-(* type naif_indexing =
- (Cic.term * ((bool * Inference.equality) list)) list
-;; *)
-
-type pos = Left | Right
-;;
-
-let head_of_term =
- function
- | Cic.Appl hd::tl -> hd
- | t -> t
-;;
-
-let index table eq =
- let (_,(_,l,r,ordering),_,_) = eq in
- let hl = head_of_term l in
- let hr = head_of_term r in
- let index x pos =
- let x_entry =
- try Hashtbl.find table x
- with Not_found -> [] in
- Hashtbl.replace table x (pos,eq)::x_entry in
- (match ordering with
- | Utils.Gt ->
- index hl Left
- | Utils.Lt ->
- index hr Right
- | _ -> index hl Left;
- index hr Right);
- table
-;;
-
-let demodulate_term env table cmp term =
- let hd_term = head_of_term term in
- let candidates = Hashtbl.find table hd_term in
+(* Copyright (C) 2005, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+let debug_print = Utils.debug_print;;
+
+
+type retrieval_mode = Matching | Unification;;
+
+
+let print_candidates mode term res =
+ let _ =
+ match mode with
+ | Matching ->
+ Printf.printf "| candidates Matching %s\n" (CicPp.ppterm term)
+ | Unification ->
+ Printf.printf "| candidates Unification %s\n" (CicPp.ppterm term)
+ in
+ print_endline
+ (String.concat "\n"
+ (List.map
+ (fun (p, e) ->
+ Printf.sprintf "| (%s, %s)" (Utils.string_of_pos p)
+ (Inference.string_of_equality e))
+ res));
+ print_endline "|";
+;;
+
+
+let indexing_retrieval_time = ref 0.;;
+
+
+let apply_subst = CicMetaSubst.apply_subst
+
+
+
+(*
+(* NO INDEXING *)
+let init_index () = ()
+let empty_table () = []
+
+let index table equality =
+ let _, _, (_, l, r, ordering), _, _ = equality in
+ match ordering with
+ | Utils.Gt -> (Utils.Left, equality)::table
+ | Utils.Lt -> (Utils.Right, equality)::table
+ | _ -> (Utils.Left, equality)::(Utils.Right, equality)::table
+;;
+
+let remove_index table equality =
+ List.filter (fun (p, e) -> e != equality) table
+;;
+
+let in_index table equality =
+ List.exists (fun (p, e) -> e == equality) table
+;;
+
+let get_candidates mode table term = table
+*)
+
+
+(*
+(* PATH INDEXING *)
+let init_index () = ()
+
+let empty_table () =
+ Path_indexing.PSTrie.empty
+;;
+
+let index = Path_indexing.index
+and remove_index = Path_indexing.remove_index
+and in_index = Path_indexing.in_index;;
+
+let get_candidates mode trie term =
+ let t1 = Unix.gettimeofday () in
+ let res =
+ let s =
+ match mode with
+ | Matching -> Path_indexing.retrieve_generalizations trie term
+ | Unification -> Path_indexing.retrieve_unifiables trie term
+(* Path_indexing.retrieve_all trie term *)
+ in
+ Path_indexing.PosEqSet.elements s
+ in
+(* print_candidates mode term res; *)
+ let t2 = Unix.gettimeofday () in
+ indexing_retrieval_time := !indexing_retrieval_time +. (t2 -. t1);
+ res
+;;
+*)
+
+
+(* DISCRIMINATION TREES *)
+let init_index () =
+ Hashtbl.clear Discrimination_tree.arities;
+;;
+
+let empty_table () =
+ Discrimination_tree.DiscriminationTree.empty
+;;
+
+let index = Discrimination_tree.index
+and remove_index = Discrimination_tree.remove_index
+and in_index = Discrimination_tree.in_index;;
+
+let get_candidates mode tree term =
+ let t1 = Unix.gettimeofday () in
+ let res =
+ let s =
+ match mode with
+ | Matching -> Discrimination_tree.retrieve_generalizations tree term
+ | Unification -> Discrimination_tree.retrieve_unifiables tree term
+ in
+ Discrimination_tree.PosEqSet.elements s
+ in
+(* print_candidates mode term res; *)
+(* print_endline (Discrimination_tree.string_of_discrimination_tree tree); *)
+(* print_newline (); *)
+ let t2 = Unix.gettimeofday () in
+ indexing_retrieval_time := !indexing_retrieval_time +. (t2 -. t1);
+ res
+;;
+
+
+let match_unif_time_ok = ref 0.;;
+let match_unif_time_no = ref 0.;;
+
+
+(*
+ finds the first equality in the index that matches "term", of type "termty"
+ termty can be Implicit if it is not needed. The result (one of the sides of
+ the equality, actually) should be not greater (wrt the term ordering) than
+ term
+*)
+let rec find_matches metasenv context ugraph lift_amount term termty =
+ let module C = Cic in
+ let module U = Utils in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let cmp = !Utils.compare_terms in
+ let check = match termty with C.Implicit None -> false | _ -> true in
+ function
+ | [] -> None
+ | candidate::tl ->
+ let pos, (_, proof, (ty, left, right, o), metas, args) = candidate in
+ if check && not (fst (CicReduction.are_convertible
+ ~metasenv context termty ty ugraph)) then (
+ find_matches metasenv context ugraph lift_amount term termty tl
+ ) else
+ let do_match c eq_URI =
+ let subst', metasenv', ugraph' =
+ let t1 = Unix.gettimeofday () in
+ try
+ let r =
+ Inference.matching (metasenv @ metas) context
+ term (S.lift lift_amount c) ugraph in
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
+ r
+ with Inference.MatchingFailure as e ->
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
+ raise e
+ in
+ Some (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
+ (candidate, eq_URI))
+ in
+ let c, other, eq_URI =
+ if pos = Utils.Left then left, right, Utils.eq_ind_URI ()
+ else right, left, Utils.eq_ind_r_URI ()
+ in
+ if o <> U.Incomparable then
+ try
+ do_match c eq_URI
+ with Inference.MatchingFailure ->
+ find_matches metasenv context ugraph lift_amount term termty tl
+ else
+ let res =
+ try do_match c eq_URI
+ with Inference.MatchingFailure -> None
+ in
+ match res with
+ | Some (_, s, _, _, _) ->
+ let c' = apply_subst s c
+ and other' = apply_subst s other in
+ let order = cmp c' other' in
+ let names = U.names_of_context context in
+ if order = U.Gt then
+ res
+ else
+ find_matches
+ metasenv context ugraph lift_amount term termty tl
+ | None ->
+ find_matches metasenv context ugraph lift_amount term termty tl
+;;
+
+
+(*
+ as above, but finds all the matching equalities, and the matching condition
+ can be either Inference.matching or Inference.unification
+*)
+let rec find_all_matches ?(unif_fun=Inference.unification)
+ metasenv context ugraph lift_amount term termty =
+ let module C = Cic in
+ let module U = Utils in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let cmp = !Utils.compare_terms in
+ function
+ | [] -> []
+ | candidate::tl ->
+ let pos, (_, _, (ty, left, right, o), metas, args) = candidate in
+ let do_match c eq_URI =
+ let subst', metasenv', ugraph' =
+ let t1 = Unix.gettimeofday () in
+ try
+ let r =
+ unif_fun (metasenv @ metas) context
+ term (S.lift lift_amount c) ugraph in
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
+ r
+ with
+ | Inference.MatchingFailure
+ | CicUnification.UnificationFailure _
+ | CicUnification.Uncertain _ as e ->
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
+ raise e
+ in
+ (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
+ (candidate, eq_URI))
+ in
+ let c, other, eq_URI =
+ if pos = Utils.Left then left, right, Utils.eq_ind_URI ()
+ else right, left, Utils.eq_ind_r_URI ()
+ in
+ if o <> U.Incomparable then
+ try
+ let res = do_match c eq_URI in
+ res::(find_all_matches ~unif_fun metasenv context ugraph
+ lift_amount term termty tl)
+ with
+ | Inference.MatchingFailure
+ | CicUnification.UnificationFailure _
+ | CicUnification.Uncertain _ ->
+ find_all_matches ~unif_fun metasenv context ugraph
+ lift_amount term termty tl
+ else
+ try
+ let res = do_match c eq_URI in
+ match res with
+ | _, s, _, _, _ ->
+ let c' = apply_subst s c
+ and other' = apply_subst s other in
+ let order = cmp c' other' in
+ let names = U.names_of_context context in
+ if order <> U.Lt && order <> U.Le then
+ res::(find_all_matches ~unif_fun metasenv context ugraph
+ lift_amount term termty tl)
+ else
+ find_all_matches ~unif_fun metasenv context ugraph
+ lift_amount term termty tl
+ with
+ | Inference.MatchingFailure
+ | CicUnification.UnificationFailure _
+ | CicUnification.Uncertain _ ->
+ find_all_matches ~unif_fun metasenv context ugraph
+ lift_amount term termty tl
+;;
+
+
+(*
+ returns true if target is subsumed by some equality in table
+*)
+let subsumption env table target =
+ let _, _, (ty, left, right, _), tmetas, _ = target in
+ let metasenv, context, ugraph = env in
+ let metasenv = metasenv @ tmetas in
+ let samesubst subst subst' =
+ let tbl = Hashtbl.create (List.length subst) in
+ List.iter (fun (m, (c, t1, t2)) -> Hashtbl.add tbl m (c, t1, t2)) subst;
+ List.for_all
+ (fun (m, (c, t1, t2)) ->
+ try
+ let c', t1', t2' = Hashtbl.find tbl m in
+ if (c = c') && (t1 = t1') && (t2 = t2') then true
+ else false
+ with Not_found ->
+ true)
+ subst'
+ in
+ let leftr =
+ match left with
+ | Cic.Meta _ -> []
+ | _ ->
+ let leftc = get_candidates Matching table left in
+ find_all_matches ~unif_fun:Inference.matching
+ metasenv context ugraph 0 left ty leftc
+ in
+ let rec ok what = function
+ | [] -> false, []
+ | (_, subst, menv, ug, ((pos, (_, _, (_, l, r, o), m, _)), _))::tl ->
+ try
+ let other = if pos = Utils.Left then r else l in
+ let subst', menv', ug' =
+ let t1 = Unix.gettimeofday () in
+ try
+ let r =
+ Inference.matching (metasenv @ menv @ m) context what other ugraph
+ in
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
+ r
+ with Inference.MatchingFailure as e ->
+ let t2 = Unix.gettimeofday () in
+ match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
+ raise e
+ in
+ if samesubst subst subst' then
+ true, subst
+ else
+ ok what tl
+ with Inference.MatchingFailure ->
+ ok what tl
+ in
+ let r, subst = ok right leftr in
+ let r, s =
+ if r then
+ true, subst
+ else
+ let rightr =
+ match right with
+ | Cic.Meta _ -> []
+ | _ ->
+ let rightc = get_candidates Matching table right in
+ find_all_matches ~unif_fun:Inference.matching
+ metasenv context ugraph 0 right ty rightc
+ in
+ ok left rightr
+ in
+ (if r then
+ debug_print
+ (lazy
+ (Printf.sprintf "SUBSUMPTION! %s\n%s\n"
+ (Inference.string_of_equality target) (Utils.print_subst s))));
+ r, s
+;;
+
+
+let rec demodulation_aux ?(typecheck=false)
+ metasenv context ugraph table lift_amount term =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let candidates = get_candidates Matching table term in
+ match term with
+ | C.Meta _ -> None
+ | term ->
+ let termty, ugraph =
+ if typecheck then
+ CicTypeChecker.type_of_aux' metasenv context term ugraph
+ else
+ C.Implicit None, ugraph
+ in
+ let res =
+ find_matches metasenv context ugraph lift_amount term termty candidates
+ in
+ if res <> None then
+ res
+ else
+ match term with
+ | C.Appl l ->
+ let res, ll =
+ List.fold_left
+ (fun (res, tl) t ->
+ if res <> None then
+ (res, tl @ [S.lift 1 t])
+ else
+ let r =
+ demodulation_aux metasenv context ugraph table
+ lift_amount t
+ in
+ match r with
+ | None -> (None, tl @ [S.lift 1 t])
+ | Some (rel, _, _, _, _) -> (r, tl @ [rel]))
+ (None, []) l
+ in (
+ match res with
+ | None -> None
+ | Some (_, subst, menv, ug, eq_found) ->
+ Some (C.Appl ll, subst, menv, ug, eq_found)
+ )
+ | C.Prod (nn, s, t) ->
+ let r1 =
+ demodulation_aux metasenv context ugraph table lift_amount s in (
+ match r1 with
+ | None ->
+ let r2 =
+ demodulation_aux metasenv
+ ((Some (nn, C.Decl s))::context) ugraph
+ table (lift_amount+1) t
+ in (
+ match r2 with
+ | None -> None
+ | Some (t', subst, menv, ug, eq_found) ->
+ Some (C.Prod (nn, (S.lift 1 s), t'),
+ subst, menv, ug, eq_found)
+ )
+ | Some (s', subst, menv, ug, eq_found) ->
+ Some (C.Prod (nn, s', (S.lift 1 t)),
+ subst, menv, ug, eq_found)
+ )
+ | C.Lambda (nn, s, t) ->
+ let r1 =
+ demodulation_aux metasenv context ugraph table lift_amount s in (
+ match r1 with
+ | None ->
+ let r2 =
+ demodulation_aux metasenv
+ ((Some (nn, C.Decl s))::context) ugraph
+ table (lift_amount+1) t
+ in (
+ match r2 with
+ | None -> None
+ | Some (t', subst, menv, ug, eq_found) ->
+ Some (C.Lambda (nn, (S.lift 1 s), t'),
+ subst, menv, ug, eq_found)
+ )
+ | Some (s', subst, menv, ug, eq_found) ->
+ Some (C.Lambda (nn, s', (S.lift 1 t)),
+ subst, menv, ug, eq_found)
+ )
+ | t ->
+ None
+;;
+
+
+let build_newtarget_time = ref 0.;;
+
+
+let demod_counter = ref 1;;
+
+(** demodulation, when target is an equality *)
+let rec demodulation_equality newmeta env table sign target =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let metasenv, context, ugraph = env in
+ let _, proof, (eq_ty, left, right, order), metas, args = target in
+ let metasenv' = metasenv @ metas in
+
+ let maxmeta = ref newmeta in
+
+ let build_newtarget is_left (t, subst, menv, ug, (eq_found, eq_URI)) =
+ let time1 = Unix.gettimeofday () in
+
+ let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
+ let ty =
+ try fst (CicTypeChecker.type_of_aux' metasenv context what ugraph)
+ with CicUtil.Meta_not_found _ -> ty
+ in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ let newterm, newproof =
+ let bo = apply_subst subst (S.subst other t) in
+ let name = C.Name ("x_Demod_" ^ (string_of_int !demod_counter)) in
+ incr demod_counter;
+ let bo' =
+ let l, r = if is_left then t, S.lift 1 right else S.lift 1 left, t in
+ C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []);
+ S.lift 1 eq_ty; l; r]
+ in
+ if sign = Utils.Positive then
+ (bo,
+ Inference.ProofBlock (
+ subst, eq_URI, (name, ty), bo'(* t' *), eq_found, proof))
+ else
+ let metaproof =
+ incr maxmeta;
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ debug_print (lazy (Printf.sprintf "\nADDING META: %d\n" !maxmeta));
+ print_newline ();
+ C.Meta (!maxmeta, irl)
+ in
+ let eq_found =
+ let proof' =
+ let termlist =
+ if pos = Utils.Left then [ty; what; other]
+ else [ty; other; what]
+ in
+ Inference.ProofSymBlock (termlist, proof')
+ in
+ let what, other =
+ if pos = Utils.Left then what, other else other, what
+ in
+ pos, (0, proof', (ty, other, what, Utils.Incomparable),
+ menv', args')
+ in
+ let target_proof =
+ let pb =
+ Inference.ProofBlock (subst, eq_URI, (name, ty), bo',
+ eq_found, Inference.BasicProof metaproof)
+ in
+ match proof with
+ | Inference.BasicProof _ ->
+ print_endline "replacing a BasicProof";
+ pb
+ | Inference.ProofGoalBlock (_, parent_proof) ->
+ print_endline "replacing another ProofGoalBlock";
+ Inference.ProofGoalBlock (pb, parent_proof)
+ | _ -> assert false
+ in
+ let refl =
+ C.Appl [C.MutConstruct (* reflexivity *)
+ (LibraryObjects.eq_URI (), 0, 1, []);
+ eq_ty; if is_left then right else left]
+ in
+ (bo,
+ Inference.ProofGoalBlock (Inference.BasicProof refl, target_proof))
+ in
+ let left, right = if is_left then newterm, right else left, newterm in
+ let m = (Inference.metas_of_term left) @ (Inference.metas_of_term right) in
+ let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas
+ and newargs = args
+ in
+ let ordering = !Utils.compare_terms left right in
+
+ let time2 = Unix.gettimeofday () in
+ build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+ let res =
+ let w = Utils.compute_equality_weight eq_ty left right in
+ (w, newproof, (eq_ty, left, right, ordering), newmetasenv, newargs)
+ in
+ !maxmeta, res
+ in
+ let res = demodulation_aux metasenv' context ugraph table 0 left in
+ let newmeta, newtarget =
+ match res with
+ | Some t ->
+ let newmeta, newtarget = build_newtarget true t in
+ if (Inference.is_identity (metasenv', context, ugraph) newtarget) ||
+ (Inference.meta_convertibility_eq target newtarget) then
+ newmeta, newtarget
+ else
+ demodulation_equality newmeta env table sign newtarget
+ | None ->
+ let res = demodulation_aux metasenv' context ugraph table 0 right in
+ match res with
+ | Some t ->
+ let newmeta, newtarget = build_newtarget false t in
+ if (Inference.is_identity (metasenv', context, ugraph) newtarget) ||
+ (Inference.meta_convertibility_eq target newtarget) then
+ newmeta, newtarget
+ else
+ demodulation_equality newmeta env table sign newtarget
+ | None ->
+ newmeta, target
+ in
+ (* newmeta, newtarget *)
+ (* tentiamo di ridurre usando CicReduction.normalize *)
+ let w, p, (ty, left, right, o), m, a = newtarget in
+ let left' = ProofEngineReduction.simpl context left in
+ let right' = ProofEngineReduction.simpl context right in
+ let newleft =
+ if !Utils.compare_terms left' left = Utils.Lt then left' else left in
+ let newright =
+ if !Utils.compare_terms right' right = Utils.Lt then right' else right in
+ if newleft != left || newright != right then (
+ debug_print
+ (lazy
+ (Printf.sprintf "left: %s, left': %s\nright: %s, right': %s\n"
+ (CicPp.ppterm left) (CicPp.ppterm left') (CicPp.ppterm right)
+ (CicPp.ppterm right')))
+ );
+ let w' = Utils.compute_equality_weight ty newleft newright in
+ let o' = !Utils.compare_terms newleft newright in
+ newmeta, (w', p, (ty, newleft, newright, o'), m, a)
+;;
+
+
+(**
+ Performs the beta expansion of the term "term" w.r.t. "table",
+ i.e. returns the list of all the terms t s.t. "(t term) = t2", for some t2
+ in table.
+*)
+let rec betaexpand_term metasenv context ugraph table lift_amount term =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let candidates = get_candidates Unification table term in
+ let res, lifted_term =
+ match term with
+ | C.Meta (i, l) ->
+ let l', lifted_l =
+ List.fold_right
+ (fun arg (res, lifted_tl) ->
+ match arg with
+ | Some arg ->
+ let arg_res, lifted_arg =
+ betaexpand_term metasenv context ugraph table
+ lift_amount arg in
+ let l1 =
+ List.map
+ (fun (t, s, m, ug, eq_found) ->
+ (Some t)::lifted_tl, s, m, ug, eq_found)
+ arg_res
+ in
+ (l1 @
+ (List.map
+ (fun (l, s, m, ug, eq_found) ->
+ (Some lifted_arg)::l, s, m, ug, eq_found)
+ res),
+ (Some lifted_arg)::lifted_tl)
+ | None ->
+ (List.map
+ (fun (r, s, m, ug, eq_found) ->
+ None::r, s, m, ug, eq_found) res,
+ None::lifted_tl)
+ ) l ([], [])
+ in
+ let e =
+ List.map
+ (fun (l, s, m, ug, eq_found) ->
+ (C.Meta (i, l), s, m, ug, eq_found)) l'
+ in
+ e, C.Meta (i, lifted_l)
+
+ | C.Rel m ->
+ [], if m <= lift_amount then C.Rel m else C.Rel (m+1)
+
+ | C.Prod (nn, s, t) ->
+ let l1, lifted_s =
+ betaexpand_term metasenv context ugraph table lift_amount s in
+ let l2, lifted_t =
+ betaexpand_term metasenv ((Some (nn, C.Decl s))::context) ugraph
+ table (lift_amount+1) t in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug, eq_found) ->
+ C.Prod (nn, t, lifted_t), s, m, ug, eq_found) l1
+ and l2' =
+ List.map
+ (fun (t, s, m, ug, eq_found) ->
+ C.Prod (nn, lifted_s, t), s, m, ug, eq_found) l2 in
+ l1' @ l2', C.Prod (nn, lifted_s, lifted_t)
+
+ | C.Lambda (nn, s, t) ->
+ let l1, lifted_s =
+ betaexpand_term metasenv context ugraph table lift_amount s in
+ let l2, lifted_t =
+ betaexpand_term metasenv ((Some (nn, C.Decl s))::context) ugraph
+ table (lift_amount+1) t in
+ let l1' =
+ List.map
+ (fun (t, s, m, ug, eq_found) ->
+ C.Lambda (nn, t, lifted_t), s, m, ug, eq_found) l1
+ and l2' =
+ List.map
+ (fun (t, s, m, ug, eq_found) ->
+ C.Lambda (nn, lifted_s, t), s, m, ug, eq_found) l2 in
+ l1' @ l2', C.Lambda (nn, lifted_s, lifted_t)
+
+ | C.Appl l ->
+ let l', lifted_l =
+ List.fold_right
+ (fun arg (res, lifted_tl) ->
+ let arg_res, lifted_arg =
+ betaexpand_term metasenv context ugraph table lift_amount arg
+ in
+ let l1 =
+ List.map
+ (fun (a, s, m, ug, eq_found) ->
+ a::lifted_tl, s, m, ug, eq_found)
+ arg_res
+ in
+ (l1 @
+ (List.map
+ (fun (r, s, m, ug, eq_found) ->
+ lifted_arg::r, s, m, ug, eq_found)
+ res),
+ lifted_arg::lifted_tl)
+ ) l ([], [])
+ in
+ (List.map
+ (fun (l, s, m, ug, eq_found) -> (C.Appl l, s, m, ug, eq_found)) l',
+ C.Appl lifted_l)
+
+ | t -> [], (S.lift lift_amount t)
+ in
+ match term with
+ | C.Meta (i, l) -> res, lifted_term
+ | term ->
+ let termty, ugraph =
+ C.Implicit None, ugraph
+(* CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+ in
+ let r =
+ find_all_matches
+ metasenv context ugraph lift_amount term termty candidates
+ in
+ r @ res, lifted_term
+;;
+
+
+let sup_l_counter = ref 1;;
+
+(**
+ superposition_left
+ returns a list of new clauses inferred with a left superposition step
+ the negative equation "target" and one of the positive equations in "table"
+*)
+let superposition_left newmeta (metasenv, context, ugraph) table target =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let module CR = CicReduction in
+ let module U = Utils in
+ let weight, proof, (eq_ty, left, right, ordering), _, _ = target in
+ let expansions, _ =
+ let term = if ordering = U.Gt then left else right in
+ betaexpand_term metasenv context ugraph table 0 term
+ in
+ let maxmeta = ref newmeta in
+ let build_new (bo, s, m, ug, (eq_found, eq_URI)) =
+
+ debug_print (lazy "\nSUPERPOSITION LEFT\n");
+
+ let time1 = Unix.gettimeofday () in
+ let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ let newgoal, newproof =
+ let bo' = apply_subst s (S.subst other bo) in
+ let name = C.Name ("x_SupL_" ^ (string_of_int !sup_l_counter)) in
+ incr sup_l_counter;
+ let bo'' =
+ let l, r =
+ if ordering = U.Gt then bo, S.lift 1 right else S.lift 1 left, bo in
+ C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []);
+ S.lift 1 eq_ty; l; r]
+ in
+ incr maxmeta;
+ let metaproof =
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ C.Meta (!maxmeta, irl)
+ in
+ let eq_found =
+ let proof' =
+ let termlist =
+ if pos = Utils.Left then [ty; what; other]
+ else [ty; other; what]
+ in
+ Inference.ProofSymBlock (termlist, proof')
+ in
+ let what, other =
+ if pos = Utils.Left then what, other else other, what
+ in
+ pos, (0, proof', (ty, other, what, Utils.Incomparable), menv', args')
+ in
+ let target_proof =
+ let pb =
+ Inference.ProofBlock (s, eq_URI, (name, ty), bo'', eq_found,
+ Inference.BasicProof metaproof)
+ in
+ match proof with
+ | Inference.BasicProof _ ->
+ debug_print (lazy "replacing a BasicProof");
+ pb
+ | Inference.ProofGoalBlock (_, parent_proof) ->
+ debug_print (lazy "replacing another ProofGoalBlock");
+ Inference.ProofGoalBlock (pb, parent_proof)
+ | _ -> assert false
+ in
+ let refl =
+ C.Appl [C.MutConstruct (* reflexivity *)
+ (LibraryObjects.eq_URI (), 0, 1, []);
+ eq_ty; if ordering = U.Gt then right else left]
+ in
+ (bo',
+ Inference.ProofGoalBlock (Inference.BasicProof refl, target_proof))
+ in
+ let left, right =
+ if ordering = U.Gt then newgoal, right else left, newgoal in
+ let neworder = !Utils.compare_terms left right in
+
+ let time2 = Unix.gettimeofday () in
+ build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+ let res =
+ let w = Utils.compute_equality_weight eq_ty left right in
+ (w, newproof, (eq_ty, left, right, neworder), [], [])
+ in
+ res
+ in
+ !maxmeta, List.map build_new expansions
+;;
+
+
+let sup_r_counter = ref 1;;
+
+(**
+ superposition_right
+ returns a list of new clauses inferred with a right superposition step
+ between the positive equation "target" and one in the "table" "newmeta" is
+ the first free meta index, i.e. the first number above the highest meta
+ index: its updated value is also returned
+*)
+let superposition_right newmeta (metasenv, context, ugraph) table target =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let module CR = CicReduction in
+ let module U = Utils in
+ let _, eqproof, (eq_ty, left, right, ordering), newmetas, args = target in
+ let metasenv' = metasenv @ newmetas in
+ let maxmeta = ref newmeta in
+ let res1, res2 =
+ match ordering with
+ | U.Gt -> fst (betaexpand_term metasenv' context ugraph table 0 left), []
+ | U.Lt -> [], fst (betaexpand_term metasenv' context ugraph table 0 right)
+ | _ ->
+ let res l r =
+ List.filter
+ (fun (_, subst, _, _, _) ->
+ let subst = apply_subst subst in
+ let o = !Utils.compare_terms (subst l) (subst r) in
+ o <> U.Lt && o <> U.Le)
+ (fst (betaexpand_term metasenv' context ugraph table 0 l))
+ in
+ (res left right), (res right left)
+ in
+ let build_new ordering (bo, s, m, ug, (eq_found, eq_URI)) =
+
+ let time1 = Unix.gettimeofday () in
-
-
+ let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ let newgoal, newproof =
+ let bo' = apply_subst s (S.subst other bo) in
+ let t' =
+ let name = C.Name ("x_SupR_" ^ (string_of_int !sup_r_counter)) in
+ incr sup_r_counter;
+ let l, r =
+ if ordering = U.Gt then bo, S.lift 1 right else S.lift 1 left, bo in
+ (name, ty, S.lift 1 eq_ty, l, r)
+ in
+ let name = C.Name ("x_SupR_" ^ (string_of_int !sup_r_counter)) in
+ incr sup_r_counter;
+ let bo'' =
+ let l, r =
+ if ordering = U.Gt then bo, S.lift 1 right else S.lift 1 left, bo in
+ C.Appl [C.MutInd (LibraryObjects.eq_URI (), 0, []);
+ S.lift 1 eq_ty; l; r]
+ in
+ bo',
+ Inference.ProofBlock (s, eq_URI, (name, ty), bo'', eq_found, eqproof)
+ in
+ let newmeta, newequality =
+ let left, right =
+ if ordering = U.Gt then newgoal, apply_subst s right
+ else apply_subst s left, newgoal in
+ let neworder = !Utils.compare_terms left right
+ and newmenv = newmetas @ menv'
+ and newargs = args @ args' in
+ let eq' =
+ let w = Utils.compute_equality_weight eq_ty left right in
+ (w, newproof, (eq_ty, left, right, neworder), newmenv, newargs)
+ and env = (metasenv, context, ugraph) in
+ let newm, eq' = Inference.fix_metas !maxmeta eq' in
+ newm, eq'
+ in
+ maxmeta := newmeta;
+
+ let time2 = Unix.gettimeofday () in
+ build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+ newequality
+ in
+ let new1 = List.map (build_new U.Gt) res1
+ and new2 = List.map (build_new U.Lt) res2 in
+ let ok e = not (Inference.is_identity (metasenv, context, ugraph) e) in
+ (!maxmeta,
+ (List.filter ok (new1 @ new2)))
+;;
+
+
+(** demodulation, when the target is a goal *)
+let rec demodulation_goal newmeta env table goal =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let metasenv, context, ugraph = env in
+ let maxmeta = ref newmeta in
+ let proof, metas, term = goal in
+ let metasenv' = metasenv @ metas in
+
+ let build_newgoal (t, subst, menv, ug, (eq_found, eq_URI)) =
+ let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ let ty =
+ try fst (CicTypeChecker.type_of_aux' metasenv context what ugraph)
+ with CicUtil.Meta_not_found _ -> ty
+ in
+ let newterm, newproof =
+ let bo = apply_subst subst (S.subst other t) in
+ let bo' = apply_subst subst t in
+ let name = C.Name ("x_DemodGoal_" ^ (string_of_int !demod_counter)) in
+ incr demod_counter;
+ let metaproof =
+ incr maxmeta;
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ debug_print (lazy (Printf.sprintf "\nADDING META: %d\n" !maxmeta));
+ C.Meta (!maxmeta, irl)
+ in
+ let eq_found =
+ let proof' =
+ let termlist =
+ if pos = Utils.Left then [ty; what; other]
+ else [ty; other; what]
+ in
+ Inference.ProofSymBlock (termlist, proof')
+ in
+ let what, other =
+ if pos = Utils.Left then what, other else other, what
+ in
+ pos, (0, proof', (ty, other, what, Utils.Incomparable), menv', args')
+ in
+ let goal_proof =
+ let pb =
+ Inference.ProofBlock (subst, eq_URI, (name, ty), bo',
+ eq_found, Inference.BasicProof metaproof)
+ in
+ let rec repl = function
+ | Inference.NoProof ->
+ debug_print (lazy "replacing a NoProof");
+ pb
+ | Inference.BasicProof _ ->
+ debug_print (lazy "replacing a BasicProof");
+ pb
+ | Inference.ProofGoalBlock (_, parent_proof) ->
+ debug_print (lazy "replacing another ProofGoalBlock");
+ Inference.ProofGoalBlock (pb, parent_proof)
+ | (Inference.SubProof (term, meta_index, p) as subproof) ->
+ debug_print
+ (lazy
+ (Printf.sprintf "replacing %s"
+ (Inference.string_of_proof subproof)));
+ Inference.SubProof (term, meta_index, repl p)
+ | _ -> assert false
+ in repl proof
+ in
+ bo, Inference.ProofGoalBlock (Inference.NoProof, goal_proof)
+ in
+ let m = Inference.metas_of_term newterm in
+ let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas in
+ !maxmeta, (newproof, newmetasenv, newterm)
+ in
+ let res =
+ demodulation_aux ~typecheck:true metasenv' context ugraph table 0 term
+ in
+ match res with
+ | Some t ->
+ let newmeta, newgoal = build_newgoal t in
+ let _, _, newg = newgoal in
+ if Inference.meta_convertibility term newg then
+ newmeta, newgoal
+ else
+ demodulation_goal newmeta env table newgoal
+ | None ->
+ newmeta, goal
+;;
+
+
+(** demodulation, when the target is a theorem *)
+let rec demodulation_theorem newmeta env table theorem =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let module M = CicMetaSubst in
+ let module HL = HelmLibraryObjects in
+ let metasenv, context, ugraph = env in
+ let maxmeta = ref newmeta in
+ let proof, metas, term = theorem in
+ let term, termty, metas = theorem in
+ let metasenv' = metasenv @ metas in
+
+ let build_newtheorem (t, subst, menv, ug, (eq_found, eq_URI)) =
+ let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ let newterm, newty =
+ let bo = apply_subst subst (S.subst other t) in
+ let bo' = apply_subst subst t in
+ let name = C.Name ("x_DemodThm_" ^ (string_of_int !demod_counter)) in
+ incr demod_counter;
+ let newproof =
+ Inference.ProofBlock (subst, eq_URI, (name, ty), bo', eq_found,
+ Inference.BasicProof term)
+ in
+ (Inference.build_proof_term newproof, bo)
+ in
+ let m = Inference.metas_of_term newterm in
+ let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas in
+ !maxmeta, (newterm, newty, newmetasenv)
+ in
+ let res =
+ demodulation_aux ~typecheck:true metasenv' context ugraph table 0 termty
+ in
+ match res with
+ | Some t ->
+ let newmeta, newthm = build_newtheorem t in
+ let newt, newty, _ = newthm in
+ if Inference.meta_convertibility termty newty then
+ newmeta, newthm
+ else
+ demodulation_theorem newmeta env table newthm
+ | None ->
+ newmeta, theorem
+;;
projects / helm.git / blobdiff