feat(arith): integrate simplex2 into sidekick; remove old simplex

src/arith/base-term/Base_types.ml

@@ -12,6 +12,8 @@ type 'a lra_view = 'a Sidekick_arith_lra.lra_view =
   | LRA_op of lra_op * 'a * 'a
   | LRA_mult of Q.t * 'a
   | LRA_const of Q.t
+  | LRA_simplex_var of 'a
+  | LRA_simplex_pred of 'a * Sidekick_arith_lra.S_op.t * Q.t
   | LRA_other of 'a
 
 (* main term cell. *)
@@ -238,6 +240,10 @@ let pp_term_view_gen ~pp_id ~pp_t out = function
       | LRA_mult (n, x) ->
         Fmt.fprintf out "(@[*@ %a@ %a@])" Q.pp_print n pp_t x
       | LRA_const q -> Q.pp_print out q
+      | LRA_simplex_var v -> pp_t out v
+      | LRA_simplex_pred (v, op, q) ->
+        Fmt.fprintf out "(@[%a@ %s %a@])"
+          pp_t v (Sidekick_arith_lra.S_op.to_string op) Q.pp_print q
       | LRA_other x -> pp_t out x
     end
 
@@ -593,6 +599,8 @@ end = struct
     let sub_hash = A.hash
     let sub_eq = A.equal
 
+    let hash_q q = Hash.string (Q.to_string q)
+
     let hash (t:A.t view) : int = match t with
       | Bool b -> Hash.bool b
       | App_fun (f,l) ->
@@ -607,8 +615,11 @@ end = struct
           | LRA_op (p, a, b) ->
             Hash.combine4 82 (Hash.poly p) (sub_hash a) (sub_hash b)
           | LRA_mult (n, x) ->
-            Hash.combine3 83 (Hash.string @@ Q.to_string n) (sub_hash x)
+            Hash.combine3 83 (hash_q n) (sub_hash x)
-          | LRA_const q -> Hash.combine2 84 (Hash.string @@ Q.to_string q)
+          | LRA_const q -> Hash.combine2 84 (hash_q q)
+          | LRA_simplex_var v -> Hash.combine2 99 (sub_hash v)
+          | LRA_simplex_pred (v,op,q) ->
+            Hash.combine4 120 (sub_hash v) (Hash.poly op) (hash_q q)
           | LRA_other x -> sub_hash x
         end
 
@@ -630,8 +641,11 @@ end = struct
           | LRA_const a1, LRA_const a2 -> Q.equal a1 a2
           | LRA_mult (n1,x1), LRA_mult (n2,x2) -> Q.equal n1 n2 && sub_eq x1 x2
           | LRA_other x1, LRA_other x2 -> sub_eq x1 x2
-          | (LRA_pred _ | LRA_op _ | LRA_const _
+          | LRA_simplex_var v1, LRA_simplex_var v2 -> sub_eq v1 v2
-            | LRA_mult _ | LRA_other _), _ -> false
+          | LRA_simplex_pred (v1,op1,q1), LRA_simplex_pred (v2,op2,q2) ->
+            sub_eq v1 v2 && (op1==op2) && Q.equal q1 q2
+          | (LRA_pred _ | LRA_op _ | LRA_const _ | LRA_simplex_var _
+            | LRA_mult _ | LRA_other _ | LRA_simplex_pred _), _ -> false
         end
       | (Bool _ | App_fun _ | Eq _ | Not _ | Ite _ | LRA _), _
         -> false
@@ -700,8 +714,8 @@ end = struct
       end
     | LRA l ->
       begin match l with
-        | LRA_pred _ -> Ty.bool
+        | LRA_pred _ | LRA_simplex_pred _ -> Ty.bool
-        | LRA_op _ | LRA_const _ | LRA_mult _ -> Ty.real
+        | LRA_op _ | LRA_const _ | LRA_mult _ | LRA_simplex_var _ -> Ty.real
         | LRA_other x -> x.term_ty
       end
 
@@ -716,6 +730,8 @@ end = struct
       begin match l with
         | LRA_pred (_, a, b)|LRA_op (_, a, b) -> f a; f b
         | LRA_mult (_,x) | LRA_other x -> f x
+        | LRA_simplex_var x -> f x
+        | LRA_simplex_pred (x,_,_) -> f x
         | LRA_const _ -> ()
       end
 

src/arith/lra/linear_expr.ml

@@ -4,9 +4,6 @@
 
 module type COEFF = Linear_expr_intf.COEFF
 module type VAR = Linear_expr_intf.VAR
-module type FRESH = Linear_expr_intf.FRESH
-module type VAR_GEN = Linear_expr_intf.VAR_GEN
-module type VAR_EXTENDED = Linear_expr_intf.VAR_EXTENDED
 
 module type S = Linear_expr_intf.S
 
@@ -195,33 +192,3 @@ module Make(C : COEFF)(Var : VAR) = struct
   end
 end[@@inline]
 
-module Make_var_gen(Var : VAR)
-  : VAR_EXTENDED with type user_var = Var.t
-                  and type lit = Var.lit
-= struct
-  type user_var = Var.t
-
-  type t =
-    | User of user_var
-    | Internal of int
-
-  let compare (a:t) b : int = match a, b with
-    | User a, User b -> Var.compare a b
-    | User _, Internal _ -> -1
-    | Internal _, User _ -> 1
-    | Internal i, Internal j -> CCInt.compare i j
-
-  let pp out = function
-    | User v -> Var.pp out v
-    | Internal i -> Format.fprintf out "internal_v_%d" i
-
-  type lit = Var.lit
-  let pp_lit = Var.pp_lit
-
-  module Fresh = struct
-    type t = int ref
-    let create() = ref 0
-    let copy r = ref !r
-    let fresh r = Internal (CCRef.get_then_incr r)
-  end
-end[@@inline]

src/arith/lra/linear_expr.mli

@@ -7,9 +7,6 @@
 module type COEFF = Linear_expr_intf.COEFF
 
 module type VAR = Linear_expr_intf.VAR
-module type FRESH = Linear_expr_intf.FRESH
-module type VAR_GEN = Linear_expr_intf.VAR_GEN
-module type VAR_EXTENDED = Linear_expr_intf.VAR_EXTENDED
 
 module type S = Linear_expr_intf.S
 
@@ -19,8 +16,3 @@ module Make(C : COEFF)(Var : VAR)
   : S with module C = C
        and module Var = Var
        and module Var_map = CCMap.Make(Var)
-
-module Make_var_gen(Var : VAR)
-  : VAR_EXTENDED
-    with type user_var = Var.t
-     and type lit = Var.lit

src/arith/lra/linear_expr_intf.ml

@@ -57,51 +57,6 @@ module type VAR = sig
   val pp_lit : lit Fmt.printer
 end
 
-(** {2 Fresh variables}
-
-    Standard interface for variables with an infinite number
-    of 'fresh' variables. A 'fresh' variable should be distinct
-    from any other.
-*)
-module type FRESH = sig
-  type var
-  (** The type of variables. *)
-
-  type t
-  (** A type of state for creating fresh variables. *)
-
-  val copy : t -> t
-  (** Copy state *)
-
-  val fresh : t -> var
-  (** Create a fresh variable using an existing variable as base.
-      TODO: need some explaining, about the difference with {!create}. *)
-end
-
-(** {2 Generative Variable interface}
-
-    Standard interface for variables that are meant to be used
-    in expressions. Furthermore, fresh variables can be generated
-    (which is useful to refactor and/or put problems in specific
-    formats used by algorithms).
-*)
-module type VAR_GEN = sig
-  include VAR
-
-  (** Generate fresh variables on demand *)
-  module Fresh : FRESH with type var := t
-end
-
-module type VAR_EXTENDED = sig
-  type user_var (** original variables *)
-
-  type t =
-    | User of user_var
-    | Internal of int
-
-  include VAR_GEN with type t := t
-end
-
 type bool_op = Predicate.t = Leq | Geq | Lt | Gt | Eq | Neq
 
 (** {2 Linear expressions & formulas} *)

src/arith/lra/sidekick_arith_lra.ml

@@ -6,11 +6,12 @@
 
 open Sidekick_core
 
-module Simplex = Simplex
 module Simplex2 = Simplex2
 module Predicate = Predicate
 module Linear_expr = Linear_expr
 
+module S_op = Simplex2.Op
+
 type pred = Linear_expr_intf.bool_op = Leq | Geq | Lt | Gt | Eq | Neq
 type op = Plus | Minus
 
@@ -19,6 +20,8 @@ type 'a lra_view =
   | LRA_op of op * 'a * 'a
   | LRA_mult of Q.t * 'a
   | LRA_const of Q.t
+  | LRA_simplex_var of 'a (* an opaque variable *)
+  | LRA_simplex_pred of 'a * S_op.t * Q.t (* an atomic constraint *)
   | LRA_other of 'a
 
 let map_view f (l:_ lra_view) : _ lra_view =
@@ -27,6 +30,8 @@ let map_view f (l:_ lra_view) : _ lra_view =
     | LRA_op (p, a, b) -> LRA_op (p, f a, f b)
     | LRA_mult (n,a) -> LRA_mult (n, f a)
     | LRA_const q -> LRA_const q
+    | LRA_simplex_var v -> LRA_simplex_var (f v)
+    | LRA_simplex_pred (v, op, q) -> LRA_simplex_pred (f v, op, q)
     | LRA_other x -> LRA_other (f x)
   end
 
@@ -44,6 +49,9 @@ module type ARG = sig
 
   val ty_lra : S.T.Term.state -> ty
 
+  val mk_and : S.T.Term.state -> term -> term -> term
+  val mk_or : S.T.Term.state -> term -> term -> term
+
   val has_ty_real : term -> bool
   (** Does this term have the type [Real] *)
 
@@ -98,9 +106,8 @@ module Make(A : ARG) : S with module A = A = struct
   end
 
   module SimpVar
-    : Linear_expr.VAR_GEN
+    : Linear_expr.VAR
       with type t = A.term
-       and type Fresh.t = A.Gensym.t
        and type lit = Tag.t
   = struct
     type t = A.term
@@ -108,21 +115,12 @@ module Make(A : ARG) : S with module A = A = struct
     let compare = A.S.T.Term.compare
     type lit = Tag.t
     let pp_lit = Tag.pp
-    module Fresh = struct
-      type t = A.Gensym.t
-      let copy = A.Gensym.copy
-      let fresh (st:t) =
-        let ty = A.ty_lra (A.Gensym.tst st) in
-        A.Gensym.fresh_term ~pre:"_lra" st ty
-    end
   end
 
-  module SimpSolver = Simplex.Make_full(SimpVar)
+  module LE_ = Linear_expr.Make(struct include Q let pp=pp_print end)(SimpVar)
-
+  module LE = LE_.Expr
-  (* linear expressions *)
+  module SimpSolver = Simplex2.Make(SimpVar)
-  module LComb = SimpSolver.L.Comb
+  module LConstr = SimpSolver.Constraint
-  module LE = SimpSolver.L.Expr
-  module LConstr = SimpSolver.L.Constr
 
   type state = {
     tst: T.state;
@@ -130,11 +128,13 @@ module Make(A : ARG) : S with module A = A = struct
     gensym: A.Gensym.t;
     neq_encoded: unit T.Tbl.t;
     (* if [a != b] asserted and not in this table, add clause [a = b \/ a<b \/ a>b] *)
-    needs_th_combination: LE.t T.Tbl.t; (* terms that require theory combination *)
+    needs_th_combination: LE_.Comb.t T.Tbl.t; (* terms that require theory combination *)
     t_defs: LE.t T.Tbl.t; (* term definitions *)
     pred_defs: (pred * LE.t * LE.t * T.t * T.t) T.Tbl.t; (* predicate definitions *)
     local_eqs: (N.t * N.t) Backtrack_stack.t; (* inferred by the congruence closure *)
+    simplex: SimpSolver.t;
   }
+  (* TODO *)
 
   let create tst : state =
     { tst;
@@ -145,13 +145,16 @@ module Make(A : ARG) : S with module A = A = struct
       t_defs=T.Tbl.create 8;
       pred_defs=T.Tbl.create 16;
       local_eqs = Backtrack_stack.create();
+      simplex=SimpSolver.create ();
     }
 
   let push_level self =
+    SimpSolver.push_level self.simplex;
     Backtrack_stack.push_level self.local_eqs;
     ()
 
   let pop_levels self n =
+    SimpSolver.pop_levels self.simplex n;
     Backtrack_stack.pop_levels self.local_eqs n ~f:(fun _ -> ());
     ()
 
@@ -212,7 +215,7 @@ module Make(A : ARG) : S with module A = A = struct
     let open LE.Infix in
     match A.view_as_lra t with
     | LRA_other _ -> LE.monomial1 (f t)
-    | LRA_pred _ ->
+    | LRA_pred _ | LRA_simplex_pred _ ->
       Error.errorf "type error: in linexp, LRA predicate %a" T.pp t
     | LRA_op (op, t1, t2) ->
       let t1 = as_linexp ~f t1 in
@@ -224,6 +227,7 @@ module Make(A : ARG) : S with module A = A = struct
     | LRA_mult (n, x) ->
       let t = as_linexp ~f x in
       LE.( n * t )
+    | LRA_simplex_var v -> LE.monomial1 v
     | LRA_const q -> LE.of_const q
 
   let as_linexp_id = as_linexp ~f:CCFun.id
@@ -233,98 +237,175 @@ module Make(A : ARG) : S with module A = A = struct
      *)
 
   (* preprocess linear expressions away *)
-  let preproc_lra (self:state) si ~recurse ~mk_lit:_ ~add_clause:_ (t:T.t) : T.t option =
+  let preproc_lra (self:state) si ~recurse ~mk_lit ~add_clause (t:T.t) : T.t option =
     Log.debugf 50 (fun k->k "lra.preprocess %a" T.pp t);
     let tst = SI.tst si in
+
+    let mk_eq x q =
+      let t1 = A.mk_lra tst (LRA_simplex_pred (x, Leq, q)) in
+      let t2 = A.mk_lra tst (LRA_simplex_pred (x, Geq, q)) in
+      A.mk_and tst t1 t2
+    and mk_neq x q =
+      let t1 = A.mk_lra tst (LRA_simplex_pred (x, Lt, q)) in
+      let t2 = A.mk_lra tst (LRA_simplex_pred (x, Gt, q)) in
+      A.mk_or tst t1 t2
+    in
+
     match A.view_as_lra t with
-    | LRA_pred ((Eq|Neq) as pred, t1, t2) ->
-      (* keep equality as is, needed for congruence closure *)
-      let t1 = recurse t1 in
-      let t2 = recurse t2 in
-      let u = A.mk_lra tst (LRA_pred (pred, t1, t2)) in
-      if T.equal t u then None else Some u
     | LRA_pred (pred, t1, t2) ->
       let l1 = as_linexp ~f:recurse t1 in
       let l2 = as_linexp ~f:recurse t2 in
-      let proxy = fresh_term self ~pre:"_pred_lra_" Ty.bool in
+      let le = LE.(l1 - l2) in
-      T.Tbl.add self.pred_defs proxy (pred, l1, l2, t1, t2);
+      let le_comb, le_const = LE.comb le, LE.const le in
-      Log.debugf 5 (fun k->k"@[<hv2>lra.preprocess.step %a@ :into %a@ :def %a@]"
+      let le_const = Q.neg le_const in
-                       T.pp t T.pp proxy pp_pred_def (pred,l1,l2));
+      (* now we have [le_comb <pred> le_const] *)
-      Some proxy
+
+      begin match LE_.Comb.as_singleton le_comb, pred with
+        | None, _ ->
+          (* non trivial linexp, give it a fresh name in the simplex *)
+          let proxy = fresh_term self ~pre:"_le" (T.ty t1) in
+          T.Tbl.replace self.needs_th_combination proxy le_comb;
+
+          let le_comb = LE_.Comb.to_list le_comb in
+          List.iter (fun (_,v) -> SimpSolver.add_var self.simplex v) le_comb;
+          SimpSolver.define self.simplex proxy le_comb;
+
+          let new_t =
+            match pred with
+            | Eq -> mk_eq proxy le_const
+            | Neq -> mk_neq proxy le_const
+            | Leq -> A.mk_lra tst (LRA_simplex_pred (proxy, S_op.Leq, le_const))
+            | Lt -> A.mk_lra tst (LRA_simplex_pred (proxy, S_op.Lt, le_const))
+            | Geq -> A.mk_lra tst (LRA_simplex_pred (proxy, S_op.Geq, le_const))
+            | Gt -> A.mk_lra tst (LRA_simplex_pred (proxy, S_op.Gt, le_const))
+          in
+
+          Log.debugf 10 (fun k->k "lra.preprocess@ :%a@ :into %a" T.pp t T.pp new_t);
+          Some new_t
+
+        | Some (coeff, v), Eq ->
+          let q = Q.(le_const / coeff) in
+          Some (mk_eq v q) (* turn into [c.v <= const /\ … >= ..] *)
+
+        | Some (coeff, v), Neq ->
+          let q = Q.(le_const / coeff) in
+          Some (mk_neq v q) (* turn into [c.v < const \/ … > ..] *)
+
+        | Some (coeff, v), pred ->
+          (* [c . v <= const] becomes a direct simplex constraint [v <= const/c] *)
+          let negate = Q.sign coeff < 0 in
+          let q = Q.div le_const coeff in
+
+          let op = match pred with
+            | Leq -> S_op.Leq
+            | Lt -> S_op.Lt
+            | Geq -> S_op.Geq
+            | Gt -> S_op.Gt
+            | Eq | Neq -> assert false
+          in
+          let op = if negate then S_op.neg_sign op else op in
+
+          let new_t = A.mk_lra tst (LRA_simplex_pred (v, op, q)) in
+          Log.debugf 10 (fun k->k "lra.preprocess@ :%a@ :into %a" T.pp t T.pp new_t);
+          Some new_t
+      end
+
     | LRA_op _ | LRA_mult _ ->
       let le = as_linexp ~f:recurse t in
-      let proxy = fresh_term self ~pre:"_e_lra_" (T.ty t) in
+      let le_comb, le_const = LE.comb le, LE.const le in
-      T.Tbl.add self.t_defs proxy le;
+      let le_comb = LE_.Comb.to_list le_comb in
-      T.Tbl.add self.needs_th_combination proxy le;
+      List.iter (fun (_,v) -> SimpSolver.add_var self.simplex v) le_comb;
-      Log.debugf 5 (fun k->k"@[<hv2>lra.preprocess.step %a@ :into %a@ :def %a@]"
+
-                       T.pp t T.pp proxy LE.pp le);
+      let proxy = fresh_term self ~pre:"_le" (T.ty t) in
-      Some proxy
+
+      if Q.(le_const = zero) then (
+        (* if there is no constant, define [proxy] as [proxy := le_comb] and
+           return [proxy] *)
+        SimpSolver.define self.simplex proxy le_comb;
+        Some proxy
+      ) else (
+        (* a bit more complicated: we cannot just define [proxy := le_comb]
+           because of the coefficient.
+           Instead we assert [proxy - le_comb = le_const] using a secondary
+           variable [proxy2 := le_comb - proxy]
+           and asserting [proxy2 = -le_const] *)
+        let proxy2 = fresh_term self ~pre:"_le_diff" (T.ty t) in
+        SimpSolver.define self.simplex proxy2
+          ((Q.minus_one, proxy) :: le_comb);
+
+        add_clause [
+          mk_lit (A.mk_lra tst (LRA_simplex_pred (proxy2, Leq, Q.neg le_const)))
+        ];
+        add_clause [
+          mk_lit (A.mk_lra tst (LRA_simplex_pred (proxy2, Geq, Q.neg le_const)))
+        ];
+
+        Some proxy
+      )
+
     | LRA_other t when A.has_ty_real t ->
-      let le = LE.monomial1 t in
+      let le = LE_.Comb.monomial1 t in
       T.Tbl.replace self.needs_th_combination t le;
       None
-    | LRA_const _ | LRA_other _ -> None
+    | LRA_const _ | LRA_simplex_pred _ | LRA_simplex_var _ | LRA_other _ -> None
-
-  (* ensure that [a != b] triggers the clause
-     [a=b \/ a<b \/ a>b] *)
-  let encode_neq self si acts trail : unit =
-    let tst = self.tst in
-    begin
-      trail
-      |> Iter.filter_map
-        (fun lit ->
-           let t = Lit.term lit in
-           Log.debugf 50 (fun k->k "@[lra: check lit %a@ :t %a@ :sign %B@]"
-                             Lit.pp lit T.pp t (Lit.sign lit));
-
-           let check_pred pred a b =
-             let pred = if Lit.sign lit then pred else Predicate.neg pred in
-             Log.debugf 50 (fun k->k "pred = `%s`" (Predicate.to_string pred));
-             if pred = Neq && not (T.Tbl.mem self.neq_encoded t) then (
-               Some (lit, a, b)
-             ) else None
-           in
-
-           begin match T.Tbl.find self.pred_defs t with
-             | (pred, _, _, ta, tb) -> check_pred pred ta tb
-             | exception Not_found ->
-               begin match A.view_as_lra t with
-                 | LRA_pred (pred, a, b) -> check_pred pred a b
-                 | _ -> None
-               end
-           end)
-      |> Iter.iter
-        (fun (lit,a,b) ->
-           Log.debugf 50 (fun k->k "encode neq in %a" Lit.pp lit);
-           let c = [
-             Lit.neg lit;
-             SI.mk_lit si acts (A.mk_lra tst (LRA_pred (Lt, a, b)));
-             SI.mk_lit si acts (A.mk_lra tst (LRA_pred (Lt, b, a)));
-           ] in
-           SI.add_clause_permanent si acts c;
-           T.Tbl.add self.neq_encoded (Lit.term (Lit.abs lit)) ();
-        )
-    end
 
   module Q_map = CCMap.Make(Q)
 
-  let final_check_ (self:state) si (acts:SI.actions) (trail:_ Iter.t) : unit =
+  (* raise conflict from certificate *)
+  let fail_with_cert si acts cert : 'a =
+    (* TODO: check certificate *)
+    let confl =
+      SimpSolver.Unsat_cert.lits cert
+      |> CCList.flat_map (Tag.to_lits si)
+      |>  List.rev_map SI.Lit.neg
+    in
+    SI.raise_conflict si acts confl SI.P.default
+
+  let check_simplex_ self si acts : SimpSolver.Subst.t =
+    Log.debug 5 "lra: call arith solver";
+    let res = Profile.with1 "simplex.solve" SimpSolver.check self.simplex in
+    begin match res with
+      | SimpSolver.Sat m -> m
+      | SimpSolver.Unsat cert ->
+        Log.debugf 10
+          (fun k->k "(@[lra.check.unsat@ :cert %a@])"
+              SimpSolver.Unsat_cert.pp cert);
+        fail_with_cert si acts cert
+    end
+
+  let partial_check_ self si acts trail : unit =
+    Profile.with_ "lra.partial-check" @@ fun () ->
+    trail
+      (fun lit ->
+         let sign = SI.Lit.sign lit in
+         let lit_t = SI.Lit.term lit in
+         match A.view_as_lra lit_t with
+         | LRA_simplex_pred (v, op, q) ->
+           let op = if sign then op else S_op.neg_sign op in
+           let constr = SimpSolver.Constraint.mk v op q in
+           Log.debugf 10
+             (fun k->k "(@[lra.partial-check.assert@ %a@])"
+                 SimpSolver.Constraint.pp constr);
+           begin
+             try
+               SimpSolver.add_var self.simplex v;
+               SimpSolver.add_constraint self.simplex constr (Tag.Lit lit)
+             with SimpSolver.E_unsat cert ->
+               Log.debugf 10
+                 (fun k->k "(@[lra.partial-check.unsat@ :cert %a@])"
+                     SimpSolver.Unsat_cert.pp cert);
+               fail_with_cert si acts cert
+           end
+         | _ -> ());
+
+    (* incremental check *)
+    ignore (check_simplex_ self si acts : SimpSolver.Subst.t);
+    ()
+
+  let final_check_ (self:state) si (acts:SI.actions) (_trail:_ Iter.t) : unit =
     Log.debug 5 "(th-lra.final-check)";
     Profile.with_ "lra.final-check" @@ fun () ->
-    let simplex = SimpSolver.create self.gensym in
+    (* FIXME
-    encode_neq self si acts trail;
-    (* first, add definitions *)
-    begin
-      T.Tbl.iter
-        (fun t le ->
-           let open LE.Infix in
-           let le = le - LE.monomial1 t in
-           let c = LConstr.eq0 le in
-           let lit = Tag.By_def in
-           SimpSolver.add_constr simplex c lit
-        )
-        self.t_defs
-    end;
     (* add congruence closure equalities *)
     Backtrack_stack.iter self.local_eqs
       ~f:(fun (n1,n2) ->
@@ -333,50 +414,24 @@ module Make(A : ARG) : S with module A = A = struct
          let c = LConstr.eq0 LE.(t1 -  t2) in
          let lit = Tag.CC_eq (n1,n2) in
          SimpSolver.add_constr simplex c lit);
-    (* add trail *)
+       *)
-    begin
+
-      trail
-      |> Iter.iter
-        (fun lit ->
-           let sign = Lit.sign lit in
-           let t = Lit.term lit in
-           let assert_pred pred a b =
-             let pred = if sign then pred else Predicate.neg pred in
-             if pred = Neq then (
-               Log.debugf 50 (fun k->k "(@[LRA.skip-neq@ :in %a@])" T.pp t);
-             ) else (
-               let c = LConstr.of_expr LE.(a-b) pred in
-               SimpSolver.add_constr simplex c (Tag.Lit lit);
-             )
-           in
-           begin match T.Tbl.find self.pred_defs t with
-             | (pred, a, b, _, _) -> assert_pred pred a b
-             | exception Not_found ->
-               begin match A.view_as_lra t with
-                 | LRA_pred (pred, a, b) ->
-                   let a = try T.Tbl.find self.t_defs a with _ -> as_linexp_id a in
-                   let b = try T.Tbl.find self.t_defs b with _ -> as_linexp_id b in
-                   assert_pred pred a b
-                 | _ -> ()
-               end
-           end)
-    end;
     Log.debug 5 "lra: call arith solver";
-    let res = Profile.with1 "simplex.solve" SimpSolver.solve simplex in
+    let model = check_simplex_ self si acts in
-    begin match res with
+    Log.debugf 20 (fun k->k "(@[lra.model@ %a@])" SimpSolver.Subst.pp model);
-      | SimpSolver.Solution _m ->
+    Log.debug 5 "lra: solver returns SAT";
-        Log.debug 5 "lra: solver returns SAT";
+    let n_th_comb =
-        let n_th_comb =
+      T.Tbl.keys self.needs_th_combination |> Iter.length
-          T.Tbl.keys self.needs_th_combination |> Iter.length
+    in
-        in
+    if n_th_comb > 0 then (
-        if n_th_comb > 0 then (
+      Log.debugf 5
-          Log.debugf 5
+        (fun k->k "(@[LRA.needs-th-combination@ :n-lits %d@])" n_th_comb);
-            (fun k->k "(@[LRA.needs-th-combination@ :n-lits %d@])" n_th_comb);
+    );
-        );
+    Log.debugf 50
-        Log.debugf 50
+      (fun k->k "(@[LRA.needs-th-combination@ :lits %a@])"
-          (fun k->k "(@[LRA.needs-th-combination@ :lits %a@])"
+          (Util.pp_iter @@ Fmt.within "`" "`" T.pp) (T.Tbl.keys self.needs_th_combination));
-              (Util.pp_iter @@ Fmt.within "`" "`" T.pp) (T.Tbl.keys self.needs_th_combination));
+
-        (* FIXME: theory combination
+    (* FIXME: theory combination
         let lazy model = model in
         Log.debugf 30 (fun k->k "(@[LRA.model@ %a@])" FM_A.pp_model model);
 
@@ -418,26 +473,8 @@ module Make(A : ARG) : S with module A = A = struct
             by_val;
           ()
         end;
-           *)
+    *)
-        ()
+
-      | SimpSolver.Unsatisfiable cert ->
-        let unsat_core =
-          match SimpSolver.check_cert simplex cert with
-          | `Ok unsat_core -> unsat_core (* TODO *)
-          | _ -> assert false (* some kind of fatal error ? *)
-        in
-        Log.debugf 5 (fun k->k"lra: solver returns UNSAT@ with cert %a"
-                         (Fmt.Dump.list Tag.pp) unsat_core);
-        (* TODO: produce and store a proper LRA resolution proof *)
-        let confl =
-          unsat_core
-          |> Iter.of_list
-          |> Iter.flat_map_l (fun tag -> Tag.to_lits si tag)
-          |> Iter.map Lit.neg
-          |> Iter.to_rev_list
-        in
-        SI.raise_conflict si acts confl SI.P.default
-    end;
     ()
 
   let create_and_setup si =
@@ -446,6 +483,7 @@ module Make(A : ARG) : S with module A = A = struct
     (* TODO    SI.add_simplifier si (simplify st); *)
     SI.add_preprocess si (preproc_lra st);
     SI.on_final_check si (final_check_ st);
+    SI.on_partial_check si (partial_check_ st);
     SI.on_cc_post_merge si
       (fun _ _ n1 n2 ->
          if A.has_ty_real (N.term n1) then (

src/arith/lra/simplex.ml

@@ -1,765 +0,0 @@
-(*
-  copyright (c) 2014-2018, Guillaume Bury, Simon Cruanes
-  *)
-
-(* OPTIMS:
- * - distinguish separate systems (that do not interact), such as in { 1 <= 3x = 3y <= 2; z <= 3} ?
- * - Implement gomorry cuts ?
-*)
-
-module Fmt = CCFormat
-module type VAR = Linear_expr_intf.VAR
-module type FRESH = Linear_expr_intf.FRESH
-module type VAR_GEN = Linear_expr_intf.VAR_GEN
-
-module type S = Simplex_intf.S
-module type S_FULL = Simplex_intf.S_FULL
-
-module Vec = CCVector
-
-module Matrix : sig
-  type 'a t
-
-  val create : unit -> 'a t
-  val get : 'a t -> int -> int -> 'a
-  val set : 'a t -> int -> int -> 'a -> unit
-  val get_row : 'a t -> int -> 'a Vec.vector
-  val copy : 'a t -> 'a t
-  val n_row : _ t -> int
-  val n_col : _ t -> int
-  val push_row : 'a t -> 'a -> unit (* new row, filled with element *)
-  val push_col : 'a t -> 'a -> unit (* new column, filled with element *)
-
-  (**/**)
-  val check_invariants : _ t -> bool
-  (**/**)
-end = struct
-  type 'a t = {
-    mutable n_col: int; (* num of columns *)
-    tab: 'a Vec.vector Vec.vector;
-  }
-
-  let[@inline] create() : _ = {tab=Vec.create(); n_col=0}
-
-  let[@inline] get m i j = Vec.get (Vec.get m.tab i) j
-  let[@inline] get_row m i = Vec.get m.tab i
-  let[@inline] set (m:_ t) i j x = Vec.set (Vec.get m.tab i) j x
-  let[@inline] copy m = {m with tab=Vec.map Vec.copy m.tab}
-
-  let[@inline] n_row m = Vec.length m.tab
-  let[@inline] n_col m = m.n_col
-
-  let push_row m x = Vec.push m.tab (Vec.make (n_col m) x)
-  let push_col m x =
-    m.n_col <- m.n_col + 1;
-    Vec.iter (fun row -> Vec.push row x) m.tab
-
-  let check_invariants m = Vec.for_all (fun r -> Vec.length r = n_col m) m.tab
-end
-
-(* use non-polymorphic comparison ops *)
-open CCInt.Infix
-
-(* Simplex Implementation *)
-module Make_inner
-    (Var: VAR)
-    (VMap : CCMap.S with type key=Var.t)
-    (Param: sig type t val copy : t -> t end)
-= struct
-  module Var_map = VMap
-  module M = Var_map
-
-  type param = Param.t
-  type var = Var.t
-  type lit = Var.lit
-
-  type erat = {
-    base: Q.t; (* reference number *)
-    eps_factor: Q.t; (* coefficient for epsilon, the infinitesimal *)
-  }
-
-  (** Epsilon-rationals, used for strict bounds *)
-  module Erat = struct
-    type t = erat
-
-    let zero : t = {base=Q.zero; eps_factor=Q.zero}
-
-    let[@inline] make base eps_factor : t = {base; eps_factor}
-    let[@inline] base t = t.base
-    let[@inline] eps_factor t = t.eps_factor
-    let[@inline] mul k e = make Q.(k * e.base) Q.(k * e.eps_factor)
-    let[@inline] sum e1 e2 = make Q.(e1.base + e2.base) Q.(e1.eps_factor + e2.eps_factor)
-    let[@inline] compare e1 e2 = match Q.compare e1.base e2.base with
-      | 0 -> Q.compare e1.eps_factor e2.eps_factor
-      | x -> x
-
-    let lt a b = compare a b < 0
-    let gt a b = compare a b > 0
-
-    let[@inline] min x y = if compare x y <= 0 then x else y
-    let[@inline] max x y = if compare x y >= 0 then x else y
-
-    let[@inline] evaluate (epsilon:Q.t) (e:t) : Q.t = Q.(e.base + epsilon * e.eps_factor)
-
-    let pp out e =
-      if Q.equal Q.zero (eps_factor e)
-      then Q.pp_print out (base e)
-      else
-        Fmt.fprintf out "(@[<h>%a + @<1>ε * %a@])"
-          Q.pp_print (base e) Q.pp_print (eps_factor e)
-  end
-
-  let str_of_var = Fmt.to_string Var.pp
-  let str_of_erat = Fmt.to_string Erat.pp
-  let str_of_q = Fmt.to_string Q.pp_print
-
-  type bound = {
-    value : Erat.t;
-    reason : lit option;
-  }
-
-  (* state associated with a variable *)
-  type var_state = {
-    var: var;
-    mutable assign: Erat.t option; (* current assignment *)
-    mutable l_bound: bound; (* lower bound *)
-    mutable u_bound: bound; (* upper bound *)
-    mutable idx_basic: int; (* index in [t.nbasic] *)
-    mutable idx_nbasic: int; (* index in [t.nbasic] *)
-  }
-
-  (* Exceptions *)
-  exception Unsat of var_state
-  exception AbsurdBounds of var_state
-  exception NoneSuitable
-
-  type basic_var = var_state
-  type nbasic_var = var_state
-
-  type t = {
-    param: param;
-    mutable var_states: var_state M.t; (* var -> its state *)
-    tab : Q.t Matrix.t; (* the matrix of coefficients *)
-    basic : basic_var Vec.vector; (* basic variables *)
-    nbasic : nbasic_var Vec.vector; (* non basic variables *)
-  }
-
-  type cert = {
-    cert_var: var;
-    cert_expr: (Q.t * var) list;
-  }
-
-  type res =
-    | Solution of Q.t Var_map.t
-    | Unsatisfiable of cert
-
-  let create param : t = {
-    param;
-    var_states = M.empty;
-    tab = Matrix.create ();
-    basic = Vec.create ();
-    nbasic = Vec.create ();
-  }
-
-  let[@inline] index_basic (x:basic_var) : int = x.idx_basic
-  let[@inline] index_nbasic (x:nbasic_var) : int = x.idx_nbasic
-
-  let[@inline] is_basic (x:var_state) : bool = x.idx_basic >= 0
-  let[@inline] is_nbasic (x:var_state) : bool = x.idx_nbasic >= 0
-
-  (* check invariants, for test purposes *)
-  let check_invariants (t:t) : bool =
-    Matrix.check_invariants t.tab &&
-    Vec.for_all (fun v -> is_basic v) t.basic &&
-    Vec.for_all (fun v -> is_nbasic v) t.nbasic &&
-    Vec.for_all (fun v -> not (is_nbasic v)) t.basic &&
-    Vec.for_all (fun v -> not (is_basic v)) t.nbasic &&
-    Vec.for_all (fun v -> CCOpt.is_some v.assign) t.nbasic &&
-    Vec.for_all (fun v -> CCOpt.is_none v.assign) t.basic &&
-    true
-
-  (* find the definition of the basic variable [x],
-     as a linear combination of non basic variables *)
-  let find_expr_basic_opt t (x:var_state) : Q.t Vec.vector option =
-    begin match index_basic x with
-      | -1 -> None
-      | i -> Some (Matrix.get_row t.tab i)
-    end
-
-  (* expression that defines a basic variable in terms of non-basic variables *)
-  let find_expr_basic t (x:basic_var) : Q.t Vec.vector =
-    let i = index_basic x in
-    assert (i >= 0);
-    Matrix.get_row t.tab i
-
-  (* build the expression [y = \sum_i (if x_i=y then 1 else 0)·x_i] *)
-  let find_expr_nbasic t (x:nbasic_var) : Q.t Vec.vector =
-    Vec.map
-      (fun y -> if x == y then Q.one else Q.zero)
-      t.nbasic
-
-  (* find expression of [x] *)
-  let find_expr_total (t:t) (x:var_state) : Q.t Vec.vector =
-    match find_expr_basic_opt t x with
-    | Some e -> e
-    | None ->
-      assert (is_nbasic x);
-      find_expr_nbasic t x
-
-  (* compute value of basic variable.
-     It can be computed by using [x]'s definition
-     in terms of nbasic variables, which have values *)
-  let value_basic (t:t) (x:basic_var) : Erat.t =
-    assert (is_basic x);
-    let res = ref Erat.zero in
-    let expr = find_expr_basic t x in
-    for i = 0 to Vec.length expr - 1 do
-      let val_nbasic_i =
-        match (Vec.get t.nbasic i).assign with
-        | None -> assert false
-        | Some e -> e
-      in
-      res := Erat.sum !res (Erat.mul (Vec.get expr i) val_nbasic_i)
-    done;
-    !res
-
-  (* extract a value for [x] *)
-  let[@inline] value (t:t) (x:var_state) : Erat.t =
-    match x.assign with
-    | Some e -> e
-    | None -> value_basic t x
-
-  (* trivial bounds *)
-  let empty_bounds : bound * bound =
-    { value = Erat.make Q.minus_inf Q.zero; reason = None; },
-    { value = Erat.make Q.inf Q.zero; reason = None; }
-
-  (* find bounds of [x] *)
-  let[@inline] get_bounds (x:var_state) : bound * bound =
-    x.l_bound, x.u_bound
-
-  let[@inline] get_bounds_values (x:var_state) : Erat.t * Erat.t =
-    let l, u = get_bounds x in
-    l.value, u.value
-
-  (* is [value x] within the bounds for [x]? *)
-  let is_within_bounds (t:t) (x:var_state) : bool * Erat.t =
-    let v = value t x in
-    let low, upp = get_bounds_values x in
-    if Erat.compare v low < 0 then
-      false, low
-    else if Erat.compare v upp > 0 then
-      false, upp
-    else
-      true, v
-
-  (* add [v] as a non-basic variable, or return its state if already mapped *)
-  let get_var_or_add_as_nbasic (t:t) (v:var) : var_state =
-    match M.get v t.var_states with
-    | Some v -> v
-    | None ->
-      let l_bound, u_bound = empty_bounds in
-      let idx_nbasic = Vec.length t.nbasic in
-      let vs = {
-        var=v; l_bound; u_bound;
-        assign=Some Erat.zero;
-        idx_nbasic; idx_basic=(-1);
-      } in
-      t.var_states <- M.add v vs t.var_states;
-      Vec.push t.nbasic vs;
-      Matrix.push_col t.tab Q.zero; (* new empty column *)
-      vs
-
-  (* add new variables as nbasic variables, return them, ignore
-     the already existing variables *)
-  let add_vars_as_nbasic (t:t) (l:var list) : unit =
-    List.iter
-      (fun x ->
-         if not (M.mem x t.var_states) then  (
-           (* allocate new index for [x] *)
-           ignore (get_var_or_add_as_nbasic t x : var_state)
-         ))
-      l
-
-  (* define basic variable [x] by [eq] in [t] *)
-  let add_eq (t:t) (x, eq : var * _ list) : unit =
-    let eq = List.map (fun (coeff,x) -> coeff, get_var_or_add_as_nbasic t x) eq in
-    (* add [x] as a basic var *)
-    begin match M.get x t.var_states with
-      | Some _ ->
-        invalid_arg (Fmt.sprintf "Variable `%a` already defined." Var.pp x);
-      | None ->
-        let l_bound, u_bound = empty_bounds in
-        let idx_basic = Vec.length t.basic in
-        let vs = {
-          var=x; l_bound; u_bound; assign=None; idx_basic;
-          idx_nbasic=(-1);
-        } in
-        Vec.push t.basic vs;
-        t.var_states <- M.add x vs t.var_states;
-    end;
-    (* add new row for defining [x] *)
-    assert (Matrix.n_col t.tab > 0);
-    Matrix.push_row t.tab Q.zero;
-    let row_i = Matrix.n_row t.tab - 1 in
-    assert (row_i >= 0);
-
-    (* now put into the row the coefficients corresponding to [eq],
-       expanding basic variables to their definition *)
-    List.iter
-      (fun (c, x) ->
-         (* FIXME(perf): replace with a `idx -> Q.t` function, do not allocate vector *)
-         let expr = find_expr_total t x in
-         assert (Vec.length expr = Matrix.n_col t.tab);
-         Vec.iteri
-           (fun j c' ->
-              if not (Q.equal Q.zero c') then (
-                Matrix.set t.tab row_i j Q.(Matrix.get t.tab row_i j + c * c')
-              ))
-           expr)
-      eq;
-    ()
-
-  (* add bounds to [x] in [t] *)
-  let add_bound_aux (x:var_state)
-      (low:Erat.t) (low_reason:lit option)
-      (upp:Erat.t) (upp_reason:lit option) : unit =
-    let l, u = get_bounds x in
-    let l' = if Erat.lt low l.value then l else { value = low; reason = low_reason; } in
-    let u' = if Erat.gt upp u.value then u else { value = upp; reason = upp_reason; } in
-    x.l_bound <- l';
-    x.u_bound <- u';
-    ()
-
-  let add_bounds (t:t)
-      ?strict_lower:(slow=false) ?strict_upper:(supp=false)
-      ?lower_reason ?upper_reason (x, l, u) : unit =
-    let x = get_var_or_add_as_nbasic t x in
-    let e1 = if slow then Q.one else Q.zero in
-    let e2 = if supp then Q.neg Q.one else Q.zero in
-    add_bound_aux x (Erat.make l e1) lower_reason (Erat.make u e2) upper_reason;
-    if is_nbasic x then (
-      let b, v = is_within_bounds t x in
-      if not b then (
-        x.assign <- Some v;
-      )
-    )
-
-  let add_lower_bound t ?strict ~reason x l =
-    add_bounds t ?strict_lower:strict ~lower_reason:reason (x,l,Q.inf)
-
-  let add_upper_bound t ?strict ~reason x u =
-    add_bounds t ?strict_upper:strict ~upper_reason:reason (x,Q.minus_inf,u)
-
-  let iter_all_vars (t:t) : var_state Iter.t =
-    Iter.append (Vec.to_iter t.nbasic) (Vec.to_iter t.basic)
-
-  (* full assignment *)
-  let full_assign (t:t) : (var * Erat.t) Iter.t =
-    Iter.append (Vec.to_iter t.nbasic) (Vec.to_iter t.basic)
-    |> Iter.map (fun x -> x.var, value t x)
-
-  let[@inline] min x y = if Q.compare x y < 0 then x else y
-
-  (* Find an epsilon that is small enough for finding a solution, yet
-     it must be positive.
-
-     {!Erat.t} values are used to turn strict bounds ([X > 0]) into
-     non-strict bounds ([X >= 0 + ε]), because the simplex algorithm
-     only deals with non-strict bounds.
-     When a solution is found, we need to turn {!Erat.t} into {!Q.t} by
-     finding a rational value that is small enough that it will fit into
-     all the intervals of [t]. This rational will be the actual value of [ε].
-  *)
-  let solve_epsilon (t:t) : Q.t =
-    let emax =
-      Iter.fold
-        (fun emax x ->
-           let { value = {base=low;eps_factor=e_low}; _} = x.l_bound in
-           let { value = {base=upp;eps_factor=e_upp}; _} = x.u_bound in
-           let {base=v; eps_factor=e_v} = value t x in
-           (* lower bound *)
-           let emax =
-             if Q.compare low Q.minus_inf > 0 && Q.compare e_v e_low < 0
-             then min emax Q.((low - v) / (e_v - e_low))
-             else emax
-           in
-           (* upper bound *)
-           if Q.compare upp Q.inf < 0 && Q.compare e_v e_upp > 0
-           then min emax Q.((upp - v) / (e_v - e_upp))
-           else emax)
-        Q.inf (iter_all_vars t)
-    in
-    if Q.compare emax Q.one >= 0 then Q.one else emax
-
-  let get_full_assign_seq (t:t) : _ Iter.t =
-    let e = solve_epsilon t in
-    let f = Erat.evaluate e in
-    full_assign t
-    |> Iter.map (fun (x,v) -> x, f v)
-
-  let get_full_assign t : Q.t Var_map.t = Var_map.of_iter (get_full_assign_seq t)
-
-  (* Find nbasic variable suitable for pivoting with [x].
-     A nbasic variable [y] is suitable if it "goes into the right direction"
-     (its coefficient in the definition of [x] is of the adequate sign)
-     and if it hasn't reached its bound in this direction.
-
-     precondition: [x] is a basic variable whose value in current assignment
-       is outside its bounds
-
-     We return the smallest (w.r.t Var.compare) suitable variable.
-     This is important for termination.
-  *)
-  let find_suitable_nbasic_for_pivot (t:t) (x:basic_var) : nbasic_var * Q.t =
-    Profile.with_ "simplex.find-pivot-var" @@ fun () ->
-    assert (is_basic x);
-    let _, v = is_within_bounds t x in
-    let b = Erat.compare (value t x) v < 0 in
-    (* is nbasic var [y], with coeff [a] in definition of [x], suitable? *)
-    let test (y:nbasic_var) (a:Q.t) : bool =
-      assert (is_nbasic y);
-      let v = value t y in
-      let low, upp = get_bounds_values y in
-      if b then (
-        (Erat.lt v upp && Q.compare a Q.zero > 0) ||
-        (Erat.gt v low && Q.compare a Q.zero < 0)
-      ) else (
-        (Erat.gt v low && Q.compare a Q.zero > 0) ||
-        (Erat.lt v upp && Q.compare a Q.zero < 0)
-      )
-    in
-    let nbasic_vars = t.nbasic in
-    let expr = find_expr_basic t x in
-    (* find best suitable variable *)
-    let rec aux i =
-      if i = Vec.length nbasic_vars then (
-        assert (i = Vec.length expr);
-        None
-      ) else (
-        let y = Vec.get nbasic_vars i in
-        let a = Vec.get expr i in
-        if test y a then (
-          (* see if other variables are better suited *)
-          begin match aux (i+1) with
-            | None -> Some (y,a)
-            | Some (z, _) as res_tail ->
-              if Var.compare y.var z.var <= 0
-              then Some (y,a)
-              else res_tail
-          end
-        ) else (
-          aux (i+1)
-        )
-      )
-    in
-    begin match aux 0 with
-      | Some res -> res
-      | None ->  raise NoneSuitable
-    end
-
-  (* pivot to exchange [x] and [y] *)
-  let pivot (t:t) (x:basic_var) (y:nbasic_var) (a:Q.t) : unit =
-    Profile.with_ "simplex.pivot" @@ fun () ->
-    (* swap values ([x] becomes assigned) *)
-    let val_x = value t x in
-    y.assign <- None;
-    x.assign <- Some val_x;
-    (* Matrix Pivot operation *)
-    let kx = index_basic x in
-    let ky = index_nbasic y in
-    for j = 0 to Vec.length t.nbasic - 1 do
-      if y == Vec.get t.nbasic j then (
-        Matrix.set t.tab kx j Q.(inv a)
-      ) else (
-        Matrix.set t.tab kx j Q.(neg (Matrix.get t.tab kx j) / a)
-      )
-    done;
-    for i = 0 to Vec.length t.basic - 1 do
-      if i <> kx then (
-        let c = Matrix.get t.tab i ky in
-        Matrix.set t.tab i ky Q.zero;
-        for j = 0 to Vec.length t.nbasic - 1 do
-          Matrix.set t.tab i j Q.(Matrix.get t.tab i j + c * Matrix.get t.tab kx j)
-        done
-      )
-    done;
-    (* Switch x and y in basic and nbasic vars *)
-    Vec.set t.basic kx y;
-    Vec.set t.nbasic ky x;
-    x.idx_basic <- -1;
-    y.idx_basic <- kx;
-    x.idx_nbasic <- ky;
-    y.idx_nbasic <- -1;
-    ()
-
-  (* find minimum element of [arr] (wrt [cmp]) that satisfies predicate [f] *)
-  let find_min_filter ~cmp (f:'a -> bool) (arr:('a,_) Vec.t) : 'a option =
-    (* find the first element that satisfies [f] *)
-    let rec aux_find_first i =
-      if i = Vec.length arr then None
-      else (
-        let x = Vec.get arr i in
-        if f x
-        then aux_compare_with x (i+1)
-        else aux_find_first (i+1)
-      )
-    (* find if any element of [l] satisfies [f] and is smaller than [x] *)
-    and aux_compare_with x i =
-      if i = Vec.length arr then Some x
-      else (
-        let y = Vec.get arr i in
-        let best = if f y && cmp y x < 0 then y else x in
-        aux_compare_with best (i+1)
-      )
-    in
-    aux_find_first 0
-
-  (* check bounds *)
-  let check_bounds (t:t) : unit =
-    iter_all_vars t
-      (fun x ->
-         let l = x.l_bound in
-         let u = x.u_bound in
-         if Erat.gt l.value u.value then raise (AbsurdBounds x))
-
-  let[@inline] compare_by_var x y = Var.compare x.var y.var
-
-  (* actual solving algorithm *)
-  let solve_aux (t:t) : unit =
-    Profile.instant
-      (Printf.sprintf "(simplex.solve :basic %d :non-basic %d)"
-         (Vec.length t.basic) (Vec.length t.nbasic));
-    check_bounds t;
-    (* select the smallest basic variable that is not satisfied in the current
-       assignment. *)
-    let rec aux_select_basic_var () =
-      match
-        Profile.with_ "simplex.select-basic-var" @@ fun () ->
-        find_min_filter ~cmp:compare_by_var
-          (fun x -> not (fst (is_within_bounds t x)))
-          t.basic
-      with
-        | Some x -> aux_pivot_on_basic x
-        | None -> ()
-    (* remove the basic variable *)
-    and aux_pivot_on_basic x =
-      let _b, v = is_within_bounds t x in
-      assert (not _b);
-      match find_suitable_nbasic_for_pivot t x with
-        | y, a ->
-          (* exchange [x] and [y] by pivoting *)
-          pivot t x y a;
-          (* assign [x], now a nbasic variable, to the faulty bound [v] *)
-          x.assign <- Some v;
-          (* next iteration *)
-          aux_select_basic_var ()
-        | exception NoneSuitable ->
-          raise (Unsat x)
-    in
-    aux_select_basic_var ();
-    ()
-
-  (* main method for the user to call *)
-  let solve (t:t) : res =
-    try
-      solve_aux t;
-      Solution (get_full_assign t)
-    with
-      | Unsat x ->
-        let cert_expr =
-          List.combine
-            (Vec.to_list (find_expr_basic t x))
-            (Vec.to_list t.nbasic |> CCList.map (fun x -> x.var))
-        in
-        Unsatisfiable { cert_var=x.var; cert_expr; } (* FIXME *)
-      | AbsurdBounds x ->
-        Unsatisfiable { cert_var=x.var; cert_expr=[]; }
-
-  (* add [c·x] to [m] *)
-  let add_expr_ (x:var) (c:Q.t) (m:Q.t M.t) =
-    let c' = M.get_or ~default:Q.zero x m in
-    let c' = Q.(c + c') in
-    if Q.equal Q.zero c' then M.remove x m else M.add x c' m
-
-  (* dereference basic variables from [c·x], and add the result to [m] *)
-  let rec deref_var_ t x c m =
-    match find_expr_basic_opt t x with
-    | None -> add_expr_ x.var c m
-    | Some expr_x ->
-      let m = ref m in
-      Vec.iteri
-        (fun i c_i ->
-           let y_i = Vec.get t.nbasic i in
-           m := deref_var_ t y_i Q.(c * c_i) !m)
-        expr_x;
-      !m
-
-  (* maybe invert bounds, if [c < 0] *)
-  let scale_bounds c (l,u) : bound * bound =
-    match Q.compare c Q.zero with
-      | 0 ->
-        let b = { value = Erat.zero; reason = None; } in
-        b, b
-      | n when n<0 ->
-        { u with value = Erat.mul c u.value; },
-        { l with value = Erat.mul c l.value; }
-      | _ ->
-        { l with value = Erat.mul c l.value; },
-        { u with value = Erat.mul c u.value; }
-
-  let add_to_unsat_core acc = function
-    | None -> acc
-    | Some reason -> reason :: acc
-
-  let check_cert (t:t) (c:cert) =
-    let x = M.get c.cert_var t.var_states |> CCOpt.get_lazy (fun()->assert false) in
-    let { value = low_x; reason = low_x_reason; } = x.l_bound in
-    let { value = up_x; reason = upp_x_reason; } = x.u_bound in
-    begin match c.cert_expr with
-      | [] ->
-        if Erat.compare low_x up_x > 0
-        then `Ok (add_to_unsat_core (add_to_unsat_core [] low_x_reason) upp_x_reason)
-        else `Bad_bounds (str_of_erat low_x, str_of_erat up_x)
-      | expr ->
-        let e0 = deref_var_ t x (Q.neg Q.one) M.empty in
-        (* compute bounds for the expression [c.cert_expr],
-           and also compute [c.cert_expr - x] to check if it's 0] *)
-        let low, low_unsat_core, up, up_unsat_core, expr_minus_x =
-          List.fold_left
-            (fun (l, luc, u, uuc, expr_minus_x) (c, y) ->
-               let y = M.get y t.var_states |> CCOpt.get_lazy (fun ()->assert false) in
-               let ly, uy = scale_bounds c (get_bounds y) in
-               assert (Erat.compare ly.value uy.value <= 0);
-               let expr_minus_x = deref_var_ t y c expr_minus_x in
-               let luc = add_to_unsat_core luc ly.reason in
-               let uuc = add_to_unsat_core uuc uy.reason in
-               Erat.sum l ly.value, luc, Erat.sum u uy.value, uuc, expr_minus_x)
-            (Erat.zero, [], Erat.zero, [], e0)
-            expr
-        in
-        (* check that the expanded expression is [x], and that
-           one of the bounds on [x] is incompatible with bounds of [c.cert_expr] *)
-        if M.is_empty expr_minus_x then (
-          if Erat.compare low_x up > 0
-          then `Ok (add_to_unsat_core up_unsat_core low_x_reason)
-          else if Erat.compare up_x low < 0
-          then `Ok (add_to_unsat_core low_unsat_core upp_x_reason)
-          else `Bad_bounds (str_of_erat low, str_of_erat up)
-        ) else `Diff_not_0 expr_minus_x
-    end
-
-  (* printer *)
-
-  let matrix_pp_width = ref 8
-
-  let fmt_head = format_of_string "|%*s|| "
-  let fmt_cell = format_of_string "%*s| "
-
-  let pp_cert out (c:cert) = match c.cert_expr with
-    | [] -> Fmt.fprintf out "(@[inconsistent-bounds %a@])" Var.pp c.cert_var
-    | _ ->
-      let pp_pair = Fmt.(hvbox ~i:2 @@ pair ~sep:(return "@ * ") Q.pp_print Var.pp) in
-      Fmt.fprintf out "(@[<hv>cert@ :var %a@ :linexp %a@])"
-        Var.pp c.cert_var
-        Fmt.(within "[" "]" @@ hvbox @@ list ~sep:(return "@ + ") pp_pair)
-        c.cert_expr
-
-  let pp_mat out t =
-    let open Fmt in
-    fprintf out "@[<v>";
-    (* header *)
-    fprintf out fmt_head !matrix_pp_width "";
-    Vec.iter (fun x -> fprintf out fmt_cell !matrix_pp_width (str_of_var x.var)) t.nbasic;
-    fprintf out "@,";
-    (* rows *)
-    for i=0 to Matrix.n_row t.tab-1 do
-      if i>0 then fprintf out "@,";
-      let v = Vec.get t.basic i in
-      fprintf out fmt_head !matrix_pp_width (str_of_var v.var);
-      let row = Matrix.get_row t.tab i in
-      Vec.iter (fun q -> fprintf out fmt_cell !matrix_pp_width (str_of_q q)) row;
-    done;
-    fprintf out "@]"
-
-  let pp_vars =
-    let ppv out v =
-      Fmt.fprintf out "(@[var %a@ :assign %a@ :lbound %a@ :ubound %a@])"
-        Var.pp v.var (Fmt.Dump.option Erat.pp) v.assign
-        Erat.pp v.l_bound.value Erat.pp v.u_bound.value
-    in
-    Fmt.(within "(" ")" @@ hvbox @@ iter ppv)
-
-  let pp_full_state out (t:t) : unit =
-    (* print main matrix *)
-    Fmt.fprintf out
-      "(@[<hv>simplex@ :n-row %d :n-col %d@ :mat %a@ :vars %a @])"
-      (Matrix.n_row t.tab) (Matrix.n_col t.tab) pp_mat t
-      pp_vars (iter_all_vars t)
-end
-
-module Make(Var:VAR) =
-  Make_inner(Var)(CCMap.Make(Var))(struct
-    type t = unit
-    let copy ()=()
-  end)
-
-module Make_full_for_expr(V : VAR_GEN)
-    (L : Linear_expr.S
-     with type Var.t = V.t
-      and type C.t = Q.t
-      and type Var.lit = V.lit)
-  : S_FULL with type var = V.t
-            and type lit = V.lit
-            and module L = L
-            and module Var_map = L.Var_map
-            and type L.var = V.t
-            and type L.Comb.t = L.Comb.t
-            and type param = V.Fresh.t
-= struct
-  include Make_inner(V)(L.Var_map)(V.Fresh)
-  module L = L
-
-  type op = Predicate.t = Leq | Geq | Lt | Gt | Eq | Neq
-
-  type constr = L.Constr.t
-
-  (* add a constraint *)
-  let add_constr (t:t) (c:constr) (reason:lit) : unit =
-    let e, op, q = L.Constr.split c in
-    match L.Comb.as_singleton e with
-    | Some (c0, x0) ->
-      (* no need for a fresh variable, just add constraint on [x0] *)
-      let q = Q.div q c0 in
-      let op = if Q.sign c0 < 0 then Predicate.neg_sign op else op in
-      begin match op with
-        | Leq -> add_upper_bound t ~strict:false ~reason x0 q
-        | Geq -> add_lower_bound t ~strict:false ~reason x0 q
-        | Lt -> add_upper_bound t ~strict:true ~reason x0 q
-        | Gt -> add_lower_bound t ~strict:true ~reason x0 q
-        | Eq -> add_bounds t (x0,q,q)
-                  ~strict_lower:false ~strict_upper:false
-                  ~lower_reason:reason ~upper_reason:reason
-        | Neq -> assert false
-      end
-    | None ->
-      let (x:var) = V.Fresh.fresh t.param in
-      add_eq t (x, L.Comb.to_list e);
-      begin match op with
-        | Leq -> add_upper_bound t ~strict:false ~reason x q
-        | Geq -> add_lower_bound t ~strict:false ~reason x q
-        | Lt -> add_upper_bound t ~strict:true ~reason x q
-        | Gt -> add_lower_bound t ~strict:true ~reason x q
-        | Eq -> add_bounds t (x,q,q)
-                  ~strict_lower:false ~strict_upper:false
-                  ~lower_reason:reason ~upper_reason:reason
-        | Neq -> assert false
-      end
-end
-
-module Make_full(V : VAR_GEN)
-  : S_FULL with type var = V.t
-            and type lit = V.lit
-            and type L.var = V.t
-            and type param = V.Fresh.t
-  = Make_full_for_expr(V)(Linear_expr.Make(struct include Q let pp = pp_print end)(V))

src/arith/lra/simplex.mli

@@ -1,33 +0,0 @@
-
-(** Solving Linear systems of rational equations. *)
-
-module type VAR = Linear_expr_intf.VAR
-module type FRESH = Linear_expr_intf.FRESH
-module type VAR_GEN = Linear_expr_intf.VAR_GEN
-
-module type S = Simplex_intf.S
-module type S_FULL = Simplex_intf.S_FULL
-
-(** Low level simplex interface *)
-module Make(V : VAR) :
-  S with type var = V.t
-     and type lit = V.lit
-     and type param = unit
-     and module Var_map = CCMap.Make(V)
-
-(** High-level simplex interface *)
-module Make_full_for_expr(V : VAR_GEN)
-    (L : Linear_expr.S with type Var.t = V.t and type Var.lit = V.lit and type C.t = Q.t)
-  : S_FULL with type var = V.t
-            and type lit = V.lit
-            and module L = L
-            and module Var_map = L.Var_map
-            and type L.var = V.t
-            and type L.Comb.t = L.Comb.t
-            and type param = V.Fresh.t
-
-module Make_full(V : VAR_GEN)
-  : S_FULL with type var = V.t
-            and type lit = V.lit
-            and type L.var = V.t
-            and type param = V.Fresh.t

src/arith/tests/run_tests.ml

@@ -6,7 +6,6 @@ let tests : unit Alcotest.test list = [
 let props =
   List.flatten
     [ Test_simplex2.props;
-      Test_simplex.props;
     ]
 
 let () =

src/arith/tests/test_simplex.ml

@@ -1,180 +0,0 @@
-module Fmt = CCFormat
-module QC = QCheck
-
-module Var = struct
-  include CCInt
-
-  let pp out x = Format.fprintf out "X_%d" x
-
-  let rand n : t QC.arbitrary = QC.make ~print:(Fmt.to_string pp) @@ QC.Gen.(0--n)
-  type lit = int
-  let pp_lit = Fmt.int
-
-  module Fresh = struct
-    type var = t
-    type t = int ref
-    let copy r = ref !r
-    let create() = ref ~-1
-    let fresh r = decr r; !r
-  end
-end
-
-module L = Sidekick_arith_lra.Linear_expr.Make(struct include Q let pp=pp_print end)(Var)
-module Spl = Sidekick_arith_lra.Simplex.Make_full_for_expr(Var)(L)
-module Var_map = Spl.Var_map
-
-let rand_n low n : Z.t QC.arbitrary =
-  QC.map ~rev:Z.to_int Z.of_int QC.(low -- n)
-
-let rand_q : Q.t QC.arbitrary =
-  let n1 = rand_n ~-100_000 100_000 in
-  let n2 = rand_n 1 40_000 in
-  let qc =
-    QC.map ~rev:(fun q -> Q.num q, Q.den q)
-      (fun (x,y) -> Q.make x y)
-      (QC.pair n1 n2)
-  in
-  (* avoid [undef] when shrinking *)
-  let shrink q yield =
-    CCOpt.get_exn qc.QC.shrink q (fun x -> if Q.is_real x then yield x)
-  in
-  QC.set_shrink shrink qc
-
-type subst = Spl.L.subst
-
-(* NOTE: should arrive in qcheck at some point *)
-let filter_shrink (f:'a->bool) (a:'a QC.arbitrary) : 'a QC.arbitrary =
-  match a.QC.shrink with
-    | None -> a
-    | Some shr -> QC.set_shrink (QC.Shrink.filter f shr) a
-
-module Comb = struct
-  include Spl.L.Comb
-
-  let rand n : t QC.arbitrary =
-    let a =
-      QC.map_same_type (fun e -> if is_empty e then monomial1 0 else e) @@
-      QC.map ~rev:to_list of_list @@
-      QC.list_of_size QC.Gen.(1--n) @@ QC.pair rand_q (Var.rand 10)
-    in
-    filter_shrink (fun e -> not (is_empty e)) a
-end
-
-module Expr = struct
-  include Spl.L.Expr
-
-  let rand n : t QC.arbitrary =
-    QC.map ~rev:(fun e->comb e, const e) (CCFun.uncurry make) @@
-    QC.pair (Comb.rand n) rand_q
-end
-
-module Constr = struct
-  include Spl.L.Constr
-
-  let shrink c : t QC.Iter.t =
-    let open QC.Iter in
-    CCOpt.map_or ~default:empty
-      (fun s -> s c.expr >|= fun expr -> {c with expr})
-      (Expr.rand 5).QC.shrink
-
-  let rand n : t QC.arbitrary =
-    let gen =
-      QC.Gen.(
-        return of_expr <*>
-          (Expr.rand n).QC.gen <*>
-          oneofl Sidekick_arith_lra.Predicate.([Leq;Geq;Lt;Gt;Eq])
-      )
-    in
-    QC.make ~print:(Fmt.to_string pp) ~shrink gen
-end
-
-module Problem = struct
-  type t = Constr.t list
-
-  module Infix = struct
-    let (&&) = List.rev_append
-  end
-  include Infix
-
-  let eval subst = List.for_all (L.Constr.eval subst)
-
-  let pp out pb = Fmt.(hvbox @@ list ~sep:(return "@ @<1>∧ ") L.Constr.pp) out pb
-
-  let rand ?min:(m=3) n : t QC.arbitrary =
-    let n = max m (max n 6) in
-    QC.list_of_size QC.Gen.(m -- n) @@ Constr.rand 10
-end
-
-let add_problem (t:Spl.t) (pb:Problem.t) : unit =
-  let lit = 0 in
-  List.iter (fun constr -> Spl.add_constr t constr lit) pb
-
-let pp_subst : subst Fmt.printer =
-  Fmt.(map Spl.L.Var_map.to_iter @@
-    within "{" "}" @@ hvbox @@ iter ~sep:(return ",@ ") @@
-    pair ~sep:(return "@ @<1>→ ") Var.pp Q.pp_print
-  )
-
-let check_invariants =
-  let prop pb =
-    let simplex = Spl.create (Var.Fresh.create()) in
-    add_problem simplex pb;
-    Spl.check_invariants simplex
-  in
-  QC.Test.make ~long_factor:10 ~count:50 ~name:"simplex_invariants" (Problem.rand 20) prop
-
-let check_invariants_after_solve =
-  let prop pb =
-    let simplex = Spl.create (Var.Fresh.create()) in
-    add_problem simplex pb;
-    ignore (Spl.solve simplex);
-    if Spl.check_invariants simplex then true
-    else (
-      QC.Test.fail_reportf "(@[bad-invariants@ %a@])" Spl.pp_full_state simplex
-    )
-  in
-  QC.Test.make ~long_factor:10 ~count:50 ~name:"simplex_invariants_after_solve" (Problem.rand 20) prop
-
-let check_sound =
-  let prop pb =
-    let simplex = Spl.create (Var.Fresh.create()) in
-    add_problem simplex pb;
-    begin match Spl.solve simplex with
-      | Spl.Solution subst ->
-        if Problem.eval subst pb then true
-        else (
-          QC.Test.fail_reportf
-            "(@[<hv>bad-solution@ :problem %a@ :sol %a@ :simplex %a@])"
-            Problem.pp pb pp_subst subst Spl.pp_full_state simplex
-        )
-      | Spl.Unsatisfiable cert ->
-        begin match Spl.check_cert simplex cert with
-          | `Ok _ -> true
-          | `Bad_bounds (low, up) ->
-            QC.Test.fail_reportf
-              "(@[<hv>bad-certificat@ :problem %a@ :cert %a@ :low %s :up %s@ :simplex %a@])"
-              Problem.pp pb Spl.pp_cert cert low up Spl.pp_full_state simplex
-          | `Diff_not_0 e ->
-            QC.Test.fail_reportf
-              "(@[<hv>bad-certificat@ :problem %a@ :cert %a@ :diff %a@ :simplex %a@])"
-              Problem.pp pb Spl.pp_cert cert Comb.pp (Comb.of_map e) Spl.pp_full_state simplex
-        end
-    end
-  in
-  QC.Test.make ~long_factor:10 ~count:300 ~name:"simplex_sound" (Problem.rand 20) prop
-
-let check_scalable =
-  let prop pb =
-    let simplex = Spl.create (Var.Fresh.create()) in
-    add_problem simplex pb;
-    ignore (Spl.solve simplex);
-    true
-  in
-  QC.Test.make ~long_factor:2 ~count:10 ~name:"simplex_scalable" (Problem.rand ~min:150 150) prop
-
-
-let props = [
-  check_invariants;
-  check_sound;
-  check_scalable;
-]

src/smtlib/Process.ml

@@ -312,6 +312,9 @@ module Th_lra = Sidekick_arith_lra.Make(struct
   type term = S.T.Term.t
   type ty = S.T.Ty.t
 
+  let mk_and = Form.and_
+  let mk_or = Form.or_
+
   let mk_lra = T.lra
   let view_as_lra t = match T.view t with
     | T.LRA l -> l