Added Smt module

This commit is contained in:
Guillaume Bury 2014-11-14 17:40:29 +01:00
parent b7c5b39e02
commit 566c30bdcc
16 changed files with 679 additions and 31 deletions

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@ -5,7 +5,7 @@ COMP=ocamlbuild -log $(LOG) -use-ocamlfind -classic-display
FLAGS=
DIRS=-Is sat,smt,util,util/smtlib
DOC=msat.docdir/index.html
TEST=sat_solve.native
TEST=sat_solve.native smt_solve.native
NAME=msat

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@ -1,3 +1,4 @@
# Sat Modules
Explanation
Formula_intf
Res
@ -8,6 +9,11 @@ Theory_intf
Tseitin
Tseitin_intf
# Smt Modules
Unionfind
Smt
# Old modules
#Arith
#Cc
#Combine

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@ -344,7 +344,7 @@ module Make(St : Solver_types.S) = struct
print_dot_rule "BGCOLOR=\"LIGHTBLUE\"" aux () fmt p.conclusion
| Lemma _ ->
let aux fmt () =
Format.fprintf fmt "<TR><TD colspan=\"2\"BGCOLOR=\"LIGHTBLUE\">%a</TD></TR><TR><TD>Lemma</TD><TD>%s</TD></TR>"
Format.fprintf fmt "<TR><TD colspan=\"2\" BGCOLOR=\"LIGHTBLUE\">%a</TD></TR><TR><TD>Lemma</TD><TD>%s</TD></TR>"
print_clause p.conclusion St.(p.conclusion.name)
in
print_dot_rule "BGCOLOR=\"RED\"" aux () fmt p.conclusion

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@ -1,4 +1,8 @@
(* Copyright 2014 Guillaume Bury *)
(*
MSAT is free software, using the Apache license, see file LICENSE
Copyright 2014 Guillaume Bury
Copyright 2014 Simon Cruanes
*)
module Fsat : Formula_intf.S

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@ -373,7 +373,7 @@ module Make (F : Formula_intf.S)
propagate ()
| Th.Unsat (l, p) ->
let l = List.rev_map St.add_atom l in
let c = St.make_clause (St.fresh_name ()) l (List.length l) true (History []) in
let c = St.make_clause (St.fresh_name ()) l (List.length l) true (Lemma p) in
Some c
and propagate () =
@ -501,6 +501,7 @@ module Make (F : Formula_intf.S)
let report_unsat ({atoms=atoms} as confl) =
Log.debug 5 "Unsat conflict : %a" St.pp_clause confl;
env.unsat_conflict <- Some confl;
env.is_unsat <- true;
raise Unsat
@ -646,6 +647,7 @@ module Make (F : Formula_intf.S)
if env.is_unsat then raise Unsat;
let init_name = string_of_int cnumber in
let init0 = make_clause init_name atoms (List.length atoms) false (History []) in
Log.debug 10 "New clause : %a" St.pp_clause init0;
try
let atoms, init =
if decision_level () = 0 then

8
smt/.merlin Normal file
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@ -0,0 +1,8 @@
S ./
S ../sat/
S ../util/
B ../_build/
B ../_build/sat/
B ../_build/smt/
B ../_build/util/

155
smt/smt.ml Normal file
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@ -0,0 +1,155 @@
(*
MSAT is free software, using the Apache license, see file LICENSE
Copyright 2014 Guillaume Bury
Copyright 2014 Simon Cruanes
*)
module Fsmt = struct
exception Invalid_var
type var = string
type t =
| Fresh of int
| Equal of var * var
| Distinct of var * var
let dummy = Fresh 0
let max_fresh = ref 0
let fresh () =
incr max_fresh;
Fresh !max_fresh
let mk_var i =
if i <> "" then
i
else
raise Invalid_var
let mk_eq i j = Equal (mk_var i, mk_var j)
let mk_neq i j = Distinct (mk_var i, mk_var j)
let neg = function
| Fresh i -> Fresh (-i)
| Equal (a, b) -> Distinct (a, b)
| Distinct (a, b) -> Equal (a, b)
let norm = function
| Fresh i -> Fresh (abs i), i < 0
| Equal (a, b) -> Equal (min a b, max a b), false
| Distinct (a, b) -> Equal (min a b, max a b), true
(* Only used after normalisation, so usual functions should work *)
let hash = Hashtbl.hash
let equal = (=)
let compare = Pervasives.compare
let s = Hstring.make ""
let label _ = s
let add_label _ _ = ()
let print fmt = function
| Fresh i -> Format.fprintf fmt "%sv%d" (if i < 0 then "¬ " else "") (abs i)
| Equal (a, b) -> Format.fprintf fmt "%s = %s" a b
| Distinct (a, b) -> Format.fprintf fmt "%s <> %s" a b
end
module Tseitin = Tseitin.Make(Fsmt)
module Tsmt = struct
module U = Unionfind.Make(String)
type formula = Fsmt.t
type proof = unit
type slice = {
start : int;
length : int;
get : int -> formula;
push : formula -> formula list -> proof -> unit;
}
type level = U.t
type res =
| Sat of level
| Unsat of formula list * proof
let dummy = U.empty
let env = ref U.empty
let current_level () = !env
let temp = ref []
let assume s =
try
for i = s.start to s.start + s.length - 1 do
match s.get i with
| Fsmt.Fresh _ -> ()
| Fsmt.Equal (i, j) as f ->
temp := f :: !temp;
env := U.union !env i j
| Fsmt.Distinct (i, j) as f ->
temp := f :: !temp;
env := U.forbid !env i j
| _ -> assert false
done;
Sat (current_level ())
with U.Unsat ->
match !temp with
| _ :: _ -> Unsat (List.rev_map Fsmt.neg !temp, ())
| _ -> assert false
let backtrack l = env := l
end
module Make(Dummy:sig end) = struct
module SmtSolver = Solver.Make(Fsmt)(Tsmt)
type atom = Fsmt.t
type clause = SmtSolver.St.clause
type proof = SmtSolver.Proof.proof
type res =
| Sat
| Unsat
let _i = ref 0
let make_eq = Fsmt.mk_eq
let make_neq = Fsmt.mk_neq
let neg = Fsmt.neg
let hash = Fsmt.hash
let equal = Fsmt.equal
let compare = Fsmt.compare
let solve () =
try
SmtSolver.solve ();
Sat
with SmtSolver.Unsat -> Unsat
let assume l =
incr _i;
try
SmtSolver.assume l !_i
with SmtSolver.Unsat -> ()
let get_proof () =
SmtSolver.Proof.learn (SmtSolver.history ());
match SmtSolver.unsat_conflict () with
| None -> assert false
| Some c -> SmtSolver.Proof.prove_unsat c
let unsat_core = SmtSolver.Proof.unsat_core
let print_atom = Fsmt.print
let print_clause = SmtSolver.St.print_clause
let print_proof = SmtSolver.Proof.print_dot
end

69
smt/smt.mli Normal file
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@ -0,0 +1,69 @@
(*
MSAT is free software, using the Apache license, see file LICENSE
Copyright 2014 Guillaume Bury
Copyright 2014 Simon Cruanes
*)
module Fsmt : sig
include Formula_intf.S
val mk_eq : string -> string -> t
val mk_neq : string -> string -> t
end
module Tseitin : Tseitin.S with type atom = Fsmt.t
module Make(Dummy: sig end) : sig
(** Fonctor to make a pure SAT Solver module with built-in literals. *)
type atom = Fsmt.t
(** Type for atoms, i.e boolean literals. *)
type clause
(** Abstract type for clauses *)
type proof
(** Abstract type for resolution proofs *)
type res = Sat | Unsat
(** Type of results returned by the solve function. *)
val make_eq : string -> string -> atom
(** Returns the literal corresponding to equality of the given variables
@raise Invalid_var if given [0] as argument.*)
val make_neq : string -> string -> atom
(** Returns the literal corresponding to disequality of the given variables
@raise Invalid_var if given [0] as argument.*)
val neg : atom -> atom
(** [neg a] returns the negation of a literal. Involutive, i.e [neg (neg a) = a]. *)
val hash : atom -> int
val equal : atom -> atom -> bool
val compare : atom -> atom -> int
(** Usual hash and comparison functions. For now, directly uses
[Pervasives] and [Hashtbl] builtins. *)
val solve : unit -> res
(** Returns the satisfiability status of the current set of assumptions. *)
val assume : atom list list -> unit
(** Add a list of clauses to the set of assumptions. *)
val get_proof : unit -> proof
(** Returns the resolution proof found, if [solve] returned [Unsat]. *)
val unsat_core : proof -> clause list
(** Returns the unsat-core of the proof. *)
val print_atom : Format.formatter -> atom -> unit
(** Print the atom on the given formatter. *)
val print_clause : Format.formatter -> clause -> unit
(** Print the clause on the given formatter. *)
val print_proof : Format.formatter -> proof -> unit
(** Print the given proof in dot format. *)
end

84
smt/unionfind.ml Normal file
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@ -0,0 +1,84 @@
module type OrderedType = sig
type t
val compare : t -> t -> int
end
(* Union-find Module *)
module Make(T : OrderedType) = struct
exception Unsat
type var = T.t
module M = Map.Make(T)
type t = {
rank : int M.t;
forbid : ((var * var) list);
mutable parent : var M.t;
}
let empty = {
rank = M.empty;
forbid = [];
parent = M.empty;
}
let find_map m i default =
try
M.find i m
with Not_found ->
default
let rec find_aux f i =
let fi = find_map f i i in
if fi = i then
(f, i)
else
let f, r = find_aux f fi in
let f = M.add i r f in
(f, r)
let find h x =
let f, cx = find_aux h.parent x in
h.parent <- f;
cx
(* Highly ineficient treatment of inequalities *)
let possible h =
let aux (a, b) =
let ca = find h a in
let cb = find h b in
ca != cb
in
if List.for_all aux h.forbid then
h
else
raise Unsat
let union_aux h x y =
let cx = find h x in
let cy = find h y in
if cx != cy then begin
let rx = find_map h.rank cx 0 in
let ry = find_map h.rank cy 0 in
if rx > ry then
{ h with parent = M.add cy cx h.parent }
else if ry > rx then
{ h with parent = M.add cx cy h.parent }
else
{ rank = M.add cx (rx + 1) h.rank;
parent = M.add cy cx h.parent;
forbid = h.forbid; }
end else
h
let union h x y = possible (union_aux h x y)
let forbid h x y =
let cx = find h x in
let cy = find h y in
if cx = cy then
raise Unsat
else
{ h with forbid = (x, y) :: h.forbid }
end

14
smt/unionfind.mli Normal file
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@ -0,0 +1,14 @@
module type OrderedType = sig
type t
val compare : t -> t -> int
end
module Make(T : OrderedType) : sig
type t
exception Unsat
val empty : t
val find : t -> T.t -> T.t
val union : t -> T.t -> T.t -> t
val forbid : t -> T.t -> T.t -> t
end

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@ -61,7 +61,7 @@ let format_of_filename s =
let parse_with_input file = function
| Auto -> assert false
| Dimacs -> List.rev_map (List.rev_map S.make) (Parsedimacs.parse file)
| Smtlib -> rev_flat_map Sat.Tseitin.make_cnf [] (Smtlib.parse file)
| Smtlib -> rev_flat_map Sat.Tseitin.make_cnf [] (Satlib.parse file)
let parse_input file =
parse_with_input file (match !input with

198
util/smt_solve.ml Normal file
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@ -0,0 +1,198 @@
module S = Smt.Make(struct end)
exception Out_of_time
exception Out_of_space
(* IO wrappers *)
(* Types for input/output languages *)
type sat_input =
| Auto
| Smtlib
type sat_output =
| Standard (* Only output problem status *)
| Dot
let input = ref Auto
let output = ref Standard
let input_list = [
"auto", Auto;
"smtlib", Smtlib;
]
let output_list = [
"dot", Dot;
]
let error_msg opt arg l =
Format.fprintf Format.str_formatter "'%s' is not a valid argument for '%s', valid arguments are : %a"
arg opt (fun fmt -> List.iter (fun (s, _) -> Format.fprintf fmt "%s, " s)) l;
Format.flush_str_formatter ()
let set_io opt arg flag l =
try
flag := List.assoc arg l
with Not_found ->
invalid_arg (error_msg opt arg l)
let set_input s = set_io "Input" s input input_list
let set_output s = set_io "Output" s output output_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 5 = ".smt2" then
Smtlib
else (* Default choice *)
Smtlib
let parse_with_input file = function
| Auto -> assert false
| Smtlib -> rev_flat_map Smt.Tseitin.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.fprintf std "%( fmt %)@." format
| Dot -> Format.fprintf std "/* %( fmt %) */@." format
let print_proof proof = match !output with
| Standard -> ()
| Dot -> S.print_proof std proof
let rec print_cl fmt = function
| [] -> Format.fprintf fmt "[]"
| [a] -> Smt.Fsmt.print fmt a
| a :: ((_ :: _) as r) -> Format.fprintf fmt "%a %a" Smt.Fsmt.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" S.print_clause c) l
(* Arguments parsing *)
let file = ref ""
let p_cnf = ref false
let p_proof_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 =
let arg1 = String.sub arg 0 (l-1) in
r := m *. (float_of_string arg1)
in
if l = 0 then raise (Arg.Bad "bad numeric argument")
else
try
match arg.[l-1] with
| 'k' -> multiplier 1e3
| 'M' -> multiplier 1e6
| 'G' -> multiplier 1e9
| 'T' -> multiplier 1e12
| 's' -> multiplier 1.
| 'm' -> multiplier 60.
| 'h' -> multiplier 3600.
| '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")
let setup_gc_stat () =
at_exit (fun () ->
Gc.print_stat stdout;
)
let input_file = fun s -> file := s
let usage = "Usage : main [options] <file>"
let argspec = Arg.align [
"-bt", Arg.Unit (fun () -> Printexc.record_backtrace true),
" Enable stack traces";
"-cnf", Arg.Set p_cnf,
" Prints the cnf used.";
"-check", Arg.Set p_proof_check,
" 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)";
"-size", Arg.String (int_arg size_limit),
"<s>[kMGT] Sets the size limit for the sat solver";
"-time", Arg.String (int_arg time_limit),
"<t>[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),
"<lvl> Sets the debug verbose level";
]
(* Limits alarm *)
let check () =
let t = Sys.time () in
let heap_size = (Gc.quick_stat ()).Gc.heap_words in
let s = float heap_size *. float Sys.word_size /. 8. in
if t > !time_limit then
raise Out_of_time
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;
if !file = "" then begin
Arg.usage argspec usage;
exit 2
end;
ignore(Gc.create_alarm check);
(* Interesting stuff happening *)
let cnf = get_cnf () in
if !p_cnf then
print_lcl cnf;
S.assume cnf;
match S.solve () with
| S.Sat ->
print "Sat";
| S.Unsat ->
print "Unsat";
if !p_proof_check then begin
let p = S.get_proof () in
print_proof p;
if !p_unsat_core then
print_lclause (S.unsat_core p)
end
let () =
try
main ()
with
| Out_of_time ->
print "Time limit exceeded";
exit 2
| Out_of_space ->
print "Size limit exceeded";
exit 3

103
util/smtlib/satlib.ml Normal file
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@ -0,0 +1,103 @@
(* Copyright 2014 INRIA **)
open Smtlib_syntax
module F = Sat.Fsat
module T = Sat.Tseitin
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_var =
fun 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) -> get_var 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_sort = function
| SortIdentifier(_, id) ->
let s = translate_id id in
if s <> "Bool" then raise Incomplete_translation
| _ -> 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 right_assoc s f = function
| x :: r -> List.fold_right f r x
| _ -> raise (Bad_arity s)
let rec translate_term = function
| TermSpecConst(_, const) -> translate_const const
| TermQualIdentifier(_, id) -> get_var (translate_qualid id)
| TermQualIdTerm(_, f, (_, l)) ->
begin match (translate_qualid f), (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
| _ -> raise Unknown_command
end
| _ -> raise Incomplete_translation
(* Command Translation *)
let translate_command = function
| CommandDeclareFun(_, s, (_, []), ret) ->
ignore (translate_sort ret);
ignore (get_var (translate_symbol 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

3
util/smtlib/satlib.mli Normal file
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@ -0,0 +1,3 @@
(* Copyright 2014 INRIA *)
val parse : string -> Sat.Tseitin.t list

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@ -2,8 +2,8 @@
open Smtlib_syntax
module F = Sat.Fsat
module T = Sat.Tseitin
module F = Smt.Fsmt
module T = Smt.Tseitin
exception Bad_arity of string
exception Unknown_command
@ -14,8 +14,7 @@ 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_var =
fun s ->
let get_var s =
try
Hashtbl.find env s
with Not_found ->
@ -29,7 +28,7 @@ let translate_const = function
| SpecConstNum(_, s)
| SpecConstString(_, s)
| SpecConstsHex(_, s)
| SpecConstsBinary(_, s) -> get_var s
| SpecConstsBinary(_, s) -> s
let translate_symbol = function
| Symbol(_, s)
@ -39,12 +38,6 @@ let translate_id = function
| IdSymbol(_, s) -> translate_symbol s
| IdUnderscoreSymNum(_, s, n) -> raise Incomplete_translation
let translate_sort = function
| SortIdentifier(_, id) ->
let s = translate_id id in
if s <> "Bool" then raise Incomplete_translation
| _ -> raise Incomplete_translation
let translate_qualid = function
| QualIdentifierId(_, id) -> translate_id id
| QualIdentifierAs(_, id, s) -> raise Incomplete_translation
@ -57,27 +50,36 @@ let right_assoc s f = function
| x :: r -> List.fold_right f r x
| _ -> raise (Bad_arity s)
let rec translate_term = function
let translate_atom = function
| TermSpecConst(_, const) -> translate_const const
| TermQualIdentifier(_, id) -> get_var (translate_qualid id)
| TermQualIdentifier(_, id) -> translate_qualid id
| _ -> raise Incomplete_translation
let rec translate_term = function
| TermQualIdTerm(_, f, (_, l)) ->
begin match (translate_qualid f), (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
| _ -> raise Unknown_command
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
| _ -> raise Unknown_command
end
end
| _ -> raise Incomplete_translation
(* Command Translation *)
let translate_command = function
| CommandDeclareFun(_, s, (_, []), ret) ->
ignore (translate_sort ret);
ignore (get_var (translate_symbol s));
| CommandDeclareFun(_, s, (_, []), _) ->
None
| CommandAssert(_, t) ->
Some (translate_term t)

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@ -1,3 +1,3 @@
(* Copyright 2014 INRIA *)
val parse : string -> Sat.Tseitin.t list
val parse : string -> Smt.Tseitin.t list