simplify_formula.ml 7.73 KB
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(********************************************************************)
(*                                                                  *)
(*  The Why3 Verification Platform   /   The Why3 Development Team  *)
(*  Copyright 2010-2012   --   INRIA - CNRS - Paris-Sud University  *)
(*                                                                  *)
(*  This software is distributed under the terms of the GNU Lesser  *)
(*  General Public License version 2.1, with the special exception  *)
(*  on linking described in file LICENSE.                           *)
(*                                                                  *)
(********************************************************************)
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open Term
open Decl

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let rec fmla_simpl f = TermTF.t_map_simp (fun t -> t) fmla_simpl f
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let decl_l d =
  match d.d_node with
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    | Dprop (k,pr,f) ->
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        let f = fmla_simpl f in
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        begin match f.t_node, k with
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          | Ttrue, Paxiom -> [[]]
          | Tfalse, Paxiom -> []
          | Ttrue, Pgoal -> []
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          | _ -> [[create_prop_decl k pr f]]
        end
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    | _ -> [[DeclTF.decl_map (fun t -> t) fmla_simpl d]]
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let simplify_formula = Trans.rewriteTF (fun t -> t) fmla_simpl None
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let simplify_formula_and_task = Trans.decl_l decl_l None
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let () = Trans.register_transform
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  "simplify_formula" simplify_formula
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  ~desc:"Simplify@ the@ formulas@ using@ propositional@ simplifications."
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let () = Trans.register_transform_l
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  "simplify_formula_and_task" simplify_formula_and_task
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  ~desc:"Same as simplify_formula, but also@ \
         removes@ axioms@ and@ goals@ that@ become@ trivial."
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(** remove_trivial_quantification
    Original version in the alt-ergo prover by Sylvain Conchon *)

(** transform \exists x. x == y /\ F into F[y/x] *)
(** transform \forall x. x <> y \/ F into F[y/x] *)

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(** test if the freevariable of a term
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    are included in a given set *)
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let t_boundvars_in fvars t =
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  try
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    t_v_fold (fun () u -> if Svs.mem u fvars then raise Exit) () t;
    false
  with Exit -> true
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exception Subst_found of term

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let rec fmla_find_subst boundvars var sign f =
  let fnF = fmla_find_subst boundvars var in
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  match f.t_node with
    | Tapp (ls,[{t_node=Tvar vs} as tv;t])
    | Tapp (ls,[t;{t_node=Tvar vs} as tv])
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        when sign && ls_equal ls ps_equ && vs_equal vs var
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          && not (t_equal t tv) && not (t_boundvars_in boundvars t) ->
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        raise (Subst_found t)
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    | Tbinop (Tor, f1, f2)  when not sign -> (fnF sign f1); (fnF sign f2)
    | Tbinop (Tand, f1, f2) when sign ->  (fnF sign f1); (fnF sign f2)
    | Tbinop (Timplies, f1, f2) when not sign ->
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        (fnF (not sign) f1); (fnF sign f2)
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    | Tnot f1 -> fnF (not sign) f1
    | Tquant (_,fb) ->
        let vsl,trl,f' = t_open_quant fb in
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        if trl = []
        then
          let boundvars =
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            List.fold_left (fun s v -> Svs.add v s) boundvars vsl in
          fmla_find_subst boundvars var sign f'
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    | Tlet (_,fb) ->
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        let vs,f' = t_open_bound fb in
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        let boundvars = Svs.add vs boundvars in
        fmla_find_subst boundvars var sign f'
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    | Tcase (_,fbs) ->
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        let iter_fb fb =
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          let patl,f = t_open_branch fb in
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          let boundvars = patl.pat_vars in
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          fmla_find_subst boundvars var sign f in
        List.iter iter_fb fbs
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    | Tbinop (_, _, _) | Tif ( _, _, _) | Tapp _ | Tfalse | Ttrue-> ()
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    | Tvar _ | Tconst _ | Teps _ -> raise (FmlaExpected f)
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let rec fmla_quant sign f = function
  | [] -> [], f
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  | vs::l ->
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      let vsl, f = fmla_quant sign f l in
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      try
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        fmla_find_subst (Svs.singleton vs) vs sign f;
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        vs::vsl, f
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      with Subst_found t ->
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        let f = t_subst_single vs t f in
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        vsl, fmla_simpl f
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let rec fmla_remove_quant f =
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  match f.t_node with
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    | Tquant (k,fb) ->
        let vsl,trl,f',close = t_open_quant_cb fb in
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          if trl <> []
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          then f
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          else
            let sign = match k with
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              | Tforall -> false | Texists -> true in
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            let vsl, f' = fmla_quant sign f' vsl in
            let f' = fmla_remove_quant f' in
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            t_quant k (close vsl [] f')
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    | _ -> TermTF.t_map (fun t -> t) fmla_remove_quant f
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(*let fmla_remove_quant f =
  Format.eprintf "@[<hov>%a =>|@\n" Pretty.print_fmla f;
  let f = fmla_remove_quant f in
  Format.eprintf "|=>%a@]@.@." Pretty.print_fmla f;
  Pretty.forget_all ();
  f
*)

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let simplify_trivial_quantification =
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  Trans.rewriteTF (fun t -> t) fmla_remove_quant None
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let () = Trans.register_transform
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  "simplify_trivial_quantification" simplify_trivial_quantification
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  ~desc:"@[Simplify@ trivial@ quantifications:@]@\n  \
@[\
 - @[transform \\exists x. x == y /\\ F@ into F[y/x],@]@\n\
 - @[transform \\forall x. x <> y \\/ F@ into F[y/x].@]@]"
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let simplify_trivial_quantification_in_goal =
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  Trans.goal (fun pr f -> [create_prop_decl Pgoal pr (fmla_remove_quant f)])
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let () = Trans.register_transform
  "simplify_trivial_quantification_in_goal"
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   simplify_trivial_quantification_in_goal
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  ~desc:"Same@ as@ simplify_trivial_quantification, but@ only@ in@ goals."
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(** linearize all the subformulas with the given connector (conj/disj);
    the returned array also contains the sign of each subformula *)
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let fmla_flatten conj f =
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  let terms = ref [] in
  let rec aux sign f =
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    match f.t_node with
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    | Tnot f -> aux (not sign) f
    | Tbinop (Tor, f1, f2) when sign <> conj ->
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        aux sign f2; aux sign f1
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    | Tbinop (Tand, f1, f2) when sign = conj ->
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        aux sign f2; aux sign f1
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    | Tbinop (Timplies, f1, f2) when sign <> conj ->
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        aux sign f2; aux (not sign) f1
    | _ -> terms := (f, sign)::!terms in
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  aux true f;
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  Array.of_list !terms

(** recreate the structure of a given formula with linearized subformulas *)
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let fmla_unflatten conj f formulas =
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  let i = ref 0 in
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  let rec aux sign f = t_label_copy f (match f.t_node with
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    | Tnot f -> t_not (aux (not sign) f)
    | Tbinop (Tor, f1, f2) when sign <> conj ->
        let f1' = aux sign f1 in t_or f1' (aux sign f2)
    | Tbinop (Tand, f1, f2) when sign = conj ->
        let f1' = aux sign f1 in t_and f1' (aux sign f2)
    | Tbinop (Timplies, f1, f2) when sign <> conj ->
        let f1' = aux (not sign) f1 in t_implies f1' (aux sign f2)
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    | _ ->
        let (t, s) = formulas.(!i) in
        assert (sign = s);
        incr i;
        t) in
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  aux true f
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(** substitute all the terms that appear as a side of an equality/disequality
    and that match the given filter

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    equal terms can be substituted in all the terms of surrounding
    conjunctions, while disequal terms can be substituted in all the terms
    of surrounding disjunctions
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    substitutions are not exported outside quantifiers (even if their free
    variables are untouched), so the transformation is possibly incomplete
    (but still correct) on formulas that have inner quantifiers *)
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let fmla_cond_subst filter f =
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  let rec aux f =
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    match f.t_node with
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    | Tbinop (o, _, _) when o <> Tiff ->
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        let conj = match o with
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          Tand -> true | Tor | Timplies -> false | Tiff -> assert false in
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        let subf = fmla_flatten conj f in
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        let subl = Array.length subf in
        for i = 0 to subl - 1 do
          let (f, s) = subf.(i) in
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          subf.(i) <- (aux f, s);
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        done;
        for i = 0 to subl - 1 do
          let do_subst t1 t2 =
            for j = 0 to subl - 1 do
              if j <> i then
                let (f, s) = subf.(j) in
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                subf.(j) <- (t_replace_alpha t1 t2 f, s);
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            done in
          let (f, s) = subf.(i) in
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          match f.t_node with
          | Tapp (ls,[t1;t2]) when ls_equal ls ps_equ && s = conj ->
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              if filter t1 t2 then do_subst t1 t2 else
              if filter t2 t1 then do_subst t2 t1
          | _ -> ()
        done;
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        fmla_unflatten conj f subf
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    | _ -> TermTF.t_map (fun t -> t) aux f in
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  aux f