN { CommandPop($1, $4) } - - command: - | cur_position LPAREN ASSERT term RPAREN { CommandAssert($1, $4) } - - command: - | cur_position LPAREN CHECKSAT RPAREN { CommandCheckSat($1) } - - command: - | cur_position LPAREN GETASSERT RPAREN { CommandGetAssert($1) } - - command: - | cur_position LPAREN GETPROOF RPAREN { CommandGetProof($1) } - - command: - | cur_position LPAREN GETUNSATCORE RPAREN { CommandGetUnsatCore($1) } - - command: - | cur_position LPAREN GETVALUE LPAREN commandgetvalue_command_term24 RPAREN RPAREN { CommandGetValue($1, $5) } - - command: - | cur_position LPAREN GETASSIGN RPAREN { CommandGetAssign($1) } - - command: - | cur_position LPAREN GETOPTION KEYWORD RPAREN { CommandGetOption($1, $4) } - - command: - | cur_position LPAREN GETINFO infoflag RPAREN { CommandGetInfo($1, $4) } - - command: - | cur_position LPAREN EXIT RPAREN { CommandExit($1) } - - commands: - | commands_commands_command30 { Commands(pd_commands_commands_command30 $1, $1) } - - identifier: - | symbol { IdSymbol(pd_symbol $1, $1) } - - identifier: - | cur_position LPAREN UNDERSCORE symbol idunderscoresymnum_identifier_numeral33 RPAREN { IdUnderscoreSymNum($1, $4, $5) } - - infoflag: - | cur_position KEYWORD { InfoFlagKeyword($1, $2) } - - qualidentifier: - | identifier { QualIdentifierId(pd_identifier $1, $1) } - - qualidentifier: - | cur_position LPAREN AS identifier sort RPAREN { QualIdentifierAs($1, $4, $5) } - - sexpr: - | specconstant { SexprSpecConst(pd_specconstant $1, $1) } - - sexpr: - | symbol { SexprSymbol(pd_symbol $1, $1) } - - sexpr: - | cur_position KEYWORD { SexprKeyword($1, $2) } - - sexpr: - | cur_position LPAREN sexprinparen_sexpr_sexpr41 RPAREN { SexprInParen($1, $3) } - - sort: - | identifier { SortIdentifier(pd_identifier $1, $1) } - - sort: - | cur_position LPAREN identifier sortidsortmulti_sort_sort44 RPAREN { SortIdSortMulti($1, $3, $4) } - - sortedvar: - | cur_position LPAREN symbol sort RPAREN { SortedVarSymSort($1, $3, $4) } - - specconstant: - | cur_position DECIMAL { SpecConstsDec($1, $2) } - - specconstant: - | cur_position NUMERAL { SpecConstNum($1, $2) } - - specconstant: - | cur_position STRINGLIT { SpecConstString($1, $2) } - - specconstant: - | cur_position HEXADECIMAL { SpecConstsHex($1, $2) } - - specconstant: - | cur_position BINARY { SpecConstsBinary($1, $2) } - - symbol: - | cur_position SYMBOL { Symbol($1, $2) } - - symbol: - | cur_position ASCIIWOR { SymbolWithOr($1, $2) } - - term: - | specconstant { TermSpecConst(pd_specconstant $1, $1) } - - term: - | qualidentifier { TermQualIdentifier(pd_qualidentifier $1, $1) } - - term: - | cur_position LPAREN qualidentifier termqualidterm_term_term56 RPAREN { TermQualIdTerm($1, $3, $4) } - - term: - | cur_position LPAREN LET LPAREN termletterm_term_varbinding58 RPAREN term RPAREN { TermLetTerm($1, $5, $7) } - - term: - | cur_position LPAREN FORALL LPAREN termforallterm_term_sortedvar60 RPAREN term RPAREN { TermForAllTerm($1, $5, $7) } - - term: - | cur_position LPAREN EXISTS LPAREN termexiststerm_term_sortedvar62 RPAREN term RPAREN { TermExistsTerm($1, $5, $7) } - - term: - | cur_position LPAREN EXCLIMATIONPT term termexclimationpt_term_attribute64 RPAREN { TermExclimationPt($1, $4, $5) } - - varbinding: - | cur_position LPAREN symbol term RPAREN { VarBindingSymTerm($1, $3, $4) } - - termexclimationpt_term_attribute64: - | attribute { (pd_attribute $1, ($1)::[]) } - - termexclimationpt_term_attribute64: - | attribute termexclimationpt_term_attribute64 { let (p, ( l1 )) = $2 in (pd_attribute $1, ($1)::(l1)) } - - termexiststerm_term_sortedvar62: - | sortedvar { (pd_sortedvar $1, ($1)::[]) } - - termexiststerm_term_sortedvar62: - | sortedvar termexiststerm_term_sortedvar62 { let (p, ( l1 )) = $2 in (pd_sortedvar $1, ($1)::(l1)) } - - termforallterm_term_sortedvar60: - | sortedvar { (pd_sortedvar $1, ($1)::[]) } - - termforallterm_term_sortedvar60: - | sortedvar termforallterm_term_sortedvar60 { let (p, ( l1 )) = $2 in (pd_sortedvar $1, ($1)::(l1)) } - - termletterm_term_varbinding58: - | varbinding { (pd_varbinding $1, ($1)::[]) } - - termletterm_term_varbinding58: - | varbinding termletterm_term_varbinding58 { let (p, ( l1 )) = $2 in (pd_varbinding $1, ($1)::(l1)) } - - termqualidterm_term_term56: - | term { (pd_term $1, ($1)::[]) } - - termqualidterm_term_term56: - | term termqualidterm_term_term56 { let (p, ( l1 )) = $2 in (pd_term $1, ($1)::(l1)) } - - sortidsortmulti_sort_sort44: - | sort { (pd_sort $1, ($1)::[]) } - - sortidsortmulti_sort_sort44: - | sort sortidsortmulti_sort_sort44 { let (p, ( l1 )) = $2 in (pd_sort $1, ($1)::(l1)) } - - sexprinparen_sexpr_sexpr41: - | cur_position { ($1, []) } - - sexprinparen_sexpr_sexpr41: - | sexpr sexprinparen_sexpr_sexpr41 { let (p, ( l1 )) = $2 in (pd_sexpr $1, ($1)::(l1)) } - - idunderscoresymnum_identifier_numeral33: - | cur_position NUMERAL { ($1, ($2)::[]) } - - idunderscoresymnum_identifier_numeral33: - | cur_position NUMERAL idunderscoresymnum_identifier_numeral33 { let (p, ( l1 )) = $3 in ($1, ($2)::(l1)) } - - commands_commands_command30: - | cur_position { ($1, []) } - - commands_commands_command30: - | command commands_commands_command30 { let (p, ( l1 )) = $2 in (pd_command $1, ($1)::(l1)) } - - commandgetvalue_command_term24: - | term { (pd_term $1, ($1)::[]) } - - commandgetvalue_command_term24: - | term commandgetvalue_command_term24 { let (p, ( l1 )) = $2 in (pd_term $1, ($1)::(l1)) } - - commanddefinefun_command_sortedvar15: - | cur_position { ($1, []) } - - commanddefinefun_command_sortedvar15: - | sortedvar commanddefinefun_command_sortedvar15 { let (p, ( l1 )) = $2 in (pd_sortedvar $1, ($1)::(l1)) } - - commanddeclarefun_command_sort13: - | cur_position { ($1, []) } - - commanddeclarefun_command_sort13: - | sort commanddeclarefun_command_sort13 { let (p, ( l1 )) = $2 in (pd_sort $1, ($1)::(l1)) } - - commanddefinesort_command_symbol11: - | cur_position { ($1, []) } - - commanddefinesort_command_symbol11: - | symbol commanddefinesort_command_symbol11 { let (p, ( l1 )) = $2 in (pd_symbol $1, ($1)::(l1)) } - - attributevalsexpr_attributevalue_sexpr5: - | cur_position { ($1, []) } - - attributevalsexpr_attributevalue_sexpr5: - | sexpr attributevalsexpr_attributevalue_sexpr5 { let (p, ( l1 )) = $2 in (pd_sexpr $1, ($1)::(l1)) } diff --git a/src/util/smtlib/smtlib.ml b/src/util/smtlib/smtlib.ml deleted file mode 100644 index 49057058..00000000 --- a/src/util/smtlib/smtlib.ml +++ /dev/null @@ -1,112 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -open Smtlib_syntax - -module F = Expr -module T = Cnf.S - -exception Bad_arity of string -exception Unknown_command -exception Incomplete_translation - -(* Environment *) -let env : (string, T.t) Hashtbl.t = Hashtbl.create 57;; -Hashtbl.add env "true" T.f_true;; -Hashtbl.add env "false" T.f_false;; - -let get_atom s = - try - Hashtbl.find env s - with Not_found -> - let f = T.make_atom (F.fresh ()) in - Hashtbl.add env s f; - f - -(* Term translation *) -let translate_const = function - | SpecConstsDec(_, s) - | SpecConstNum(_, s) - | SpecConstString(_, s) - | SpecConstsHex(_, s) - | SpecConstsBinary(_, s) -> s - -let translate_symbol = function - | Symbol(_, s) - | SymbolWithOr(_, s) -> s - -let translate_id = function - | IdSymbol(_, s) -> translate_symbol s - | IdUnderscoreSymNum(_, s, n) -> raise Incomplete_translation - -let translate_qualid = function - | QualIdentifierId(_, id) -> translate_id id - | QualIdentifierAs(_, id, s) -> raise Incomplete_translation - -let left_assoc s f = function - | x :: r -> List.fold_left f x r - | _ -> raise (Bad_arity s) - -let rec right_assoc s f = function - | [] -> raise (Bad_arity s) - | [x] -> x - | x :: r -> f x (right_assoc s f r) - -let translate_atom = function - | TermSpecConst(_, const) -> translate_const const - | TermQualIdentifier(_, id) -> translate_qualid id - | _ -> raise Incomplete_translation - -let rec translate_term = function - | TermQualIdTerm(_, f, (_, l)) -> - begin match (translate_qualid f) with - | "=" -> - begin match (List.map translate_atom l) with - | [a; b] -> T.make_atom (F.mk_eq a b) - | _ -> assert false - end - | s -> - begin match s, (List.map translate_term l) with - (* CORE theory translation - 'distinct','ite' not yet implemented *) - | "not", [e] -> T.make_not e - | "not", _ -> raise (Bad_arity "not") - | "and", l -> T.make_and l - | "or", l -> T.make_or l - | "xor" as s, l -> left_assoc s T.make_xor l - | "=>" as s, l -> right_assoc s T.make_imply l - | _ -> - Format.printf "unknown : %s@." s; - raise Unknown_command - end - end - | e -> (get_atom (translate_atom e)) - -(* Command Translation *) -let translate_command = function - | CommandDeclareFun(_, s, (_, []), _) -> - None - | CommandAssert(_, t) -> - Some (translate_term t) - | _ -> None - -let rec translate_command_list acc = function - | [] -> acc - | c :: r -> - begin match translate_command c with - | None -> translate_command_list acc r - | Some t -> translate_command_list (t :: acc) r - end - -let translate = function - | Some Commands (_, (_, l)) -> List.rev (translate_command_list [] l) - | None -> [] - -let parse file = - let f = open_in file in - let lexbuf = Lexing.from_channel f in - let commands = Parsesmtlib.main Lexsmtlib.token lexbuf in - close_in f; - translate commands diff --git a/src/util/smtlib/smtlib.mli b/src/util/smtlib/smtlib.mli deleted file mode 100644 index c5c5bfed..00000000 --- a/src/util/smtlib/smtlib.mli +++ /dev/null @@ -1,7 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -val parse : string -> Cnf.S.t list diff --git a/src/util/smtlib/smtlib_syntax.ml b/src/util/smtlib/smtlib_syntax.ml deleted file mode 100644 index 6f33e693..00000000 --- a/src/util/smtlib/smtlib_syntax.ml +++ /dev/null @@ -1,229 +0,0 @@ -(* auto-generated by gt *) - -open Smtlib_util;; - -type dummy = Dummy -and an_option = | AnOptionAttribute of pd * attribute -and attribute = | AttributeKeyword of pd * string | AttributeKeywordValue of pd * string * attributevalue -and attributevalue = | AttributeValSpecConst of pd * specconstant | AttributeValSymbol of pd * symbol | AttributeValSexpr of pd * attributevalsexpr_attributevalue_sexpr5 -and command = | CommandSetLogic of pd * symbol | CommandSetOption of pd * an_option | CommandSetInfo of pd * attribute | CommandDeclareSort of pd * symbol * string | CommandDefineSort of pd * symbol * commanddefinesort_command_symbol11 * sort | CommandDeclareFun of pd * symbol * commanddeclarefun_command_sort13 * sort | CommandDefineFun of pd * symbol * commanddefinefun_command_sortedvar15 * sort * term | CommandPush of pd * string | CommandPop of pd * string | CommandAssert of pd * term | CommandCheckSat of pd | CommandGetAssert of pd | CommandGetProof of pd | CommandGetUnsatCore of pd | CommandGetValue of pd * commandgetvalue_command_term24 | CommandGetAssign of pd | CommandGetOption of pd * string | CommandGetInfo of pd * infoflag | CommandExit of pd -and commands = | Commands of pd * commands_commands_command30 -and identifier = | IdSymbol of pd * symbol | IdUnderscoreSymNum of pd * symbol * idunderscoresymnum_identifier_numeral33 -and infoflag = | InfoFlagKeyword of pd * string -and qualidentifier = | QualIdentifierId of pd * identifier | QualIdentifierAs of pd * identifier * sort -and sexpr = | SexprSpecConst of pd * specconstant | SexprSymbol of pd * symbol | SexprKeyword of pd * string | SexprInParen of pd * sexprinparen_sexpr_sexpr41 -and sort = | SortIdentifier of pd * identifier | SortIdSortMulti of pd * identifier * sortidsortmulti_sort_sort44 -and sortedvar = | SortedVarSymSort of pd * symbol * sort -and specconstant = | SpecConstsDec of pd * string | SpecConstNum of pd * string | SpecConstString of pd * string | SpecConstsHex of pd * string | SpecConstsBinary of pd * string -and symbol = | Symbol of pd * string | SymbolWithOr of pd * string -and term = | TermSpecConst of pd * specconstant | TermQualIdentifier of pd * qualidentifier | TermQualIdTerm of pd * qualidentifier * termqualidterm_term_term56 | TermLetTerm of pd * termletterm_term_varbinding58 * term | TermForAllTerm of pd * termforallterm_term_sortedvar60 * term | TermExistsTerm of pd * termexiststerm_term_sortedvar62 * term | TermExclimationPt of pd * term * termexclimationpt_term_attribute64 -and varbinding = | VarBindingSymTerm of pd * symbol * term -and termexclimationpt_term_attribute64 = pd * ( attribute) list -and termexiststerm_term_sortedvar62 = pd * ( sortedvar) list -and termforallterm_term_sortedvar60 = pd * ( sortedvar) list -and termletterm_term_varbinding58 = pd * ( varbinding) list -and termqualidterm_term_term56 = pd * ( term) list -and sortidsortmulti_sort_sort44 = pd * ( sort) list -and sexprinparen_sexpr_sexpr41 = pd * ( sexpr) list -and idunderscoresymnum_identifier_numeral33 = pd * ( string) list -and commands_commands_command30 = pd * ( command) list -and commandgetvalue_command_term24 = pd * ( term) list -and commanddefinefun_command_sortedvar15 = pd * ( sortedvar) list -and commanddeclarefun_command_sort13 = pd * ( sort) list -and commanddefinesort_command_symbol11 = pd * ( symbol) list -and attributevalsexpr_attributevalue_sexpr5 = pd * ( sexpr) list;; - -(* pd stands for pos (position) and extradata *) -let dummy () = () -and pd_an_option = function - | AnOptionAttribute(d,_) -> d - -and pd_attribute = function - | AttributeKeyword(d,_) -> d - - | AttributeKeywordValue(d,_,_) -> d - -and pd_attributevalue = function - | AttributeValSpecConst(d,_) -> d - - | AttributeValSymbol(d,_) -> d - - | AttributeValSexpr(d,_) -> d - -and pd_command = function - | CommandSetLogic(d,_) -> d - - | CommandSetOption(d,_) -> d - - | CommandSetInfo(d,_) -> d - - | CommandDeclareSort(d,_,_) -> d - - | CommandDefineSort(d,_,_,_) -> d - - | CommandDeclareFun(d,_,_,_) -> d - - | CommandDefineFun(d,_,_,_,_) -> d - - | CommandPush(d,_) -> d - - | CommandPop(d,_) -> d - - | CommandAssert(d,_) -> d - - | CommandCheckSat(d) -> d - - | CommandGetAssert(d) -> d - - | CommandGetProof(d) -> d - - | CommandGetUnsatCore(d) -> d - - | CommandGetValue(d,_) -> d - - | CommandGetAssign(d) -> d - - | CommandGetOption(d,_) -> d - - | CommandGetInfo(d,_) -> d - - | CommandExit(d) -> d - -and pd_commands = function - | Commands(d,_) -> d - -and pd_identifier = function - | IdSymbol(d,_) -> d - - | IdUnderscoreSymNum(d,_,_) -> d - -and pd_infoflag = function - | InfoFlagKeyword(d,_) -> d - -and pd_qualidentifier = function - | QualIdentifierId(d,_) -> d - - | QualIdentifierAs(d,_,_) -> d - -and pd_sexpr = function - | SexprSpecConst(d,_) -> d - - | SexprSymbol(d,_) -> d - - | SexprKeyword(d,_) -> d - - | SexprInParen(d,_) -> d - -and pd_sort = function - | SortIdentifier(d,_) -> d - - | SortIdSortMulti(d,_,_) -> d - -and pd_sortedvar = function - | SortedVarSymSort(d,_,_) -> d - -and pd_specconstant = function - | SpecConstsDec(d,_) -> d - - | SpecConstNum(d,_) -> d - - | SpecConstString(d,_) -> d - - | SpecConstsHex(d,_) -> d - - | SpecConstsBinary(d,_) -> d - -and pd_symbol = function - | Symbol(d,_) -> d - - | SymbolWithOr(d,_) -> d - -and pd_term = function - | TermSpecConst(d,_) -> d - - | TermQualIdentifier(d,_) -> d - - | TermQualIdTerm(d,_,_) -> d - - | TermLetTerm(d,_,_) -> d - - | TermForAllTerm(d,_,_) -> d - - | TermExistsTerm(d,_,_) -> d - - | TermExclimationPt(d,_,_) -> d - -and pd_varbinding = function - | VarBindingSymTerm(d,_,_) -> d - -and pd_termexclimationpt_term_attribute64 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_termexiststerm_term_sortedvar62 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_termforallterm_term_sortedvar60 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_termletterm_term_varbinding58 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_termqualidterm_term_term56 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_sortidsortmulti_sort_sort44 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_sexprinparen_sexpr_sexpr41 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_idunderscoresymnum_identifier_numeral33 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_commands_commands_command30 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_commandgetvalue_command_term24 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_commanddefinefun_command_sortedvar15 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_commanddeclarefun_command_sort13 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_commanddefinesort_command_symbol11 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d - -and pd_attributevalsexpr_attributevalue_sexpr5 = function - | (d,[]) -> d - - | (d,( _ )::f1239o2) -> d -;; -let pd e = pd_commands e;; diff --git a/src/util/smtlib/smtlib_syntax.mli b/src/util/smtlib/smtlib_syntax.mli deleted file mode 100644 index 05ad8cc7..00000000 --- a/src/util/smtlib/smtlib_syntax.mli +++ /dev/null @@ -1,123 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -type dummy = Dummy -and an_option = AnOptionAttribute of Smtlib_util.pd * attribute -and attribute = - AttributeKeyword of Smtlib_util.pd * string - | AttributeKeywordValue of Smtlib_util.pd * string * attributevalue -and attributevalue = - AttributeValSpecConst of Smtlib_util.pd * specconstant - | AttributeValSymbol of Smtlib_util.pd * symbol - | AttributeValSexpr of Smtlib_util.pd * - attributevalsexpr_attributevalue_sexpr5 -and command = - CommandSetLogic of Smtlib_util.pd * symbol - | CommandSetOption of Smtlib_util.pd * an_option - | CommandSetInfo of Smtlib_util.pd * attribute - | CommandDeclareSort of Smtlib_util.pd * symbol * string - | CommandDefineSort of Smtlib_util.pd * symbol * - commanddefinesort_command_symbol11 * sort - | CommandDeclareFun of Smtlib_util.pd * symbol * - commanddeclarefun_command_sort13 * sort - | CommandDefineFun of Smtlib_util.pd * symbol * - commanddefinefun_command_sortedvar15 * sort * term - | CommandPush of Smtlib_util.pd * string - | CommandPop of Smtlib_util.pd * string - | CommandAssert of Smtlib_util.pd * term - | CommandCheckSat of Smtlib_util.pd - | CommandGetAssert of Smtlib_util.pd - | CommandGetProof of Smtlib_util.pd - | CommandGetUnsatCore of Smtlib_util.pd - | CommandGetValue of Smtlib_util.pd * commandgetvalue_command_term24 - | CommandGetAssign of Smtlib_util.pd - | CommandGetOption of Smtlib_util.pd * string - | CommandGetInfo of Smtlib_util.pd * infoflag - | CommandExit of Smtlib_util.pd -and commands = Commands of Smtlib_util.pd * commands_commands_command30 -and identifier = - IdSymbol of Smtlib_util.pd * symbol - | IdUnderscoreSymNum of Smtlib_util.pd * symbol * - idunderscoresymnum_identifier_numeral33 -and infoflag = InfoFlagKeyword of Smtlib_util.pd * string -and qualidentifier = - QualIdentifierId of Smtlib_util.pd * identifier - | QualIdentifierAs of Smtlib_util.pd * identifier * sort -and sexpr = - SexprSpecConst of Smtlib_util.pd * specconstant - | SexprSymbol of Smtlib_util.pd * symbol - | SexprKeyword of Smtlib_util.pd * string - | SexprInParen of Smtlib_util.pd * sexprinparen_sexpr_sexpr41 -and sort = - SortIdentifier of Smtlib_util.pd * identifier - | SortIdSortMulti of Smtlib_util.pd * identifier * - sortidsortmulti_sort_sort44 -and sortedvar = SortedVarSymSort of Smtlib_util.pd * symbol * sort -and specconstant = - SpecConstsDec of Smtlib_util.pd * string - | SpecConstNum of Smtlib_util.pd * string - | SpecConstString of Smtlib_util.pd * string - | SpecConstsHex of Smtlib_util.pd * string - | SpecConstsBinary of Smtlib_util.pd * string -and symbol = - Symbol of Smtlib_util.pd * string - | SymbolWithOr of Smtlib_util.pd * string -and term = - TermSpecConst of Smtlib_util.pd * specconstant - | TermQualIdentifier of Smtlib_util.pd * qualidentifier - | TermQualIdTerm of Smtlib_util.pd * qualidentifier * - termqualidterm_term_term56 - | TermLetTerm of Smtlib_util.pd * termletterm_term_varbinding58 * term - | TermForAllTerm of Smtlib_util.pd * termforallterm_term_sortedvar60 * term - | TermExistsTerm of Smtlib_util.pd * termexiststerm_term_sortedvar62 * term - | TermExclimationPt of Smtlib_util.pd * term * - termexclimationpt_term_attribute64 -and varbinding = VarBindingSymTerm of Smtlib_util.pd * symbol * term -and termexclimationpt_term_attribute64 = Smtlib_util.pd * attribute list -and termexiststerm_term_sortedvar62 = Smtlib_util.pd * sortedvar list -and termforallterm_term_sortedvar60 = Smtlib_util.pd * sortedvar list -and termletterm_term_varbinding58 = Smtlib_util.pd * varbinding list -and termqualidterm_term_term56 = Smtlib_util.pd * term list -and sortidsortmulti_sort_sort44 = Smtlib_util.pd * sort list -and sexprinparen_sexpr_sexpr41 = Smtlib_util.pd * sexpr list -and idunderscoresymnum_identifier_numeral33 = Smtlib_util.pd * string list -and commands_commands_command30 = Smtlib_util.pd * command list -and commandgetvalue_command_term24 = Smtlib_util.pd * term list -and commanddefinefun_command_sortedvar15 = Smtlib_util.pd * sortedvar list -and commanddeclarefun_command_sort13 = Smtlib_util.pd * sort list -and commanddefinesort_command_symbol11 = Smtlib_util.pd * symbol list -and attributevalsexpr_attributevalue_sexpr5 = Smtlib_util.pd * sexpr list -val dummy : unit -> unit -val pd_an_option : an_option -> Smtlib_util.pd -val pd_attribute : attribute -> Smtlib_util.pd -val pd_attributevalue : attributevalue -> Smtlib_util.pd -val pd_command : command -> Smtlib_util.pd -val pd_commands : commands -> Smtlib_util.pd -val pd_identifier : identifier -> Smtlib_util.pd -val pd_infoflag : infoflag -> Smtlib_util.pd -val pd_qualidentifier : qualidentifier -> Smtlib_util.pd -val pd_sexpr : sexpr -> Smtlib_util.pd -val pd_sort : sort -> Smtlib_util.pd -val pd_sortedvar : sortedvar -> Smtlib_util.pd -val pd_specconstant : specconstant -> Smtlib_util.pd -val pd_symbol : symbol -> Smtlib_util.pd -val pd_term : term -> Smtlib_util.pd -val pd_varbinding : varbinding -> Smtlib_util.pd -val pd_termexclimationpt_term_attribute64 : 'a * 'b list -> 'a -val pd_termexiststerm_term_sortedvar62 : 'a * 'b list -> 'a -val pd_termforallterm_term_sortedvar60 : 'a * 'b list -> 'a -val pd_termletterm_term_varbinding58 : 'a * 'b list -> 'a -val pd_termqualidterm_term_term56 : 'a * 'b list -> 'a -val pd_sortidsortmulti_sort_sort44 : 'a * 'b list -> 'a -val pd_sexprinparen_sexpr_sexpr41 : 'a * 'b list -> 'a -val pd_idunderscoresymnum_identifier_numeral33 : 'a * 'b list -> 'a -val pd_commands_commands_command30 : 'a * 'b list -> 'a -val pd_commandgetvalue_command_term24 : 'a * 'b list -> 'a -val pd_commanddefinefun_command_sortedvar15 : 'a * 'b list -> 'a -val pd_commanddeclarefun_command_sort13 : 'a * 'b list -> 'a -val pd_commanddefinesort_command_symbol11 : 'a * 'b list -> 'a -val pd_attributevalsexpr_attributevalue_sexpr5 : 'a * 'b list -> 'a -val pd : commands -> Smtlib_util.pd diff --git a/src/util/smtlib/smtlib_util.ml b/src/util/smtlib/smtlib_util.ml deleted file mode 100644 index 8e1da4d5..00000000 --- a/src/util/smtlib/smtlib_util.ml +++ /dev/null @@ -1,12 +0,0 @@ -(* auto-generated by gt *) - -(* no extra data from grammar file. *) -type extradata = unit;; -let initial_data() = ();; - -let file = ref "stdin";; -let line = ref 1;; -type pos = int;; -let string_of_pos p = "line "^(string_of_int p);; -let cur_pd() = (!line, initial_data());; (* "pd": pos + extradata *) -type pd = pos * extradata;; diff --git a/src/util/smtlib/smtlib_util.mli b/src/util/smtlib/smtlib_util.mli deleted file mode 100644 index 24ff66b8..00000000 --- a/src/util/smtlib/smtlib_util.mli +++ /dev/null @@ -1,14 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -type extradata = unit -val initial_data : unit -> unit -val file : string ref -val line : int ref -type pos = int -val string_of_pos : int -> string -val cur_pd : unit -> int * unit -type pd = pos * extradata diff --git a/src/util/type.ml b/src/util/type.ml new file mode 100644 index 00000000..584bc1aa --- /dev/null +++ b/src/util/type.ml @@ -0,0 +1,619 @@ + +(* Log&Module Init *) +(* ************************************************************************ *) + +module Ast = Dolmen.Term +module Id = Dolmen.Id +module M = Map.Make(Id) +module H = Hashtbl.Make(Id) + +(* Types *) +(* ************************************************************************ *) + +(* The type of potentially expected result type for parsing an expression *) +type expect = + | Nothing + | Type + | Typed of Expr.ty + +(* The type returned after parsing an expression. *) +type res = + | Ttype + | Ty of Expr.ty + | Term of Expr.term + | Formula of Expr.Formula.t + + +(* The local environments used for type-checking. *) +type env = { + + (* local variables (mostly quantified variables) *) + type_vars : (Expr.ttype Expr.id) M.t; + term_vars : (Expr.ty Expr.id) M.t; + + (* Bound variables (through let constructions) *) + term_lets : Expr.term M.t; + prop_lets : Expr.Formula.t M.t; + + (* Typing options *) + expect : expect; +} + +type 'a typer = env -> Dolmen.Term.t -> 'a + +(* Exceptions *) +(* ************************************************************************ *) + +(* Internal exception *) +exception Found of Ast.t + +(* Exception for typing errors *) +exception Typing_error of string * Ast.t + +(* Convenience functions *) +let _expected s t = raise (Typing_error ( + Format.asprintf "Expected a %s" s, t)) +let _bad_arity s n t = raise (Typing_error ( + Format.asprintf "Bad arity for operator '%s' (expected %d arguments)" s n, t)) +let _type_mismatch t ty ty' ast = raise (Typing_error ( + Format.asprintf "Type Mismatch: '%a' has type %a, but an expression of type %a was expected" + Expr.Print.term t Expr.Print.ty ty Expr.Print.ty ty', ast)) +let _fo_term s t = raise (Typing_error ( + Format.asprintf "Let-bound variable '%a' is applied to terms" Id.print s, t)) + +(* Global Environment *) +(* ************************************************************************ *) + +(* Global identifier table; stores declared types and aliases. *) +let global_env = H.create 42 + +let find_global name = + try H.find global_env name + with Not_found -> `Not_found + +(* Symbol declarations *) +let decl_ty_cstr id c = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Ty c); + Log.debugf 1 "New type constructor : %a" (fun k -> k Expr.Print.const_ttype c) + +let decl_term id c = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Term c); + Log.debugf 1 "New constant : %a" (fun k -> k Expr.Print.const_ty c) + +(* Symbol definitions *) +let def_ty id args body = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Ty_alias (args, body)) + +let def_term id ty_args args body = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Term_alias (ty_args, args, body)) + +(* Local Environment *) +(* ************************************************************************ *) + +(* Make a new empty environment *) +let empty_env ?(expect=Nothing) = { + type_vars = M.empty; + term_vars = M.empty; + term_lets = M.empty; + prop_lets = M.empty; + expect; +} + +let expect env expect = { env with expect = expect } + +(* Generate new fresh names for shadowed variables *) +let new_name pre = + let i = ref 0 in + (fun () -> incr i; pre ^ (string_of_int !i)) + +let new_ty_name = new_name "ty#" +let new_term_name = new_name "term#" + +(* Add local variables to environment *) +let add_type_var env id v = + let v' = + if M.mem id env.type_vars then + Expr.Id.ttype (new_ty_name ()) + else + v + in + Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Expr.Print.id_ttype v'); + v', { env with type_vars = M.add id v' env.type_vars } + +let add_type_vars env l = + let l', env' = List.fold_left (fun (l, acc) (id, v) -> + let v', acc' = add_type_var acc id v in + v' :: l, acc') ([], env) l in + List.rev l', env' + +let add_term_var env id v = + let v' = + if M.mem id env.type_vars then + Expr.Id.ty (new_term_name ()) Expr.(v.id_type) + else + v + in + Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Expr.Print.id_ty v'); + v', { env with term_vars = M.add id v' env.term_vars } + +let find_var env name = + try `Ty (M.find name env.type_vars) + with Not_found -> + begin + try + `Term (M.find name env.term_vars) + with Not_found -> + `Not_found + end + +(* Add local bound variables to env *) +let add_let_term env id t = + Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Expr.Print.term t); + { env with term_lets = M.add id t env.term_lets } + +let add_let_prop env id t = + Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Expr.Formula.print t); + { env with prop_lets = M.add id t env.prop_lets } + +let find_let env name = + try `Term (M.find name env.term_lets) + with Not_found -> + begin + try + `Prop (M.find name env.prop_lets) + with Not_found -> + `Not_found + end + +let pp_expect fmt = function + | Nothing -> Format.fprintf fmt "<>" + | Type -> Format.fprintf fmt "" + | Typed ty -> Expr.Print.ty fmt ty + +let pp_map pp fmt map = + M.iter (fun k v -> + Format.fprintf fmt "%s->%a;" k.Id.name pp v) map + +let pp_env fmt env = + Format.fprintf fmt "(%a) %a%a%a%a" + pp_expect env.expect + (pp_map Expr.Print.id_ttype) env.type_vars + (pp_map Expr.Print.id_ty) env.term_vars + (pp_map Expr.Print.term) env.term_lets + (pp_map Expr.Formula.print) env.prop_lets + +(* Some helper functions *) +(* ************************************************************************ *) + +let flat_map f l = List.flatten (List.map f l) + +let take_drop n l = + let rec aux acc = function + | 0, _ | _, [] -> List.rev acc, [] + | m, x :: r -> aux (x :: acc) (m - 1, r) + in + aux [] (n, l) + +let diagonal l = + let rec single x acc = function + | [] -> acc + | y :: r -> single x ((x, y) :: acc) r + and aux acc = function + | [] -> acc + | x :: r -> aux (single x acc r) r + in + aux [] l + +(* Wrappers for expression building *) +(* ************************************************************************ *) + +let arity f = + List.length Expr.(f.id_type.fun_vars) + + List.length Expr.(f.id_type.fun_args) + +let ty_apply env ast f args = + try + Expr.Ty.apply f args + with Expr.Bad_ty_arity _ -> + _bad_arity Expr.(f.id_name) (arity f) ast + +let term_apply env ast f ty_args t_args = + try + Expr.Term.apply f ty_args t_args + with + | Expr.Bad_arity _ -> + _bad_arity Expr.(f.id_name) (arity f) ast + | Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast + +let ty_subst ast_term id args f_args body = + let aux s v ty = Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Expr.Subst.empty f_args args with + | subst -> + Expr.Ty.subst subst body + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_args) ast_term + +let term_subst ast_term id ty_args t_args f_ty_args f_t_args body = + let aux s v ty = Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Expr.Subst.empty f_ty_args ty_args with + | ty_subst -> + begin + let aux s v t = Expr.Subst.Id.bind v t s in + match List.fold_left2 aux Expr.Subst.empty f_t_args t_args with + | t_subst -> + Expr.Term.subst ty_subst t_subst body + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term + end + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term + +let make_eq ast_term a b = + try + Expr.Formula.make_atom @@ Expr.Atom.eq a b + with Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast_term + +let make_pred ast_term p = + try + Expr.Formula.make_atom @@ Expr.Atom.pred p + with Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast_term + +let infer env s args = + match env.expect with + | Nothing -> `Nothing + | Type -> + let n = List.length args in + let res = Expr.Id.ty_fun s.Id.name n in + decl_ty_cstr s res; + `Ty res + | Typed ty -> + let n = List.length args in + let rec replicate acc n = + if n <= 0 then acc else replicate (Expr.Ty.base :: acc) (n - 1) + in + let res = Expr.Id.term_fun s.Id.name [] (replicate [] n) ty in + decl_term s res; + `Term res + +(* Expression parsing *) +(* ************************************************************************ *) + +let rec parse_expr (env : env) t = + match t with + + (* Basic formulas *) + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.True }, []) } + | { Ast.term = Ast.Builtin Ast.True } -> + Formula Expr.Formula.f_true + + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.False }, []) } + | { Ast.term = Ast.Builtin Ast.False } -> + Formula Expr.Formula.f_false + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } -> + Formula (Expr.Formula.make_and (List.map (parse_formula env) l)) + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } -> + Formula (Expr.Formula.make_or (List.map (parse_formula env) l)) + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_not (Expr.Formula.make_equiv f g)) + | _ -> _bad_arity "xor" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_imply f g) + | _ -> _bad_arity "=>" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_equiv f g) + | _ -> _bad_arity "<=>" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t -> + begin match l with + | [p] -> + Formula (Expr.Formula.make_not (parse_formula env p)) + | _ -> _bad_arity "not" 1 t + end + + (* (Dis)Equality *) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, l) } as t -> + begin match l with + | [a; b] -> + Formula ( + make_eq t + (parse_term env a) + (parse_term env b) + ) + | _ -> _bad_arity "=" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Distinct}, args) } as t -> + let l' = List.map (parse_term env) args in + let l'' = diagonal l' in + Formula ( + Expr.Formula.make_and + (List.map (fun (a, b) -> + Expr.Formula.make_not + (make_eq t a b)) l'') + ) + + (* General case: application *) + | { Ast.term = Ast.Symbol s } as ast -> + parse_app env ast s [] + | { Ast.term = Ast.App ({ Ast.term = Ast.Symbol s }, l) } as ast -> + parse_app env ast s l + + (* Local bindings *) + | { Ast.term = Ast.Binder (Ast.Let, vars, f) } -> + parse_let env f vars + + (* Other cases *) + | ast -> raise (Typing_error ("Couldn't parse the expression", ast)) + +and parse_var env = function + | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> + begin match parse_expr env e with + | Ttype -> `Ty (s, Expr.Id.ttype s.Id.name) + | Ty ty -> `Term (s, Expr.Id.ty s.Id.name ty) + | _ -> _expected "type (or Ttype)" e + end + | { Ast.term = Ast.Symbol s } -> + begin match env.expect with + | Nothing -> assert false + | Type -> `Ty (s, Expr.Id.ttype s.Id.name) + | Typed ty -> `Term (s, Expr.Id.ty s.Id.name ty) + end + | t -> _expected "(typed) variable" t + +and parse_quant_vars env l = + let ttype_vars, typed_vars, env' = List.fold_left ( + fun (l1, l2, acc) v -> + match parse_var acc v with + | `Ty (id, v') -> + let v'', acc' = add_type_var acc id v' in + (v'' :: l1, l2, acc') + | `Term (id, v') -> + let v'', acc' = add_term_var acc id v' in + (l1, v'' :: l2, acc') + ) ([], [], env) l in + List.rev ttype_vars, List.rev typed_vars, env' + +and parse_let env f = function + | [] -> parse_expr env f + | x :: r -> + begin match x with + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, [ + { Ast.term = Ast.Symbol s }; e]) } -> + let t = parse_term env e in + let env' = add_let_term env s t in + parse_let env' f r + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, [ + { Ast.term = Ast.Symbol s }; e]) } -> + let t = parse_formula env e in + let env' = add_let_prop env s t in + parse_let env' f r + | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> + begin match parse_expr env e with + | Term t -> + let env' = add_let_term env s t in + parse_let env' f r + | Formula t -> + let env' = add_let_prop env s t in + parse_let env' f r + | _ -> _expected "term of formula" e + end + | t -> _expected "let-binding" t + end + +and parse_app env ast s args = + match find_let env s with + | `Term t -> + if args = [] then Term t + else _fo_term s ast + | `Prop p -> + if args = [] then Formula p + else _fo_term s ast + | `Not_found -> + begin match find_var env s with + | `Ty f -> + if args = [] then Ty (Expr.Ty.of_id f) + else _fo_term s ast + | `Term f -> + if args = [] then Term (Expr.Term.of_id f) + else _fo_term s ast + | `Not_found -> + begin match find_global s with + | `Ty f -> + parse_app_ty env ast f args + | `Term f -> + parse_app_term env ast f args + | `Ty_alias (f_args, body) -> + parse_app_subst_ty env ast s args f_args body + | `Term_alias (f_ty_args, f_t_args, body) -> + parse_app_subst_term env ast s args f_ty_args f_t_args body + | `Not_found -> + begin match infer env s args with + | `Ty f -> parse_app_ty env ast f args + | `Term f -> parse_app_term env ast f args + | `Nothing -> + raise (Typing_error ( + Format.asprintf "Scoping error: '%a' not found" Id.print s, ast)) + end + end + end + +and parse_app_ty env ast f args = + let l = List.map (parse_ty env) args in + Ty (ty_apply env ast f l) + +and parse_app_term env ast f args = + let n = List.length Expr.(f.id_type.fun_vars) in + let ty_l, t_l = take_drop n args in + let ty_args = List.map (parse_ty env) ty_l in + let t_args = List.map (parse_term env) t_l in + Term (term_apply env ast f ty_args t_args) + +and parse_app_subst_ty env ast id args f_args body = + let l = List.map (parse_ty env) args in + Ty (ty_subst ast id l f_args body) + +and parse_app_subst_term env ast id args f_ty_args f_t_args body = + let n = List.length f_ty_args in + let ty_l, t_l = take_drop n args in + let ty_args = List.map (parse_ty env) ty_l in + let t_args = List.map (parse_term env) t_l in + Term (term_subst ast id ty_args t_args f_ty_args f_t_args body) + +and parse_ty env ast = + match parse_expr { env with expect = Type } ast with + | Ty ty -> ty + | _ -> _expected "type" ast + +and parse_term env ast = + match parse_expr { env with expect = Typed Expr.Ty.base } ast with + | Term t -> t + | _ -> _expected "term" ast + +and parse_formula env ast = + match parse_expr { env with expect = Typed Expr.Ty.prop } ast with + | Term t when Expr.(Ty.equal Ty.prop t.t_type) -> + make_pred ast t + | Formula p -> p + | _ -> _expected "formula" ast + +let parse_ttype_var env t = + match parse_var env t with + | `Ty (id, v) -> (id, v) + | `Term _ -> _expected "type variable" t + +let rec parse_sig_quant env = function + | { Ast.term = Ast.Binder (Ast.Pi, vars, t) } -> + let ttype_vars = List.map (parse_ttype_var env) vars in + let ttype_vars', env' = add_type_vars env ttype_vars in + let l = List.combine vars ttype_vars' in + parse_sig_arrow l [] env' t + | t -> + parse_sig_arrow [] [] env t + +and parse_sig_arrow ttype_vars (ty_args: (Ast.t * res) list) env = function + | { Ast.term = Ast.Binder (Ast.Arrow, args, ret) } -> + let t_args = parse_sig_args env args in + parse_sig_arrow ttype_vars (ty_args @ t_args) env ret + | t -> + begin match parse_expr env t with + | Ttype -> + begin match ttype_vars with + | (h, _) :: _ -> + raise (Typing_error ( + "Type constructor signatures cannot have quantified type variables", h)) + | [] -> + let aux n = function + | (_, Ttype) -> n + 1 + | (ast, _) -> raise (Found ast) + in + begin + match List.fold_left aux 0 ty_args with + | n -> `Ty_cstr n + | exception Found err -> + raise (Typing_error ( + Format.asprintf + "Type constructor signatures cannot have non-ttype arguments,", err)) + end + end + | Ty ret -> + let aux acc = function + | (_, Ty t) -> t :: acc + | (ast, _) -> raise (Found ast) + in + begin + match List.fold_left aux [] ty_args with + | exception Found err -> _expected "type" err + | l -> `Fun_ty (List.map snd ttype_vars, List.rev l, ret) + end + | _ -> _expected "Ttype of type" t + end + +and parse_sig_args env l = + flat_map (parse_sig_arg env) l + +and parse_sig_arg env = function + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.Product}, l) } -> + List.map (fun x -> x, parse_expr env x) l + | t -> + [t, parse_expr env t] + +let parse_sig = parse_sig_quant + +let rec parse_fun ty_args t_args env = function + | { Ast.term = Ast.Binder (Ast.Fun, l, ret) } -> + let ty_args', t_args', env' = parse_quant_vars env l in + parse_fun (ty_args @ ty_args') (t_args @ t_args') env' ret + | ast -> + begin match parse_expr env ast with + | Ttype -> raise (Typing_error ("Cannot redefine Ttype", ast)) + | Ty body -> + if t_args = [] then `Ty (ty_args, body) + else _expected "term" ast + | Term body -> `Term (ty_args, t_args, body) + | Formula _ -> _expected "type or term" ast + end + +(* High-level parsing functions *) +(* ************************************************************************ *) + +let new_decl env t id = + Log.debugf 5 "Typing declaration: %s : %a" + (fun k -> k id.Id.name Ast.print t); + begin match parse_sig env t with + | `Ty_cstr n -> decl_ty_cstr id (Expr.Id.ty_fun id.Id.name n) + | `Fun_ty (vars, args, ret) -> + decl_term id (Expr.Id.term_fun id.Id.name vars args ret) + end + +let new_def env t id = + Log.debugf 5 "Typing definition: %s = %a" + (fun k -> k id.Id.name Ast.print t); + begin match parse_fun [] [] env t with + | `Ty (ty_args, body) -> def_ty id ty_args body + | `Term (ty_args, t_args, body) -> def_term id ty_args t_args body + end + +let new_formula env t = + Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); + let res = parse_formula env t in + res + diff --git a/src/util/type.mli b/src/util/type.mli new file mode 100644 index 00000000..26fd6ad6 --- /dev/null +++ b/src/util/type.mli @@ -0,0 +1,15 @@ + +(** Typechecking of terms from Dolmen.Term.t + This module provides functions to parse terms from the untyped syntax tree + defined in Dolmen, and generate formulas as defined in the Expr module. *) + +exception Typing_error of string * Dolmen.Term.t + +(** {2 High-level functions} *) + +val new_decl : Dolmen.Id.t -> Dolmen.Term.t -> unit + +val new_def : Dolmen.Id.t -> Dolmen.Term.t -> unit + +val new_formula : Dolmen.Term.t -> Expr.Formula.t + From 954892ac4aa9130e77915429e7f5e492c9697a4b Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 9 Sep 2016 12:07:13 +0200 Subject: [PATCH 04/25] [WIP] Strange compiler bug --- src/main.ml | 23 +++++++++++++++++++++++ src/util/type.ml | 11 +++++++---- 2 files changed, 30 insertions(+), 4 deletions(-) diff --git a/src/main.ml b/src/main.ml index 0a8676db..6ea9a86e 100644 --- a/src/main.ml +++ b/src/main.ml @@ -115,6 +115,29 @@ let check () = else if s > !size_limit then raise Out_of_space +let do_task + (module S : Msat.External.S + with type St.formula = Expr.atom) s = + match s.Dolmen.Statement.descr with + | Dolmen.Statement.Def (id, t) -> Type.new_def id t + | Dolmen.Statement.Decl (id, t) -> Type.new_decl id t + | Dolmen.Statement.Consequent t -> + let f = Type.new_formula t in + let cnf = Expr.Formula.make_cnf f in + S.assume cnf + | Dolmen.Statement.Antecedent t -> + let f = Expr.Formula.make_not @@ Type.new_formula t in + let cnf = Expr.Formula.make_cnf f in + S.assume cnf + | Dolmen.Statement.Prove -> + begin match S.solve () with + | S.Sat _ -> () + | S.Unsat _ -> () + end + | _ -> + Format.printf "Command not supported:@\n%a@." + Dolmen.Statement.print s + let main () = (* Administrative duties *) Arg.parse argspec input_file usage; diff --git a/src/util/type.ml b/src/util/type.ml index 584bc1aa..5065c4be 100644 --- a/src/util/type.ml +++ b/src/util/type.ml @@ -103,7 +103,7 @@ let def_term id ty_args args body = (* ************************************************************************ *) (* Make a new empty environment *) -let empty_env ?(expect=Nothing) = { +let empty_env ?(expect=Nothing) () = { type_vars = M.empty; term_vars = M.empty; term_lets = M.empty; @@ -595,7 +595,8 @@ let rec parse_fun ty_args t_args env = function (* High-level parsing functions *) (* ************************************************************************ *) -let new_decl env t id = +let new_decl id t = + let env = empty_env () in Log.debugf 5 "Typing declaration: %s : %a" (fun k -> k id.Id.name Ast.print t); begin match parse_sig env t with @@ -604,7 +605,8 @@ let new_decl env t id = decl_term id (Expr.Id.term_fun id.Id.name vars args ret) end -let new_def env t id = +let new_def id t = + let env = empty_env () in Log.debugf 5 "Typing definition: %s = %a" (fun k -> k id.Id.name Ast.print t); begin match parse_fun [] [] env t with @@ -612,7 +614,8 @@ let new_def env t id = | `Term (ty_args, t_args, body) -> def_term id ty_args t_args body end -let new_formula env t = +let new_formula t = + let env = empty_env () in Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); let res = parse_formula env t in res From 9d509241ad045bbd264a1d813abb7ad387ef43e0 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 9 Sep 2016 18:09:04 +0200 Subject: [PATCH 05/25] [WIP] Some drastic cleanup of code Some of these changes are to be reverted, among other the structure of terms used for the instantiation of the pure SAT solver --- Makefile | 8 ++- _tags | 5 +- src/main.ml | 14 ++-- src/msat.mlpack | 6 +- src/msat_sat.mlpack | 1 - src/msat_smt.mlpack | 13 +--- src/sat/sat.ml | 94 ++----------------------- src/sat/sat.mli | 55 +-------------- src/smt/ID.ml | 39 ----------- src/smt/ID.mli | 25 ------- src/smt/smt.ml | 2 - src/smt/symbols.ml | 62 ----------------- src/smt/symbols.mli | 33 --------- src/smt/term.ml | 101 --------------------------- src/smt/term.mli | 46 ------------- src/smt/ty.ml | 60 ---------------- src/smt/ty.mli | 29 -------- src/util/expr.ml | 6 +- src/util/expr.mli | 11 ++- src/util/type.ml | 164 ++++++++++++++++++++------------------------ src/util/type.mli | 2 +- 21 files changed, 116 insertions(+), 660 deletions(-) delete mode 100644 src/smt/ID.ml delete mode 100644 src/smt/ID.mli delete mode 100644 src/smt/symbols.ml delete mode 100644 src/smt/symbols.mli delete mode 100644 src/smt/term.ml delete mode 100644 src/smt/term.mli delete mode 100644 src/smt/ty.ml delete mode 100644 src/smt/ty.mli diff --git a/Makefile b/Makefile index 92f4bc5e..dd764e92 100644 --- a/Makefile +++ b/Makefile @@ -3,7 +3,7 @@ LOG=build.log COMP=ocamlbuild -log $(LOG) -use-ocamlfind FLAGS= -DOC=msat.docdir/index.html msat_smt.docdir/index.html +DOC=msat.docdir/index.html msat_sat.docdir/index.html msat_smt.docdir/index.html BIN=main.native TEST_BIN=tests/test_api.native @@ -12,11 +12,13 @@ NAME_BIN=msat NAME_CORE=msat NAME_SAT=msat_sat NAME_SMT=msat_smt +NAME_MCSAT=msat_mcsat LIB_CORE=$(addprefix $(NAME_CORE), .cma .cmxa .cmxs) LIB_SAT=$(addprefix $(NAME_SAT), .cma .cmxa .cmxs) LIB_SMT=$(addprefix $(NAME_SMT), .cma .cmxa .cmxs) -LIB=$(LIB_CORE) $(LIB_SAT) $(LIB_SMT) +LIB_MCSAT=$(addprefix $(NAME_MCSAT), .cma .cmxa .cmxs) +LIB=$(LIB_CORE) $(LIB_SAT) # $(LIB_SMT) $(LIB_MCSAT) all: lib test @@ -26,7 +28,7 @@ lib: doc: $(COMP) $(FLAGS) $(DOC) -bin: +bin: lib $(COMP) $(FLAGS) $(BIN) cp $(BIN) $(NAME_BIN) && rm $(BIN) diff --git a/_tags b/_tags index 47e25776..c1554407 100644 --- a/_tags +++ b/_tags @@ -11,6 +11,7 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : include : include : include +: include : include # Pack options @@ -18,10 +19,12 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : for-pack(Msat) : for-pack(Msat) : for-pack(Msat) + : for-pack(Msat_sat) : for-pack(Msat_smt) +: for-pack(Msat_mcsat) -# Bin options +# Testing dependencies : package(dolmen) : package(dolmen) diff --git a/src/main.ml b/src/main.ml index 6ea9a86e..e770c77b 100644 --- a/src/main.ml +++ b/src/main.ml @@ -4,10 +4,8 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module F = Expr - (* -module T = Msat_smt.Cnf.S module Sat = Msat_sat.Sat.Make(struct end) + (* module Smt = Msat_smt.Smt.Make(struct end) module Mcsat = Msat_smt.Mcsat.Make(struct end) *) @@ -101,7 +99,7 @@ let argspec = Arg.align [ "[smhd] Sets the time limit for the sat solver"; "-u", Arg.Set p_unsat_core, " Prints the unsat-core explanation of the unsat proof (if used with -check)"; - "-v", Arg.Int (fun i -> Log.set_debug i), + "-v", Arg.Int (fun i -> Msat.Log.set_debug i), " Sets the debug verbose level"; ] @@ -117,17 +115,17 @@ let check () = let do_task (module S : Msat.External.S - with type St.formula = Expr.atom) s = + with type St.formula = Msat.Expr.atom) s = match s.Dolmen.Statement.descr with | Dolmen.Statement.Def (id, t) -> Type.new_def id t | Dolmen.Statement.Decl (id, t) -> Type.new_decl id t | Dolmen.Statement.Consequent t -> let f = Type.new_formula t in - let cnf = Expr.Formula.make_cnf f in + let cnf = Msat.Expr.Formula.make_cnf f in S.assume cnf | Dolmen.Statement.Antecedent t -> - let f = Expr.Formula.make_not @@ Type.new_formula t in - let cnf = Expr.Formula.make_cnf f in + let f = Msat.Expr.Formula.make_not @@ Type.new_formula t in + let cnf = Msat.Expr.Formula.make_cnf f in S.assume cnf | Dolmen.Statement.Prove -> begin match S.solve () with diff --git a/src/msat.mlpack b/src/msat.mlpack index b07295d9..4968dec6 100644 --- a/src/msat.mlpack +++ b/src/msat.mlpack @@ -18,12 +18,12 @@ Solver Mcsolver Solver_types -# Backends +# Proofs & Backends +Res Backend_intf Dot Dedukti # Auxiliary modules -Res +Expr Tseitin -Hashcons diff --git a/src/msat_sat.mlpack b/src/msat_sat.mlpack index 492570c2..dc169686 100644 --- a/src/msat_sat.mlpack +++ b/src/msat_sat.mlpack @@ -1,2 +1 @@ Sat - diff --git a/src/msat_smt.mlpack b/src/msat_smt.mlpack index cfd8b1ba..1bba977f 100644 --- a/src/msat_smt.mlpack +++ b/src/msat_smt.mlpack @@ -1,12 +1,3 @@ -Cc -Cnf -Explanation -Expr -ID -Literal -Mcsat Smt -Symbols -Term -Ty -Unionfind +Cc +Explanation diff --git a/src/sat/sat.ml b/src/sat/sat.ml index 448cecb4..07f948ee 100644 --- a/src/sat/sat.ml +++ b/src/sat/sat.ml @@ -4,92 +4,10 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -open Msat +module Make(Dummy : sig end) = + Msat.Solver.Make + (Msat.Expr.Atom) + (Msat.Solver.DummyTheory + (Msat.Expr.Atom)) + (struct end) -module FI = Formula_intf - -module Fsat = struct - - exception Bad_atom - - type t = int - type proof = unit - - let max_lit = max_int - let max_fresh = ref (-1) - let max_index = ref 0 - - let _make i = - if i <> 0 && (abs i) < max_lit then begin - max_index := max !max_index (abs i); - i - end else - raise Bad_atom - - let dummy = 0 - - let neg a = - a - let norm a = abs a, if a < 0 then FI.Negated else FI.Same_sign - let abs = abs - let sign i = i > 0 - let apply_sign b i = if b then i else neg i - let set_sign b i = if b then abs i else neg (abs i) - - let hash (a:int) = a land max_int - let equal (a:int) b = a=b - let compare (a:int) b = Pervasives.compare a b - - let make i = _make (2 * i) - - let fresh, iter = - let create () = - incr max_fresh; - _make (2 * !max_fresh + 1) - in - let iter: (t -> unit) -> unit = fun f -> - for j = 1 to !max_index do - f j - done - in - create, iter - - let print fmt a = - Format.fprintf fmt "%s%s%d" - (if a < 0 then "~" else "") - (if a mod 2 = 0 then "v" else "f") - ((abs a) / 2) - -end - -module Tseitin = Tseitin.Make(Fsat) - -module Make(Dummy : sig end) = struct - - module Tsat = Solver.DummyTheory(Fsat) - include Solver.Make(Fsat)(Tsat)(struct end) - - let print_atom = Fsat.print - let print_clause = St.print_clause - let print_proof out p = - let module Dot = Dot.Make(Proof)(struct - let clause_name c = St.(c.name) - let print_atom = St.print_atom - let lemma_info () = "()", None, [] - end) - in - Dot.print out p - - let print_dimacs_clause fmt l = - Format.fprintf fmt "%a0" (fun fmt l -> - List.iter (fun i -> Format.fprintf fmt "%d " i) l) l - - let print_dimacs fmt l = - let l = List.map (fun c -> - List.map (fun a -> a.St.lit) (Proof.to_list c)) l in - let n, m = List.fold_left (fun (n, m) c -> - let m' = List.fold_left (fun i j -> max i (abs j)) m c in - (n + 1, m')) (0, 0) l in - Format.fprintf fmt "p cnf %d %d@\n" n m; - List.iter (fun c -> Format.fprintf fmt "%a@\n" print_dimacs_clause c) l - -end diff --git a/src/sat/sat.mli b/src/sat/sat.mli index 06e4185b..cab12d63 100644 --- a/src/sat/sat.mli +++ b/src/sat/sat.mli @@ -6,59 +6,6 @@ Copyright 2014 Simon Cruanes open Msat -module Fsat : sig +module Make(Dummy : sig end) : Solver.S with type St.formula = Expr.Atom.t - include Formula_intf.S with type t = private int - - exception Bad_atom - (** Exception raised when a problem with atomic formula encoding is detected. *) - - val make : int -> t - (** Returns the literal corresponding to the integer. - @raise Bad_atom if given [0] as argument.*) - - val fresh : unit -> t - (** [new_atom ()] returns a fresh literal. - @raise Bad_atom if there are no more integer available to represent new atoms. *) - - val neg : t -> t - (** [neg a] returns the negation of a literal. Involutive, i.e [neg (neg a) = a]. *) - - val abs : t -> t - val sign : t -> bool - val apply_sign : bool -> t -> t - val set_sign : bool -> t -> t - (** Convenienc functions for manipulating literals. *) - - val hash : t -> int - val equal : t -> t -> bool - val compare : t -> t -> int - (** Usual hash and comparison functions. For now, directly uses - [Pervasives] and [Hashtbl] builtins. *) - - val iter : (t -> unit) -> unit - (** Allows iteration over all atoms created (even if unused). *) - -end - -module Tseitin : Tseitin.S with type atom = Fsat.t - -module Make(Dummy : sig end) : sig - (** Fonctor to make a pure SAT Solver module with built-in literals. *) - - include Solver.S with type St.formula = Fsat.t - - val print_atom : Format.formatter -> atom -> unit - (** Print the atom on the given formatter. *) - - val print_clause : Format.formatter -> St.clause -> unit - (** Print the clause on the given formatter. *) - - val print_proof : Format.formatter -> Proof.proof -> unit - (** Print the given proof in dot format. *) - - val print_dimacs : Format.formatter -> St.clause list -> unit - (** Prints a cnf in dimacs format on the given formatter *) - -end diff --git a/src/smt/ID.ml b/src/smt/ID.ml deleted file mode 100644 index fb0f64d4..00000000 --- a/src/smt/ID.ml +++ /dev/null @@ -1,39 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2016 Guillaume Bury -Copyright 2016 Simon Cruanes -*) - -type t = { - id: int; - name: string; -} - -let make = - let n = ref 0 in - fun name -> - let x = { id= !n; name; } in - incr n; - x - -let copy {name;_} = make name - -let to_string id = id.name - -let equal a b = a.id=b.id -let compare a b = Pervasives.compare a.id b.id -let hash a = a.id land max_int -let pp out a = Format.fprintf out "%s/%d" a.name a.id -let pp_name out a = Format.pp_print_string out a.name - -module AsKey = struct - type t_ = t - type t = t_ - let equal = equal - let compare = compare - let hash = hash -end - -module Map = Map.Make(AsKey) -module Set = Set.Make(AsKey) -module Tbl = Hashtbl.Make(AsKey) diff --git a/src/smt/ID.mli b/src/smt/ID.mli deleted file mode 100644 index f0ac869d..00000000 --- a/src/smt/ID.mli +++ /dev/null @@ -1,25 +0,0 @@ - -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2016 Guillaume Bury -Copyright 2016 Simon Cruanes -*) - -(** {1 Unique Identifiers} *) - -type t - -val make : string -> t -val copy : t -> t - -val to_string : t -> string - -val equal : t -> t -> bool -val compare : t -> t -> int -val hash : t -> int - -val pp_name : Format.formatter -> t -> unit - -module Map : Map.S with type key = t -module Set : Set.S with type elt = t -module Tbl : Hashtbl.S with type key = t diff --git a/src/smt/smt.ml b/src/smt/smt.ml index 10eafb4c..b42478fc 100644 --- a/src/smt/smt.ml +++ b/src/smt/smt.ml @@ -4,8 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Fsmt = Expr - module Tsmt = struct module CC = Cc.Make(String) diff --git a/src/smt/symbols.ml b/src/smt/symbols.ml deleted file mode 100644 index c39e60ab..00000000 --- a/src/smt/symbols.ml +++ /dev/null @@ -1,62 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -type name_kind = Constructor | Other - -type t = - | True - | False - | Name of ID.t * name_kind - | Var of ID.t - -let name ?(kind=Other) s = Name (s, kind) -let var s = Var s - -let compare_kind k1 k2 = match k1, k2 with - | Other, Other -> 0 - | Other, _ -> 1 - | _ , Other -> -1 - | Constructor, Constructor -> 0 - -let compare s1 s2 = match s1, s2 with - | Name (n1,k1), Name (n2,k2) -> - let c = compare_kind k1 k2 in - if c = 0 then ID.compare n1 n2 else c - | Name _, _ -> -1 - | _, Name _ -> 1 - | Var n1, Var n2 -> ID.compare n1 n2 - | Var _, _ -> -1 - | _ ,Var _ -> 1 - | _ -> Pervasives.compare s1 s2 - -let equal s1 s2 = compare s1 s2 = 0 - -let hash = function - | Name (n,_) -> ID.hash n * 19 - | Var n (*| Int n*) -> ID.hash n * 19 + 1 - | s -> Hashtbl.hash s - -let to_string = function - | Name (n,_) -> ID.to_string n - | Var x -> "*var* "^(ID.to_string x) - | True -> "true" - | False -> "false" - -let print fmt s = Format.fprintf fmt "%s" (to_string s) - -module Map = - Map.Make(struct type t' = t type t=t' let compare=compare end) - -module Set = - Set.Make(struct type t' = t type t=t' let compare=compare end) - diff --git a/src/smt/symbols.mli b/src/smt/symbols.mli deleted file mode 100644 index 17dd3e0b..00000000 --- a/src/smt/symbols.mli +++ /dev/null @@ -1,33 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -type name_kind = Constructor | Other - -type t = - | True - | False - | Name of ID.t * name_kind - | Var of ID.t - -val name : ?kind:name_kind -> ID.t -> t -val var : ID.t -> t - -val equal : t -> t -> bool -val compare : t -> t -> int -val hash : t -> int - -val print : Format.formatter -> t -> unit - -module Map : Map.S with type key = t -module Set : Set.S with type elt = t - diff --git a/src/smt/term.ml b/src/smt/term.ml deleted file mode 100644 index 8a670468..00000000 --- a/src/smt/term.ml +++ /dev/null @@ -1,101 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -open Msat - -module Sy = Symbols - -type view = { - head: head; - ty: Ty.t; - mutable tag: int; -} - -and head = - | App of Symbols.t * t list - | Ite of t * t * t - -and t = view - -module H = struct - type t = view - let equal t1 t2 = match t1.head, t2.head with - | App (f1,l1), App (f2,l2) -> - begin try - Sy.equal f1 f2 - && List.for_all2 (==) l1 l2 - && Ty.equal t1.ty t2.ty - with Invalid_argument _ -> - false - end - | Ite (a1,b1,c1), Ite (a2,b2,c2) -> - a1==a2 && b1==b2 && c1==c2 - | App _, Ite _ - | Ite _, App _ -> false - - let hash t = match t.head with - | Ite (a,b,c) -> - abs - (List.fold_left - (fun acc x-> acc*19 +x.tag) 17 [a;b;c]) - | App (f,l) -> - abs - (List.fold_left - (fun acc x-> acc*19 +x.tag) (Sy.hash f + Ty.hash t.ty) - l) - let set_id x tag = x.tag <- tag -end - -module T = Hashcons.Make(H) - -let view t = t -let head t = t.head - -let rec print fmt t = match t.head with - | Ite (a,b,c) -> - Format.fprintf fmt "(@[<2>ite@ %a@ %a@ %a@])" print a print b print c - | App (x, l) -> - match x, l with - | _, [] -> Format.fprintf fmt "%a" Sy.print x - | _, _ -> Format.fprintf fmt "%a(%a)" Sy.print x print_list l - -and print_list fmt = function - | [] -> () - | [t] -> print fmt t - | t::l -> Format.fprintf fmt "%a,%a" print t print_list l - -let compare t1 t2 = - let c = Pervasives.compare t2.tag t1.tag in - if c = 0 then c - else match t1.head, t2.head with - | App ((Sy.True | Sy.False), _), App ((Sy.True | Sy.False), _) -> c - | App ((Sy.True | Sy.False), _), _ -> -1 - | _, App ((Sy.True | Sy.False), _) -> 1 - | _,_ -> c - -let app s l ty = T.hashcons {head=App(s,l); ty=ty; tag= -1; } -let const s ty = app s [] ty -let ite a b c = T.hashcons {head=Ite (a,b,c); ty=b.ty; tag= -1; } - -let true_ = app (Sy.True) [] Ty.Tbool -let false_ = app (Sy.False) [] Ty.Tbool - -let equal t1 t2 = t1 == t2 - -let hash t = t.tag - -module Set = - Set.Make(struct type t' = t type t=t' let compare=compare end) - -module Map = - Map.Make(struct type t' = t type t=t' let compare=compare end) diff --git a/src/smt/term.mli b/src/smt/term.mli deleted file mode 100644 index 92defc96..00000000 --- a/src/smt/term.mli +++ /dev/null @@ -1,46 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -open Msat - -type t - -type view = private { - head: head; - ty: Ty.t; - mutable tag: int; -} - -and head = - | App of Symbols.t * t list - | Ite of t * t * t - -val view : t -> view -val head : t -> head - -val app : Symbols.t -> t list -> Ty.t -> t -val const : Symbols.t -> Ty.t -> t -val ite : t -> t -> t -> t - -val true_ : t -val false_ : t - -val compare : t -> t -> int -val equal : t -> t -> bool -val hash : t -> int - -val print : Format.formatter -> t -> unit - -module Map : Map.S with type key = t -module Set : Set.S with type elt = t - diff --git a/src/smt/ty.ml b/src/smt/ty.ml deleted file mode 100644 index a3af5bd7..00000000 --- a/src/smt/ty.ml +++ /dev/null @@ -1,60 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) - -open Msat - -type symbol = Symbols.t - -type t = - | Tbool - | Tabstract of ID.t - | Tsum of ID.t * symbol list - -let bool = Tbool -let abstract i = Tabstract i -let sum i l = Tsum (i, l) - -let hash t = - match t with - | Tabstract s -> ID.hash s - | Tsum (s, l) -> - let h = - List.fold_left - (fun h x -> 13 * h + Symbols.hash x) (ID.hash s) l - in - abs h - | _ -> Hashtbl.hash t - -let equal t1 t2 = - match t1, t2 with - | Tabstract s1, Tabstract s2 - | Tsum (s1, _), Tsum (s2, _) -> - ID.equal s1 s2 - | Tbool, Tbool -> true - | _ -> false - -let compare t1 t2 = - match t1, t2 with - | Tabstract s1, Tabstract s2 -> - ID.compare s1 s2 - | Tabstract _, _ -> -1 | _ , Tabstract _ -> 1 - | Tsum (s1, _), Tsum(s2, _) -> - ID.compare s1 s2 - | Tsum _, _ -> -1 | _ , Tsum _ -> 1 - | t1, t2 -> Pervasives.compare t1 t2 - -let print fmt ty = - match ty with - | Tbool -> Format.fprintf fmt "bool" - | Tabstract s -> Format.fprintf fmt "%s" (ID.to_string s) - | Tsum (s, _) -> Format.fprintf fmt "%s" (ID.to_string s) diff --git a/src/smt/ty.mli b/src/smt/ty.mli deleted file mode 100644 index 0c94cf71..00000000 --- a/src/smt/ty.mli +++ /dev/null @@ -1,29 +0,0 @@ -(**************************************************************************) -(* *) -(* Cubicle *) -(* Combining model checking algorithms and SMT solvers *) -(* *) -(* Sylvain Conchon and Alain Mebsout *) -(* Universite Paris-Sud 11 *) -(* *) -(* Copyright 2011. This file is distributed under the terms of the *) -(* Apache Software License version 2.0 *) -(* *) -(**************************************************************************) -open Msat - -type symbol = Symbols.t - -type t = - | Tbool - | Tabstract of ID.t - | Tsum of ID.t * symbol list - -val bool : t -val abstract : ID.t -> t -val sum : ID.t -> symbol list -> t - -val hash : t -> int -val equal : t -> t -> bool -val compare : t -> t -> int -val print : Format.formatter -> t -> unit diff --git a/src/util/expr.ml b/src/util/expr.ml index 752b55e7..9270d741 100644 --- a/src/util/expr.ml +++ b/src/util/expr.ml @@ -513,10 +513,10 @@ module Atom = struct let norm f = { f with sign = true }, - if f.sign then Msat.Formula_intf.Same_sign - else Msat.Formula_intf.Negated + if f.sign then Formula_intf.Same_sign + else Formula_intf.Negated end -module Formula = Msat.Tseitin.Make(Atom) +module Formula = Tseitin.Make(Atom) diff --git a/src/util/expr.mli b/src/util/expr.mli index 1f819b2c..229cf51b 100644 --- a/src/util/expr.mli +++ b/src/util/expr.mli @@ -290,6 +290,7 @@ end module Atom : sig type t = atom + type proof = unit (** Type alias *) val hash : t -> int @@ -300,6 +301,12 @@ module Atom : sig val print : Format.formatter -> t -> unit (** Printing functions *) + val dummy : atom + (** A dummy atom, different from any other atom. *) + + val fresh : unit -> atom + (** Create a fresh propositional atom. *) + val eq : term -> term -> atom (** Create an equality over two terms. The two given terms must have the same type [t], which must be different from {!Ty.prop} *) @@ -310,10 +317,10 @@ module Atom : sig val neg : atom -> atom (** Returns the negation of the given atom *) - val norm : atom -> atom * Msat.Formula_intf.negated + val norm : atom -> atom * Formula_intf.negated (** Normalization functions as required by msat. *) end -module Formula : Msat.Tseitin.S with type atom = atom +module Formula : Tseitin.S with type atom = atom diff --git a/src/util/type.ml b/src/util/type.ml index 5065c4be..5727a03e 100644 --- a/src/util/type.ml +++ b/src/util/type.ml @@ -14,33 +14,31 @@ module H = Hashtbl.Make(Id) type expect = | Nothing | Type - | Typed of Expr.ty + | Typed of Msat.Expr.ty (* The type returned after parsing an expression. *) type res = | Ttype - | Ty of Expr.ty - | Term of Expr.term - | Formula of Expr.Formula.t + | Ty of Msat.Expr.ty + | Term of Msat.Expr.term + | Formula of Msat.Expr.Formula.t (* The local environments used for type-checking. *) type env = { (* local variables (mostly quantified variables) *) - type_vars : (Expr.ttype Expr.id) M.t; - term_vars : (Expr.ty Expr.id) M.t; + type_vars : (Msat.Expr.ttype Msat.Expr.id) M.t; + term_vars : (Msat.Expr.ty Msat.Expr.id) M.t; (* Bound variables (through let constructions) *) - term_lets : Expr.term M.t; - prop_lets : Expr.Formula.t M.t; + term_lets : Msat.Expr.term M.t; + prop_lets : Msat.Expr.Formula.t M.t; (* Typing options *) expect : expect; } -type 'a typer = env -> Dolmen.Term.t -> 'a - (* Exceptions *) (* ************************************************************************ *) @@ -57,7 +55,7 @@ let _bad_arity s n t = raise (Typing_error ( Format.asprintf "Bad arity for operator '%s' (expected %d arguments)" s n, t)) let _type_mismatch t ty ty' ast = raise (Typing_error ( Format.asprintf "Type Mismatch: '%a' has type %a, but an expression of type %a was expected" - Expr.Print.term t Expr.Print.ty ty Expr.Print.ty ty', ast)) + Msat.Expr.Print.term t Msat.Expr.Print.ty ty Msat.Expr.Print.ty ty', ast)) let _fo_term s t = raise (Typing_error ( Format.asprintf "Let-bound variable '%a' is applied to terms" Id.print s, t)) @@ -74,28 +72,28 @@ let find_global name = (* Symbol declarations *) let decl_ty_cstr id c = if H.mem global_env id then - Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" (fun k -> k Id.print id); H.add global_env id (`Ty c); - Log.debugf 1 "New type constructor : %a" (fun k -> k Expr.Print.const_ttype c) + Msat.Log.debugf 1 "New type constructor : %a" (fun k -> k Msat.Expr.Print.const_ttype c) let decl_term id c = if H.mem global_env id then - Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" (fun k -> k Id.print id); H.add global_env id (`Term c); - Log.debugf 1 "New constant : %a" (fun k -> k Expr.Print.const_ty c) + Msat.Log.debugf 1 "New constant : %a" (fun k -> k Msat.Expr.Print.const_ty c) (* Symbol definitions *) let def_ty id args body = if H.mem global_env id then - Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" (fun k -> k Id.print id); H.add global_env id (`Ty_alias (args, body)) let def_term id ty_args args body = if H.mem global_env id then - Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" (fun k -> k Id.print id); H.add global_env id (`Term_alias (ty_args, args, body)) @@ -111,8 +109,6 @@ let empty_env ?(expect=Nothing) () = { expect; } -let expect env expect = { env with expect = expect } - (* Generate new fresh names for shadowed variables *) let new_name pre = let i = ref 0 in @@ -125,12 +121,12 @@ let new_term_name = new_name "term#" let add_type_var env id v = let v' = if M.mem id env.type_vars then - Expr.Id.ttype (new_ty_name ()) + Msat.Expr.Id.ttype (new_ty_name ()) else v in - Log.debugf 1 "New binding : %a -> %a" - (fun k -> k Id.print id Expr.Print.id_ttype v'); + Msat.Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Msat.Expr.Print.id_ttype v'); v', { env with type_vars = M.add id v' env.type_vars } let add_type_vars env l = @@ -142,12 +138,12 @@ let add_type_vars env l = let add_term_var env id v = let v' = if M.mem id env.type_vars then - Expr.Id.ty (new_term_name ()) Expr.(v.id_type) + Msat.Expr.Id.ty (new_term_name ()) Msat.Expr.(v.id_type) else v in - Log.debugf 1 "New binding : %a -> %a" - (fun k -> k Id.print id Expr.Print.id_ty v'); + Msat.Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Msat.Expr.Print.id_ty v'); v', { env with term_vars = M.add id v' env.term_vars } let find_var env name = @@ -162,13 +158,13 @@ let find_var env name = (* Add local bound variables to env *) let add_let_term env id t = - Log.debugf 1 "New let-binding : %s -> %a" - (fun k -> k id.Id.name Expr.Print.term t); + Msat.Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Msat.Expr.Print.term t); { env with term_lets = M.add id t env.term_lets } let add_let_prop env id t = - Log.debugf 1 "New let-binding : %s -> %a" - (fun k -> k id.Id.name Expr.Formula.print t); + Msat.Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Msat.Expr.Formula.print t); { env with prop_lets = M.add id t env.prop_lets } let find_let env name = @@ -184,20 +180,12 @@ let find_let env name = let pp_expect fmt = function | Nothing -> Format.fprintf fmt "<>" | Type -> Format.fprintf fmt "" - | Typed ty -> Expr.Print.ty fmt ty + | Typed ty -> Msat.Expr.Print.ty fmt ty let pp_map pp fmt map = M.iter (fun k v -> Format.fprintf fmt "%s->%a;" k.Id.name pp v) map -let pp_env fmt env = - Format.fprintf fmt "(%a) %a%a%a%a" - pp_expect env.expect - (pp_map Expr.Print.id_ttype) env.type_vars - (pp_map Expr.Print.id_ty) env.term_vars - (pp_map Expr.Print.term) env.term_lets - (pp_map Expr.Formula.print) env.prop_lets - (* Some helper functions *) (* ************************************************************************ *) @@ -224,41 +212,41 @@ let diagonal l = (* ************************************************************************ *) let arity f = - List.length Expr.(f.id_type.fun_vars) + - List.length Expr.(f.id_type.fun_args) + List.length Msat.Expr.(f.id_type.fun_vars) + + List.length Msat.Expr.(f.id_type.fun_args) let ty_apply env ast f args = try - Expr.Ty.apply f args - with Expr.Bad_ty_arity _ -> - _bad_arity Expr.(f.id_name) (arity f) ast + Msat.Expr.Ty.apply f args + with Msat.Expr.Bad_ty_arity _ -> + _bad_arity Msat.Expr.(f.id_name) (arity f) ast let term_apply env ast f ty_args t_args = try - Expr.Term.apply f ty_args t_args + Msat.Expr.Term.apply f ty_args t_args with - | Expr.Bad_arity _ -> - _bad_arity Expr.(f.id_name) (arity f) ast - | Expr.Type_mismatch (t, ty, ty') -> + | Msat.Expr.Bad_arity _ -> + _bad_arity Msat.Expr.(f.id_name) (arity f) ast + | Msat.Expr.Type_mismatch (t, ty, ty') -> _type_mismatch t ty ty' ast let ty_subst ast_term id args f_args body = - let aux s v ty = Expr.Subst.Id.bind v ty s in - match List.fold_left2 aux Expr.Subst.empty f_args args with + let aux s v ty = Msat.Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Msat.Expr.Subst.empty f_args args with | subst -> - Expr.Ty.subst subst body + Msat.Expr.Ty.subst subst body | exception Invalid_argument _ -> _bad_arity id.Id.name (List.length f_args) ast_term let term_subst ast_term id ty_args t_args f_ty_args f_t_args body = - let aux s v ty = Expr.Subst.Id.bind v ty s in - match List.fold_left2 aux Expr.Subst.empty f_ty_args ty_args with + let aux s v ty = Msat.Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Msat.Expr.Subst.empty f_ty_args ty_args with | ty_subst -> begin - let aux s v t = Expr.Subst.Id.bind v t s in - match List.fold_left2 aux Expr.Subst.empty f_t_args t_args with + let aux s v t = Msat.Expr.Subst.Id.bind v t s in + match List.fold_left2 aux Msat.Expr.Subst.empty f_t_args t_args with | t_subst -> - Expr.Term.subst ty_subst t_subst body + Msat.Expr.Term.subst ty_subst t_subst body | exception Invalid_argument _ -> _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term end @@ -267,14 +255,14 @@ let term_subst ast_term id ty_args t_args f_ty_args f_t_args body = let make_eq ast_term a b = try - Expr.Formula.make_atom @@ Expr.Atom.eq a b - with Expr.Type_mismatch (t, ty, ty') -> + Msat.Expr.Formula.make_atom @@ Msat.Expr.Atom.eq a b + with Msat.Expr.Type_mismatch (t, ty, ty') -> _type_mismatch t ty ty' ast_term let make_pred ast_term p = try - Expr.Formula.make_atom @@ Expr.Atom.pred p - with Expr.Type_mismatch (t, ty, ty') -> + Msat.Expr.Formula.make_atom @@ Msat.Expr.Atom.pred p + with Msat.Expr.Type_mismatch (t, ty, ty') -> _type_mismatch t ty ty' ast_term let infer env s args = @@ -282,19 +270,19 @@ let infer env s args = | Nothing -> `Nothing | Type -> let n = List.length args in - let res = Expr.Id.ty_fun s.Id.name n in + let res = Msat.Expr.Id.ty_fun s.Id.name n in decl_ty_cstr s res; `Ty res | Typed ty -> let n = List.length args in let rec replicate acc n = - if n <= 0 then acc else replicate (Expr.Ty.base :: acc) (n - 1) + if n <= 0 then acc else replicate (Msat.Expr.Ty.base :: acc) (n - 1) in - let res = Expr.Id.term_fun s.Id.name [] (replicate [] n) ty in + let res = Msat.Expr.Id.term_fun s.Id.name [] (replicate [] n) ty in decl_term s res; `Term res -(* Expression parsing *) +(* Msat.Expression parsing *) (* ************************************************************************ *) let rec parse_expr (env : env) t = @@ -303,24 +291,24 @@ let rec parse_expr (env : env) t = (* Basic formulas *) | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.True }, []) } | { Ast.term = Ast.Builtin Ast.True } -> - Formula Expr.Formula.f_true + Formula Msat.Expr.Formula.f_true | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.False }, []) } | { Ast.term = Ast.Builtin Ast.False } -> - Formula Expr.Formula.f_false + Formula Msat.Expr.Formula.f_false | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } -> - Formula (Expr.Formula.make_and (List.map (parse_formula env) l)) + Formula (Msat.Expr.Formula.make_and (List.map (parse_formula env) l)) | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } -> - Formula (Expr.Formula.make_or (List.map (parse_formula env) l)) + Formula (Msat.Expr.Formula.make_or (List.map (parse_formula env) l)) | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor}, l) } as t -> begin match l with | [p; q] -> let f = parse_formula env p in let g = parse_formula env q in - Formula (Expr.Formula.make_not (Expr.Formula.make_equiv f g)) + Formula (Msat.Expr.Formula.make_not (Msat.Expr.Formula.make_equiv f g)) | _ -> _bad_arity "xor" 2 t end @@ -329,7 +317,7 @@ let rec parse_expr (env : env) t = | [p; q] -> let f = parse_formula env p in let g = parse_formula env q in - Formula (Expr.Formula.make_imply f g) + Formula (Msat.Expr.Formula.make_imply f g) | _ -> _bad_arity "=>" 2 t end @@ -338,14 +326,14 @@ let rec parse_expr (env : env) t = | [p; q] -> let f = parse_formula env p in let g = parse_formula env q in - Formula (Expr.Formula.make_equiv f g) + Formula (Msat.Expr.Formula.make_equiv f g) | _ -> _bad_arity "<=>" 2 t end | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t -> begin match l with | [p] -> - Formula (Expr.Formula.make_not (parse_formula env p)) + Formula (Msat.Expr.Formula.make_not (parse_formula env p)) | _ -> _bad_arity "not" 1 t end @@ -365,9 +353,9 @@ let rec parse_expr (env : env) t = let l' = List.map (parse_term env) args in let l'' = diagonal l' in Formula ( - Expr.Formula.make_and + Msat.Expr.Formula.make_and (List.map (fun (a, b) -> - Expr.Formula.make_not + Msat.Expr.Formula.make_not (make_eq t a b)) l'') ) @@ -387,15 +375,15 @@ let rec parse_expr (env : env) t = and parse_var env = function | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> begin match parse_expr env e with - | Ttype -> `Ty (s, Expr.Id.ttype s.Id.name) - | Ty ty -> `Term (s, Expr.Id.ty s.Id.name ty) + | Ttype -> `Ty (s, Msat.Expr.Id.ttype s.Id.name) + | Ty ty -> `Term (s, Msat.Expr.Id.ty s.Id.name ty) | _ -> _expected "type (or Ttype)" e end | { Ast.term = Ast.Symbol s } -> begin match env.expect with | Nothing -> assert false - | Type -> `Ty (s, Expr.Id.ttype s.Id.name) - | Typed ty -> `Term (s, Expr.Id.ty s.Id.name ty) + | Type -> `Ty (s, Msat.Expr.Id.ttype s.Id.name) + | Typed ty -> `Term (s, Msat.Expr.Id.ty s.Id.name ty) end | t -> _expected "(typed) variable" t @@ -450,10 +438,10 @@ and parse_app env ast s args = | `Not_found -> begin match find_var env s with | `Ty f -> - if args = [] then Ty (Expr.Ty.of_id f) + if args = [] then Ty (Msat.Expr.Ty.of_id f) else _fo_term s ast | `Term f -> - if args = [] then Term (Expr.Term.of_id f) + if args = [] then Term (Msat.Expr.Term.of_id f) else _fo_term s ast | `Not_found -> begin match find_global s with @@ -481,7 +469,7 @@ and parse_app_ty env ast f args = Ty (ty_apply env ast f l) and parse_app_term env ast f args = - let n = List.length Expr.(f.id_type.fun_vars) in + let n = List.length Msat.Expr.(f.id_type.fun_vars) in let ty_l, t_l = take_drop n args in let ty_args = List.map (parse_ty env) ty_l in let t_args = List.map (parse_term env) t_l in @@ -504,13 +492,13 @@ and parse_ty env ast = | _ -> _expected "type" ast and parse_term env ast = - match parse_expr { env with expect = Typed Expr.Ty.base } ast with + match parse_expr { env with expect = Typed Msat.Expr.Ty.base } ast with | Term t -> t | _ -> _expected "term" ast and parse_formula env ast = - match parse_expr { env with expect = Typed Expr.Ty.prop } ast with - | Term t when Expr.(Ty.equal Ty.prop t.t_type) -> + match parse_expr { env with expect = Typed Msat.Expr.Ty.prop } ast with + | Term t when Msat.Expr.(Ty.equal Ty.prop t.t_type) -> make_pred ast t | Formula p -> p | _ -> _expected "formula" ast @@ -597,17 +585,17 @@ let rec parse_fun ty_args t_args env = function let new_decl id t = let env = empty_env () in - Log.debugf 5 "Typing declaration: %s : %a" + Msat.Log.debugf 5 "Typing declaration: %s : %a" (fun k -> k id.Id.name Ast.print t); begin match parse_sig env t with - | `Ty_cstr n -> decl_ty_cstr id (Expr.Id.ty_fun id.Id.name n) + | `Ty_cstr n -> decl_ty_cstr id (Msat.Expr.Id.ty_fun id.Id.name n) | `Fun_ty (vars, args, ret) -> - decl_term id (Expr.Id.term_fun id.Id.name vars args ret) + decl_term id (Msat.Expr.Id.term_fun id.Id.name vars args ret) end let new_def id t = let env = empty_env () in - Log.debugf 5 "Typing definition: %s = %a" + Msat.Log.debugf 5 "Typing definition: %s = %a" (fun k -> k id.Id.name Ast.print t); begin match parse_fun [] [] env t with | `Ty (ty_args, body) -> def_ty id ty_args body @@ -616,7 +604,7 @@ let new_def id t = let new_formula t = let env = empty_env () in - Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); + Msat.Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); let res = parse_formula env t in res diff --git a/src/util/type.mli b/src/util/type.mli index 26fd6ad6..a0414e29 100644 --- a/src/util/type.mli +++ b/src/util/type.mli @@ -11,5 +11,5 @@ val new_decl : Dolmen.Id.t -> Dolmen.Term.t -> unit val new_def : Dolmen.Id.t -> Dolmen.Term.t -> unit -val new_formula : Dolmen.Term.t -> Expr.Formula.t +val new_formula : Dolmen.Term.t -> Msat.Expr.Formula.t From dfff903f8cafc250b4c2bef78fe4bdcfa163601d Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Mon, 12 Sep 2016 15:32:22 +0200 Subject: [PATCH 06/25] Removed additional libs. --- Makefile | 16 +- src/main.ml | 151 ++++++----- src/sat/sat.ml | 6 +- src/sat/sat.mli | 2 - src/smt/cc.ml | 2 - src/smt/mcsat.ml | 2 - src/util/type.ml | 619 ++---------------------------------------- src/util/type.mli | 15 - src/util/type_smt.ml | 615 +++++++++++++++++++++++++++++++++++++++++ src/util/type_smt.mli | 7 + 10 files changed, 725 insertions(+), 710 deletions(-) delete mode 100644 src/util/type.mli create mode 100644 src/util/type_smt.ml create mode 100644 src/util/type_smt.mli diff --git a/Makefile b/Makefile index dd764e92..328cc6dc 100644 --- a/Makefile +++ b/Makefile @@ -10,15 +10,15 @@ TEST_BIN=tests/test_api.native NAME_OCAMLFIND=msat NAME_BIN=msat NAME_CORE=msat -NAME_SAT=msat_sat -NAME_SMT=msat_smt -NAME_MCSAT=msat_mcsat +#NAME_SAT=msat_sat +#NAME_SMT=msat_smt +#NAME_MCSAT=msat_mcsat LIB_CORE=$(addprefix $(NAME_CORE), .cma .cmxa .cmxs) -LIB_SAT=$(addprefix $(NAME_SAT), .cma .cmxa .cmxs) -LIB_SMT=$(addprefix $(NAME_SMT), .cma .cmxa .cmxs) -LIB_MCSAT=$(addprefix $(NAME_MCSAT), .cma .cmxa .cmxs) -LIB=$(LIB_CORE) $(LIB_SAT) # $(LIB_SMT) $(LIB_MCSAT) +#LIB_SAT=$(addprefix $(NAME_SAT), .cma .cmxa .cmxs) +#LIB_SMT=$(addprefix $(NAME_SMT), .cma .cmxa .cmxs) +#LIB_MCSAT=$(addprefix $(NAME_MCSAT), .cma .cmxa .cmxs) +LIB=$(LIB_CORE) # $(LIB_SAT) $(LIB_SMT) $(LIB_MCSAT) all: lib test @@ -28,7 +28,7 @@ lib: doc: $(COMP) $(FLAGS) $(DOC) -bin: lib +bin: $(COMP) $(FLAGS) $(BIN) cp $(BIN) $(NAME_BIN) && rm $(BIN) diff --git a/src/main.ml b/src/main.ml index e770c77b..b3e0450d 100644 --- a/src/main.ml +++ b/src/main.ml @@ -4,10 +4,11 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Sat = Msat_sat.Sat.Make(struct end) +module Sat = Sat.Make(struct end) +module Dummy = Sat (* -module Smt = Msat_smt.Smt.Make(struct end) -module Mcsat = Msat_smt.Mcsat.Make(struct end) +module Smt = Smt.Make(struct end) +module Mcsat = Mcsat.Make(struct end) *) module P = @@ -99,7 +100,7 @@ let argspec = Arg.align [ "[smhd] Sets the time limit for the sat solver"; "-u", Arg.Set p_unsat_core, " Prints the unsat-core explanation of the unsat proof (if used with -check)"; - "-v", Arg.Int (fun i -> Msat.Log.set_debug i), + "-v", Arg.Int (fun i -> Log.set_debug i), " Sets the debug verbose level"; ] @@ -113,28 +114,30 @@ let check () = else if s > !size_limit then raise Out_of_space -let do_task - (module S : Msat.External.S - with type St.formula = Msat.Expr.atom) s = - match s.Dolmen.Statement.descr with - | Dolmen.Statement.Def (id, t) -> Type.new_def id t - | Dolmen.Statement.Decl (id, t) -> Type.new_decl id t - | Dolmen.Statement.Consequent t -> - let f = Type.new_formula t in - let cnf = Msat.Expr.Formula.make_cnf f in - S.assume cnf - | Dolmen.Statement.Antecedent t -> - let f = Msat.Expr.Formula.make_not @@ Type.new_formula t in - let cnf = Msat.Expr.Formula.make_cnf f in - S.assume cnf - | Dolmen.Statement.Prove -> - begin match S.solve () with - | S.Sat _ -> () - | S.Unsat _ -> () - end - | _ -> - Format.printf "Command not supported:@\n%a@." - Dolmen.Statement.print s +module Make + (T : Type.S) + (S : External.S with type St.formula = T.atom) = struct + + let do_task s = + match s.Dolmen.Statement.descr with + | Dolmen.Statement.Def (id, t) -> T.def id t + | Dolmen.Statement.Decl (id, t) -> T.decl id t + | Dolmen.Statement.Consequent t -> + let cnf = T.consequent t in + S.assume cnf + | Dolmen.Statement.Antecedent t -> + let cnf = T.antecedent t in + S.assume cnf + | Dolmen.Statement.Prove -> + begin match S.solve () with + | S.Sat _ -> () + | S.Unsat _ -> () + end + | _ -> + Format.printf "Command not supported:@\n%a@." + Dolmen.Statement.print s +end + let main () = (* Administrative duties *) @@ -150,55 +153,55 @@ let main () = Gc.delete_alarm al; () - (* Old code ... +(* Old code ... - let cnf = get_cnf () in - if !p_cnf then - print_cnf cnf; - match !solver with - | Smt -> - Smt.assume cnf; - let res = Smt.solve () in - Gc.delete_alarm al; - begin match res with - | Smt.Sat sat -> - let t = Sys.time () in - if !p_check then - if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then - raise Incorrect_model; - print "Sat (%f/%f)" t (Sys.time () -. t) - | Smt.Unsat us -> - let t = Sys.time () in - if !p_check then begin - let p = us.Solver_intf.get_proof () in - Smt.Proof.check p; - print_proof p; - if !p_unsat_core then - print_unsat_core (Smt.unsat_core p) - end; - print "Unsat (%f/%f)" t (Sys.time () -. t) - end - | Mcsat -> - Mcsat.assume cnf; - let res = Mcsat.solve () in - begin match res with - | Mcsat.Sat sat -> - let t = Sys.time () in - if !p_check then - if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then - raise Incorrect_model; - print "Sat (%f/%f)" t (Sys.time () -. t) - | Mcsat.Unsat us -> - let t = Sys.time () in - if !p_check then begin - let p = us.Solver_intf.get_proof () in - Mcsat.Proof.check p; - print_mcproof p; - if !p_unsat_core then - print_mc_unsat_core (Mcsat.unsat_core p) - end; - print "Unsat (%f/%f)" t (Sys.time () -. t) - end + let cnf = get_cnf () in + if !p_cnf then + print_cnf cnf; + match !solver with + | Smt -> + Smt.assume cnf; + let res = Smt.solve () in + Gc.delete_alarm al; + begin match res with + | Smt.Sat sat -> + let t = Sys.time () in + if !p_check then + if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then + raise Incorrect_model; + print "Sat (%f/%f)" t (Sys.time () -. t) + | Smt.Unsat us -> + let t = Sys.time () in + if !p_check then begin + let p = us.Solver_intf.get_proof () in + Smt.Proof.check p; + print_proof p; + if !p_unsat_core then + print_unsat_core (Smt.unsat_core p) + end; + print "Unsat (%f/%f)" t (Sys.time () -. t) + end + | Mcsat -> + Mcsat.assume cnf; + let res = Mcsat.solve () in + begin match res with + | Mcsat.Sat sat -> + let t = Sys.time () in + if !p_check then + if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then + raise Incorrect_model; + print "Sat (%f/%f)" t (Sys.time () -. t) + | Mcsat.Unsat us -> + let t = Sys.time () in + if !p_check then begin + let p = us.Solver_intf.get_proof () in + Mcsat.Proof.check p; + print_mcproof p; + if !p_unsat_core then + print_mc_unsat_core (Mcsat.unsat_core p) + end; + print "Unsat (%f/%f)" t (Sys.time () -. t) + end *) diff --git a/src/sat/sat.ml b/src/sat/sat.ml index 07f948ee..2c91c65f 100644 --- a/src/sat/sat.ml +++ b/src/sat/sat.ml @@ -5,9 +5,5 @@ Copyright 2014 Simon Cruanes *) module Make(Dummy : sig end) = - Msat.Solver.Make - (Msat.Expr.Atom) - (Msat.Solver.DummyTheory - (Msat.Expr.Atom)) - (struct end) + Solver.Make(Expr.Atom)(Solver.DummyTheory(Expr.Atom))(struct end) diff --git a/src/sat/sat.mli b/src/sat/sat.mli index cab12d63..79c9b6b0 100644 --- a/src/sat/sat.mli +++ b/src/sat/sat.mli @@ -4,8 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -open Msat - module Make(Dummy : sig end) : Solver.S with type St.formula = Expr.Atom.t diff --git a/src/smt/cc.ml b/src/smt/cc.ml index a4114398..b0b3f19a 100644 --- a/src/smt/cc.ml +++ b/src/smt/cc.ml @@ -12,8 +12,6 @@ (* *) (**************************************************************************) -open Msat - let max_split = 1000000 let cc_active = ref true diff --git a/src/smt/mcsat.ml b/src/smt/mcsat.ml index 9a5b67fc..9be8e7bc 100644 --- a/src/smt/mcsat.ml +++ b/src/smt/mcsat.ml @@ -4,8 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -open Msat - module Fsmt = Expr module Tsmt = struct diff --git a/src/util/type.ml b/src/util/type.ml index 5727a03e..788328a3 100644 --- a/src/util/type.ml +++ b/src/util/type.ml @@ -1,610 +1,25 @@ -(* Log&Module Init *) -(* ************************************************************************ *) +(** Typechecking of terms from Dolmen.Term.t + This module defines the requirements for typing expre'ssions from dolmen. *) -module Ast = Dolmen.Term -module Id = Dolmen.Id -module M = Map.Make(Id) -module H = Hashtbl.Make(Id) +module type S = sig -(* Types *) -(* ************************************************************************ *) + type atom + (** The type of atoms that will be fed to tha sovler. *) -(* The type of potentially expected result type for parsing an expression *) -type expect = - | Nothing - | Type - | Typed of Msat.Expr.ty + exception Typing_error of string * Dolmen.Term.t + (** Exception raised during typechecking. *) -(* The type returned after parsing an expression. *) -type res = - | Ttype - | Ty of Msat.Expr.ty - | Term of Msat.Expr.term - | Formula of Msat.Expr.Formula.t + val decl : Dolmen.Id.t -> Dolmen.Term.t -> unit + (** New declaration, i.e an identifier and its type. *) + val def : Dolmen.Id.t -> Dolmen.Term.t -> unit + (** New definition, i.e an identifier and the term it is equal to. *) -(* The local environments used for type-checking. *) -type env = { - - (* local variables (mostly quantified variables) *) - type_vars : (Msat.Expr.ttype Msat.Expr.id) M.t; - term_vars : (Msat.Expr.ty Msat.Expr.id) M.t; - - (* Bound variables (through let constructions) *) - term_lets : Msat.Expr.term M.t; - prop_lets : Msat.Expr.Formula.t M.t; - - (* Typing options *) - expect : expect; -} - -(* Exceptions *) -(* ************************************************************************ *) - -(* Internal exception *) -exception Found of Ast.t - -(* Exception for typing errors *) -exception Typing_error of string * Ast.t - -(* Convenience functions *) -let _expected s t = raise (Typing_error ( - Format.asprintf "Expected a %s" s, t)) -let _bad_arity s n t = raise (Typing_error ( - Format.asprintf "Bad arity for operator '%s' (expected %d arguments)" s n, t)) -let _type_mismatch t ty ty' ast = raise (Typing_error ( - Format.asprintf "Type Mismatch: '%a' has type %a, but an expression of type %a was expected" - Msat.Expr.Print.term t Msat.Expr.Print.ty ty Msat.Expr.Print.ty ty', ast)) -let _fo_term s t = raise (Typing_error ( - Format.asprintf "Let-bound variable '%a' is applied to terms" Id.print s, t)) - -(* Global Environment *) -(* ************************************************************************ *) - -(* Global identifier table; stores declared types and aliases. *) -let global_env = H.create 42 - -let find_global name = - try H.find global_env name - with Not_found -> `Not_found - -(* Symbol declarations *) -let decl_ty_cstr id c = - if H.mem global_env id then - Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" - (fun k -> k Id.print id); - H.add global_env id (`Ty c); - Msat.Log.debugf 1 "New type constructor : %a" (fun k -> k Msat.Expr.Print.const_ttype c) - -let decl_term id c = - if H.mem global_env id then - Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" - (fun k -> k Id.print id); - H.add global_env id (`Term c); - Msat.Log.debugf 1 "New constant : %a" (fun k -> k Msat.Expr.Print.const_ty c) - -(* Symbol definitions *) -let def_ty id args body = - if H.mem global_env id then - Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" - (fun k -> k Id.print id); - H.add global_env id (`Ty_alias (args, body)) - -let def_term id ty_args args body = - if H.mem global_env id then - Msat.Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" - (fun k -> k Id.print id); - H.add global_env id (`Term_alias (ty_args, args, body)) - -(* Local Environment *) -(* ************************************************************************ *) - -(* Make a new empty environment *) -let empty_env ?(expect=Nothing) () = { - type_vars = M.empty; - term_vars = M.empty; - term_lets = M.empty; - prop_lets = M.empty; - expect; -} - -(* Generate new fresh names for shadowed variables *) -let new_name pre = - let i = ref 0 in - (fun () -> incr i; pre ^ (string_of_int !i)) - -let new_ty_name = new_name "ty#" -let new_term_name = new_name "term#" - -(* Add local variables to environment *) -let add_type_var env id v = - let v' = - if M.mem id env.type_vars then - Msat.Expr.Id.ttype (new_ty_name ()) - else - v - in - Msat.Log.debugf 1 "New binding : %a -> %a" - (fun k -> k Id.print id Msat.Expr.Print.id_ttype v'); - v', { env with type_vars = M.add id v' env.type_vars } - -let add_type_vars env l = - let l', env' = List.fold_left (fun (l, acc) (id, v) -> - let v', acc' = add_type_var acc id v in - v' :: l, acc') ([], env) l in - List.rev l', env' - -let add_term_var env id v = - let v' = - if M.mem id env.type_vars then - Msat.Expr.Id.ty (new_term_name ()) Msat.Expr.(v.id_type) - else - v - in - Msat.Log.debugf 1 "New binding : %a -> %a" - (fun k -> k Id.print id Msat.Expr.Print.id_ty v'); - v', { env with term_vars = M.add id v' env.term_vars } - -let find_var env name = - try `Ty (M.find name env.type_vars) - with Not_found -> - begin - try - `Term (M.find name env.term_vars) - with Not_found -> - `Not_found - end - -(* Add local bound variables to env *) -let add_let_term env id t = - Msat.Log.debugf 1 "New let-binding : %s -> %a" - (fun k -> k id.Id.name Msat.Expr.Print.term t); - { env with term_lets = M.add id t env.term_lets } - -let add_let_prop env id t = - Msat.Log.debugf 1 "New let-binding : %s -> %a" - (fun k -> k id.Id.name Msat.Expr.Formula.print t); - { env with prop_lets = M.add id t env.prop_lets } - -let find_let env name = - try `Term (M.find name env.term_lets) - with Not_found -> - begin - try - `Prop (M.find name env.prop_lets) - with Not_found -> - `Not_found - end - -let pp_expect fmt = function - | Nothing -> Format.fprintf fmt "<>" - | Type -> Format.fprintf fmt "" - | Typed ty -> Msat.Expr.Print.ty fmt ty - -let pp_map pp fmt map = - M.iter (fun k v -> - Format.fprintf fmt "%s->%a;" k.Id.name pp v) map - -(* Some helper functions *) -(* ************************************************************************ *) - -let flat_map f l = List.flatten (List.map f l) - -let take_drop n l = - let rec aux acc = function - | 0, _ | _, [] -> List.rev acc, [] - | m, x :: r -> aux (x :: acc) (m - 1, r) - in - aux [] (n, l) - -let diagonal l = - let rec single x acc = function - | [] -> acc - | y :: r -> single x ((x, y) :: acc) r - and aux acc = function - | [] -> acc - | x :: r -> aux (single x acc r) r - in - aux [] l - -(* Wrappers for expression building *) -(* ************************************************************************ *) - -let arity f = - List.length Msat.Expr.(f.id_type.fun_vars) + - List.length Msat.Expr.(f.id_type.fun_args) - -let ty_apply env ast f args = - try - Msat.Expr.Ty.apply f args - with Msat.Expr.Bad_ty_arity _ -> - _bad_arity Msat.Expr.(f.id_name) (arity f) ast - -let term_apply env ast f ty_args t_args = - try - Msat.Expr.Term.apply f ty_args t_args - with - | Msat.Expr.Bad_arity _ -> - _bad_arity Msat.Expr.(f.id_name) (arity f) ast - | Msat.Expr.Type_mismatch (t, ty, ty') -> - _type_mismatch t ty ty' ast - -let ty_subst ast_term id args f_args body = - let aux s v ty = Msat.Expr.Subst.Id.bind v ty s in - match List.fold_left2 aux Msat.Expr.Subst.empty f_args args with - | subst -> - Msat.Expr.Ty.subst subst body - | exception Invalid_argument _ -> - _bad_arity id.Id.name (List.length f_args) ast_term - -let term_subst ast_term id ty_args t_args f_ty_args f_t_args body = - let aux s v ty = Msat.Expr.Subst.Id.bind v ty s in - match List.fold_left2 aux Msat.Expr.Subst.empty f_ty_args ty_args with - | ty_subst -> - begin - let aux s v t = Msat.Expr.Subst.Id.bind v t s in - match List.fold_left2 aux Msat.Expr.Subst.empty f_t_args t_args with - | t_subst -> - Msat.Expr.Term.subst ty_subst t_subst body - | exception Invalid_argument _ -> - _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term - end - | exception Invalid_argument _ -> - _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term - -let make_eq ast_term a b = - try - Msat.Expr.Formula.make_atom @@ Msat.Expr.Atom.eq a b - with Msat.Expr.Type_mismatch (t, ty, ty') -> - _type_mismatch t ty ty' ast_term - -let make_pred ast_term p = - try - Msat.Expr.Formula.make_atom @@ Msat.Expr.Atom.pred p - with Msat.Expr.Type_mismatch (t, ty, ty') -> - _type_mismatch t ty ty' ast_term - -let infer env s args = - match env.expect with - | Nothing -> `Nothing - | Type -> - let n = List.length args in - let res = Msat.Expr.Id.ty_fun s.Id.name n in - decl_ty_cstr s res; - `Ty res - | Typed ty -> - let n = List.length args in - let rec replicate acc n = - if n <= 0 then acc else replicate (Msat.Expr.Ty.base :: acc) (n - 1) - in - let res = Msat.Expr.Id.term_fun s.Id.name [] (replicate [] n) ty in - decl_term s res; - `Term res - -(* Msat.Expression parsing *) -(* ************************************************************************ *) - -let rec parse_expr (env : env) t = - match t with - - (* Basic formulas *) - | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.True }, []) } - | { Ast.term = Ast.Builtin Ast.True } -> - Formula Msat.Expr.Formula.f_true - - | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.False }, []) } - | { Ast.term = Ast.Builtin Ast.False } -> - Formula Msat.Expr.Formula.f_false - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } -> - Formula (Msat.Expr.Formula.make_and (List.map (parse_formula env) l)) - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } -> - Formula (Msat.Expr.Formula.make_or (List.map (parse_formula env) l)) - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor}, l) } as t -> - begin match l with - | [p; q] -> - let f = parse_formula env p in - let g = parse_formula env q in - Formula (Msat.Expr.Formula.make_not (Msat.Expr.Formula.make_equiv f g)) - | _ -> _bad_arity "xor" 2 t - end - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply}, l) } as t -> - begin match l with - | [p; q] -> - let f = parse_formula env p in - let g = parse_formula env q in - Formula (Msat.Expr.Formula.make_imply f g) - | _ -> _bad_arity "=>" 2 t - end - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, l) } as t -> - begin match l with - | [p; q] -> - let f = parse_formula env p in - let g = parse_formula env q in - Formula (Msat.Expr.Formula.make_equiv f g) - | _ -> _bad_arity "<=>" 2 t - end - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t -> - begin match l with - | [p] -> - Formula (Msat.Expr.Formula.make_not (parse_formula env p)) - | _ -> _bad_arity "not" 1 t - end - - (* (Dis)Equality *) - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, l) } as t -> - begin match l with - | [a; b] -> - Formula ( - make_eq t - (parse_term env a) - (parse_term env b) - ) - | _ -> _bad_arity "=" 2 t - end - - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Distinct}, args) } as t -> - let l' = List.map (parse_term env) args in - let l'' = diagonal l' in - Formula ( - Msat.Expr.Formula.make_and - (List.map (fun (a, b) -> - Msat.Expr.Formula.make_not - (make_eq t a b)) l'') - ) - - (* General case: application *) - | { Ast.term = Ast.Symbol s } as ast -> - parse_app env ast s [] - | { Ast.term = Ast.App ({ Ast.term = Ast.Symbol s }, l) } as ast -> - parse_app env ast s l - - (* Local bindings *) - | { Ast.term = Ast.Binder (Ast.Let, vars, f) } -> - parse_let env f vars - - (* Other cases *) - | ast -> raise (Typing_error ("Couldn't parse the expression", ast)) - -and parse_var env = function - | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> - begin match parse_expr env e with - | Ttype -> `Ty (s, Msat.Expr.Id.ttype s.Id.name) - | Ty ty -> `Term (s, Msat.Expr.Id.ty s.Id.name ty) - | _ -> _expected "type (or Ttype)" e - end - | { Ast.term = Ast.Symbol s } -> - begin match env.expect with - | Nothing -> assert false - | Type -> `Ty (s, Msat.Expr.Id.ttype s.Id.name) - | Typed ty -> `Term (s, Msat.Expr.Id.ty s.Id.name ty) - end - | t -> _expected "(typed) variable" t - -and parse_quant_vars env l = - let ttype_vars, typed_vars, env' = List.fold_left ( - fun (l1, l2, acc) v -> - match parse_var acc v with - | `Ty (id, v') -> - let v'', acc' = add_type_var acc id v' in - (v'' :: l1, l2, acc') - | `Term (id, v') -> - let v'', acc' = add_term_var acc id v' in - (l1, v'' :: l2, acc') - ) ([], [], env) l in - List.rev ttype_vars, List.rev typed_vars, env' - -and parse_let env f = function - | [] -> parse_expr env f - | x :: r -> - begin match x with - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, [ - { Ast.term = Ast.Symbol s }; e]) } -> - let t = parse_term env e in - let env' = add_let_term env s t in - parse_let env' f r - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, [ - { Ast.term = Ast.Symbol s }; e]) } -> - let t = parse_formula env e in - let env' = add_let_prop env s t in - parse_let env' f r - | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> - begin match parse_expr env e with - | Term t -> - let env' = add_let_term env s t in - parse_let env' f r - | Formula t -> - let env' = add_let_prop env s t in - parse_let env' f r - | _ -> _expected "term of formula" e - end - | t -> _expected "let-binding" t - end - -and parse_app env ast s args = - match find_let env s with - | `Term t -> - if args = [] then Term t - else _fo_term s ast - | `Prop p -> - if args = [] then Formula p - else _fo_term s ast - | `Not_found -> - begin match find_var env s with - | `Ty f -> - if args = [] then Ty (Msat.Expr.Ty.of_id f) - else _fo_term s ast - | `Term f -> - if args = [] then Term (Msat.Expr.Term.of_id f) - else _fo_term s ast - | `Not_found -> - begin match find_global s with - | `Ty f -> - parse_app_ty env ast f args - | `Term f -> - parse_app_term env ast f args - | `Ty_alias (f_args, body) -> - parse_app_subst_ty env ast s args f_args body - | `Term_alias (f_ty_args, f_t_args, body) -> - parse_app_subst_term env ast s args f_ty_args f_t_args body - | `Not_found -> - begin match infer env s args with - | `Ty f -> parse_app_ty env ast f args - | `Term f -> parse_app_term env ast f args - | `Nothing -> - raise (Typing_error ( - Format.asprintf "Scoping error: '%a' not found" Id.print s, ast)) - end - end - end - -and parse_app_ty env ast f args = - let l = List.map (parse_ty env) args in - Ty (ty_apply env ast f l) - -and parse_app_term env ast f args = - let n = List.length Msat.Expr.(f.id_type.fun_vars) in - let ty_l, t_l = take_drop n args in - let ty_args = List.map (parse_ty env) ty_l in - let t_args = List.map (parse_term env) t_l in - Term (term_apply env ast f ty_args t_args) - -and parse_app_subst_ty env ast id args f_args body = - let l = List.map (parse_ty env) args in - Ty (ty_subst ast id l f_args body) - -and parse_app_subst_term env ast id args f_ty_args f_t_args body = - let n = List.length f_ty_args in - let ty_l, t_l = take_drop n args in - let ty_args = List.map (parse_ty env) ty_l in - let t_args = List.map (parse_term env) t_l in - Term (term_subst ast id ty_args t_args f_ty_args f_t_args body) - -and parse_ty env ast = - match parse_expr { env with expect = Type } ast with - | Ty ty -> ty - | _ -> _expected "type" ast - -and parse_term env ast = - match parse_expr { env with expect = Typed Msat.Expr.Ty.base } ast with - | Term t -> t - | _ -> _expected "term" ast - -and parse_formula env ast = - match parse_expr { env with expect = Typed Msat.Expr.Ty.prop } ast with - | Term t when Msat.Expr.(Ty.equal Ty.prop t.t_type) -> - make_pred ast t - | Formula p -> p - | _ -> _expected "formula" ast - -let parse_ttype_var env t = - match parse_var env t with - | `Ty (id, v) -> (id, v) - | `Term _ -> _expected "type variable" t - -let rec parse_sig_quant env = function - | { Ast.term = Ast.Binder (Ast.Pi, vars, t) } -> - let ttype_vars = List.map (parse_ttype_var env) vars in - let ttype_vars', env' = add_type_vars env ttype_vars in - let l = List.combine vars ttype_vars' in - parse_sig_arrow l [] env' t - | t -> - parse_sig_arrow [] [] env t - -and parse_sig_arrow ttype_vars (ty_args: (Ast.t * res) list) env = function - | { Ast.term = Ast.Binder (Ast.Arrow, args, ret) } -> - let t_args = parse_sig_args env args in - parse_sig_arrow ttype_vars (ty_args @ t_args) env ret - | t -> - begin match parse_expr env t with - | Ttype -> - begin match ttype_vars with - | (h, _) :: _ -> - raise (Typing_error ( - "Type constructor signatures cannot have quantified type variables", h)) - | [] -> - let aux n = function - | (_, Ttype) -> n + 1 - | (ast, _) -> raise (Found ast) - in - begin - match List.fold_left aux 0 ty_args with - | n -> `Ty_cstr n - | exception Found err -> - raise (Typing_error ( - Format.asprintf - "Type constructor signatures cannot have non-ttype arguments,", err)) - end - end - | Ty ret -> - let aux acc = function - | (_, Ty t) -> t :: acc - | (ast, _) -> raise (Found ast) - in - begin - match List.fold_left aux [] ty_args with - | exception Found err -> _expected "type" err - | l -> `Fun_ty (List.map snd ttype_vars, List.rev l, ret) - end - | _ -> _expected "Ttype of type" t - end - -and parse_sig_args env l = - flat_map (parse_sig_arg env) l - -and parse_sig_arg env = function - | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.Product}, l) } -> - List.map (fun x -> x, parse_expr env x) l - | t -> - [t, parse_expr env t] - -let parse_sig = parse_sig_quant - -let rec parse_fun ty_args t_args env = function - | { Ast.term = Ast.Binder (Ast.Fun, l, ret) } -> - let ty_args', t_args', env' = parse_quant_vars env l in - parse_fun (ty_args @ ty_args') (t_args @ t_args') env' ret - | ast -> - begin match parse_expr env ast with - | Ttype -> raise (Typing_error ("Cannot redefine Ttype", ast)) - | Ty body -> - if t_args = [] then `Ty (ty_args, body) - else _expected "term" ast - | Term body -> `Term (ty_args, t_args, body) - | Formula _ -> _expected "type or term" ast - end - -(* High-level parsing functions *) -(* ************************************************************************ *) - -let new_decl id t = - let env = empty_env () in - Msat.Log.debugf 5 "Typing declaration: %s : %a" - (fun k -> k id.Id.name Ast.print t); - begin match parse_sig env t with - | `Ty_cstr n -> decl_ty_cstr id (Msat.Expr.Id.ty_fun id.Id.name n) - | `Fun_ty (vars, args, ret) -> - decl_term id (Msat.Expr.Id.term_fun id.Id.name vars args ret) - end - -let new_def id t = - let env = empty_env () in - Msat.Log.debugf 5 "Typing definition: %s = %a" - (fun k -> k id.Id.name Ast.print t); - begin match parse_fun [] [] env t with - | `Ty (ty_args, body) -> def_ty id ty_args body - | `Term (ty_args, t_args, body) -> def_term id ty_args t_args body - end - -let new_formula t = - let env = empty_env () in - Msat.Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); - let res = parse_formula env t in - res + val consequent : Dolmen.Term.t -> atom list list + val antecedent : Dolmen.Term.t -> atom list list + (** Parse a formula, and return a cnf ready to be given to the solver. + Consequent is for hypotheses (left of the sequent), while antecedent + is for goals (i.e formulas on the right of a sequent). *) +end diff --git a/src/util/type.mli b/src/util/type.mli deleted file mode 100644 index a0414e29..00000000 --- a/src/util/type.mli +++ /dev/null @@ -1,15 +0,0 @@ - -(** Typechecking of terms from Dolmen.Term.t - This module provides functions to parse terms from the untyped syntax tree - defined in Dolmen, and generate formulas as defined in the Expr module. *) - -exception Typing_error of string * Dolmen.Term.t - -(** {2 High-level functions} *) - -val new_decl : Dolmen.Id.t -> Dolmen.Term.t -> unit - -val new_def : Dolmen.Id.t -> Dolmen.Term.t -> unit - -val new_formula : Dolmen.Term.t -> Msat.Expr.Formula.t - diff --git a/src/util/type_smt.ml b/src/util/type_smt.ml new file mode 100644 index 00000000..65127dcf --- /dev/null +++ b/src/util/type_smt.ml @@ -0,0 +1,615 @@ + +(* Log&Module Init *) +(* ************************************************************************ *) + +module Ast = Dolmen.Term +module Id = Dolmen.Id +module M = Map.Make(Id) +module H = Hashtbl.Make(Id) + +(* Types *) +(* ************************************************************************ *) + +(* The type of potentially expected result type for parsing an expression *) +type expect = + | Nothing + | Type + | Typed of Expr.ty + +(* The type returned after parsing an expression. *) +type res = + | Ttype + | Ty of Expr.ty + | Term of Expr.term + | Formula of Expr.Formula.t + + +(* The local environments used for type-checking. *) +type env = { + + (* local variables (mostly quantified variables) *) + type_vars : (Expr.ttype Expr.id) M.t; + term_vars : (Expr.ty Expr.id) M.t; + + (* Bound variables (through let constructions) *) + term_lets : Expr.term M.t; + prop_lets : Expr.Formula.t M.t; + + (* Typing options *) + expect : expect; +} + +(* Exceptions *) +(* ************************************************************************ *) + +(* Internal exception *) +exception Found of Ast.t + +(* Exception for typing errors *) +exception Typing_error of string * Ast.t + +(* Convenience functions *) +let _expected s t = raise (Typing_error ( + Format.asprintf "Expected a %s" s, t)) +let _bad_arity s n t = raise (Typing_error ( + Format.asprintf "Bad arity for operator '%s' (expected %d arguments)" s n, t)) +let _type_mismatch t ty ty' ast = raise (Typing_error ( + Format.asprintf "Type Mismatch: '%a' has type %a, but an expression of type %a was expected" + Expr.Print.term t Expr.Print.ty ty Expr.Print.ty ty', ast)) +let _fo_term s t = raise (Typing_error ( + Format.asprintf "Let-bound variable '%a' is applied to terms" Id.print s, t)) + +(* Global Environment *) +(* ************************************************************************ *) + +(* Global identifier table; stores declared types and aliases. *) +let global_env = H.create 42 + +let find_global name = + try H.find global_env name + with Not_found -> `Not_found + +(* Symbol declarations *) +let decl_ty_cstr id c = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Ty c); + Log.debugf 1 "New type constructor : %a" (fun k -> k Expr.Print.const_ttype c) + +let decl_term id c = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Term c); + Log.debugf 1 "New constant : %a" (fun k -> k Expr.Print.const_ty c) + +(* Symbol definitions *) +let def_ty id args body = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Ty_alias (args, body)) + +let def_term id ty_args args body = + if H.mem global_env id then + Log.debugf 0 "Symbol '%a' has already been defined, overwriting previous definition" + (fun k -> k Id.print id); + H.add global_env id (`Term_alias (ty_args, args, body)) + +(* Local Environment *) +(* ************************************************************************ *) + +(* Make a new empty environment *) +let empty_env ?(expect=Nothing) () = { + type_vars = M.empty; + term_vars = M.empty; + term_lets = M.empty; + prop_lets = M.empty; + expect; +} + +(* Generate new fresh names for shadowed variables *) +let new_name pre = + let i = ref 0 in + (fun () -> incr i; pre ^ (string_of_int !i)) + +let new_ty_name = new_name "ty#" +let new_term_name = new_name "term#" + +(* Add local variables to environment *) +let add_type_var env id v = + let v' = + if M.mem id env.type_vars then + Expr.Id.ttype (new_ty_name ()) + else + v + in + Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Expr.Print.id_ttype v'); + v', { env with type_vars = M.add id v' env.type_vars } + +let add_type_vars env l = + let l', env' = List.fold_left (fun (l, acc) (id, v) -> + let v', acc' = add_type_var acc id v in + v' :: l, acc') ([], env) l in + List.rev l', env' + +let add_term_var env id v = + let v' = + if M.mem id env.type_vars then + Expr.Id.ty (new_term_name ()) Expr.(v.id_type) + else + v + in + Log.debugf 1 "New binding : %a -> %a" + (fun k -> k Id.print id Expr.Print.id_ty v'); + v', { env with term_vars = M.add id v' env.term_vars } + +let find_var env name = + try `Ty (M.find name env.type_vars) + with Not_found -> + begin + try + `Term (M.find name env.term_vars) + with Not_found -> + `Not_found + end + +(* Add local bound variables to env *) +let add_let_term env id t = + Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Expr.Print.term t); + { env with term_lets = M.add id t env.term_lets } + +let add_let_prop env id t = + Log.debugf 1 "New let-binding : %s -> %a" + (fun k -> k id.Id.name Expr.Formula.print t); + { env with prop_lets = M.add id t env.prop_lets } + +let find_let env name = + try `Term (M.find name env.term_lets) + with Not_found -> + begin + try + `Prop (M.find name env.prop_lets) + with Not_found -> + `Not_found + end + +let pp_expect fmt = function + | Nothing -> Format.fprintf fmt "<>" + | Type -> Format.fprintf fmt "" + | Typed ty -> Expr.Print.ty fmt ty + +let pp_map pp fmt map = + M.iter (fun k v -> + Format.fprintf fmt "%s->%a;" k.Id.name pp v) map + +(* Some helper functions *) +(* ************************************************************************ *) + +let flat_map f l = List.flatten (List.map f l) + +let take_drop n l = + let rec aux acc = function + | 0, _ | _, [] -> List.rev acc, [] + | m, x :: r -> aux (x :: acc) (m - 1, r) + in + aux [] (n, l) + +let diagonal l = + let rec single x acc = function + | [] -> acc + | y :: r -> single x ((x, y) :: acc) r + and aux acc = function + | [] -> acc + | x :: r -> aux (single x acc r) r + in + aux [] l + +(* Wrappers for expression building *) +(* ************************************************************************ *) + +let arity f = + List.length Expr.(f.id_type.fun_vars) + + List.length Expr.(f.id_type.fun_args) + +let ty_apply env ast f args = + try + Expr.Ty.apply f args + with Expr.Bad_ty_arity _ -> + _bad_arity Expr.(f.id_name) (arity f) ast + +let term_apply env ast f ty_args t_args = + try + Expr.Term.apply f ty_args t_args + with + | Expr.Bad_arity _ -> + _bad_arity Expr.(f.id_name) (arity f) ast + | Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast + +let ty_subst ast_term id args f_args body = + let aux s v ty = Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Expr.Subst.empty f_args args with + | subst -> + Expr.Ty.subst subst body + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_args) ast_term + +let term_subst ast_term id ty_args t_args f_ty_args f_t_args body = + let aux s v ty = Expr.Subst.Id.bind v ty s in + match List.fold_left2 aux Expr.Subst.empty f_ty_args ty_args with + | ty_subst -> + begin + let aux s v t = Expr.Subst.Id.bind v t s in + match List.fold_left2 aux Expr.Subst.empty f_t_args t_args with + | t_subst -> + Expr.Term.subst ty_subst t_subst body + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term + end + | exception Invalid_argument _ -> + _bad_arity id.Id.name (List.length f_ty_args + List.length f_t_args) ast_term + +let make_eq ast_term a b = + try + Expr.Formula.make_atom @@ Expr.Atom.eq a b + with Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast_term + +let make_pred ast_term p = + try + Expr.Formula.make_atom @@ Expr.Atom.pred p + with Expr.Type_mismatch (t, ty, ty') -> + _type_mismatch t ty ty' ast_term + +let infer env s args = + match env.expect with + | Nothing -> `Nothing + | Type -> + let n = List.length args in + let res = Expr.Id.ty_fun s.Id.name n in + decl_ty_cstr s res; + `Ty res + | Typed ty -> + let n = List.length args in + let rec replicate acc n = + if n <= 0 then acc else replicate (Expr.Ty.base :: acc) (n - 1) + in + let res = Expr.Id.term_fun s.Id.name [] (replicate [] n) ty in + decl_term s res; + `Term res + +(* Expression parsing *) +(* ************************************************************************ *) + +let rec parse_expr (env : env) t = + match t with + + (* Basic formulas *) + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.True }, []) } + | { Ast.term = Ast.Builtin Ast.True } -> + Formula Expr.Formula.f_true + + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.False }, []) } + | { Ast.term = Ast.Builtin Ast.False } -> + Formula Expr.Formula.f_false + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } -> + Formula (Expr.Formula.make_and (List.map (parse_formula env) l)) + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } -> + Formula (Expr.Formula.make_or (List.map (parse_formula env) l)) + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_not (Expr.Formula.make_equiv f g)) + | _ -> _bad_arity "xor" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_imply f g) + | _ -> _bad_arity "=>" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, l) } as t -> + begin match l with + | [p; q] -> + let f = parse_formula env p in + let g = parse_formula env q in + Formula (Expr.Formula.make_equiv f g) + | _ -> _bad_arity "<=>" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t -> + begin match l with + | [p] -> + Formula (Expr.Formula.make_not (parse_formula env p)) + | _ -> _bad_arity "not" 1 t + end + + (* (Dis)Equality *) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, l) } as t -> + begin match l with + | [a; b] -> + Formula ( + make_eq t + (parse_term env a) + (parse_term env b) + ) + | _ -> _bad_arity "=" 2 t + end + + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Distinct}, args) } as t -> + let l' = List.map (parse_term env) args in + let l'' = diagonal l' in + Formula ( + Expr.Formula.make_and + (List.map (fun (a, b) -> + Expr.Formula.make_not + (make_eq t a b)) l'') + ) + + (* General case: application *) + | { Ast.term = Ast.Symbol s } as ast -> + parse_app env ast s [] + | { Ast.term = Ast.App ({ Ast.term = Ast.Symbol s }, l) } as ast -> + parse_app env ast s l + + (* Local bindings *) + | { Ast.term = Ast.Binder (Ast.Let, vars, f) } -> + parse_let env f vars + + (* Other cases *) + | ast -> raise (Typing_error ("Couldn't parse the expression", ast)) + +and parse_var env = function + | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> + begin match parse_expr env e with + | Ttype -> `Ty (s, Expr.Id.ttype s.Id.name) + | Ty ty -> `Term (s, Expr.Id.ty s.Id.name ty) + | _ -> _expected "type (or Ttype)" e + end + | { Ast.term = Ast.Symbol s } -> + begin match env.expect with + | Nothing -> assert false + | Type -> `Ty (s, Expr.Id.ttype s.Id.name) + | Typed ty -> `Term (s, Expr.Id.ty s.Id.name ty) + end + | t -> _expected "(typed) variable" t + +and parse_quant_vars env l = + let ttype_vars, typed_vars, env' = List.fold_left ( + fun (l1, l2, acc) v -> + match parse_var acc v with + | `Ty (id, v') -> + let v'', acc' = add_type_var acc id v' in + (v'' :: l1, l2, acc') + | `Term (id, v') -> + let v'', acc' = add_term_var acc id v' in + (l1, v'' :: l2, acc') + ) ([], [], env) l in + List.rev ttype_vars, List.rev typed_vars, env' + +and parse_let env f = function + | [] -> parse_expr env f + | x :: r -> + begin match x with + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, [ + { Ast.term = Ast.Symbol s }; e]) } -> + let t = parse_term env e in + let env' = add_let_term env s t in + parse_let env' f r + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv}, [ + { Ast.term = Ast.Symbol s }; e]) } -> + let t = parse_formula env e in + let env' = add_let_prop env s t in + parse_let env' f r + | { Ast.term = Ast.Colon ({ Ast.term = Ast.Symbol s }, e) } -> + begin match parse_expr env e with + | Term t -> + let env' = add_let_term env s t in + parse_let env' f r + | Formula t -> + let env' = add_let_prop env s t in + parse_let env' f r + | _ -> _expected "term of formula" e + end + | t -> _expected "let-binding" t + end + +and parse_app env ast s args = + match find_let env s with + | `Term t -> + if args = [] then Term t + else _fo_term s ast + | `Prop p -> + if args = [] then Formula p + else _fo_term s ast + | `Not_found -> + begin match find_var env s with + | `Ty f -> + if args = [] then Ty (Expr.Ty.of_id f) + else _fo_term s ast + | `Term f -> + if args = [] then Term (Expr.Term.of_id f) + else _fo_term s ast + | `Not_found -> + begin match find_global s with + | `Ty f -> + parse_app_ty env ast f args + | `Term f -> + parse_app_term env ast f args + | `Ty_alias (f_args, body) -> + parse_app_subst_ty env ast s args f_args body + | `Term_alias (f_ty_args, f_t_args, body) -> + parse_app_subst_term env ast s args f_ty_args f_t_args body + | `Not_found -> + begin match infer env s args with + | `Ty f -> parse_app_ty env ast f args + | `Term f -> parse_app_term env ast f args + | `Nothing -> + raise (Typing_error ( + Format.asprintf "Scoping error: '%a' not found" Id.print s, ast)) + end + end + end + +and parse_app_ty env ast f args = + let l = List.map (parse_ty env) args in + Ty (ty_apply env ast f l) + +and parse_app_term env ast f args = + let n = List.length Expr.(f.id_type.fun_vars) in + let ty_l, t_l = take_drop n args in + let ty_args = List.map (parse_ty env) ty_l in + let t_args = List.map (parse_term env) t_l in + Term (term_apply env ast f ty_args t_args) + +and parse_app_subst_ty env ast id args f_args body = + let l = List.map (parse_ty env) args in + Ty (ty_subst ast id l f_args body) + +and parse_app_subst_term env ast id args f_ty_args f_t_args body = + let n = List.length f_ty_args in + let ty_l, t_l = take_drop n args in + let ty_args = List.map (parse_ty env) ty_l in + let t_args = List.map (parse_term env) t_l in + Term (term_subst ast id ty_args t_args f_ty_args f_t_args body) + +and parse_ty env ast = + match parse_expr { env with expect = Type } ast with + | Ty ty -> ty + | _ -> _expected "type" ast + +and parse_term env ast = + match parse_expr { env with expect = Typed Expr.Ty.base } ast with + | Term t -> t + | _ -> _expected "term" ast + +and parse_formula env ast = + match parse_expr { env with expect = Typed Expr.Ty.prop } ast with + | Term t when Expr.(Ty.equal Ty.prop t.t_type) -> + make_pred ast t + | Formula p -> p + | _ -> _expected "formula" ast + +let parse_ttype_var env t = + match parse_var env t with + | `Ty (id, v) -> (id, v) + | `Term _ -> _expected "type variable" t + +let rec parse_sig_quant env = function + | { Ast.term = Ast.Binder (Ast.Pi, vars, t) } -> + let ttype_vars = List.map (parse_ttype_var env) vars in + let ttype_vars', env' = add_type_vars env ttype_vars in + let l = List.combine vars ttype_vars' in + parse_sig_arrow l [] env' t + | t -> + parse_sig_arrow [] [] env t + +and parse_sig_arrow ttype_vars (ty_args: (Ast.t * res) list) env = function + | { Ast.term = Ast.Binder (Ast.Arrow, args, ret) } -> + let t_args = parse_sig_args env args in + parse_sig_arrow ttype_vars (ty_args @ t_args) env ret + | t -> + begin match parse_expr env t with + | Ttype -> + begin match ttype_vars with + | (h, _) :: _ -> + raise (Typing_error ( + "Type constructor signatures cannot have quantified type variables", h)) + | [] -> + let aux n = function + | (_, Ttype) -> n + 1 + | (ast, _) -> raise (Found ast) + in + begin + match List.fold_left aux 0 ty_args with + | n -> `Ty_cstr n + | exception Found err -> + raise (Typing_error ( + Format.asprintf + "Type constructor signatures cannot have non-ttype arguments,", err)) + end + end + | Ty ret -> + let aux acc = function + | (_, Ty t) -> t :: acc + | (ast, _) -> raise (Found ast) + in + begin + match List.fold_left aux [] ty_args with + | exception Found err -> _expected "type" err + | l -> `Fun_ty (List.map snd ttype_vars, List.rev l, ret) + end + | _ -> _expected "Ttype of type" t + end + +and parse_sig_args env l = + flat_map (parse_sig_arg env) l + +and parse_sig_arg env = function + | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.Product}, l) } -> + List.map (fun x -> x, parse_expr env x) l + | t -> + [t, parse_expr env t] + +let parse_sig = parse_sig_quant + +let rec parse_fun ty_args t_args env = function + | { Ast.term = Ast.Binder (Ast.Fun, l, ret) } -> + let ty_args', t_args', env' = parse_quant_vars env l in + parse_fun (ty_args @ ty_args') (t_args @ t_args') env' ret + | ast -> + begin match parse_expr env ast with + | Ttype -> raise (Typing_error ("Cannot redefine Ttype", ast)) + | Ty body -> + if t_args = [] then `Ty (ty_args, body) + else _expected "term" ast + | Term body -> `Term (ty_args, t_args, body) + | Formula _ -> _expected "type or term" ast + end + +(* High-level parsing functions *) +(* ************************************************************************ *) + +let decl id t = + let env = empty_env () in + Log.debugf 5 "Typing declaration: %s : %a" + (fun k -> k id.Id.name Ast.print t); + begin match parse_sig env t with + | `Ty_cstr n -> decl_ty_cstr id (Expr.Id.ty_fun id.Id.name n) + | `Fun_ty (vars, args, ret) -> + decl_term id (Expr.Id.term_fun id.Id.name vars args ret) + end + +let def id t = + let env = empty_env () in + Log.debugf 5 "Typing definition: %s = %a" + (fun k -> k id.Id.name Ast.print t); + begin match parse_fun [] [] env t with + | `Ty (ty_args, body) -> def_ty id ty_args body + | `Term (ty_args, t_args, body) -> def_term id ty_args t_args body + end + +let formula t = + let env = empty_env () in + Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); + parse_formula env t + +let consequent t = + Expr.Formula.make_cnf (formula t) + +let antecedent t = + Expr.Formula.make_cnf (Expr.Formula.make_not (formula t)) + diff --git a/src/util/type_smt.mli b/src/util/type_smt.mli new file mode 100644 index 00000000..3a2429c4 --- /dev/null +++ b/src/util/type_smt.mli @@ -0,0 +1,7 @@ + +(** Typechecking of terms from Dolmen.Term.t + This module provides functions to parse terms from the untyped syntax tree + defined in Dolmen, and generate formulas as defined in the Expr module. *) + +include Type.S with type atom = Expr.atom + From fa8957784ac8b4bcde64dcdae397d179e6805faa Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Mon, 12 Sep 2016 15:37:06 +0200 Subject: [PATCH 07/25] Restored simple expressions for pure SAT --- src/sat/expr_sat.ml | 64 ++++++++++++++++++++++++++++++++++++++++++++ src/sat/expr_sat.mli | 8 ++++++ src/sat/sat.ml | 2 +- src/sat/sat.mli | 2 +- 4 files changed, 74 insertions(+), 2 deletions(-) create mode 100644 src/sat/expr_sat.ml create mode 100644 src/sat/expr_sat.mli diff --git a/src/sat/expr_sat.ml b/src/sat/expr_sat.ml new file mode 100644 index 00000000..23c0498d --- /dev/null +++ b/src/sat/expr_sat.ml @@ -0,0 +1,64 @@ +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2016 Guillaume Bury +Copyright 2016 Simon Cruanes +*) + +exception Bad_atom + +type t = int +type proof = unit + +let max_lit = max_int +let max_fresh = ref (-1) +let max_index = ref 0 + +let _make i = + if i <> 0 && (abs i) < max_lit then begin + max_index := max !max_index (abs i); + i + end else + raise Bad_atom + +let dummy = 0 + +let neg a = - a + +let norm a = + abs a, if a < 0 then + Formula_intf.Negated + else + Formula_intf.Same_sign + +let abs = abs + +let sign i = i > 0 + +let apply_sign b i = if b then i else neg i + +let set_sign b i = if b then abs i else neg (abs i) + +let hash (a:int) = a land max_int +let equal (a:int) b = a=b +let compare (a:int) b = Pervasives.compare a b + +let make i = _make (2 * i) + +let fresh, iter = + let create () = + incr max_fresh; + _make (2 * !max_fresh + 1) + in + let iter: (t -> unit) -> unit = fun f -> + for j = 1 to !max_index do + f j + done + in + create, iter + +let print fmt a = + Format.fprintf fmt "%s%s%d" + (if a < 0 then "~" else "") + (if a mod 2 = 0 then "v" else "f") + ((abs a) / 2) + diff --git a/src/sat/expr_sat.mli b/src/sat/expr_sat.mli new file mode 100644 index 00000000..f4b72e48 --- /dev/null +++ b/src/sat/expr_sat.mli @@ -0,0 +1,8 @@ +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2016 Guillaume Bury +Copyright 2016 Simon Cruanes +*) + +include Formula_intf.S + diff --git a/src/sat/sat.ml b/src/sat/sat.ml index 2c91c65f..9e0442f3 100644 --- a/src/sat/sat.ml +++ b/src/sat/sat.ml @@ -5,5 +5,5 @@ Copyright 2014 Simon Cruanes *) module Make(Dummy : sig end) = - Solver.Make(Expr.Atom)(Solver.DummyTheory(Expr.Atom))(struct end) + Solver.Make(Expr_sat)(Solver.DummyTheory(Expr_sat))(struct end) diff --git a/src/sat/sat.mli b/src/sat/sat.mli index 79c9b6b0..dc20113a 100644 --- a/src/sat/sat.mli +++ b/src/sat/sat.mli @@ -4,6 +4,6 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Make(Dummy : sig end) : Solver.S with type St.formula = Expr.Atom.t +module Make(Dummy : sig end) : Solver.S with type St.formula = Expr_sat.t From 0631135bd5769e09c3226e490ddb7d93327b81c6 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Mon, 12 Sep 2016 15:43:57 +0200 Subject: [PATCH 08/25] Smt solver with dummy theory now builds --- src/main.ml | 2 +- src/{util/expr.ml => smt/expr_smt.ml} | 0 src/{util/expr.mli => smt/expr_smt.mli} | 0 src/smt/smt.ml | 24 +++++------------------- src/smt/smt.mli | 16 +--------------- src/{util => smt}/type_smt.ml | 0 src/{util => smt}/type_smt.mli | 0 7 files changed, 7 insertions(+), 35 deletions(-) rename src/{util/expr.ml => smt/expr_smt.ml} (100%) rename src/{util/expr.mli => smt/expr_smt.mli} (100%) rename src/{util => smt}/type_smt.ml (100%) rename src/{util => smt}/type_smt.mli (100%) diff --git a/src/main.ml b/src/main.ml index b3e0450d..521f5c6c 100644 --- a/src/main.ml +++ b/src/main.ml @@ -6,8 +6,8 @@ Copyright 2014 Simon Cruanes module Sat = Sat.Make(struct end) module Dummy = Sat - (* module Smt = Smt.Make(struct end) + (* module Mcsat = Mcsat.Make(struct end) *) diff --git a/src/util/expr.ml b/src/smt/expr_smt.ml similarity index 100% rename from src/util/expr.ml rename to src/smt/expr_smt.ml diff --git a/src/util/expr.mli b/src/smt/expr_smt.mli similarity index 100% rename from src/util/expr.mli rename to src/smt/expr_smt.mli diff --git a/src/smt/smt.ml b/src/smt/smt.ml index b42478fc..f80984fb 100644 --- a/src/smt/smt.ml +++ b/src/smt/smt.ml @@ -4,8 +4,9 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Tsmt = struct +module Th = Solver.DummyTheory(Expr_smt.Atom) + (* struct module CC = Cc.Make(String) type formula = Fsmt.t @@ -49,22 +50,7 @@ module Tsmt = struct let if_sat _ = () end + *) -module Make(Dummy:sig end) = struct - - include Solver.Make(Fsmt)(Tsmt)(struct end) - module Dot = Dot.Make(Proof)(struct - let print_atom = St.print_atom - let lemma_info () = "Proof", Some "PURPLE", [] - end) - module Dedukti = Dedukti.Make(Proof)(struct - let print _ _ = () - let prove _ _ = () - let context _ _ = () - end) - - let print_clause = St.print_clause - let print_dot = Dot.print - let print_dedukti = Dedukti.print - -end +module Make(Dummy:sig end) = + Solver.Make(Expr_smt.Atom)(Th)(struct end) diff --git a/src/smt/smt.mli b/src/smt/smt.mli index f703efe4..edb13401 100644 --- a/src/smt/smt.mli +++ b/src/smt/smt.mli @@ -4,19 +4,5 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Make(Dummy: sig end) : sig - (** Fonctor to make a SMT Solver module with built-in literals. *) - - include Solver.S with type St.formula = Expr.t - - val print_clause : Format.formatter -> St.clause -> unit - (** Print the clause on the given formatter. *) - - val print_dot : Format.formatter -> Proof.proof -> unit - (** Print the given proof in dot format. *) - - val print_dedukti : Format.formatter -> Proof.proof -> unit - (** Print the given proof in dot format. *) - -end +module Make(Dummy: sig end) : Solver.S with type St.formula = Expr_smt.atom diff --git a/src/util/type_smt.ml b/src/smt/type_smt.ml similarity index 100% rename from src/util/type_smt.ml rename to src/smt/type_smt.ml diff --git a/src/util/type_smt.mli b/src/smt/type_smt.mli similarity index 100% rename from src/util/type_smt.mli rename to src/smt/type_smt.mli From a0d8bd54570678a0e78e6ade6bd0fd385cdc7e5f Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Mon, 12 Sep 2016 17:11:05 +0200 Subject: [PATCH 09/25] Added dolmen dependency --- .travis.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index c707458b..aa50feaf 100644 --- a/.travis.yml +++ b/.travis.yml @@ -19,7 +19,7 @@ before_install: - opam switch ${OCAML_VERSION} - eval `opam config env` install: - - opam install ocamlfind ocamlbuild + - opam install dolmen ocamlfind ocamlbuild - make bin lib script: - make test From 4522aa3ddccb82a83c5257dc23bbc0f4c3548976 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Mon, 12 Sep 2016 17:54:10 +0200 Subject: [PATCH 10/25] Removed Expr module from msat lib --- _tags | 4 ---- src/msat.mlpack | 1 - 2 files changed, 5 deletions(-) diff --git a/_tags b/_tags index c1554407..f350c48a 100644 --- a/_tags +++ b/_tags @@ -20,10 +20,6 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : for-pack(Msat) : for-pack(Msat) -: for-pack(Msat_sat) -: for-pack(Msat_smt) -: for-pack(Msat_mcsat) - # Testing dependencies : package(dolmen) : package(dolmen) diff --git a/src/msat.mlpack b/src/msat.mlpack index 4968dec6..eb1182bc 100644 --- a/src/msat.mlpack +++ b/src/msat.mlpack @@ -25,5 +25,4 @@ Dot Dedukti # Auxiliary modules -Expr Tseitin From 2a3353431251ef0ef6e141033597f9c251da7f67 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Wed, 14 Sep 2016 19:55:57 +0200 Subject: [PATCH 11/25] Added (dummy) mcsat module for test binary --- Makefile | 3 +- _tags | 2 +- src/main.ml | 3 -- src/mcsat/mcsat.ml | 11 +++++ src/mcsat/mcsat.mli | 8 ++++ src/smt/mcsat.ml | 114 -------------------------------------------- src/smt/smt.ml | 47 +----------------- 7 files changed, 23 insertions(+), 165 deletions(-) create mode 100644 src/mcsat/mcsat.ml create mode 100644 src/mcsat/mcsat.mli delete mode 100644 src/smt/mcsat.ml diff --git a/Makefile b/Makefile index 328cc6dc..498c8e7d 100644 --- a/Makefile +++ b/Makefile @@ -53,8 +53,9 @@ log: clean: $(COMP) -clean + rm -rf $(NAME_BIN) -ALL_NAMES = $(NAME_CORE) $(NAME_SAT) $(NAME_SMT) +ALL_NAMES = $(NAME_CORE) # $(NAME_SAT) $(NAME_SMT) $(NAME_MCAT) TO_INSTALL_LIB=$(addsuffix .a, $(ALL_NAMES)) \ $(addsuffix .cmi, $(ALL_NAMES)) TO_INSTALL=META $(addprefix _build/src/,$(LIB) $(TO_INSTALL_LIB)) diff --git a/_tags b/_tags index f350c48a..e737cd45 100644 --- a/_tags +++ b/_tags @@ -9,10 +9,10 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) : include : include : include +: include : include : include : include -: include # Pack options : for-pack(Msat) diff --git a/src/main.ml b/src/main.ml index 521f5c6c..3ce4dd3f 100644 --- a/src/main.ml +++ b/src/main.ml @@ -5,11 +5,8 @@ Copyright 2014 Simon Cruanes *) module Sat = Sat.Make(struct end) -module Dummy = Sat module Smt = Smt.Make(struct end) - (* module Mcsat = Mcsat.Make(struct end) - *) module P = Dolmen.Logic.Make(Dolmen.ParseLocation) diff --git a/src/mcsat/mcsat.ml b/src/mcsat/mcsat.ml new file mode 100644 index 00000000..5acf092d --- /dev/null +++ b/src/mcsat/mcsat.ml @@ -0,0 +1,11 @@ +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2014 Guillaume Bury +Copyright 2014 Simon Cruanes +*) + +module Th = Solver.DummyTheory(Expr_smt.Atom) + +module Make(Dummy:sig end) = + Solver.Make(Expr_smt.Atom)(Th)(struct end) + diff --git a/src/mcsat/mcsat.mli b/src/mcsat/mcsat.mli new file mode 100644 index 00000000..edb13401 --- /dev/null +++ b/src/mcsat/mcsat.mli @@ -0,0 +1,8 @@ +(* +MSAT is free software, using the Apache license, see file LICENSE +Copyright 2014 Guillaume Bury +Copyright 2014 Simon Cruanes +*) + +module Make(Dummy: sig end) : Solver.S with type St.formula = Expr_smt.atom + diff --git a/src/smt/mcsat.ml b/src/smt/mcsat.ml deleted file mode 100644 index 9be8e7bc..00000000 --- a/src/smt/mcsat.ml +++ /dev/null @@ -1,114 +0,0 @@ -(* -MSAT is free software, using the Apache license, see file LICENSE -Copyright 2014 Guillaume Bury -Copyright 2014 Simon Cruanes -*) - -module Fsmt = Expr - -module Tsmt = struct - - module M = Map.Make(Fsmt.Term) - module CC = Cc.Make(String) - - (* Type definitions *) - type term = Fsmt.Term.t - type formula = Fsmt.t - type proof = unit - - type level = { - cc : CC.t; - assign : (term * int) M.t; - } - - (* Functions *) - let dummy = { cc = CC.empty; assign = M.empty; } - - let env = ref dummy - - let current_level () = !env - - let to_clause (a, b, l) = - Log.debugf 10 "@[<2>Expl : %s; %s@ %a@]" - (fun k->k a b - (fun out () -> List.iter (Format.fprintf out " |- %s@ ") l) ()); - let rec aux acc = function - | [] | [_] -> acc - | x :: ((y :: _) as r) -> - aux (Fsmt.mk_eq x y :: acc) r - in - (Fsmt.mk_eq a b) :: (List.rev_map Fsmt.neg (aux [] l)) - - let assume s = - let open Plugin_intf in - try - for i = s.start to s.start + s.length - 1 do - match s.get i with - | Assign (x, v, lvl) -> - env := { !env with assign = M.add x (v, lvl) !env.assign } - | Lit f -> - Log.debugf 10 "Propagating in th :@ @[%a@]" (fun k->k Fsmt.print f); - match f with - | Fsmt.Prop _ -> () - | Fsmt.Equal (i, j) -> - env := { !env with cc = CC.add_eq !env.cc i j } - | Fsmt.Distinct (i, j) -> - env := { !env with cc = CC.add_neq !env.cc i j } - done; - Sat - with CC.Unsat x -> - Log.debug 8 "Making explanation clause..."; - Unsat (to_clause x, ()) - - let backtrack l = env := l - - let assign t = CC.repr !env.cc t - - let iter_assignable f = function - | Fsmt.Prop _ -> () - | Fsmt.Equal(a, b) - | Fsmt.Distinct (a, b) -> f a; f b - - let max (a: int) (b: int) = if a < b then b else a - - let eval = function - | Fsmt.Prop _ -> Plugin_intf.Unknown - | Fsmt.Equal (a, b) -> - begin try - let a', lvl_a = M.find a !env.assign in - let b', lvl_b = M.find b !env.assign in - Plugin_intf.Valued (Fsmt.Term.equal a' b', max lvl_a lvl_b) - with Not_found -> - Plugin_intf.Unknown - end - | Fsmt.Distinct (a, b) -> - begin try - let a', lvl_a = M.find a !env.assign in - let b', lvl_b = M.find b !env.assign in - Plugin_intf.Valued (not (Fsmt.Term.equal a' b'), max lvl_a lvl_b) - with Not_found -> - Plugin_intf.Unknown - end - - let if_sat _ = () - -end - -module Make(Dummy:sig end) = struct - - include Mcsolver.Make(Fsmt)(Tsmt)(struct end) - module Dot = Dot.Make(Proof)(struct - let print_atom = St.print_atom - let lemma_info () = "Proof", Some "PURPLE", [] - end) - module Dedukti = Dedukti.Make(Proof)(struct - let print _ _ = () - let prove _ _ = () - let context _ _ = () - end) - - let print_clause = St.print_clause - let print_dot = Dot.print - let print_dedukti = Dedukti.print - -end diff --git a/src/smt/smt.ml b/src/smt/smt.ml index f80984fb..5acf092d 100644 --- a/src/smt/smt.ml +++ b/src/smt/smt.ml @@ -6,51 +6,6 @@ Copyright 2014 Simon Cruanes module Th = Solver.DummyTheory(Expr_smt.Atom) - (* struct - module CC = Cc.Make(String) - - type formula = Fsmt.t - type proof = unit - type level = CC.t - - let dummy = CC.empty - - let env = ref dummy - - let current_level () = !env - - let to_clause (a, b, l) = - Log.debugf 10 "@[Expl : %s; %s@ %a@]" - (fun k->k a b - (fun out () -> List.iter (Format.fprintf out "|- %s@ ") l) ()); - let rec aux acc = function - | [] | [_] -> acc - | x :: ((y :: _) as r) -> - aux (Fsmt.mk_eq x y :: acc) r - in - (Fsmt.mk_eq a b) :: (List.rev_map Fsmt.neg (aux [] l)) - - let assume s = - let open Theory_intf in - try - for i = s.start to s.start + s.length - 1 do - Log.debugf 10 "Propagating in th :@ @[%a@]" (fun k->k Fsmt.print (s.get i)); - match s.get i with - | Fsmt.Prop _ -> () - | Fsmt.Equal (i, j) -> env := CC.add_eq !env i j - | Fsmt.Distinct (i, j) -> env := CC.add_neq !env i j - done; - Sat - with CC.Unsat x -> - Log.debug 8 "Making explanation clause..."; - Unsat (to_clause x, ()) - - let backtrack l = env := l - - let if_sat _ = () - -end - *) - module Make(Dummy:sig end) = Solver.Make(Expr_smt.Atom)(Th)(struct end) + From 4f5bb640ca24cb97d74c041dddedbc5207c15e00 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 16 Sep 2016 15:49:33 +0200 Subject: [PATCH 12/25] [WIP] All is setup, remains to have real theories Architecture is now all setup, but theories for the smt and mcsat solvers are currently dummy ones that are not doing anything. --- .merlin | 2 + _tags | 2 + src/main.ml | 183 +++++++++++++++++++------------------------ src/sat/expr_sat.mli | 3 + src/sat/type_sat.ml | 73 +++++++++++++++++ src/sat/type_sat.mli | 7 ++ src/smt/expr_smt.ml | 7 +- src/smt/type_smt.ml | 20 +++-- src/smt/type_smt.mli | 4 +- tests/test_api.ml | 87 +++++++------------- 10 files changed, 217 insertions(+), 171 deletions(-) create mode 100644 src/sat/type_sat.ml create mode 100644 src/sat/type_sat.mli diff --git a/.merlin b/.merlin index 6457aa65..cfd63256 100644 --- a/.merlin +++ b/.merlin @@ -2,6 +2,7 @@ S src/core S src/solver S src/sat S src/smt +S src/mcsat S src/backend S src/util S tests @@ -11,6 +12,7 @@ B _build/src/core B _build/src/solver B _build/src/sat B _build/src/smt +B _build/src/mcsat B _build/src/util B _build/src/backend B _build/tests diff --git a/_tags b/_tags index e737cd45..3714ec07 100644 --- a/_tags +++ b/_tags @@ -23,6 +23,8 @@ true: inline(100), optimize(3), unbox_closures, unbox_closures_factor(20) # Testing dependencies : package(dolmen) : package(dolmen) +: package(dolmen) +: package(dolmen) # more warnings : warn_K, warn_Y, warn_X diff --git a/src/main.ml b/src/main.ml index 3ce4dd3f..0dbc9031 100644 --- a/src/main.ml +++ b/src/main.ml @@ -4,28 +4,77 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Sat = Sat.Make(struct end) -module Smt = Smt.Make(struct end) -module Mcsat = Mcsat.Make(struct end) +exception Incorrect_model +exception Out_of_time +exception Out_of_space + +let file = ref "" +let p_cnf = ref false +let p_check = ref false +let p_proof_print = ref false +let p_unsat_core = ref false +let time_limit = ref 300. +let size_limit = ref 1000_000_000. module P = Dolmen.Logic.Make(Dolmen.ParseLocation) (Dolmen.Id)(Dolmen.Term)(Dolmen.Statement) -exception Incorrect_model -exception Out_of_time -exception Out_of_space +module type S = sig + val do_task : Dolmen.Statement.t -> unit +end -type solver = - | Sat - | Smt - | Mcsat +module Make + (S : External.S) + (T : Type.S with type atom := S.atom) += struct -let solver = ref Smt + let hyps = ref [] + + let do_task s = + match s.Dolmen.Statement.descr with + | Dolmen.Statement.Def (id, t) -> T.def id t + | Dolmen.Statement.Decl (id, t) -> T.decl id t + | Dolmen.Statement.Consequent t -> + let cnf = T.consequent t in + hyps := cnf @ !hyps; + S.assume cnf + | Dolmen.Statement.Antecedent t -> + let cnf = T.antecedent t in + hyps := cnf @ !hyps; + S.assume cnf + | Dolmen.Statement.Prove -> + let res = S.solve () in + let t = Sys.time () in + begin match res with + | S.Sat state -> + if !p_check then + if not (List.for_all (List.exists state.Solver_intf.eval) !hyps) then + raise Incorrect_model; + let t' = Sys.time () -. t in + Format.printf "Sat (%f/%f)@." t t' + | S.Unsat state -> + if !p_check then begin + let p = state.Solver_intf.get_proof () in + S.Proof.check p; + end; + let t' = Sys.time () -. t in + Format.printf "Unsat (%f/%f)@." t t' + end + | _ -> + Format.printf "Command not supported:@\n%a@." + Dolmen.Statement.print s +end + +module Sat = Make(Sat.Make(struct end))(Type_sat) +module Smt = Make(Smt.Make(struct end))(Type_smt) +module Mcsat = Make(Mcsat.Make(struct end))(Type_smt) + +let solver = ref (module Sat : S) let solver_list = [ - "sat", Sat; - "smt", Smt; - "mcsat", Mcsat; + "sat", (module Sat : S); + "smt", (module Smt : S); + "mcsat", (module Mcsat : S); ] let error_msg opt arg l = @@ -42,14 +91,6 @@ let set_flag opt arg flag l = let set_solver s = set_flag "Solver" s solver solver_list (* Arguments parsing *) -let file = ref "" -let p_cnf = ref false -let p_check = ref false -let p_proof_print = ref false -let p_unsat_core = ref false -let time_limit = ref 300. -let size_limit = ref 1000_000_000. - let int_arg r arg = let l = String.length arg in let multiplier m = @@ -111,30 +152,6 @@ let check () = else if s > !size_limit then raise Out_of_space -module Make - (T : Type.S) - (S : External.S with type St.formula = T.atom) = struct - - let do_task s = - match s.Dolmen.Statement.descr with - | Dolmen.Statement.Def (id, t) -> T.def id t - | Dolmen.Statement.Decl (id, t) -> T.decl id t - | Dolmen.Statement.Consequent t -> - let cnf = T.consequent t in - S.assume cnf - | Dolmen.Statement.Antecedent t -> - let cnf = T.antecedent t in - S.assume cnf - | Dolmen.Statement.Prove -> - begin match S.solve () with - | S.Sat _ -> () - | S.Unsat _ -> () - end - | _ -> - Format.printf "Command not supported:@\n%a@." - Dolmen.Statement.print s -end - let main () = (* Administrative duties *) @@ -146,73 +163,35 @@ let main () = let al = Gc.create_alarm check in (* Interesting stuff happening *) - let _, _input = P.parse_file !file in + let lang, input = P.parse_file !file in + let module S = (val !solver : S) in + List.iter S.do_task input; + (* Small hack for dimacs, which do not output a "Prove" statement *) + begin match lang with + | P.Dimacs -> S.do_task @@ Dolmen.Statement.check_sat () + | _ -> () + end; Gc.delete_alarm al; () -(* Old code ... - - let cnf = get_cnf () in - if !p_cnf then - print_cnf cnf; - match !solver with - | Smt -> - Smt.assume cnf; - let res = Smt.solve () in - Gc.delete_alarm al; - begin match res with - | Smt.Sat sat -> - let t = Sys.time () in - if !p_check then - if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then - raise Incorrect_model; - print "Sat (%f/%f)" t (Sys.time () -. t) - | Smt.Unsat us -> - let t = Sys.time () in - if !p_check then begin - let p = us.Solver_intf.get_proof () in - Smt.Proof.check p; - print_proof p; - if !p_unsat_core then - print_unsat_core (Smt.unsat_core p) - end; - print "Unsat (%f/%f)" t (Sys.time () -. t) - end - | Mcsat -> - Mcsat.assume cnf; - let res = Mcsat.solve () in - begin match res with - | Mcsat.Sat sat -> - let t = Sys.time () in - if !p_check then - if not (List.for_all (List.exists sat.Solver_intf.eval) cnf) then - raise Incorrect_model; - print "Sat (%f/%f)" t (Sys.time () -. t) - | Mcsat.Unsat us -> - let t = Sys.time () in - if !p_check then begin - let p = us.Solver_intf.get_proof () in - Mcsat.Proof.check p; - print_mcproof p; - if !p_unsat_core then - print_mc_unsat_core (Mcsat.unsat_core p) - end; - print "Unsat (%f/%f)" t (Sys.time () -. t) - end - -*) - let () = try main () with - | Incorrect_model -> - Format.printf "Internal error : incorrect *sat* model@."; - exit 4 | Out_of_time -> Format.printf "Timeout@."; exit 2 | Out_of_space -> Format.printf "Spaceout@."; exit 3 + | Incorrect_model -> + Format.printf "Internal error : incorrect *sat* model@."; + exit 4 + | Type_sat.Typing_error (msg, t) + | Type_smt.Typing_error (msg, t) -> + let loc = match t.Dolmen.Term.loc with + | Some l -> l | None -> Dolmen.ParseLocation.mk "<>" 0 0 0 0 + in + Format.fprintf Format.std_formatter "While typing:@\n%a@\n%a: typing error\n%s@." + Dolmen.Term.print t Dolmen.ParseLocation.fmt loc msg diff --git a/src/sat/expr_sat.mli b/src/sat/expr_sat.mli index f4b72e48..4e1b70ab 100644 --- a/src/sat/expr_sat.mli +++ b/src/sat/expr_sat.mli @@ -6,3 +6,6 @@ Copyright 2016 Simon Cruanes include Formula_intf.S +val make : int -> t +(** Make a proposition from an integer. *) + diff --git a/src/sat/type_sat.ml b/src/sat/type_sat.ml new file mode 100644 index 00000000..6689f7f6 --- /dev/null +++ b/src/sat/type_sat.ml @@ -0,0 +1,73 @@ + +(* Log&Module Init *) +(* ************************************************************************ *) + +module Id = Dolmen.Id +module Ast = Dolmen.Term +module H = Hashtbl.Make(Id) +module Formula = Tseitin.Make(Expr_sat) + +(* Exceptions *) +(* ************************************************************************ *) + +exception Typing_error of string * Dolmen.Term.t + +(* Identifiers *) +(* ************************************************************************ *) + +let symbols = H.create 42 + +let find_id id = + try + H.find symbols id + with Not_found -> + let res = Expr_sat.fresh () in + H.add symbols id res; + res + +(* Actual parsing *) +(* ************************************************************************ *) + +let rec parse = function + | { Ast.term = Ast.Builtin Ast.True } -> + Formula.f_true + | { Ast.term = Ast.Builtin Ast.False } -> + Formula.f_false + | { Ast.term = Ast.Symbol id } -> + let s = find_id id in + Formula.make_atom s + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not }, [p]) } + | { Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "not" } }, [p]) } -> + Formula.make_not (parse p) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And }, l) } + | { Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "and" } }, l) } -> + Formula.make_and (List.map parse l) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or }, l) } + | { Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "or" } }, l) } -> + Formula.make_or (List.map parse l) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply }, [p; q]) } -> + Formula.make_imply (parse p) (parse q) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Equiv }, [p; q]) } -> + Formula.make_equiv (parse p) (parse q) + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor }, [p; q]) } -> + Formula.make_xor (parse p) (parse q) + | t -> + raise (Typing_error ("Term is not a pure proposition", t)) + +(* Exported functions *) +(* ************************************************************************ *) + +let decl _ t = + raise (Typing_error ("Declarations are not allowed in pure sat", t)) + +let def _ t = + raise (Typing_error ("Definitions are not allowed in pure sat", t)) + +let antecedent t = + let f = parse t in + Formula.make_cnf f + +let consequent t = + let f = parse t in + Formula.make_cnf @@ Formula.make_not f + diff --git a/src/sat/type_sat.mli b/src/sat/type_sat.mli new file mode 100644 index 00000000..6d295a52 --- /dev/null +++ b/src/sat/type_sat.mli @@ -0,0 +1,7 @@ + +(** Typechecking of terms from Dolmen.Term.t + This module provides functions to parse terms from the untyped syntax tree + defined in Dolmen, and generate formulas as defined in the Expr_sat module. *) + +include Type.S with type atom := Expr_sat.t + diff --git a/src/smt/expr_smt.ml b/src/smt/expr_smt.ml index 9270d741..5fb8acfe 100644 --- a/src/smt/expr_smt.ml +++ b/src/smt/expr_smt.ml @@ -133,8 +133,11 @@ module Print = struct let atom_aux fmt f = match f.atom with - | Equal (a, b) -> Format.fprintf fmt "%a = %a" term a term b - | Pred t -> Format.fprintf fmt "%a" term t + | Equal (a, b) -> + Format.fprintf fmt "%a %s %a" + term a (if f.sign then "=" else "<>") term b + | Pred t -> + Format.fprintf fmt "%s%a" (if f.sign then "" else "¬ ") term t let atom fmt f = Format.fprintf fmt "⟦%a⟧" atom_aux f diff --git a/src/smt/type_smt.ml b/src/smt/type_smt.ml index 65127dcf..529cff89 100644 --- a/src/smt/type_smt.ml +++ b/src/smt/type_smt.ml @@ -6,6 +6,7 @@ module Ast = Dolmen.Term module Id = Dolmen.Id module M = Map.Make(Id) module H = Hashtbl.Make(Id) +module Expr = Expr_smt (* Types *) (* ************************************************************************ *) @@ -287,6 +288,9 @@ let infer env s args = let rec parse_expr (env : env) t = match t with + (* Base Type *) + | { Ast.term = Ast.Symbol { Id.name = "Bool" } } -> + Ty (Expr_smt.Ty.prop) (* Basic formulas *) | { Ast.term = Ast.App ({ Ast.term = Ast.Builtin Ast.True }, []) } @@ -297,10 +301,12 @@ let rec parse_expr (env : env) t = | { Ast.term = Ast.Builtin Ast.False } -> Formula Expr.Formula.f_false - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } -> + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.And}, l) } + | { Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "and" }}, l) } -> Formula (Expr.Formula.make_and (List.map (parse_formula env) l)) - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } -> + | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Or}, l) } + | { Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "or" }}, l) } -> Formula (Expr.Formula.make_or (List.map (parse_formula env) l)) | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Xor}, l) } as t -> @@ -330,7 +336,8 @@ let rec parse_expr (env : env) t = | _ -> _bad_arity "<=>" 2 t end - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t -> + | ({ Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Not}, l) } as t) + | ({ Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "not" }}, l) } as t) -> begin match l with | [p] -> Formula (Expr.Formula.make_not (parse_formula env p)) @@ -338,7 +345,8 @@ let rec parse_expr (env : env) t = end (* (Dis)Equality *) - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, l) } as t -> + | ({ Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Eq}, l) } as t) + | ({ Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "=" }}, l) } as t) -> begin match l with | [a; b] -> Formula ( @@ -607,9 +615,9 @@ let formula t = Log.debugf 5 "Typing top-level formula: %a" (fun k -> k Ast.print t); parse_formula env t -let consequent t = +let antecedent t = Expr.Formula.make_cnf (formula t) -let antecedent t = +let consequent t = Expr.Formula.make_cnf (Expr.Formula.make_not (formula t)) diff --git a/src/smt/type_smt.mli b/src/smt/type_smt.mli index 3a2429c4..51957bc8 100644 --- a/src/smt/type_smt.mli +++ b/src/smt/type_smt.mli @@ -1,7 +1,7 @@ (** Typechecking of terms from Dolmen.Term.t This module provides functions to parse terms from the untyped syntax tree - defined in Dolmen, and generate formulas as defined in the Expr module. *) + defined in Dolmen, and generate formulas as defined in the Expr_smt module. *) -include Type.S with type atom = Expr.atom +include Type.S with type atom := Expr_smt.Atom.t diff --git a/tests/test_api.ml b/tests/test_api.ml index 74f36e37..75ae7fd2 100644 --- a/tests/test_api.ml +++ b/tests/test_api.ml @@ -6,18 +6,11 @@ Copyright 2014 Simon Cruanes (* Tests that require the API *) -module F = Expr -module T = Cnf.S +module F = Expr_sat +module T = Tseitin.Make(F) let (|>) x f = f x -type solver = Smt | Mcsat -let solver_list = [ - "smt", Smt; - "mcsat", Mcsat; -] - -let solver = ref Smt let p_check = ref false let time_limit = ref 300. let size_limit = ref 1000_000_000. @@ -32,59 +25,38 @@ let set_flag opt arg flag l = flag := List.assoc arg l with Not_found -> invalid_arg (error_msg opt arg l) -let set_solver s = set_flag "Solver" s solver solver_list let usage = "Usage : test_api [options]" let argspec = Arg.align [ "-check", Arg.Set p_check, " Build, check and print the proof (if output is set), if unsat"; - "-s", Arg.String set_solver, - "{smt,mcsat} Sets the solver to use (default smt)"; "-v", Arg.Int (fun i -> Log.set_debug i), " Sets the debug verbose level"; ] -let string_of_solver = function - | Mcsat -> "mcsat" - | Smt -> "smt" - type solver_res = | R_sat | R_unsat +exception Incorrect_model + module type BASIC_SOLVER = sig val solve : ?assumptions:F.t list -> unit -> solver_res val assume : ?tag:int -> F.t list list -> unit end -exception Incorrect_model - -let mk_solver (s:solver): (module BASIC_SOLVER) = - match s with - | Smt -> - let module S = struct - include Smt.Make(struct end) - let solve ?assumptions ()= match solve ?assumptions() with - | Sat _ -> - R_sat - | Unsat us -> - let p = us.Solver_intf.get_proof () in - Proof.check p; - R_unsat - end - in (module S) - | Mcsat -> - let module S = struct - include Mcsat.Make(struct end) - let solve ?assumptions ()= match solve ?assumptions() with - | Sat _ -> - R_sat - | Unsat us -> - let p = us.Solver_intf.get_proof () in - Proof.check p; - R_unsat - end - in (module S) +let mk_solver (): (module BASIC_SOLVER) = + let module S = struct + include Sat.Make(struct end) + let solve ?assumptions ()= match solve ?assumptions() with + | Sat _ -> + R_sat + | Unsat us -> + let p = us.Solver_intf.get_proof () in + Proof.check p; + R_unsat + end + in (module S) exception Error of string @@ -102,19 +74,19 @@ module Test = struct } let mk_test name l = {name; actions=l} - let assume l = A_assume (List.map (List.map F.mk_prop) l) + let assume l = A_assume (List.map (List.map F.make) l) let assume1 c = assume [c] let solve ?(assumptions=[]) e = - let assumptions = List.map F.mk_prop assumptions in + let assumptions = List.map F.make assumptions in A_solve (assumptions, e) type result = | Pass | Fail of string - let run (solver:solver) (t:t): result = + let run (t:t): result = (* Interesting stuff happening *) - let (module S: BASIC_SOLVER) = mk_solver solver in + let (module S: BASIC_SOLVER) = mk_solver () in try List.iter (function @@ -190,17 +162,14 @@ let main () = Arg.parse argspec (fun _ -> ()) usage; let failed = ref false in List.iter - (fun solver -> - List.iter - (fun test -> - Printf.printf "(%-6s) %-10s... %!" (string_of_solver solver) test.Test.name; - match Test.run solver test with - | Test.Pass -> Printf.printf "ok\n%!" - | Test.Fail msg -> - failed := true; - Printf.printf "fail (%s)\n%!" msg) - Test.suite) - [Smt; Mcsat]; + (fun test -> + Printf.printf "%-10s... %!" test.Test.name; + match Test.run test with + | Test.Pass -> Printf.printf "ok\n%!" + | Test.Fail msg -> + failed := true; + Printf.printf "fail (%s)\n%!" msg) + Test.suite; if !failed then exit 1 let () = main() From 9cf13bd7a2c4db7a4557c3012798db0a35ab7a81 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Thu, 22 Sep 2016 18:31:22 +0200 Subject: [PATCH 13/25] Mcsat now works (for pure equality problems) --- Makefile | 2 +- src/core/expr_intf.ml | 59 +++++----- src/core/formula_intf.ml | 14 +-- src/core/solver_types.ml | 6 +- src/mcsat/eclosure.ml | 231 +++++++++++++++++++++++++++++++++++++ src/mcsat/eclosure.mli | 60 ++++++++++ src/mcsat/mcsat.ml | 8 +- src/mcsat/theory_mcsat.ml | 118 +++++++++++++++++++ src/sat/expr_sat.mli | 3 + src/smt/type_smt.ml | 3 +- src/solver/tseitin.ml | 2 +- src/solver/tseitin.mli | 3 +- src/solver/tseitin_intf.ml | 16 +++ src/util/backtrack.ml | 99 ++++++++++++++++ src/util/backtrack.mli | 77 +++++++++++++ 15 files changed, 655 insertions(+), 46 deletions(-) create mode 100644 src/mcsat/eclosure.ml create mode 100644 src/mcsat/eclosure.mli create mode 100644 src/mcsat/theory_mcsat.ml create mode 100644 src/util/backtrack.ml create mode 100644 src/util/backtrack.mli diff --git a/Makefile b/Makefile index 498c8e7d..8f9d6531 100644 --- a/Makefile +++ b/Makefile @@ -39,7 +39,7 @@ test: bin test_bin @echo "run API tests…" @./test_api.native @echo "run benchmarks…" - @/usr/bin/time -f "%e" ./tests/run smt + # @/usr/bin/time -f "%e" ./tests/run smt @/usr/bin/time -f "%e" ./tests/run mcsat enable_log: diff --git a/src/core/expr_intf.ml b/src/core/expr_intf.ml index a718e935..84fe946f 100644 --- a/src/core/expr_intf.ml +++ b/src/core/expr_intf.ml @@ -11,39 +11,44 @@ type negated = Formula_intf.negated = module type S = sig (** Signature of formulas that parametrises the Mcsat Solver Module. *) - module Term : sig - (** The type of terms *) - type t - val hash : t -> int - val equal : t -> t -> bool - val print : Format.formatter -> t -> unit - end - - module Formula : sig - (** The type of atomic formulas over terms. *) - type t - val hash : t -> int - val equal : t -> t -> bool - val print : Format.formatter -> t -> unit - end - type proof (** An abstract type for proofs *) - val dummy : Formula.t - (** Formula constants. A valid formula should never be physically equal to [dummy] *) + module Term : sig - val fresh : unit -> Formula.t - (** Returns a fresh litteral, distinct from any other literal (used in cnf conversion) *) + type t + (** The type of terms *) - val neg : Formula.t -> Formula.t - (** Formula negation *) + val hash : t -> int + val equal : t -> t -> bool + val print : Format.formatter -> t -> unit + (** Common functions *) + + end + + module Formula : sig + + type t + (** The type of atomic formulas over terms. *) + + val hash : t -> int + val equal : t -> t -> bool + val print : Format.formatter -> t -> unit + (** Common functions *) + + val dummy : t + (** Formula constants. A valid formula should never be physically equal to [dummy] *) + + val neg : t -> t + (** Formula negation *) + + val norm : t -> t * negated + (** Returns a 'normalized' form of the formula, possibly negated + (in which case return [Negated]). + [norm] must be so that [a] and [neg a] normalise to the same formula, + but one returns [Negated] and the other [Same_sign]. *) + end - val norm : Formula.t -> Formula.t * negated - (** Returns a 'normalized' form of the formula, possibly negated - (in which case return [Negated]). - [norm] must be so that [a] and [neg a] normalise to the same formula, - but one returns [Negated] and the other [Same_sign]. *) end diff --git a/src/core/formula_intf.ml b/src/core/formula_intf.ml index 360fde32..366b2f46 100644 --- a/src/core/formula_intf.ml +++ b/src/core/formula_intf.ml @@ -17,12 +17,14 @@ module type S = sig type proof (** An abstract type for proofs *) + val hash : t -> int + val equal : t -> t -> bool + val print : Format.formatter -> t -> unit + (** Common functions *) + val dummy : t (** Formula constants. A valid formula should never be physically equal to [dummy] *) - val fresh : unit -> t - (** Returns a fresh literal, distinct from any other literal (used in cnf conversion) *) - val neg : t -> t (** Formula negation *) @@ -32,11 +34,5 @@ module type S = sig [norm] must be so that [a] and [neg a] normalise to the same formula, but one returns [Same_sign] and one returns [Negated] *) - val hash : t -> int - val equal : t -> t -> bool - (** Usual hash and comparison functions. Given to Hashtbl functors. *) - - val print : Format.formatter -> t -> unit - (** Printing function used for debugging. *) end diff --git a/src/core/solver_types.ml b/src/core/solver_types.ml index 8a1dc92c..3ce9a01d 100644 --- a/src/core/solver_types.ml +++ b/src/core/solver_types.ml @@ -80,7 +80,7 @@ module McMake (E : Expr_intf.S)(Dummy : sig end) = struct | E_var of var (* Dummy values *) - let dummy_lit = E.dummy + let dummy_lit = E.Formula.dummy let rec dummy_var = { vid = -101; @@ -144,7 +144,7 @@ module McMake (E : Expr_intf.S)(Dummy : sig end) = struct let make_boolean_var : formula -> var * Expr_intf.negated = fun t -> - let lit, negated = E.norm t in + let lit, negated = E.Formula.norm t in try MF.find f_map lit, negated with Not_found -> @@ -168,7 +168,7 @@ module McMake (E : Expr_intf.S)(Dummy : sig end) = struct aid = cpt_fois_2 (* aid = vid*2 *) } and na = { var = var; - lit = E.neg lit; + lit = E.Formula.neg lit; watched = Vec.make 10 dummy_clause; neg = pa; is_true = false; diff --git a/src/mcsat/eclosure.ml b/src/mcsat/eclosure.ml new file mode 100644 index 00000000..2fbbedb4 --- /dev/null +++ b/src/mcsat/eclosure.ml @@ -0,0 +1,231 @@ + +module type Key = sig + type t + val hash : t -> int + val equal : t -> t -> bool + val compare : t -> t -> int + val print : Format.formatter -> t -> unit +end + +module type S = sig + type t + type var + + exception Unsat of var * var * var list + + val create : Backtrack.Stack.t -> t + + val find : t -> var -> var + + val add_eq : t -> var -> var -> unit + val add_neq : t -> var -> var -> unit + val add_tag : t -> var -> var -> unit + + val find_tag : t -> var -> var * (var * var) option + +end + +module Make(T : Key) = struct + + module M = Map.Make(T) + module H = Backtrack.Hashtbl(T) + + type var = T.t + + exception Equal of var * var + exception Same_tag of var * var + exception Unsat of var * var * var list + + type repr_info = { + rank : int; + tag : (T.t * T.t) option; + forbidden : (var * var) M.t; + } + + type node = + | Follow of var + | Repr of repr_info + + type t = { + size : int H.t; + expl : var H.t; + repr : node H.t; + } + + let create s = { + size = H.create s; + expl = H.create s; + repr = H.create s; + } + + (* Union-find algorithm with path compression *) + let self_repr = Repr { rank = 0; tag = None; forbidden = M.empty } + + let find_hash m i default = + try H.find m i + with Not_found -> default + + let rec find_aux m i = + match find_hash m i self_repr with + | Repr r -> r, i + | Follow j -> + let r, k = find_aux m j in + H.add m i (Follow k); + r, k + + let get_repr h x = + let r, y = find_aux h.repr x in + y, r + + let tag h x v = + let r, y = find_aux h.repr x in + let new_m = + { r with + tag = match r.tag with + | Some (_, v') when not (T.equal v v') -> raise (Equal (x, y)) + | (Some _) as t -> t + | None -> Some (x, v) } + in + H.add h.repr y (Repr new_m) + + let find h x = fst (get_repr h x) + + let find_tag h x = + let r, y = find_aux h.repr x in + y, r.tag + + let forbid_aux m x = + try + let a, b = M.find x m in + raise (Equal (a, b)) + with Not_found -> () + + let link h x mx y my = + let new_m = { + rank = if mx.rank = my.rank then mx.rank + 1 else mx.rank; + tag = (match mx.tag, my.tag with + | Some (z, t1), Some (w, t2) -> + if not (T.equal t1 t2) then begin + Log.debugf 3 "Tag shenanigan : %a (%a) <> %a (%a)" (fun k -> + k T.print t1 T.print z T.print t2 T.print w); + raise (Equal (z, w)) + end else Some (z, t1) + | Some t, None | None, Some t -> Some t + | None, None -> None); + forbidden = M.merge (fun _ b1 b2 -> match b1, b2 with + | Some r, _ | None, Some r -> Some r | _ -> assert false) + mx.forbidden my.forbidden;} + in + let aux m z eq = + match H.find m z with + | Repr r -> + let r' = { r with + forbidden = M.add x eq (M.remove y r.forbidden) } + in + H.add m z (Repr r') + | _ -> assert false + in + M.iter (aux h.repr) my.forbidden; + H.add h.repr y (Follow x); + H.add h.repr x (Repr new_m) + + let union h x y = + let rx, mx = get_repr h x in + let ry, my = get_repr h y in + if T.compare rx ry <> 0 then begin + forbid_aux mx.forbidden ry; + forbid_aux my.forbidden rx; + if mx.rank > my.rank then begin + link h rx mx ry my + end else begin + link h ry my rx mx + end + end + + let forbid h x y = + let rx, mx = get_repr h x in + let ry, my = get_repr h y in + if T.compare rx ry = 0 then + raise (Equal (x, y)) + else match mx.tag, my.tag with + | Some (a, v), Some (b, v') when T.compare v v' = 0 -> + raise (Same_tag(a, b)) + | _ -> + H.add h.repr ry (Repr { my with forbidden = M.add rx (x, y) my.forbidden }); + H.add h.repr rx (Repr { mx with forbidden = M.add ry (x, y) mx.forbidden }) + + (* Equivalence closure with explanation output *) + let find_parent v m = find_hash m v v + + let rec root m acc curr = + let parent = find_parent curr m in + if T.compare curr parent = 0 then + curr :: acc + else + root m (curr :: acc) parent + + let rec rev_root m curr = + let next = find_parent curr m in + if T.compare curr next = 0 then + curr + else begin + H.remove m curr; + let res = rev_root m next in + H.add m next curr; + res + end + + let expl t a b = + let rec aux last = function + | x :: r, y :: r' when T.compare x y = 0 -> + aux (Some x) (r, r') + | l, l' -> begin match last with + | Some z -> List.rev_append (z :: l) l' + | None -> List.rev_append l l' + end + in + aux None (root t.expl [] a, root t.expl [] b) + + let add_eq_aux t i j = + if T.compare (find t i) (find t j) = 0 then + () + else begin + let old_root_i = rev_root t.expl i in + let old_root_j = rev_root t.expl j in + let nb_i = find_hash t.size old_root_i 0 in + let nb_j = find_hash t.size old_root_j 0 in + if nb_i < nb_j then begin + H.add t.expl i j; + H.add t.size j (nb_i + nb_j + 1) + end else begin + H.add t.expl j i; + H.add t.size i (nb_i + nb_j + 1) + end + end + + (* Functions wrapped to produce explanation in case + * something went wrong *) + let add_tag t x v = + match tag t x v with + | () -> () + | exception Equal (a, b) -> + raise (Unsat (a, b, expl t a b)) + + let add_eq t i j = + add_eq_aux t i j; + match union t i j with + | () -> () + | exception Equal (a, b) -> + raise (Unsat (a, b, expl t a b)) + + let add_neq t i j = + match forbid t i j with + | () -> () + | exception Equal (a, b) -> + raise (Unsat (a, b, expl t a b)) + | exception Same_tag (x, y) -> + add_eq_aux t i j; + let res = expl t i j in + raise (Unsat (i, j, res)) + +end diff --git a/src/mcsat/eclosure.mli b/src/mcsat/eclosure.mli new file mode 100644 index 00000000..d4d5f32c --- /dev/null +++ b/src/mcsat/eclosure.mli @@ -0,0 +1,60 @@ + +(** Equality closure using an union-find structure. + This module implements a equality closure algorithm using an union-find structure. + It supports adding of equality as well as inequalities, and raises exceptions + when trying to build an incoherent closure. + Please note that this does not implement congruence closure, as we do not + look inside the terms we are given. *) + +module type Key = sig + (** The type of keys used by the equality closure algorithm *) + + type t + val hash : t -> int + val equal : t -> t -> bool + val compare : t -> t -> int + val print : Format.formatter -> t -> unit +end + +module type S = sig + (** Type signature for the equality closure algorithm *) + + type t + (** Mutable state of the equality closure algorithm. *) + + type var + (** The type of expressions on which equality closure is built *) + + exception Unsat of var * var * var list + (** Raise when trying to build an incoherent equality closure, with an explanation + of the incoherence. + [Unsat (a, b, l)] is such that: + - [a <> b] has been previously added to the closure. + - [l] start with [a] and ends with [b] + - for each consecutive terms [p] and [q] in [l], + an equality [p = q] has been added to the closure. + *) + + val create : Backtrack.Stack.t -> t + (** Creates an empty state which uses the given backtrack stack *) + + val find : t -> var -> var + (** Returns the representative of the given expression in the current closure state *) + + val add_eq : t -> var -> var -> unit + val add_neq : t -> var -> var -> unit + (** Add an equality of inequality to the closure. *) + + val add_tag : t -> var -> var -> unit + (** Add a tag to an expression. The algorithm ensures that each equality class + only has one tag. If incoherent tags are added, an exception is raised. *) + + val find_tag : t -> var -> var * (var * var) option + (** Returns the tag associated with the equality class of the given term, if any. + More specifically, [find_tag e] returns a pair [(repr, o)] where [repr] is the representant of the equality + class of [e]. If the class has a tag, then [o = Some (e', t)] such that [e'] has been tagged with [t] previously. *) + +end + +module Make(T : Key) : S with type var = T.t + diff --git a/src/mcsat/mcsat.ml b/src/mcsat/mcsat.ml index 5acf092d..91e3dbfe 100644 --- a/src/mcsat/mcsat.ml +++ b/src/mcsat/mcsat.ml @@ -4,8 +4,10 @@ Copyright 2014 Guillaume Bury Copyright 2014 Simon Cruanes *) -module Th = Solver.DummyTheory(Expr_smt.Atom) - module Make(Dummy:sig end) = - Solver.Make(Expr_smt.Atom)(Th)(struct end) + Mcsolver.Make(struct + type proof = unit + module Term = Expr_smt.Term + module Formula = Expr_smt.Atom + end)(Theory_mcsat)(struct end) diff --git a/src/mcsat/theory_mcsat.ml b/src/mcsat/theory_mcsat.ml new file mode 100644 index 00000000..187eac68 --- /dev/null +++ b/src/mcsat/theory_mcsat.ml @@ -0,0 +1,118 @@ + +(* Module initialization *) + +module E = Eclosure.Make(Expr_smt.Term) +module H = Backtrack.Hashtbl(Expr_smt.Term) + +(* Type definitions *) + +type proof = unit +type term = Expr_smt.Term.t +type formula = Expr_smt.Atom.t + +type level = Backtrack.Stack.level + + +(* Backtracking *) + +let stack = Backtrack.Stack.create () + +let dummy = Backtrack.Stack.dummy_level + +let current_level () = Backtrack.Stack.level stack + +let backtrack = Backtrack.Stack.backtrack stack + +(* Equality closure *) + +let uf = E.create stack + +let assign t = + match E.find_tag uf t with + | _, None -> t + | _, Some (_, v) -> v + +(* Uninterpreted functions and predicates *) + +let map = H.create stack + +let true_ = Expr_smt.(Term.of_id (Id.ty "true" Ty.prop)) +let false_ = Expr_smt.(Term.of_id (Id.ty "false" Ty.prop)) + +let add_assign t v lvl = + H.add map t (v, lvl) + +(* Assignemnts *) + +let rec iter_aux f = function + | { Expr_smt.term = Expr_smt.Var _ } as t -> + f t + | { Expr_smt.term = Expr_smt.App (_, _, l) } as t -> + List.iter (iter_aux f) l; + f t + +let iter_assignable f = function + | { Expr_smt.atom = Expr_smt.Pred p } -> + iter_aux f p; + | { Expr_smt.atom = Expr_smt.Equal (a, b) } -> + iter_aux f a; iter_aux f b + +let eval = function + | { Expr_smt.atom = Expr_smt.Pred t } -> + begin try + let v, lvl = H.find map t in + if Expr_smt.Term.equal v true_ then + Plugin_intf.Valued (true, lvl) + else if Expr_smt.Term.equal v false_ then + Plugin_intf.Valued (false, lvl) + else + Plugin_intf.Unknown + with Not_found -> + Plugin_intf.Unknown + end + | { Expr_smt.atom = Expr_smt.Equal (a, b); sign } -> + begin try + let v_a, a_lvl = H.find map a in + let v_b, b_lvl = H.find map a in + if Expr_smt.Term.equal v_a v_b then + Plugin_intf.Valued(sign, max a_lvl b_lvl) + else + Plugin_intf.Valued(not sign, max a_lvl b_lvl) + with Not_found -> + Plugin_intf.Unknown + end + + +(* Theory propagation *) + +let if_sat _ = () + +let rec chain_eq = function + | [] | [_] -> [] + | a :: ((b :: r) as l) -> (Expr_smt.Atom.eq a b) :: chain_eq l + +let assume s = + let open Plugin_intf in + try + for i = s.start to s.start + s.length - 1 do + match s.get i with + | Assign (t, v, lvl) -> + add_assign t v lvl; + E.add_tag uf t v + | Lit f -> + begin match f with + | { Expr_smt.atom = Expr_smt.Equal (u, v); sign = true } -> + E.add_eq uf u v + | { Expr_smt.atom = Expr_smt.Equal (u, v); sign = false } -> + E.add_neq uf u v + | { Expr_smt.atom = Expr_smt.Pred p; sign } -> + let v = if sign then true_ else false_ in + add_assign p v ~-1 + end + done; + Plugin_intf.Sat + with + | E.Unsat (a, b, l) -> + let c = Expr_smt.Atom.eq a b :: List.map Expr_smt.Atom.neg (chain_eq l) in + Plugin_intf.Unsat (c, ()) + diff --git a/src/sat/expr_sat.mli b/src/sat/expr_sat.mli index 4e1b70ab..7026d8e4 100644 --- a/src/sat/expr_sat.mli +++ b/src/sat/expr_sat.mli @@ -9,3 +9,6 @@ include Formula_intf.S val make : int -> t (** Make a proposition from an integer. *) +val fresh : unit -> t +(** Make a fresh atom *) + diff --git a/src/smt/type_smt.ml b/src/smt/type_smt.ml index 529cff89..a0587aa7 100644 --- a/src/smt/type_smt.ml +++ b/src/smt/type_smt.ml @@ -318,7 +318,8 @@ let rec parse_expr (env : env) t = | _ -> _bad_arity "xor" 2 t end - | { Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply}, l) } as t -> + | ({ Ast.term = Ast.App ({Ast.term = Ast.Builtin Ast.Imply}, l) } as t) + | ({ Ast.term = Ast.App ({Ast.term = Ast.Symbol { Id.name = "=>" }}, l) } as t) -> begin match l with | [p; q] -> let f = parse_formula env p in diff --git a/src/solver/tseitin.ml b/src/solver/tseitin.ml index b4ea0dbb..fa124f83 100644 --- a/src/solver/tseitin.ml +++ b/src/solver/tseitin.ml @@ -12,7 +12,7 @@ module type S = Tseitin_intf.S -module Make (F : Formula_intf.S) = struct +module Make (F : Tseitin_intf.Arg) = struct exception Empty_Or type combinator = And | Or | Imp | Not diff --git a/src/solver/tseitin.mli b/src/solver/tseitin.mli index 1eb9dc6c..bd52ffeb 100644 --- a/src/solver/tseitin.mli +++ b/src/solver/tseitin.mli @@ -6,4 +6,5 @@ Copyright 2014 Simon Cruanes module type S = Tseitin_intf.S -module Make : functor (F : Formula_intf.S) -> S with type atom = F.t +module Make : functor + (F : Tseitin_intf.Arg) -> S with type atom = F.t diff --git a/src/solver/tseitin_intf.ml b/src/solver/tseitin_intf.ml index 22f7cac9..3f02b4f8 100644 --- a/src/solver/tseitin_intf.ml +++ b/src/solver/tseitin_intf.ml @@ -10,6 +10,22 @@ (* *) (**************************************************************************) +module type Arg = sig + + type t + (** Type of atomic formulas *) + + val neg : t -> t + (** Negation of atomic formulas *) + + val fresh : unit -> t + (** Generate fresh formulas *) + + val print : Format.formatter -> t -> unit + (** Print the given formula *) + +end + module type S = sig (** The type of ground formulas *) diff --git a/src/util/backtrack.ml b/src/util/backtrack.ml new file mode 100644 index 00000000..aff629cc --- /dev/null +++ b/src/util/backtrack.ml @@ -0,0 +1,99 @@ + +module Stack = struct + + type op = + (* Stack structure *) + | Nil : op + | Level : op * int -> op + (* Undo operations *) + | Set : 'a ref * 'a * op -> op + | Call1 : ('a -> unit) * 'a * op -> op + | Call2 : ('a -> 'b -> unit) * 'a * 'b * op -> op + | Call3 : ('a -> 'b -> 'c -> unit) * 'a * 'b * 'c * op -> op + | CallUnit : (unit -> unit) * op -> op + + type t = { + mutable stack : op; + mutable last : int; + } + + type level = int + + let dummy_level = -1 + + let create () = { + stack = Nil; + last = dummy_level; + } + + let register_set t ref value = t.stack <- Set(ref, value, t.stack) + let register_undo t f = t.stack <- CallUnit (f, t.stack) + let register1 t f x = t.stack <- Call1 (f, x, t.stack) + let register2 t f x y = t.stack <- Call2 (f, x, y, t.stack) + let register3 t f x y z = t.stack <- Call3 (f, x, y, z, t.stack) + + let curr = ref 0 + + let push t = + let level = !curr in + t.stack <- Level (t.stack, level); + t.last <- level; + incr curr + + let rec level t = + match t.stack with + | Level (_, lvl) -> lvl + | _ -> push t; level t + + let backtrack t lvl = + let rec pop = function + | Nil -> assert false + | Level (op, level) as current -> + if level = lvl then begin + t.stack <- current; + t.last <- level + end else + pop op + | Set (ref, x, op) -> ref := x; pop op + | CallUnit (f, op) -> f (); pop op + | Call1 (f, x, op) -> f x; pop op + | Call2 (f, x, y, op) -> f x y; pop op + | Call3 (f, x, y, z, op) -> f x y z; pop op + in + pop t.stack + + let pop t = backtrack t (t.last) + +end + +module Hashtbl(K : Hashtbl.HashedType) = struct + + module H = Hashtbl.Make(K) + + type key = K.t + type 'a t = { + tbl : 'a H.t; + stack : Stack.t; + } + + let create ?(size=256) stack = {tbl = H.create size; stack; } + + let mem {tbl; _} x = H.mem tbl x + let find {tbl; _} k = H.find tbl k + + let add t k v = + Stack.register2 t.stack H.remove t.tbl k; + H.add t.tbl k v + + let remove t k = + try + let v = find t k in + Stack.register3 t.stack H.add t.tbl k v; + H.remove t.tbl k + with Not_found -> () + + let fold t f acc = H.fold f t.tbl acc + + let iter f t = H.iter f t.tbl +end + diff --git a/src/util/backtrack.mli b/src/util/backtrack.mli new file mode 100644 index 00000000..6480cf63 --- /dev/null +++ b/src/util/backtrack.mli @@ -0,0 +1,77 @@ + +(** Provides helpers for backtracking. + This module defines backtracking stacks, i.e stacks of undo actions + to perform when backtracking to a certain point. This allows for + side-effect backtracking, and so to have backtracking automatically + handled by extensions without the need for explicit synchronisation + between the dispatcher and the extensions. +*) + +module Stack : sig + (** A backtracking stack is a stack of undo actions to perform + in order to revert back to a (mutable) state. *) + + type t + (** The type for a stack. *) + + type level + (** The type of backtracking point. *) + + val create : unit -> t + (** Creates an empty stack. *) + + val dummy_level : level + (** A dummy level. *) + + val push : t -> unit + (** Creates a backtracking point at the top of the stack. *) + + val pop : t -> unit + (** Pop all actions in the undo stack until the first backtracking point. *) + + val level : t -> level + (** Insert a named backtracking point at the top of the stack. *) + + val backtrack : t -> level -> unit + (** Backtrack to the given named backtracking point. *) + + val register_undo : t -> (unit -> unit) -> unit + (** Adds a callback at the top of the stack. *) + + val register1 : t -> ('a -> unit) -> 'a -> unit + val register2 : t -> ('a -> 'b -> unit) -> 'a -> 'b -> unit + val register3 : t -> ('a -> 'b -> 'c -> unit) -> 'a -> 'b -> 'c -> unit + (** Register functions to be called on the given arguments at the top of the stack. + Allows to save some space by not creating too much closure as would be the case if + only [unit -> unit] callbacks were stored. *) + + val register_set : t -> 'a ref -> 'a -> unit + (** Registers a ref to be set to the given value upon backtracking. *) + +end + +module Hashtbl : + functor (K : Hashtbl.HashedType) -> + sig + (** Provides wrappers around hastables in order to have + very simple integration with backtraking stacks. + All actions performed on this table register the corresponding + undo operations so that backtracking is automatic. *) + + type key = K.t + (** The type of keys of the Hashtbl. *) + + type 'a t + (** The type of hastable from keys to values of type ['a]. *) + + val create : ?size:int -> Stack.t -> 'a t + (** Creates an empty hashtable, that registers undo operations on the given stack. *) + + val add : 'a t -> key -> 'a -> unit + val mem : 'a t -> key -> bool + val find : 'a t -> key -> 'a + val remove : 'a t -> key -> unit + val iter : (key -> 'a -> unit) -> 'a t -> unit + val fold : 'a t -> (key -> 'a -> 'b -> 'b) -> 'b -> 'b + (** Usual operations on the hashtabl. For more information see the Hashtbl module of the stdlib. *) + end From 41f1ec0e8283174101d1c351142cff3881d2fb02 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 23 Sep 2016 13:30:19 +0200 Subject: [PATCH 14/25] For travis, dolmen is now pinned to github/dev version --- .travis.yml | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index aa50feaf..93b8adb5 100644 --- a/.travis.yml +++ b/.travis.yml @@ -18,8 +18,9 @@ before_install: - opam init - opam switch ${OCAML_VERSION} - eval `opam config env` + - opam install ocamlfind ocamlbuild + - opam pin add dolmen https://github.com/Gbury/dolmen.git install: - - opam install dolmen ocamlfind ocamlbuild - make bin lib script: - make test From 88b8c9f89533a01c1f5b0b28ae080ed2311bf3e4 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 23 Sep 2016 13:30:51 +0200 Subject: [PATCH 15/25] Optimisation for mcsat solver --- src/mcsat/theory_mcsat.ml | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/src/mcsat/theory_mcsat.ml b/src/mcsat/theory_mcsat.ml index 187eac68..8ff16e8f 100644 --- a/src/mcsat/theory_mcsat.ml +++ b/src/mcsat/theory_mcsat.ml @@ -52,8 +52,9 @@ let rec iter_aux f = function f t let iter_assignable f = function - | { Expr_smt.atom = Expr_smt.Pred p } -> - iter_aux f p; + | { Expr_smt.atom = Expr_smt.Pred { Expr_smt.term = Expr_smt.Var _ } } -> () + | { Expr_smt.atom = Expr_smt.Pred { Expr_smt.term = Expr_smt.App (_, _, l) } } -> + List.iter (iter_aux f) l; | { Expr_smt.atom = Expr_smt.Equal (a, b) } -> iter_aux f a; iter_aux f b From 4fae86c81dfcc4aff98bd3cd7313ae1040b6beb8 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 23 Sep 2016 14:02:12 +0200 Subject: [PATCH 16/25] Fixed typo in smt typechecker --- src/smt/type_smt.ml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/smt/type_smt.ml b/src/smt/type_smt.ml index a0587aa7..fd95c77f 100644 --- a/src/smt/type_smt.ml +++ b/src/smt/type_smt.ml @@ -194,7 +194,7 @@ let flat_map f l = List.flatten (List.map f l) let take_drop n l = let rec aux acc = function - | 0, _ | _, [] -> List.rev acc, [] + | 0, res | _, ([] as res) -> List.rev acc, res | m, x :: r -> aux (x :: acc) (m - 1, r) in aux [] (n, l) From 1656995097aae43293066480e8792ae0481dd264 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 23 Sep 2016 15:39:23 +0200 Subject: [PATCH 17/25] Added uninterpreted functions to mcsat solver --- src/core/internal.ml | 3 +- src/core/solver_types.ml | 6 +-- src/main.ml | 5 ++- src/mcsat/theory_mcsat.ml | 87 ++++++++++++++++++++++++++++++++++++--- tests/unsat/test-012.smt2 | 2 + 5 files changed, 93 insertions(+), 10 deletions(-) create mode 100644 tests/unsat/test-012.smt2 diff --git a/src/core/internal.ml b/src/core/internal.ml index db29c488..18dfb011 100644 --- a/src/core/internal.ml +++ b/src/core/internal.ml @@ -494,7 +494,8 @@ module Make l.assigned <- Some value; l.l_level <- lvl; Vec.push env.elt_queue (of_lit l); - () + Log.debugf 20 "Enqueue (%d): %a" + (fun k -> k (Vec.size env.elt_queue) pp_lit l) (* evaluate an atom for MCsat, if it's not assigned by boolean propagation/decision *) diff --git a/src/core/solver_types.ml b/src/core/solver_types.ml index 3ce9a01d..9eed6bf0 100644 --- a/src/core/solver_types.ml +++ b/src/core/solver_types.ml @@ -282,14 +282,14 @@ module McMake (E : Expr_intf.S)(Dummy : sig end) = struct let pp_assign out = function | None -> () - | Some t -> Format.fprintf out " ->@ %a" E.Term.print t + | Some t -> Format.fprintf out " ->@ @[%a@]" E.Term.print t let pp_lit out v = - Format.fprintf out "%d [lit:%a%a]" + Format.fprintf out "%d [lit:@[%a%a@]]" (v.lid+1) E.Term.print v.term pp_assign v.assigned let pp_atom out a = - Format.fprintf out "%s%d%s[atom:%a]@ " + Format.fprintf out "%s%d%s[atom:@[%a@]]@ " (sign a) (a.var.vid+1) (value a) E.Formula.print a.lit let pp_atoms_vec out vec = diff --git a/src/main.ml b/src/main.ml index 0dbc9031..bc40bb32 100644 --- a/src/main.ml +++ b/src/main.ml @@ -189,9 +189,12 @@ let () = exit 4 | Type_sat.Typing_error (msg, t) | Type_smt.Typing_error (msg, t) -> + let b = Printexc.get_backtrace () in let loc = match t.Dolmen.Term.loc with | Some l -> l | None -> Dolmen.ParseLocation.mk "<>" 0 0 0 0 in Format.fprintf Format.std_formatter "While typing:@\n%a@\n%a: typing error\n%s@." - Dolmen.Term.print t Dolmen.ParseLocation.fmt loc msg + Dolmen.Term.print t Dolmen.ParseLocation.fmt loc msg; + if Printexc.backtrace_status () then + Format.fprintf Format.std_formatter "%s@." b diff --git a/src/mcsat/theory_mcsat.ml b/src/mcsat/theory_mcsat.ml index 8ff16e8f..46b718ae 100644 --- a/src/mcsat/theory_mcsat.ml +++ b/src/mcsat/theory_mcsat.ml @@ -3,15 +3,16 @@ module E = Eclosure.Make(Expr_smt.Term) module H = Backtrack.Hashtbl(Expr_smt.Term) +module M = Hashtbl.Make(Expr_smt.Term) (* Type definitions *) type proof = unit type term = Expr_smt.Term.t type formula = Expr_smt.Atom.t - type level = Backtrack.Stack.level +exception Absurd of Expr_smt.Atom.t list (* Backtracking *) @@ -32,23 +33,97 @@ let assign t = | _, None -> t | _, Some (_, v) -> v -(* Uninterpreted functions and predicates *) - -let map = H.create stack +(* Propositional constants *) let true_ = Expr_smt.(Term.of_id (Id.ty "true" Ty.prop)) let false_ = Expr_smt.(Term.of_id (Id.ty "false" Ty.prop)) +(* Uninterpreted functions and predicates *) + +let map = H.create stack +let watch = M.create 4096 +let interpretation = H.create stack + +let pop_watches t = + try + let l = M.find watch t in + M.remove watch t; + l + with Not_found -> + [] + +let add_job j x = + let l = try M.find watch x with Not_found -> [] in + M.add watch x (j :: l) + +let update_job x ((t, watchees) as job) = + try + let y = List.find (fun y -> not (H.mem map y)) watchees in + add_job job y + with Not_found -> + add_job job x; + begin match t with + | { Expr_smt.term = Expr_smt.App (f, tys, l) } -> + let is_prop = Expr_smt.(Ty.equal t.t_type Ty.prop) in + let t_v, _ = H.find map t in + let l' = List.map (fun x -> fst (H.find map x)) l in + let u = Expr_smt.Term.apply f tys l' in + begin try + let t', u_v = H.find interpretation u in + if not (Expr_smt.Term.equal t_v u_v) then begin + match t' with + | { Expr_smt.term = Expr_smt.App (_, _, r) } when is_prop -> + let eqs = List.map2 (fun a b -> Expr_smt.Atom.neg (Expr_smt.Atom.eq a b)) l r in + if Expr_smt.(Term.equal u_v true_) then begin + let res = Expr_smt.Atom.pred t :: + Expr_smt.Atom.neg (Expr_smt.Atom.pred t') :: eqs in + raise (Absurd res) + end else begin + let res = Expr_smt.Atom.pred t' :: + Expr_smt.Atom.neg (Expr_smt.Atom.pred t) :: eqs in + raise (Absurd res) + end + | { Expr_smt.term = Expr_smt.App (_, _, r) } -> + let eqs = List.map2 (fun a b -> Expr_smt.Atom.neg (Expr_smt.Atom.eq a b)) l r in + let res = Expr_smt.Atom.eq t t' :: eqs in + raise (Absurd res) + | _ -> assert false + end + with Not_found -> + H.add interpretation u (t, t_v); + end + | _ -> assert false + end + +let rec update_watches x = function + | [] -> () + | job :: r -> + begin + try + update_job x job; + with exn -> + List.iter (fun j -> add_job j x) r; + raise exn + end; + update_watches x r + +let add_watch t l = + update_job t (t, l) + let add_assign t v lvl = - H.add map t (v, lvl) + H.add map t (v, lvl); + update_watches t (pop_watches t) (* Assignemnts *) let rec iter_aux f = function | { Expr_smt.term = Expr_smt.Var _ } as t -> + Log.debugf 10 "Adding %a as assignable" (fun k -> k Expr_smt.Term.print t); f t | { Expr_smt.term = Expr_smt.App (_, _, l) } as t -> + if l <> [] then add_watch t (t :: l); List.iter (iter_aux f) l; + Log.debugf 10 "Adding %a as assignable" (fun k -> k Expr_smt.Term.print t); f t let iter_assignable f = function @@ -113,6 +188,8 @@ let assume s = done; Plugin_intf.Sat with + | Absurd l -> + Plugin_intf.Unsat (l, ()) | E.Unsat (a, b, l) -> let c = Expr_smt.Atom.eq a b :: List.map Expr_smt.Atom.neg (chain_eq l) in Plugin_intf.Unsat (c, ()) diff --git a/tests/unsat/test-012.smt2 b/tests/unsat/test-012.smt2 new file mode 100644 index 00000000..1a2946b1 --- /dev/null +++ b/tests/unsat/test-012.smt2 @@ -0,0 +1,2 @@ +(assert (and (= a b) (not (= (f a) (f b))))) +(check-sat) From f35d3a9f23fdca8bd8adba91e1c4217e55df650a Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 23 Sep 2016 15:57:38 +0200 Subject: [PATCH 18/25] Fixed uninterpreted predicates for mcsat solver --- src/mcsat/theory_mcsat.ml | 3 ++- tests/unsat/test-013.smt2 | 2 ++ 2 files changed, 4 insertions(+), 1 deletion(-) create mode 100644 tests/unsat/test-013.smt2 diff --git a/src/mcsat/theory_mcsat.ml b/src/mcsat/theory_mcsat.ml index 46b718ae..cc0afcf3 100644 --- a/src/mcsat/theory_mcsat.ml +++ b/src/mcsat/theory_mcsat.ml @@ -128,7 +128,8 @@ let rec iter_aux f = function let iter_assignable f = function | { Expr_smt.atom = Expr_smt.Pred { Expr_smt.term = Expr_smt.Var _ } } -> () - | { Expr_smt.atom = Expr_smt.Pred { Expr_smt.term = Expr_smt.App (_, _, l) } } -> + | { Expr_smt.atom = Expr_smt.Pred ({ Expr_smt.term = Expr_smt.App (_, _, l) } as t) } -> + if l <> [] then add_watch t (t :: l); List.iter (iter_aux f) l; | { Expr_smt.atom = Expr_smt.Equal (a, b) } -> iter_aux f a; iter_aux f b diff --git a/tests/unsat/test-013.smt2 b/tests/unsat/test-013.smt2 new file mode 100644 index 00000000..d67c8f07 --- /dev/null +++ b/tests/unsat/test-013.smt2 @@ -0,0 +1,2 @@ +(assert (and (= a b) (not (p a)) (p b))) +(check-sat) From ff6e9cb8f08d59dfa07ed59b354c36d2416b2204 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Wed, 12 Oct 2016 19:11:08 +0200 Subject: [PATCH 19/25] [wip] adding documentation about msat --- docs/macros.tex | 10 ++ docs/msat.tex | 415 ++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 425 insertions(+) create mode 100644 docs/macros.tex create mode 100644 docs/msat.tex diff --git a/docs/macros.tex b/docs/macros.tex new file mode 100644 index 00000000..9932a704 --- /dev/null +++ b/docs/macros.tex @@ -0,0 +1,10 @@ + +\def\ocaml{\textsf{OCaml}} + +\def\sat{\textsf{Sat}} +\def\smt{\textsf{SMT}} +\def\mcsat{\textsf{McSat}} + +\def\msat{\textsf{mSAT}} + + diff --git a/docs/msat.tex b/docs/msat.tex new file mode 100644 index 00000000..0d2a7cd7 --- /dev/null +++ b/docs/msat.tex @@ -0,0 +1,415 @@ + +\documentclass{article} + +\usepackage[T1]{fontenc} +\usepackage{makeidx} +\usepackage{bussproofs} +\usepackage{amsmath,amssymb} +\usepackage{tabularx} +\usepackage{pgf, tikz} + +\usepackage{listings} +\lstset{language=[Objective]caml} + +\input{macros} + +\usetikzlibrary{arrows, automata} + +\begin{document} + +\title{\msat{}: a SAT/SMT/McSAT library} +\author{Guillaume~Bury} + +\maketitle + +\section{Introduction} + +The goal if the \msat{} library is to provide a way to easily +create atomated theorem provers based on a \sat{} solver. More precisely, +the library, written in \ocaml{}, provides functors which, once instantiated, +provide a \sat{}, \smt{} or \mcsat{} solver. + +Given the current state of the art of \smt{} solvers, where most \sat{} solvers +are written in C and heavily optimised\footnote{Some solvers now have instructions +to manage a processor's cache}, the \msat{} library does not aim to provide solvers +competitive with the existing implementations, but rather a + +\section{McSat: An extension of SMT Solvers} + +\subsection{Introduction} + + +Mcsat is an extension of usual SMT solvers, introduced in~\cite{VMCAI13} and~\cite{FMCAD13}. +In usual SMT Solvers, interaction between the core SAT Solver and the Theory is pretty limited~: +the SAT Solver make boolean decision, and sends them to the theory, whose role is in return to +stop the SAT Solver as soon as the current set of assumptions is incoherent. This means +that the information that theories can give the SAT Solver is pretty limited, and furthermore +it limits the ability of theories to guide the proof search. + +While it appears to leave a reasonably simple job to the theory, since it completely +hides the propositional structure of the problem, this simple interaction between the +SAT Solver and the theory makes it harder to combine multiple theories into one. Usual +techniques for combining theories in SMT solvers typically require to keep track of +equality congruence classes and require of theories to propagate any equality they discover. + +McSat extends the SAT paradigm by allowing more exchange of information between the theory +and the SAT Solver. This is achieved by allowing the solver to not only decide on the truth value +of atomic propositions, but also to decide assignments for terms that appear in the problem. +For instance, if the SAT Solver assumes a formula $x = 0$, +an arithmetic theory could propagate to the SAT Solver that the formula $x < 1$ must also hold, +instead of waiting for the SAT Solver to guess the truth value of $x < 1$ and then +inform the SAT Solver that the conjunction~: $x = 0 \land \neg x < 1$ is incoherent. + +This exchange of information between the SAT Solver and the theories results in +the construction of a model throughout the proof search (which explains the name +Model Constructing SAT). + +\subsection{SMT Solver architecture} + +We can represent a simplified version of the information flow (not taking into +account backtracking) of usual SMT Solvers, using the graph in fig~\ref{fig:smt_flow}. +In a pure Sat solver, the solver starts by doing +boolean propagation until no more literal can be propagated, at which point it +makes a decision and assign a truth value to a literal not yet assigned. It then +loops to its starting point and does boolean propagation. In an SMT solver, +after each propagation and decision, the solver sends the newly assigned literals +to the theory. The theory then has the possibility to declare the current set of +literals incoherent, and give the solver a tautology in which all literals are currently +assigned to $\bot$, thus prompting the solver to backtrack. + +\begin{figure} + \begin{center} + \begin{tikzpicture}[ + ->, % Arrow style + > = stealth, % arrow head style + shorten > = 1pt, % don't touch arrow head to node + node distance = 2cm, % distance between nodes + semithick, % line style + auto + ] + + \tikzstyle{state}=[rectangle,draw=black!75] + + \node (sat) {SAT Core}; + \node (th) [right of=sat, node distance=6cm] {Theory}; + \node[state] (d) [below of=sat, node distance=1cm] {Decision (boolean)}; + \node[state] (bp) [below of=d, node distance=2cm] {Boolean propagation}; + \node[state] (tp) [right of=bp, node distance=6cm] {Theory propagation}; + + \draw (d) edge [bend left=30] (bp); + \draw (bp) edge [bend left=30] (d); + \draw (bp) edge (tp); + + \draw[black!50] (-2,1) rectangle (2,-4); + \draw[black!50] (4,1) rectangle (8,-4); + + \end{tikzpicture} + \end{center} + \caption{Simplified SMT Solver architecture}\label{fig:smt_flow} +\end{figure} + +The main addition of McSat is that when the solver makes a decision, instead of +being restricted to making boolean assignment of formulas, the solver now can +decide to assign a value to a term belonging to one of the literals. In order to do so, +the solver first chooses a term that has not yet been assigned, and then asks +the theory for a possible assignment. Like in usual SMT Solvers, a McSat solver +only exchange information with one theory, but, as we will see, combination +of theories into one becomes easier in this framework. + +Using the assignments on terms, the theory can very easily do efficient +propagation of formulas implied by the current assignments. +The information flow then looks like fig~\ref{fig:mcsat_flow}. +For a more detailed presentation, see~\cite{FMCAD13} and~\cite{VMCAI13}. + +\begin{figure} + \begin{center} + \begin{tikzpicture}[ + ->, % Arrow style + > = stealth, % arrow head style + shorten > = 1pt, % don't touch arrow head to node + node distance = 2cm, % distance between nodes + semithick, % line style + auto + ] + + \tikzstyle{state}=[rectangle,draw=black!75] + + \node (sat) {SAT Core}; + \node (th) [right of=sat, node distance=6cm] {Theory}; + \node[state] (d) [below of=sat, node distance=1cm] {Decision}; + \node[state] (ass) [right of=d, node distance=6cm] {Assignment}; + \node[state] (bp) [below of=d, node distance=2cm] {Boolean propagation}; + \node[state] (tp) [right of=bp, node distance=6cm] {Theory propagation}; + + \draw (bp)[right] edge [bend left=5] (tp); + \draw (tp) edge [bend left=5] (bp); + \draw (bp) edge [bend left=30] (d); + \draw (ass) edge [bend left=5] (d); + \draw (d) edge [bend left=5] (ass); + \draw (d) edge [bend left=30] (bp); + \draw[<->] (ass) edge (tp); + + \draw[black!50] (-2,1) rectangle (2,-4); + \draw[black!50] (4,1) rectangle (8,-4); + + \end{tikzpicture} + \end{center} + \caption{Simplified McSat Solver architecture}\label{fig:mcsat_flow} +\end{figure} + +\subsection{Decisions and propagations} + +In this document, semantic propagations are a bit different from the propagations +used in traditional SMT Solvers. In the case of McSat (or at least the version presented here), +semantic propagations strictly correspond to the evaluation of formulas in the +current assignment. Moreover, in order to be able to correctly handle these semantic +propagations during backtrack, they are assigned a level: each decision is given a level +(typically, it is the number of previous decisions in in the scope when a decision is made), +and a formula is propagated at the maximum level of decision used to evaluate it. + +For instance, if the current trail is $\{x \mapsto_1 0, x + y + z = 0 \mapsto_2 \top, y\mapsto_3 0\}$, +then $x + y = 0$ can be propagated at level $3$, but $z = 0$ can not be propagated (at least not +given to the sat solver, however nothing prevents the theory from propagating and using it internally). + +\subsection{Algorithm formalization} + +\subsubsection{SAT} + +The SAT algorithm can be formalized as follows. During the search, the solver keeps +a set of clauses, containing the problem hypotheses and the learnt clauses, and +a trail, which is the current ordered list of assumptions and/or decisions made by +the solver. + +Each element in the trail (decision or propagation) has a level, which is the number of decision +appearing in the trail up to (and including) it. So for instance, propagations made before any +decisions have level $0$, and the first decision has level $1$. Propagations are written +$a \leadsto_C \top$, with $C$ the clause that caused the propagation, and decisions +$a \mapsto_n \top$, with $n$ the level of the decision. Trails are read +chronologically from left to right. + +In the following, given a trail $t$ and an atomic formula $a$, we will use the following notation: +$a \in t$ if $a \mapsto_n \top$ or $a \leadsto_C \top$ is in $t$, i.e $a\ in t$ is $a$ is true +in the trail $t$. In this context, the negation $\neg$ is supposed to be involutive (i.e $\neg \neg a = a$), +so that, if $a \in t$ then $\neg \neg a = a \in t$. + +The SAT algorithm has two states: first, it starts in the $\text{Solve}$ state, where propagations +and decisions are made, until a conflict is detected, at which point it enters in the $\text{Analyse}$ +state, where it analyzes the conflict, backtracks, and re-enter the $\text{Solve}$ state. +The $\text{Solve}$ state take as argument the set of hypotheses and the trail, while +the $\text{Analyze}$ state also take as argument the current conflict clause. + +The following invariants are maintained by the transition system: +\begin{description} + \item[Equivalence] During transitions between states $s_1$ and $s_2$, the set of hypotheses + (usually written $\mathbb{S}$) in $s_1$ is equivalent to that of $s_2$. + \item[Trail Soundness] In $\text{Solve}(\mathbb{S}, t)$, if $a \in t$ then $\neg a \notin t$ + \item[Conflict Analysis] In $\text{Analyze}(\mathbb{S}, t, C)$, $C$ is a clause implied by the + clauses in $\mathbb{S}$, and $\forall a \in C, \neg a \in t$ (i.e $C$ is entailed, yet false + in the partial model formed by the trail $t$). +\end{description} + +\subsection{First order terms} + +In the following, we use the following notations: +\begin{itemize} + \item $\mathbb{V}$ is an infinite set of variables + \item $\mathbb{C}$ is a possibly infinite set of constants defined + by a problem's logic\footnote{For instance, the theory of arithmetic + defines the usual operators $+, -, *, /$ as well as the constants + $0, -5, \frac{1}{2}, -2.3, \ldots$} + \item $\mathbb{S}$ is a finite set of constants defined by a problem's type definitions + \item $\mathbb{T}(\mathbb{X})$ for the (infinite) set of first-order terms over $\mathbb{X}$ + (for instance $a, f(0), x + y, \ldots$) + \item $\mathbb{F}(\mathbb{T})$ for the (infinite) set of first order quantified formulas + over the terms in $\mathbb{T}$ +\end{itemize} + +\subsection{Models} + +A model traditionally is a triplet which comprises a domain, a signature and an interpretation function. +Most problems define their signature using type definitions, and builtin theories such as arithmetic +usually have canonic models, so in the following we consider the domain and siganture constant, and +talk about the interpretation, more specifically, about the interpretation of symbols not defined +by the theory\footnote{Since theory-defined symbols, such as addition, already have an intepretation +in the canonical domain.}, i.e non-interpreted functions. An intepretation $\mathcal{I}$ can easily +be extended to a function from ground terms to model value by recursively applying it: +\[ + \mathcal{I}( f ( {(e_i)}_{1\leq i \leq n})) = \mathcal{I}_f ( {( \mathcal{I}(e_i) )}_{1 \leq i \leq n} ) +\] + +Before formalizing the SAT, SMT and McSat algorithms as inference rules, we need to formalize the notion +of partial interpretation. Indeed, during the proof search, the McSat algorithm maintains a partial mapping from +expressions to model values. The intention of this mapping is to represent a partial interpretation of the input +problem, so that if the mapping is complete (i.e all variables are assigned), then it directly gives an interpretation +of the input problem (quantified formula notwithstanding). + +More than simply an incomplete interpretation, we also want to be able to give partial function (instead of complete functions) as interpretation of +constants with positive arity. And even further, we'd like to specify these partial interpretations in a somewhat +abstract way, using mappings from expressions to model values instead of a function from model values to model +values. For instance, given a function symbol $f$ of type $\text{int} \rightarrow \text{int}$ and an integer constant $a$, we'd like to specify that in our mapping, +$f(a) \mapsto 0$, regardless of the values that $f$ takes on other argument, and also regardless +of the value mapped to $a$. To that end we introduce a notion of abstract partial interpretation. + +An abstract partial interpretation $\sigma$ is a mapping from ground expressions to model values. To each abstract partial +interpretation correspond a set of complete models that realize it. More precisely, any mapping $\sigma$ can be completed +in various ways, leading to a set of potential interpretations: +\[ + \text{Complete}(\sigma) = + \left\{ + \mathcal{I} + \; | \; + \forall f( {(e_i)}_{1 \leq i \leq n} ) \mapsto v \in \sigma , + \mathcal{I}_f ( {( \mathcal{I}(e_i) )}_{1 \leq i \leq n} ) = v + \right\} +\] + +We can then consider that the natural interpretation corresponding to a given mapping is the +partial interpretation on which all completion of the mapping agrees, i.e the intersection of +all potential candidates: +\[ + \sigma_\mathcal{I} = \bigcap_{ \mathcal{I} \in \text{Complete}(\sigma) } \mathcal{I} +\] + +Of course, it might happen that a mapping does not admit any potential interpretation, +and thus has no natural interpretation, for instance there is no possible completion of the +following mapping: +\[ + \sigma = \left\{ + \begin{matrix} + a \mapsto 0 \\ + b \mapsto 0 \\ + f(a) \mapsto 0 \\ + f(b) \mapsto 1 \\ + \end{matrix} + \right. +\] + +\begin{figure} + + Sat Solving + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Propagation (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Sove}(\mathbb{S}, t :: a \leadsto_C \top)$} + \DP{} & + $a \in C, C \in \mathbb{S}, \neg a \notin t, \forall b \neq a \in C. \neg b \in t $ + \\ \\ + % Decide (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n \top)$} + \DP{} & + $a \notin t, \neg a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ + \\ \\ + % Conflict (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + $C \in \mathbb{S}, \forall a \in C. \neg a \in t$ + \\ \\ + \end{tabular} + \end{center} + + Conflict Analysis + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Analyze (propagation) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} + \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} + \DP{} & + $\neg a \notin D$ + \\ \\ + % Analyze (decision) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_n \top, D)$} + \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} + \DP{} & + $\neg a \notin D$ + \\ \\ + % Resolution + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} + \UIC{$\text{Analyze}(\mathbb{S}, t, (C - \{a\}) \cup (D - \{ \neg a\}))$} + \DP{} & + $\neg a \in D$ + \\ \\ + % BackJump + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_d \top :: t', C)$} + \UIC{$\text{Solve}(\mathbb{S} \cup \{ C \}, t)$} + \DP{} & + $\text{is\_uip}(C), d = \text{uip\_level}(C)$ + \\ \\ + \end{tabular} + \end{center} + + SMT Solving + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Conflict (theory) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + $\mathcal{T} \vdash C, \forall a \in C, \neg a \in t$ + \\ \\ + \end{tabular} + \end{center} + + McSat Solving + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Decide (assignment) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n v)$} + \DP{} & + $a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ + \\ \\ + % Propagation (semantic) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \leadsto_n \top)$} + \DP{} & + $ $ + \\ \\ + \end{tabular} + \end{center} + + \caption{SAT, SMT and McSat inference rules}\label{fig:transitions} +\end{figure} + +\subsection{Expected theory invariants} + +TODO: rewrite this section. + +During proof search are maintained a set of assertions $\mathcal{S}$ +and a partial assignment $\sigma$ as a partial function from $\mathbb{T}(\mathbb{V, C, S})$ +to $\mathbb{T}(\mathbb{C})$. $\sigma$ is easily extended to a complete substitution function of +$\mathbb{T}(\mathbb{V, C, S})$. + +We say that $\sigma$ is compatible with $\mathcal{S}$ iff for every $\varphi \in \mathcal{S}$, +$\varphi\sigma$ is satisfiable (independently from the rest of the formulas in $\mathcal{S}$). +Intuitively, this represents the fact that the substitution $\sigma$ does not imply any +ground contradictions. + +A theory then has to ensure that for every expression $e \in \mathbb{T}(\mathbb{V,C,S})$ +there exists $v \in \mathbb{T}(\mathbb{C})$ such that $\sigma' = \sigma \cup \{ e \rightarrow v \}$ +is coherent, and compatible with $\mathcal{S}$\footnote{Note that in particular, this implies +that $\sigma$ is coherent with $\mathcal{S}$}. As soon as the current assignment is not coherent, +compatible with the current assertions, or that there is a term $e$ with no viable assignment, the theory +should inform the SAT Solver to backtrack, since the current branch is clearly not satisfiable. +If we reach the point where all expressions of the problem have been assigned, then we +have a ground model for the current set of assertions, which is then also a model +of the input problem. + +Of interest if the fact that theories that respect this invariant can easily be combined +to create a theory that also respect this invariant, as long as for any expression $e$, +there is exactly one theory responsible for finding an assignment for $e$\footnote{this +is similar to the usual criterion for combining SMT theories which is that they do not +share symbols other than equality.}. + + +\clearpage + +\bibliographystyle{plain} +\bibliography{biblio} + +\clearpage +\appendix + +\end{document} From ee2a80bc4fc3dbff6135764c56be30ac99336097 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Fri, 14 Oct 2016 14:12:29 +0200 Subject: [PATCH 20/25] [wip] Documentation update --- docs/articles/mcsat-vmcai2013.pdf | Bin 0 -> 371980 bytes docs/articles/mcsat_design.pdf | Bin 0 -> 378980 bytes docs/articles/minisat.pdf | Bin 0 -> 327416 bytes docs/biblio.bib | 13 + docs/macros.tex | 3 + docs/msat.pdf | Bin 0 -> 335008 bytes docs/msat.tex | 430 ++++++++++++++++++------------ 7 files changed, 280 insertions(+), 166 deletions(-) create mode 100644 docs/articles/mcsat-vmcai2013.pdf create mode 100644 docs/articles/mcsat_design.pdf create mode 100644 docs/articles/minisat.pdf create mode 100644 docs/biblio.bib create mode 100644 docs/msat.pdf diff --git a/docs/articles/mcsat-vmcai2013.pdf b/docs/articles/mcsat-vmcai2013.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e89e32d7a8482b538a2a577540120b61ebfaafe0 GIT binary patch literal 371980 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de Moura, Leonardo", + title = "The Design and Implementation of the Model Constructing Satisfiability Calculus", + year = 2013 +} + +@inproceedings{VMCAI13, + author = "Jovanovic, Devan and de Moura, Leonardo", + title = "A Model-Constructing Satisfiability Calculus", + year = 2013 +} diff --git a/docs/macros.tex b/docs/macros.tex index 9932a704..bc2f609b 100644 --- a/docs/macros.tex +++ b/docs/macros.tex @@ -7,4 +7,7 @@ \def\msat{\textsf{mSAT}} +\newcommand{\irule}[1]{{\small\textsc{#1}}} +\EnableBpAbbreviations{} +\newcommand{\LLc}[1]{\LL{\irule{#1}}} diff --git a/docs/msat.pdf b/docs/msat.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0d856f01a28fabcb725e90c45e45604a91e92637 GIT binary patch literal 335008 zcmb5V!;&b#qAj?~wr$(CZQHhO+qP}nwr$(4dZ#hFC!%lXC_f-$IZ5P&MQIplSs+Q~ zmq*qiS@G%d?F=m;xw#?fq)lwioXznW7}+`S|L+4yCu(8sY~qMdCu(irY$9x8WM^yw z$;%7rxbk)>_{q7S@c5#4KtM-%b3AH zq}db%d>g-}ORvNg&7^N52%pyrVC9g_Z`j~9Im(ts{ 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c39cca5d..87cb2d2c 100644 --- a/docs/msat.tex +++ b/docs/msat.tex @@ -7,7 +7,7 @@ \usepackage{amsmath,amssymb} \usepackage{tabularx} \usepackage{pgf, tikz} -\usepackage[margin=4cm]{geometry} +% \usepackage[margin=4cm]{geometry} \usepackage{float} \floatstyle{boxed} @@ -22,15 +22,15 @@ \begin{document} -\title{\msat{}: a SAT/SMT/McSAT library} +\title{\msat{}: a \sat{}/\smt{}/\mcsat{} library} \author{Guillaume~Bury} \maketitle \section{Introduction} -The goal if the \msat{} library is to provide a way to easily -create atomated theorem provers based on a \sat{} solver. More precisely, +The goal of the \msat{} library is to provide a way to easily +create automated theorem provers based on a \sat{} solver. More precisely, the library, written in \ocaml{}, provides functors which, once instantiated, provide a \sat{}, \smt{} or \mcsat{} solver. @@ -38,7 +38,7 @@ Given the current state of the art of \smt{} solvers, where most \sat{} solvers are written in C and heavily optimised\footnote{Some solvers now have instructions to manage a processor's cache}, the \msat{} library does not aim to provide solvers competitive with the existing implementations, but rather an easy way to create -reasonably eficient solvers. +reasonably efficient solvers. \msat{} currently uses the following techniques: \begin{itemize} @@ -60,11 +60,11 @@ Additionally, \msat{} has the following features: \clearpage -\section{\sat{} Solvers: principles and formalization} +\section{\sat{} Solvers: principles and formalization}\label{sec:sat} \subsection{Idea} -\subsection{Inference rules} +\subsection{Inference rules}\label{sec:trail} The SAT algorithm can be formalized as follows. During the search, the solver keeps a set of clauses, containing the problem hypotheses and the learnt clauses, and @@ -79,17 +79,23 @@ $a \mapsto_n \top$, with $n$ the level of the decision. Trails are read chronologically from left to right. In the following, given a trail $t$ and an atomic formula $a$, we will use the following notation: -$a \in t$ if $a \mapsto_n \top$ or $a \leadsto_C \top$ is in $t$, i.e $a \in t$ is $a$ is true -in the trail $t$. In this context, the negation $\neg$ is supposed to be involutive (i.e $\neg \neg a = a$), -so that, if $a \in t$ then $\neg \neg a = a \in t$. +$a \in t$ if $a \mapsto_n \top$ or $a \leadsto_C \top$ is in $t$, i.e.~$a \in t$ is $a$ is true +in the trail $t$. In this context, the negation $\neg$ is supposed to be involutive +(i.e.~$\neg \neg a = a$), so that, if $a \in t$ then $\neg \neg a = a \in t$. -The SAT algorithm has two states: first, it starts in the $\text{Solve}$ state, where propagations -and decisions are made, until a conflict is detected, at which point it enters in the $\text{Analyse}$ -state, where it analyzes the conflict, backtracks, and re-enter the $\text{Solve}$ state. +There exists two main \sat{} algorithms: \dpll{} and \cdcl{}. In both, there exists +two states: first, the starting state $\text{Solve}$, where propagations +and decisions are made, until a conflict is detected, at which point the algorithm +enters in the $\text{Analyse}$ state, where it analyzes the conflict, backtracks, +and re-enter the $\text{Solve}$ state. The difference between \dpll{} and \cdcl{} +is the treatment of conflicts during the $\text{Analyze}$ phase: \dpll{} will use +the conflict only to known where to backtrack/backjump, while in \cdcl{} the result +of the conflict analysis will be added to the set of hypotheses, so that the same +conflict does not occur again. The $\text{Solve}$ state take as argument the set of hypotheses and the trail, while the $\text{Analyze}$ state also take as argument the current conflict clause. -We can now formalize the \sat{} algorithm using the inference rules +We can now formalize the \cdcl{} algorithm using the inference rules in Figure~\ref{fig:rules}. In order to completely recover the \sat{} algorithm, one must apply the rules with the following precedence and termination conditions, depending on the current state: @@ -110,7 +116,7 @@ depending on the current state: \irule{Analyze}. We now have the choice of when to apply the \irule{Backjump} rule compared to the \irule{Analyze} rule: using \irule{Backjump} eagerly will result in the first UIP strategy, while delaying it - until later will yield the last UIP strategy, both of which are valid. + until later will yield other strategies, both of which are valid. \end{itemize} \begin{figure} @@ -169,6 +175,10 @@ depending on the current state: \DP{} & $\neg a \in D$ \\ \\ + \end{tabular} + \end{center} + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} % BackJump \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_d \top :: t', C)$} \LLc{Backjump} @@ -176,7 +186,7 @@ depending on the current state: \DP{} & \begin{tabular}{l} $\text{is\_uip}(C)$ \\ - $d = \text{uip\_level}(C)$ \\ + $d \leq \text{uip\_level}(C)$ \\ \end{tabular} \\ \\ \end{tabular} @@ -192,7 +202,7 @@ depending on the current state: \DP{} & \begin{tabular}{l} $\mathcal{T} \vdash C$ \\ - $\forall a \in C, \neg a \in t$ \\ + $\forall a \in C. \neg a \in t$ \\ \end{tabular} \\ \\ \end{tabular} @@ -224,49 +234,61 @@ The following invariants are maintained by the inference rules in Figure~\ref{fi \begin{description} \item[Trail Soundness] In $\text{Solve}(\mathbb{S}, t)$, if $a \in t$ then $\neg a \notin t$ \item[Conflict Analysis] In $\text{Analyze}(\mathbb{S}, t, C)$, $C$ is a clause implied by the - clauses in $\mathbb{S}$, and $\forall a \in C, \neg a \in t$ (i.e $C$ is entailed, yet false - in the partial model formed by the trail $t$). + clauses in $\mathbb{S}$, and $\forall a \in C. \neg a \in t$ (i.e.~$C$ is entailed by the + hypotheses, yet false in the partial model formed by the trail $t$). \item[Equivalence] In any rule \AXC{$s_1$}\UIC{$s_2$}\DP{}, the set of hypotheses (usually written $\mathbb{S}$) in $s_1$ is equivalent to that of $s_2$. \end{description} These invariants are relatively easy to prove, and provide an easy proof of correctness for -the \sat{} algorithm. Termination can be proved by observing that the same trail appears +the \cdcl{} algorithm. Termination can be proved by observing that the same trail appears at most twice during proof search (once during propagation, and eventually a second time right after backjumping\footnote{This could be avoided by making the \irule{Backjump} rule -directly propagate the relevant litteral of the conflict clause, but it needlessly +directly propagate the relevant literal of the conflict clause, but it needlessly complicates the rule.}). Correctness and termination implies completeness of the \sat{} algorithm. -\section{\smt{} solver architecture} +\section{\smt{} solver architecture}\label{sec:smt} -\subsection{Idea} +\subsection{Idea}\label{sec:smt_flow} -We can represent a simplified version of the information flow (not taking into -account backtracking) of usual SMT Solvers, using the graph in fig~\ref{fig:smt_flow}. In a \smt{} solver, after each propagation and decision, the solver sends the newly assigned literals to the theory. The theory then has the possibility to declare the current set of literals incoherent, and give the solver a tautology in which all literals are currently assigned to $\bot$\footnote{or rather for each literal, its negation is assigned to $\top$}, thus prompting the solver to backtrack. +We can represent a simplified version of the information flow (not taking into +account backtracking) of usual \smt{} Solvers, using the graph in fig~\ref{fig:smt_flow}. + +Contrary to what the Figure~\ref{fig:smt_flow} could suggest, it is not impossible +for the theory to propagate information back to the \sat{} solver. Indeed, +some \smt{} solvers already allow the theory to propagate entailed literals back to the +\sat{} solver. However, these propagations are in practice limited by the complexity +of deciding entailment. Moreover, procedures in a \smt{} solver should be incremental +in order to get decent performances, and deciding entailment in an incremental manner +is not easy (TODO~: ref nécessaire). Doing efficient, incremental entailment is exactly +what \mcsat{} allows (see Section~\ref{sec:mcsat}). \subsection{Formalization and Theory requirements} -An \smt{} solver is the combinaison of a \sat{} solver, and a theory $\mathcal{T}$. +An \smt{} solver is the combination of a \sat{} solver, and a theory $\mathcal{T}$. The role of the theory $\mathcal{T}$ is to stop the proof search as soon as the trail -of the \sat{} solver is inconsistent. Thus, we can add the \irule{Conflict-Theory} rule -to the \sat{} ifnerence rules in order to get a \smt{} solver. We give a slightly lower -precedence than the \irule{Conflict} rule for performance reason (detecting boolean -conflict is faster than theory specifi conflicts). +of the \sat{} solver is inconsistent. A trail is inconsistent iff there exists a clause +$C$, which is a tautology of $\mathcal{T}$ (thus $\mathcal{T} \vdash C$), but is not +satisfied in the current trail (each of its literals has either been decided or +propagated to false). Thus, we can add the \irule{Conflict-Theory} rule (see +Figure~\ref{fig:rules}) to the \cdcl{} inference rules in order to get a \smt{} solver. +We give the \irule{Conflict-Theory} rule a slightly lower precedence than the +\irule{Conflict} rule for performance reason (detecting boolean conflict is +faster than theory specific conflicts). -So, what is the minimum that a theory must implement to be used in a \smt{} solver~? -Given its precedence, all a theory has to do in a \smt{} sovler, is to ensure that -the current trail is consistent (when seens as a conjunction of literals). This -reflects the fact that the \sat{} core takes care of the purely propositional content -of the input problem, and leaves the theory specific reasoning to the theory, which -then does not have to deal with propositional content such as disjunction. The theory, -however, must have a global reasoning to ensure that the whole trail is consistent. +So, what is the minimum that a theory must implement in practice to be used in a +\smt{} solver~? The theory has to ensure that the current trail is consistent +(when seen as a conjunction of literals), that is to say, given a trail $t$, +it must ensure that there exists a model $\mathcal{M}$ of $\mathcal{T} $so that +$\forall a \in t. \mathcal{M} \vDash a$, or if it is impossible (i.e.~the trail +is inconsistent) produce a conflict. \begin{figure} \begin{center} @@ -296,33 +318,33 @@ however, must have a global reasoning to ensure that the whole trail is consiste \end{tikzpicture} \end{center} - \caption{Simplified SMT Solver architecture}\label{fig:smt_flow} + \caption{Simplified \smt{} Solver architecture}\label{fig:smt_flow} \end{figure} +\section{\mcsat{}: An extension of \smt{} Solvers}\label{sec:mcsat} +\subsection{Motivation and idea} -\section{McSat: An extension of SMT Solvers} - -\subsection{Introduction} - - -Mcsat is an extension of usual SMT solvers, introduced in~\cite{VMCAI13} and~\cite{FMCAD13}. -In usual SMT Solvers, interaction between the core SAT Solver and the Theory is pretty limited~: -the SAT Solver make boolean decision, and sends them to the theory, whose role is in return to -stop the SAT Solver as soon as the current set of assumptions is incoherent. This means -that the information that theories can give the SAT Solver is pretty limited, and furthermore -it limits the ability of theories to guide the proof search. +\mcsat{} is an extension of usual \smt{} solvers, introduced in~\cite{VMCAI13} and~\cite{FMCAD13}. +In usual \smt{} Solvers, interaction between the core SAT Solver and the Theory is pretty limited~: +the SAT Solver make boolean decisions and propagations, and sends them to the theory, +whose role is in return to stop the SAT Solver as soon as the current set of assumptions +is incoherent. This means that the information that theories can give the SAT Solver is +pretty limited, and furthermore it heavily restricts the ability of theories to guide +the proof search (see Section~\ref{sec:smt_flow}). While it appears to leave a reasonably simple job to the theory, since it completely hides the propositional structure of the problem, this simple interaction between the SAT Solver and the theory makes it harder to combine multiple theories into one. Usual -techniques for combining theories in SMT solvers typically require to keep track of -equality congruence classes and require of theories to propagate any equality they discover. +techniques for combining theories in \smt{} solvers typically require to keep track of +equivalence classes (with respect to the congruence closure) and for instance +in the Nelson-Oppen method for combining theories (TODO~: ref nécessaire) require of +theories to propagate any equality implied by the current assertions. -McSat extends the SAT paradigm by allowing more exchange of information between the theory +\mcsat{} extends the SAT paradigm by allowing more exchange of information between the theory and the SAT Solver. This is achieved by allowing the solver to not only decide on the truth value of atomic propositions, but also to decide assignments for terms that appear in the problem. -For instance, if the SAT Solver assumes a formula $x = 0$, +For instance, if the SAT Solver assigns a variable $x$ to $0$, an arithmetic theory could propagate to the SAT Solver that the formula $x < 1$ must also hold, instead of waiting for the SAT Solver to guess the truth value of $x < 1$ and then inform the SAT Solver that the conjunction~: $x = 0 \land \neg x < 1$ is incoherent. @@ -331,16 +353,17 @@ This exchange of information between the SAT Solver and the theories results in the construction of a model throughout the proof search (which explains the name Model Constructing SAT). -The main addition of McSat is that when the solver makes a decision, instead of +The main addition of \mcsat{} is that when the solver makes a decision, instead of being restricted to making boolean assignment of formulas, the solver now can decide to assign a value to a term belonging to one of the literals. In order to do so, the solver first chooses a term that has not yet been assigned, and then asks -the theory for a possible assignment. Like in usual SMT Solvers, a McSat solver +the theory for a possible assignment. Like in usual SMT Solvers, a \mcsat{} solver only exchange information with one theory, but, as we will see, combination -of theories into one becomes easier in this framework. +of theories into one becomes easier in this framework, because assignments are +actually a very good way to exchange information. -Using the assignments on terms, the theory can very easily do efficient -propagation of formulas implied by the current assignments: is suffices to +Using the assignments on terms, the theory can then very easily do efficient +propagation of formulas implied by the current assignments: it is enough to evaluate formulas using the current partial assignment. The information flow then looks like fig~\ref{fig:mcsat_flow}. @@ -377,13 +400,13 @@ The information flow then looks like fig~\ref{fig:mcsat_flow}. \end{tikzpicture} \end{center} - \caption{Simplified McSat Solver architecture}\label{fig:mcsat_flow} + \caption{Simplified \mcsat{} Solver architecture}\label{fig:mcsat_flow} \end{figure} \subsection{Decisions and propagations} -In this document, semantic propagations are a bit different from the propagations -used in traditional SMT Solvers. In the case of McSat (or at least the version presented here), +In \mcsat{}, semantic propagations are a bit different from the propagations +used in traditional \smt{} Solvers. In the case of \mcsat{} (or at least the version presented here), semantic propagations strictly correspond to the evaluation of formulas in the current assignment. Moreover, in order to be able to correctly handle these semantic propagations during backtrack, they are assigned a level: each decision is given a level @@ -391,74 +414,82 @@ propagations during backtrack, they are assigned a level: each decision is given previous to it, plus one), and a formula is propagated at the maximum level of the decisions used to evaluate it. +We can thus extend the notations introduced in Section~\ref{sec:trail}: $t \mapsto_n v$ is +a semantic decision which assign $t$ to a concrete value $v$, $a \leadsto_n \top$ is a +semantic propagation at level $n$. + For instance, if the current trail is $\{x \mapsto_1 0, x + y + z = 0 \mapsto_2 \top, y\mapsto_3 0\}$, -then $x + y = 0$ can be propagated at level $3$, but $z = 0$ can not be propagated (at least not -given to the sat solver, however nothing prevents the theory from propagating and using it internally). -\subsection{First order terms} +then $x + y = 0$ can be propagated at level $3$, but $z = 0$ can not be propagated, because +$z$ is not assigned yet, even if there is only one remaining valid value for $z$. +The problem with assignments as propagations is that it is not clear what to do with +them during the $\text{Analyze}$ phase of the solver, see later. + +\subsection{First order terms \& Models} + +A model traditionally is a triplet which comprises a domain, a signature and an interpretation +function. Since most problems define their signature using type definitions at the beginning, and +built-in theories such as arithmetic usually have canonic domain and signature, +we will consider in the following that the domain $\mathbb{D}$ and signature are given (and constant). +Additionally, we consider a fixed interpretation of the theory-defined symbols (which +usually does along with the domain). In the following, we use the following notations: \begin{itemize} - \item $\mathbb{V}$ is an infinite set of variables - \item $\mathbb{C}$ is a possibly infinite set of constants defined - by a problem's logic\footnote{For instance, the theory of arithmetic - defines the usual operators $+, -, *, /$ as well as the constants - $0, -5, \frac{1}{2}, -2.3, \ldots$} - \item $\mathbb{S}$ is a finite set of constants defined by a problem's type definitions - \item $\mathbb{T}(\mathbb{X})$ for the (infinite) set of first-order terms over $\mathbb{X}$ - (for instance $a, f(0), x + y, \ldots$) - \item $\mathbb{F}(\mathbb{T})$ for the (infinite) set of first order quantified formulas - over the terms in $\mathbb{T}$ + \item $\mathbb{V}$ is an infinite set of variables; + \item $\mathbb{C}$ is the possibly infinite set of constants defined + by the input problem's theories\footnote{For instance, the theory of arithmetic + defines the usual operators $+, -, *, /$ as well as $0, -5, \frac{1}{2}, -2.3, \ldots$}; + \item $\mathbb{S}$ is the finite set of constants defined by the input problem's type + definitions; + \item $\mathbb{T}$ is the (infinite) set of first-order terms over $\mathbb{V}$, $\mathbb{C}$ + and $\mathbb{S}$ (for instance $a, f(0), x + y, \ldots$); + \item $\mathbb{F}$ is the (infinite) set of first order quantified formulas + over the terms in $\mathbb{T}$. \end{itemize} -\subsection{Models} - -A model traditionally is a triplet which comprises a domain, a signature and an interpretation function. -Most problems define their signature using type definitions, and builtin theories such as arithmetic -usually have canonic models, so in the following we consider the domain and siganture constant, and -talk about the interpretation, more specifically, about the interpretation of symbols not defined -by the theory\footnote{Since theory-defined symbols, such as addition, already have an intepretation -in the canonical domain.}, i.e non-interpreted functions. An intepretation $\mathcal{I}$ can easily -be extended to a function from ground terms to model value by recursively applying it: +We are therefore interested in finding an interpretation of a problem, and more +specifically an interpretation of the symbols in $\mathbb{S}$ not defined by +the theory, i.e.~non-interpreted functions. An interpretation +$\mathcal{I}$ can easily be extended to a function from ground terms and formulas +to model value by recursively applying it: \[ - \mathcal{I}( f ( {(e_i)}_{1\leq i \leq n})) = \mathcal{I}_f ( {( \mathcal{I}(e_i) )}_{1 \leq i \leq n} ) + \mathcal{I}( f ( e_1, \ldots, e_n ) ) = + \mathcal{I}_f ( \mathcal{I}(e_1), \ldots, \mathcal{I}(e_n) ) \] -Before formalizing the SAT, SMT and McSat algorithms as inference rules, we need to formalize the notion -of partial interpretation. Indeed, during the proof search, the McSat algorithm maintains a partial mapping from -expressions to model values. The intention of this mapping is to represent a partial interpretation of the input -problem, so that if the mapping is complete (i.e all variables are assigned), then it directly gives an interpretation -of the input problem (quantified formula notwithstanding). +\paragraph{Partial Interpretation} +The goal of \mcsat{} is to construct a first-order model of the input formulas. To do so, +it has to build what we will call partial interpretations: intuitively, a partial +interpretation is a partial function from the constants symbols to the model values. +It is, however, not so simple: during proof search, the \mcsat{} algorithm maintains +a partial mapping from expressions to model values (and not from constant symbols +to model values). The intention of this mapping is to represent a set of constraints +on the partial interpretation that the algorithm is building. +For instance, given a function symbol $f$ of type $(\text{int} \rightarrow \text{int})$ and an +integer constant $a$, one such constraint that we would like to be able to express in +our mapping is the following: $f(a) \mapsto 0$, regardless of the values that $f$ takes on +other argument, and also regardless of the value mapped to $a$. To that end we introduce +the notion of abstract partial interpretation. -More than simply an incomplete interpretation, we also want to be able to give partial function (instead of complete functions) as interpretation of -constants with positive arity. And even further, we'd like to specify these partial interpretations in a somewhat -abstract way, using mappings from expressions to model values instead of a function from model values to model -values. For instance, given a function symbol $f$ of type $\text{int} \rightarrow \text{int}$ and an integer constant $a$, we'd like to specify that in our mapping, -$f(a) \mapsto 0$, regardless of the values that $f$ takes on other argument, and also regardless -of the value mapped to $a$. To that end we introduce a notion of abstract partial interpretation. - -An abstract partial interpretation $\sigma$ is a mapping from ground expressions to model values. To each abstract partial -interpretation correspond a set of complete models that realize it. More precisely, any mapping $\sigma$ can be completed -in various ways, leading to a set of potential interpretations: +An abstract partial interpretation $\sigma$ is a mapping from ground expressions to model values. +To each abstract partial interpretation correspond a set of complete models that realize it. +More precisely, any mapping $\sigma$ can be completed in various ways, leading to a set of +potential interpretations: \[ \text{Complete}(\sigma) = \left\{ \mathcal{I} \; | \; - \forall f( {(e_i)}_{1 \leq i \leq n} ) \mapsto v \in \sigma , - \mathcal{I}_f ( {( \mathcal{I}(e_i) )}_{1 \leq i \leq n} ) = v + \forall t \mapsto v \in \sigma , \mathcal{I} ( t ) = v \right\} \] -We can then consider that the natural interpretation corresponding to a given mapping is the -partial interpretation on which all completion of the mapping agrees, i.e the intersection of -all potential candidates: -\[ - \sigma_\mathcal{I} = \bigcap_{ \mathcal{I} \in \text{Complete}(\sigma) } \mathcal{I} -\] - -Of course, it might happen that a mapping does not admit any potential interpretation, -and thus has no natural interpretation, for instance there is no possible completion of the -following mapping: +\paragraph{Coherence} +An abstract partial interpretation $\sigma$ is said to be coherent iff +there exists at least one model that completes it, +i.e.~$\text{Complete}(\sigma) \neq \emptyset$. One example +of incoherent abstract partial interpretation is the following +mapping: \[ \sigma = \left\{ \begin{matrix} @@ -470,39 +501,49 @@ following mapping: \right. \] +\paragraph{Compatibility} +In order to do semantic propagations, we want to have some kind of notion +of evaluation for abstract partial interpretations, and we thus define the +partial interpretation function in the following way: +\[ + \forall t \in \mathbb{T} \cup \mathbb{F}. \forall v \in \mathbb{D}. + \left( + \forall \mathcal{I} \in \text{Complete}(\sigma). + \mathcal{I}(t) = v + \right) \rightarrow + \sigma(t) = v +\] -\subsection{Expected theory invariants} +The partial interpretation function is the intersection of the interpretation +functions of all the completions of $\sigma$, i.e.~it is the interpretation +where all completions agree. We can now say that a mapping $\sigma$ is compatible +with a trail $t$ iff $\sigma$ is coherent, and +$\forall a \in t. \not (\sigma(a) = \bot)$, or in other words, for every literal $a$ +true in the trail, there exists at least one model that completes $\sigma$ and where +$a$ is satisfied. -TODO: rewrite this section. +\paragraph{Completeness} +We need one last property on abstract partial interpretations, which is to +specify the relation between the terms in a mapping, and the terms it can evaluate, +according to its partial interpretation function defined above. Indeed, at the end +of proof search, we want all terms (and sub-terms) of the initial problem to be +evaluated using the final mapping returned by the algorithm when it finds that the +problem is satisfiable: that is what we will call completeness of a mapping. +To that end we will here enumerate some sufficient conditions on the mapping domain +$\text{Dom}(\sigma)$ compared to the finite set of terms (and sub-terms) $T$ that +appear in the problem. -During proof search are maintained a set of assertions $\mathcal{S}$ -and a partial assignment $\sigma$ as a partial function from $\mathbb{T}(\mathbb{V, C, S})$ -to $\mathbb{T}(\mathbb{C})$. $\sigma$ is easily extended to a complete substitution function of -$\mathbb{T}(\mathbb{V, C, S})$. +A first way, is to have $\text{Dom}(\sigma) = T$, i.e.~all terms (and sub-terms) of the +initial problem are present in the mapping. While this is the simplest way to ensure that +the mapping is complete, it might be a bit heavy: for instance, we might have to assign +both $x$ and $2x$, which is redundant. The problem in that case is that we try and assign +a term for which we could actually compute the value from its arguments: indeed, +since the multiplication is interpreted, we do not need to interpret it in our mapping. +This leads to another way to have a complete mapping: if $\text{Dom}(\sigma)$ is the +set of terms of $T$ whose head symbol is uninterpreted (i.e.~not defined by the theory), +it is enough to ensure that the mapping is complete, because the theory will automatically +constrain the value of terms whose head symbol is interpreted. -We say that $\sigma$ is compatible with $\mathcal{S}$ iff for every $\varphi \in \mathcal{S}$, -$\varphi\sigma$ is satisfiable (independently from the rest of the formulas in $\mathcal{S}$). -Intuitively, this represents the fact that the substitution $\sigma$ does not imply any -ground contradictions. - -A theory then has to ensure that for every expression $e \in \mathbb{T}(\mathbb{V,C,S})$ -there exists $v \in \mathbb{T}(\mathbb{C})$ such that $\sigma' = \sigma \cup \{ e \rightarrow v \}$ -is coherent, and compatible with $\mathcal{S}$\footnote{Note that in particular, this implies -that $\sigma$ is coherent with $\mathcal{S}$}. As soon as the current assignment is not coherent, -compatible with the current assertions, or that there is a term $e$ with no viable assignment, the theory -should inform the SAT Solver to backtrack, since the current branch is clearly not satisfiable. -If we reach the point where all expressions of the problem have been assigned, then we -have a ground model for the current set of assertions, which is then also a model -of the input problem. - -Of interest if the fact that theories that respect this invariant can easily be combined -to create a theory that also respect this invariant, as long as for any expression $e$, -there is exactly one theory responsible for finding an assignment for $e$\footnote{this -is similar to the usual criterion for combining SMT theories which is that they do not -share symbols other than equality.}. - - -\clearpage \bibliographystyle{plain} \bibliography{biblio} From 64af6363418431df21f1634f7602ca82b871a2aa Mon Sep 17 00:00:00 2001 From: Guillaume Bury 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We can now formalize the \cdcl{} algorithm using the inference rules -in Figure~\ref{fig:rules}. In order to completely recover the \sat{} algorithm, +in Figure~\ref{fig:smt_rules}. In order to completely recover the \sat{} algorithm, one must apply the rules with the following precedence and termination conditions, depending on the current state: \begin{itemize} @@ -153,7 +153,7 @@ depending on the current state: \end{tabular} \end{center} \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} + \begin{tabular}{c@{\hspace{.5cm}}l} % Analyze (propagation) \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} \LLc{Analyze-propagation} @@ -197,7 +197,7 @@ depending on the current state: \begin{tabular}{c@{\hspace{1cm}}l} % Conflict (theory) \AXC{$\text{Solve}(\mathbb{S}, t)$} - \LLc{Conflict-Theory} + \LLc{Conflict-Smt} \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} \DP{} & \begin{tabular}{l} @@ -207,30 +207,79 @@ depending on the current state: \\ \\ \end{tabular} \end{center} + \caption{Inference rules for \sat{} and \smt{}}\label{fig:smt_rules} +\end{figure} +\begin{figure} \center{\underline{\mcsat{}}} \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} + \begin{tabular}{c@{\hspace{.2cm}}l} % Decide (assignment) \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Theory-Decide} \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n v)$} \DP{} & - $a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ + \begin{tabular}{l} + $a \mapsto_k \_ \notin t$ \\ + $n = \text{max\_level}(t) + 1$ \\ + $\sigma_{t :: a \mapsto_n v} \text{ compatible with } t$ + \end{tabular} \\ \\ % Propagation (semantic) \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Propagate-Theory} \UIC{$\text{Solve}(\mathbb{S}, t :: a \leadsto_n \top)$} \DP{} & - $ $ + $\sigma_t(a) = \top$ + \\ \\ + % Conflict (semantic) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Conflict-Mcsat} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + \begin{tabular}{l} + $\mathcal{T} \vdash C$ \\ + $\forall a \in C, \neg a \in t \lor \sigma_t(a) = \bot$ + \end{tabular} \\ \\ \end{tabular} \end{center} - \caption{Inference rules}\label{fig:rules} + \begin{center} + \begin{tabular}{c@{\hspace{.2cm}}l} + % Analyze (assign) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_n v, C)$} + \LLc{Analyze-Assign} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + \\ \\ + % Analyze (semantic) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_n \top, C)$} + \LLc{Analyze-Semantic} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + \\ \\ + \end{tabular} + \end{center} + \begin{center} + \begin{tabular}{c@{\hspace{.2cm}}l} + % Backjump (semantic) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_n \_ :: \_, C)$} + \LLc{Backjump-Semantic} + \UIC{$\text{Solve}(\mathbb{S}, t)$} + \DP{} & + \begin{tabular}{l} + $\text{is\_semantic}(C)$ \\ + $n = \text{slevel}(C)$ \\ + \end{tabular} + \\ \\ + \end{tabular} + \end{center} + \caption{\mcsat{} specific inference rules}\label{fig:mcsat_rules} \end{figure} \subsection{Invariants, correctness and completeness} -The following invariants are maintained by the inference rules in Figure~\ref{fig:rules}: +The following invariants are maintained by the inference rules in Figure~\ref{fig:smt_rules}: \begin{description} \item[Trail Soundness] In $\text{Solve}(\mathbb{S}, t)$, if $a \in t$ then $\neg a \notin t$ \item[Conflict Analysis] In $\text{Analyze}(\mathbb{S}, t, C)$, $C$ is a clause implied by the @@ -277,9 +326,9 @@ The role of the theory $\mathcal{T}$ is to stop the proof search as soon as the of the \sat{} solver is inconsistent. A trail is inconsistent iff there exists a clause $C$, which is a tautology of $\mathcal{T}$ (thus $\mathcal{T} \vdash C$), but is not satisfied in the current trail (each of its literals has either been decided or -propagated to false). Thus, we can add the \irule{Conflict-Theory} rule (see -Figure~\ref{fig:rules}) to the \cdcl{} inference rules in order to get a \smt{} solver. -We give the \irule{Conflict-Theory} rule a slightly lower precedence than the +propagated to false). Thus, we can add the \irule{Conflict-Smt} rule (see +Figure~\ref{fig:smt_rules}) to the \cdcl{} inference rules in order to get a \smt{} solver. +We give the \irule{Conflict-Smt} rule a slightly lower precedence than the \irule{Conflict} rule for performance reason (detecting boolean conflict is faster than theory specific conflicts). @@ -544,6 +593,13 @@ set of terms of $T$ whose head symbol is uninterpreted (i.e.~not defined by the it is enough to ensure that the mapping is complete, because the theory will automatically constrain the value of terms whose head symbol is interpreted. +\subsection{Inference rules} + +In \mcsat{}, a trail $t$ contains boolean decision and propagations as well as semantic +decisions (assignments) and propagations. We can thus define $\sigma_t$ as the mapping +formed by all assignments in $t$. This lets us define the last rules in Figure~\ref{fig:mcsat_rules}, +that, together with the other rules, define the \mcsat{} algorithm. + \bibliographystyle{plain} \bibliography{biblio} From 66f250a57e60779d295b2819fbe3638a80aa93e1 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Wed, 16 Nov 2016 19:52:26 +0100 Subject: [PATCH 23/25] [travis] Changed ocaml test versions --- .travis.yml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.travis.yml b/.travis.yml index 93b8adb5..6ad16f51 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,10 +1,10 @@ language: c env: - - OCAML_VERSION=4.00.1 - - OCAML_VERSION=4.01.0 - OCAML_VERSION=4.02.3 - OCAML_VERSION=4.03.0 - OCAML_VERSION=4.03.0+flambda + - OCAML_VERSION=4.04.0 + - OCAML_VERSION=4.04.0+flambda addons: apt: sources: From c2887b2e29210f6a9927701308f5e083de66f7b5 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Thu, 17 Nov 2016 00:11:26 +0100 Subject: [PATCH 24/25] [travis] Try and build on old ocaml versions --- .travis.yml | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/.travis.yml b/.travis.yml index 6ad16f51..cf295755 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,10 +1,12 @@ language: c env: - - OCAML_VERSION=4.02.3 - - OCAML_VERSION=4.03.0 - - OCAML_VERSION=4.03.0+flambda - - OCAML_VERSION=4.04.0 - - OCAML_VERSION=4.04.0+flambda + - RUN_TEST=false OCAML_VERSION=4.00.1 + - RUN_TEST=false OCAML_VERSION=4.01.0 + - RUN_TEST=true OCAML_VERSION=4.02.3 + - RUN_TEST=true OCAML_VERSION=4.03.0 + - RUN_TEST=true OCAML_VERSION=4.03.0+flambda + - RUN_TEST=true OCAML_VERSION=4.04.0 + - RUN_TEST=true OCAML_VERSION=4.04.0+flambda addons: apt: sources: @@ -19,8 +21,8 @@ before_install: - opam switch ${OCAML_VERSION} - eval `opam config env` - opam install ocamlfind ocamlbuild - - opam pin add dolmen https://github.com/Gbury/dolmen.git + - if ${RUN_TEST}; then opam pin add dolmen https://github.com/Gbury/dolmen.git; fi install: - make bin lib script: - - make test + - if ${RUN_TEST}; then make test; fi From 7dd04204edcf832d321590fdcb9985d74312295b Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Thu, 17 Nov 2016 00:19:40 +0100 Subject: [PATCH 25/25] [travis] Only build the bin for tests --- .travis.yml | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index cf295755..6256da54 100644 --- a/.travis.yml +++ b/.travis.yml @@ -23,6 +23,7 @@ before_install: - opam install ocamlfind ocamlbuild - if ${RUN_TEST}; then opam pin add dolmen https://github.com/Gbury/dolmen.git; fi install: - - make bin lib + - make lib + - if ${RUN_TEST}; then make bin; fi script: - if ${RUN_TEST}; then make test; fi

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zfgZWyxh*elnblCsviiiSj!#}?SI4L5=2wd=WQ5Hjp3KtG^rI|eXvy)Q<9CVEqqaPJh|%YA|Nc* fRQCUK(4T@KQ>bKa(rIc!HM!L6a&o3NX2O2}oUOhK literal 0 HcmV?d00001 diff --git a/docs/msat.tex b/docs/msat.tex index 0d2a7cd7..c39cca5d 100644 --- a/docs/msat.tex +++ b/docs/msat.tex @@ -7,6 +7,11 @@ \usepackage{amsmath,amssymb} \usepackage{tabularx} \usepackage{pgf, tikz} +\usepackage[margin=4cm]{geometry} + +\usepackage{float} +\floatstyle{boxed} +\restylefloat{figure} \usepackage{listings} \lstset{language=[Objective]caml} @@ -32,50 +37,236 @@ provide a \sat{}, \smt{} or \mcsat{} solver. Given the current state of the art of \smt{} solvers, where most \sat{} solvers are written in C and heavily optimised\footnote{Some solvers now have instructions to manage a processor's cache}, the \msat{} library does not aim to provide solvers -competitive with the existing implementations, but rather a +competitive with the existing implementations, but rather an easy way to create +reasonably eficient solvers. -\section{McSat: An extension of SMT Solvers} +\msat{} currently uses the following techniques: +\begin{itemize} + \item 2-watch literals scheme + \item Activity based decisions + \item Restarts +\end{itemize} -\subsection{Introduction} +Additionally, \msat{} has the following features: +\begin{itemize} + \item Local assumptions + \item Proof/Model output + \item Adding clauses during proof search +\end{itemize} + +\clearpage + +\tableofcontents{} + +\clearpage + +\section{\sat{} Solvers: principles and formalization} + +\subsection{Idea} + +\subsection{Inference rules} + +The SAT algorithm can be formalized as follows. During the search, the solver keeps +a set of clauses, containing the problem hypotheses and the learnt clauses, and +a trail, which is the current ordered list of assumptions and/or decisions made by +the solver. + +Each element in the trail (decision or propagation) has a level, which is the number of decision +appearing in the trail up to (and including) it. So for instance, propagations made before any +decisions have level $0$, and the first decision has level $1$. Propagations are written +$a \leadsto_C \top$, with $C$ the clause that caused the propagation, and decisions +$a \mapsto_n \top$, with $n$ the level of the decision. Trails are read +chronologically from left to right. + +In the following, given a trail $t$ and an atomic formula $a$, we will use the following notation: +$a \in t$ if $a \mapsto_n \top$ or $a \leadsto_C \top$ is in $t$, i.e $a \in t$ is $a$ is true +in the trail $t$. In this context, the negation $\neg$ is supposed to be involutive (i.e $\neg \neg a = a$), +so that, if $a \in t$ then $\neg \neg a = a \in t$. + +The SAT algorithm has two states: first, it starts in the $\text{Solve}$ state, where propagations +and decisions are made, until a conflict is detected, at which point it enters in the $\text{Analyse}$ +state, where it analyzes the conflict, backtracks, and re-enter the $\text{Solve}$ state. +The $\text{Solve}$ state take as argument the set of hypotheses and the trail, while +the $\text{Analyze}$ state also take as argument the current conflict clause. + +We can now formalize the \sat{} algorithm using the inference rules +in Figure~\ref{fig:rules}. In order to completely recover the \sat{} algorithm, +one must apply the rules with the following precedence and termination conditions, +depending on the current state: +\begin{itemize} + \item If the empty clause is in $\mathbb{S}$, then the problem is unsat. + If there is no more rule to apply, the problem is sat. + \item If we are in $\text{Solve}$ mode: + \begin{enumerate} + \item First is the rule \irule{Conflict}; + \item Then the try and use \irule{Propagate}; + \item Finally, is there is nothing left to be propagated, the \irule{Decide} + rule is used. + \end{enumerate} + \item If we are in $\text{Analyze}$ mode, we have a choice concerning + the order of application. First we can observe that the rules + \irule{Analyze-Propagate}, \irule{Analyze-Decision} and \irule{Analyze-Resolution} + can not apply simultaneously, and we will thus group them in a super-rule + \irule{Analyze}. We now have the choice of when to apply the \irule{Backjump} rule + compared to the \irule{Analyze} rule: + using \irule{Backjump} eagerly will result in the first UIP strategy, while delaying it + until later will yield the last UIP strategy, both of which are valid. +\end{itemize} + +\begin{figure} + \center{\underline{\sat{}}} + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Propagation (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Propagate} + \UIC{$\text{Sove}(\mathbb{S}, t :: a \leadsto_C \top)$} + \DP{} & + \begin{tabular}{l} + $a \in C, C \in \mathbb{S}, \neg a \notin t$ \\ + $\forall b \in C. b \neq a \rightarrow \neg b \in t$ \\ + \end{tabular} + \\ \\ + % Decide (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Decide} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n \top)$} + \DP{} & + \begin{tabular}{l} + $a \notin t, \neg a \notin t, a \in \mathbb{S}$ \\ + $n = \text{max\_level}(t) + 1$ \\ + \end{tabular} + \\ \\ + % Conflict (boolean) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Conflict} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + $C \in \mathbb{S}, \forall a \in C. \neg a \in t$ + \\ \\ + \end{tabular} + \end{center} + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Analyze (propagation) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} + \LLc{Analyze-propagation} + \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} + \DP{} & + $\neg a \notin D$ + \\ \\ + % Analyze (decision) + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_n \top, D)$} + \LLc{Analyze-decision} + \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} + \DP{} & + $\neg a \notin D$ + \\ \\ + % Resolution + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} + \LLc{Analyze-Resolution} + \UIC{$\text{Analyze}(\mathbb{S}, t, (C - \{a\}) \cup (D - \{ \neg a\}))$} + \DP{} & + $\neg a \in D$ + \\ \\ + % BackJump + \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_d \top :: t', C)$} + \LLc{Backjump} + \UIC{$\text{Solve}(\mathbb{S} \cup \{ C \}, t)$} + \DP{} & + \begin{tabular}{l} + $\text{is\_uip}(C)$ \\ + $d = \text{uip\_level}(C)$ \\ + \end{tabular} + \\ \\ + \end{tabular} + \end{center} + + \center{\underline{\smt{}}} + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Conflict (theory) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \LLc{Conflict-Theory} + \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} + \DP{} & + \begin{tabular}{l} + $\mathcal{T} \vdash C$ \\ + $\forall a \in C, \neg a \in t$ \\ + \end{tabular} + \\ \\ + \end{tabular} + \end{center} + + \center{\underline{\mcsat{}}} + \begin{center} + \begin{tabular}{c@{\hspace{1cm}}l} + % Decide (assignment) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n v)$} + \DP{} & + $a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ + \\ \\ + % Propagation (semantic) + \AXC{$\text{Solve}(\mathbb{S}, t)$} + \UIC{$\text{Solve}(\mathbb{S}, t :: a \leadsto_n \top)$} + \DP{} & + $ $ + \\ \\ + \end{tabular} + \end{center} + \caption{Inference rules}\label{fig:rules} +\end{figure} + +\subsection{Invariants, correctness and completeness} + +The following invariants are maintained by the inference rules in Figure~\ref{fig:rules}: +\begin{description} + \item[Trail Soundness] In $\text{Solve}(\mathbb{S}, t)$, if $a \in t$ then $\neg a \notin t$ + \item[Conflict Analysis] In $\text{Analyze}(\mathbb{S}, t, C)$, $C$ is a clause implied by the + clauses in $\mathbb{S}$, and $\forall a \in C, \neg a \in t$ (i.e $C$ is entailed, yet false + in the partial model formed by the trail $t$). + \item[Equivalence] In any rule \AXC{$s_1$}\UIC{$s_2$}\DP{}, the set of hypotheses + (usually written $\mathbb{S}$) in $s_1$ is equivalent to that of $s_2$. +\end{description} + +These invariants are relatively easy to prove, and provide an easy proof of correctness for +the \sat{} algorithm. Termination can be proved by observing that the same trail appears +at most twice during proof search (once during propagation, and eventually a second time +right after backjumping\footnote{This could be avoided by making the \irule{Backjump} rule +directly propagate the relevant litteral of the conflict clause, but it needlessly +complicates the rule.}). Correctness and termination implies completeness of the \sat{} +algorithm. -Mcsat is an extension of usual SMT solvers, introduced in~\cite{VMCAI13} and~\cite{FMCAD13}. -In usual SMT Solvers, interaction between the core SAT Solver and the Theory is pretty limited~: -the SAT Solver make boolean decision, and sends them to the theory, whose role is in return to -stop the SAT Solver as soon as the current set of assumptions is incoherent. This means -that the information that theories can give the SAT Solver is pretty limited, and furthermore -it limits the ability of theories to guide the proof search. +\section{\smt{} solver architecture} -While it appears to leave a reasonably simple job to the theory, since it completely -hides the propositional structure of the problem, this simple interaction between the -SAT Solver and the theory makes it harder to combine multiple theories into one. Usual -techniques for combining theories in SMT solvers typically require to keep track of -equality congruence classes and require of theories to propagate any equality they discover. - -McSat extends the SAT paradigm by allowing more exchange of information between the theory -and the SAT Solver. This is achieved by allowing the solver to not only decide on the truth value -of atomic propositions, but also to decide assignments for terms that appear in the problem. -For instance, if the SAT Solver assumes a formula $x = 0$, -an arithmetic theory could propagate to the SAT Solver that the formula $x < 1$ must also hold, -instead of waiting for the SAT Solver to guess the truth value of $x < 1$ and then -inform the SAT Solver that the conjunction~: $x = 0 \land \neg x < 1$ is incoherent. - -This exchange of information between the SAT Solver and the theories results in -the construction of a model throughout the proof search (which explains the name -Model Constructing SAT). - -\subsection{SMT Solver architecture} +\subsection{Idea} We can represent a simplified version of the information flow (not taking into account backtracking) of usual SMT Solvers, using the graph in fig~\ref{fig:smt_flow}. -In a pure Sat solver, the solver starts by doing -boolean propagation until no more literal can be propagated, at which point it -makes a decision and assign a truth value to a literal not yet assigned. It then -loops to its starting point and does boolean propagation. In an SMT solver, -after each propagation and decision, the solver sends the newly assigned literals -to the theory. The theory then has the possibility to declare the current set of -literals incoherent, and give the solver a tautology in which all literals are currently -assigned to $\bot$, thus prompting the solver to backtrack. +In a \smt{} solver, after each propagation and decision, the solver sends the newly +assigned literals to the theory. The theory then has the possibility to declare the +current set of literals incoherent, and give the solver a tautology in which all +literals are currently assigned to $\bot$\footnote{or rather for each literal, its negation +is assigned to $\top$}, thus prompting the solver to backtrack. + +\subsection{Formalization and Theory requirements} + +An \smt{} solver is the combinaison of a \sat{} solver, and a theory $\mathcal{T}$. +The role of the theory $\mathcal{T}$ is to stop the proof search as soon as the trail +of the \sat{} solver is inconsistent. Thus, we can add the \irule{Conflict-Theory} rule +to the \sat{} ifnerence rules in order to get a \smt{} solver. We give a slightly lower +precedence than the \irule{Conflict} rule for performance reason (detecting boolean +conflict is faster than theory specifi conflicts). + +So, what is the minimum that a theory must implement to be used in a \smt{} solver~? +Given its precedence, all a theory has to do in a \smt{} sovler, is to ensure that +the current trail is consistent (when seens as a conjunction of literals). This +reflects the fact that the \sat{} core takes care of the purely propositional content +of the input problem, and leaves the theory specific reasoning to the theory, which +then does not have to deal with propositional content such as disjunction. The theory, +however, must have a global reasoning to ensure that the whole trail is consistent. \begin{figure} \begin{center} @@ -108,6 +299,38 @@ assigned to $\bot$, thus prompting the solver to backtrack. \caption{Simplified SMT Solver architecture}\label{fig:smt_flow} \end{figure} + + +\section{McSat: An extension of SMT Solvers} + +\subsection{Introduction} + + +Mcsat is an extension of usual SMT solvers, introduced in~\cite{VMCAI13} and~\cite{FMCAD13}. +In usual SMT Solvers, interaction between the core SAT Solver and the Theory is pretty limited~: +the SAT Solver make boolean decision, and sends them to the theory, whose role is in return to +stop the SAT Solver as soon as the current set of assumptions is incoherent. This means +that the information that theories can give the SAT Solver is pretty limited, and furthermore +it limits the ability of theories to guide the proof search. + +While it appears to leave a reasonably simple job to the theory, since it completely +hides the propositional structure of the problem, this simple interaction between the +SAT Solver and the theory makes it harder to combine multiple theories into one. Usual +techniques for combining theories in SMT solvers typically require to keep track of +equality congruence classes and require of theories to propagate any equality they discover. + +McSat extends the SAT paradigm by allowing more exchange of information between the theory +and the SAT Solver. This is achieved by allowing the solver to not only decide on the truth value +of atomic propositions, but also to decide assignments for terms that appear in the problem. +For instance, if the SAT Solver assumes a formula $x = 0$, +an arithmetic theory could propagate to the SAT Solver that the formula $x < 1$ must also hold, +instead of waiting for the SAT Solver to guess the truth value of $x < 1$ and then +inform the SAT Solver that the conjunction~: $x = 0 \land \neg x < 1$ is incoherent. + +This exchange of information between the SAT Solver and the theories results in +the construction of a model throughout the proof search (which explains the name +Model Constructing SAT). + The main addition of McSat is that when the solver makes a decision, instead of being restricted to making boolean assignment of formulas, the solver now can decide to assign a value to a term belonging to one of the literals. In order to do so, @@ -117,9 +340,9 @@ only exchange information with one theory, but, as we will see, combination of theories into one becomes easier in this framework. Using the assignments on terms, the theory can very easily do efficient -propagation of formulas implied by the current assignments. +propagation of formulas implied by the current assignments: is suffices to +evaluate formulas using the current partial assignment. The information flow then looks like fig~\ref{fig:mcsat_flow}. -For a more detailed presentation, see~\cite{FMCAD13} and~\cite{VMCAI13}. \begin{figure} \begin{center} @@ -164,50 +387,13 @@ used in traditional SMT Solvers. In the case of McSat (or at least the version p semantic propagations strictly correspond to the evaluation of formulas in the current assignment. Moreover, in order to be able to correctly handle these semantic propagations during backtrack, they are assigned a level: each decision is given a level -(typically, it is the number of previous decisions in in the scope when a decision is made), -and a formula is propagated at the maximum level of decision used to evaluate it. +(using the same process as in a \sat{} solvers: a decision level is the number of decision +previous to it, plus one), and a formula is propagated at the maximum level of the decisions +used to evaluate it. For instance, if the current trail is $\{x \mapsto_1 0, x + y + z = 0 \mapsto_2 \top, y\mapsto_3 0\}$, then $x + y = 0$ can be propagated at level $3$, but $z = 0$ can not be propagated (at least not given to the sat solver, however nothing prevents the theory from propagating and using it internally). - -\subsection{Algorithm formalization} - -\subsubsection{SAT} - -The SAT algorithm can be formalized as follows. During the search, the solver keeps -a set of clauses, containing the problem hypotheses and the learnt clauses, and -a trail, which is the current ordered list of assumptions and/or decisions made by -the solver. - -Each element in the trail (decision or propagation) has a level, which is the number of decision -appearing in the trail up to (and including) it. So for instance, propagations made before any -decisions have level $0$, and the first decision has level $1$. Propagations are written -$a \leadsto_C \top$, with $C$ the clause that caused the propagation, and decisions -$a \mapsto_n \top$, with $n$ the level of the decision. Trails are read -chronologically from left to right. - -In the following, given a trail $t$ and an atomic formula $a$, we will use the following notation: -$a \in t$ if $a \mapsto_n \top$ or $a \leadsto_C \top$ is in $t$, i.e $a\ in t$ is $a$ is true -in the trail $t$. In this context, the negation $\neg$ is supposed to be involutive (i.e $\neg \neg a = a$), -so that, if $a \in t$ then $\neg \neg a = a \in t$. - -The SAT algorithm has two states: first, it starts in the $\text{Solve}$ state, where propagations -and decisions are made, until a conflict is detected, at which point it enters in the $\text{Analyse}$ -state, where it analyzes the conflict, backtracks, and re-enter the $\text{Solve}$ state. -The $\text{Solve}$ state take as argument the set of hypotheses and the trail, while -the $\text{Analyze}$ state also take as argument the current conflict clause. - -The following invariants are maintained by the transition system: -\begin{description} - \item[Equivalence] During transitions between states $s_1$ and $s_2$, the set of hypotheses - (usually written $\mathbb{S}$) in $s_1$ is equivalent to that of $s_2$. - \item[Trail Soundness] In $\text{Solve}(\mathbb{S}, t)$, if $a \in t$ then $\neg a \notin t$ - \item[Conflict Analysis] In $\text{Analyze}(\mathbb{S}, t, C)$, $C$ is a clause implied by the - clauses in $\mathbb{S}$, and $\forall a \in C, \neg a \in t$ (i.e $C$ is entailed, yet false - in the partial model formed by the trail $t$). -\end{description} - \subsection{First order terms} In the following, we use the following notations: @@ -284,94 +470,6 @@ following mapping: \right. \] -\begin{figure} - - Sat Solving - \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} - % Propagation (boolean) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Sove}(\mathbb{S}, t :: a \leadsto_C \top)$} - \DP{} & - $a \in C, C \in \mathbb{S}, \neg a \notin t, \forall b \neq a \in C. \neg b \in t $ - \\ \\ - % Decide (boolean) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n \top)$} - \DP{} & - $a \notin t, \neg a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ - \\ \\ - % Conflict (boolean) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} - \DP{} & - $C \in \mathbb{S}, \forall a \in C. \neg a \in t$ - \\ \\ - \end{tabular} - \end{center} - - Conflict Analysis - \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} - % Analyze (propagation) - \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} - \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} - \DP{} & - $\neg a \notin D$ - \\ \\ - % Analyze (decision) - \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_n \top, D)$} - \UIC{$\text{Analyze}(\mathbb{S}, t, D)$} - \DP{} & - $\neg a \notin D$ - \\ \\ - % Resolution - \AXC{$\text{Analyze}(\mathbb{S}, t :: a \leadsto_C \top, D)$} - \UIC{$\text{Analyze}(\mathbb{S}, t, (C - \{a\}) \cup (D - \{ \neg a\}))$} - \DP{} & - $\neg a \in D$ - \\ \\ - % BackJump - \AXC{$\text{Analyze}(\mathbb{S}, t :: a \mapsto_d \top :: t', C)$} - \UIC{$\text{Solve}(\mathbb{S} \cup \{ C \}, t)$} - \DP{} & - $\text{is\_uip}(C), d = \text{uip\_level}(C)$ - \\ \\ - \end{tabular} - \end{center} - - SMT Solving - \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} - % Conflict (theory) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Analyze}(\mathbb{S}, t, C)$} - \DP{} & - $\mathcal{T} \vdash C, \forall a \in C, \neg a \in t$ - \\ \\ - \end{tabular} - \end{center} - - McSat Solving - \begin{center} - \begin{tabular}{c@{\hspace{1cm}}l} - % Decide (assignment) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Solve}(\mathbb{S}, t :: a \mapsto_n v)$} - \DP{} & - $a \notin t, a \in \mathbb{S}, n = \text{max\_level}(t) + 1$ - \\ \\ - % Propagation (semantic) - \AXC{$\text{Solve}(\mathbb{S}, t)$} - \UIC{$\text{Solve}(\mathbb{S}, t :: a \leadsto_n \top)$} - \DP{} & - $ $ - \\ \\ - \end{tabular} - \end{center} - - \caption{SAT, SMT and McSat inference rules}\label{fig:transitions} -\end{figure} \subsection{Expected theory invariants} From f237851e8941ce4c8e243a256db2365d01d35656 Mon Sep 17 00:00:00 2001 From: Guillaume Bury Date: Tue, 18 Oct 2016 17:39:10 +0200 Subject: [PATCH 21/25] Added Model definitions in msat doc --- docs/macros.tex | 4 + docs/mcsat-vmcai2013.pdf | Bin 371980 -> 0 bytes docs/mcsat_design.pdf | Bin 378980 -> 0 bytes docs/minisat.pdf | Bin 327416 -> 0 bytes docs/msat.pdf | Bin 335008 -> 332781 bytes docs/msat.tex | 321 ++++++++++++++++++++++----------------- 6 files changed, 185 insertions(+), 140 deletions(-) delete mode 100644 docs/mcsat-vmcai2013.pdf delete mode 100644 docs/mcsat_design.pdf delete mode 100644 docs/minisat.pdf diff --git a/docs/macros.tex b/docs/macros.tex index bc2f609b..a21ad2fb 100644 --- a/docs/macros.tex +++ b/docs/macros.tex @@ -1,10 +1,14 @@ \def\ocaml{\textsf{OCaml}} + \def\sat{\textsf{Sat}} \def\smt{\textsf{SMT}} \def\mcsat{\textsf{McSat}} +\def\dpll{\textsf{DPLL}} +\def\cdcl{\textsf{CDCL}} + \def\msat{\textsf{mSAT}} \newcommand{\irule}[1]{{\small\textsc{#1}}} diff --git a/docs/mcsat-vmcai2013.pdf b/docs/mcsat-vmcai2013.pdf deleted file mode 100644 index e89e32d7a8482b538a2a577540120b61ebfaafe0..0000000000000000000000000000000000000000 GIT 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