X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fparamodulation%2Findexing.ml;h=c964e3a78c882f525df690c230ec60e18abd1eb4;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=85821097df286ed60d3e14c3e7f600ca709d449e;hpb=acf29bdbdcdc6ad8c2d9d27e8a47500981b605cd;p=helm.git diff --git a/helm/ocaml/paramodulation/indexing.ml b/helm/ocaml/paramodulation/indexing.ml index 85821097d..c964e3a78 100644 --- a/helm/ocaml/paramodulation/indexing.ml +++ b/helm/ocaml/paramodulation/indexing.ml @@ -1,107 +1,395 @@ -(* type naif_indexing = - (Cic.term * ((bool * Inference.equality) list)) list -;; *) +(* 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/. + *) -type pos = Left | Right ;; +let debug_print = Utils.debug_print;; -let head_of_term = function - | Cic.Appl (hd::tl) -> hd - | t -> t + +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 index table (sign, 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, sign, eq)::x_entry) +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 -(* (match ordering with *) -(* | Utils.Gt -> *) -(* index hl Left *) -(* | Utils.Lt -> *) -(* index hr Right *) -(* | _ -> index hl Left; *) -(* index hr Right); *) - index hl Left; - index hr Right; - table +(* print_candidates mode term res; *) + let t2 = Unix.gettimeofday () in + indexing_retrieval_time := !indexing_retrieval_time +. (t2 -. t1); + res ;; +*) -let remove_index table (sign, eq) = - let _, (_, l, r, ordering), _, _ = eq in - let hl = head_of_term l - and hr = head_of_term r in - let remove_index x pos = - let x_entry = try Hashtbl.find table x with Not_found -> [] in - let newentry = List.filter (fun e -> e <> (pos, sign, eq)) x_entry in - Hashtbl.replace table x newentry +(* 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 - remove_index hl Left; - remove_index hr Right; - table +(* 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 rec find_matches metasenv context ugraph lift_amount term = +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 - | (_, U.Negative, _)::tl -> - find_matches metasenv context ugraph lift_amount term tl - | (pos, U.Positive, (_, (_, _, _, o), _, _))::tl - when (pos = Left && o = U.Lt) || (pos = Right && o = U.Gt) -> - find_matches metasenv context ugraph lift_amount term tl - | (pos, U.Positive, (proof, (ty, left, right, o), metas, args))::tl -> - let do_match c other eq_URI = + | 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' = - Inference.matching (metasenv @ metas) context term - (S.lift lift_amount c) 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 - Some (C.Rel (1 + lift_amount), subst', metasenv', ugraph', - (proof, ty, c, other, eq_URI)) + (C.Rel (1 + lift_amount), subst', metasenv', ugraph', + (candidate, eq_URI)) in let c, other, eq_URI = - if pos = Left then left, right, HL.Logic.eq_ind_URI - else right, left, HL.Logic.eq_ind_r_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 other eq_URI - with e -> find_matches metasenv context ugraph lift_amount term tl + 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 - let res = try do_match c other eq_URI with e -> None in - match res with - | Some (_, s, _, _, _) -> - if cmp (M.apply_subst s left) (M.apply_subst s right) = - (if pos = Left then U.Gt else U.Lt) then - res - else - find_matches metasenv context ugraph lift_amount term tl - | None -> - find_matches metasenv context ugraph lift_amount term tl + 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 ;; -let rec demodulate_term metasenv context ugraph table lift_amount term = +(* + 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 hd_term = head_of_term term in - let candidates = try Hashtbl.find table hd_term with Not_found -> [] 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 candidates + find_matches metasenv context ugraph lift_amount term termty candidates in if res <> None then res @@ -115,7 +403,7 @@ let rec demodulate_term metasenv context ugraph table lift_amount term = (res, tl @ [S.lift 1 t]) else let r = - demodulate_term metasenv context ugraph table + demodulation_aux metasenv context ugraph table lift_amount t in match r with @@ -125,111 +413,246 @@ let rec demodulate_term metasenv context ugraph table lift_amount term = in ( match res with | None -> None - | Some (_, subst, menv, ug, info) -> - Some (C.Appl ll, subst, menv, ug, info) + | Some (_, subst, menv, ug, eq_found) -> + Some (C.Appl ll, subst, menv, ug, eq_found) ) | C.Prod (nn, s, t) -> let r1 = - demodulate_term metasenv context ugraph table lift_amount s in ( + demodulation_aux metasenv context ugraph table lift_amount s in ( match r1 with | None -> let r2 = - demodulate_term metasenv + 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, info) -> + | Some (t', subst, menv, ug, eq_found) -> Some (C.Prod (nn, (S.lift 1 s), t'), - subst, menv, ug, info) + 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, info) -> - Some (C.Prod (nn, s', (S.lift 1 t)), subst, menv, ug, info) + | Some (s', subst, menv, ug, eq_found) -> + Some (C.Lambda (nn, s', (S.lift 1 t)), + subst, menv, ug, eq_found) ) | t -> - Printf.printf "Ne` Appl ne` Prod: %s\n" - (CicPp.pp t (Utils.names_of_context context)); None ;; -let rec demodulate newmeta env table target = +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 build_newtarget is_left - (t, subst, menv, ug, (proof', ty, what, other, eq_URI)) = + 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 = S.subst (M.apply_subst subst other) t in - let bo'' = - C.Appl ([C.MutInd (HL.Logic.eq_URI, 0, []); - S.lift 1 eq_ty] @ - if is_left then [bo; S.lift 1 right] else [S.lift 1 left; bo]) + 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 - let t' = C.Lambda (C.Anonymous, ty, bo'') in - bo, - M.apply_subst subst (C.Appl [C.Const (eq_URI, []); ty; what; t'; - proof; other; proof']) + 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 newmeta, newtarget = - 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 = - List.filter - (function C.Meta (i, _) -> List.mem i m | _ -> assert false) - args - in - let ordering = !Utils.compare_terms left right in - newmeta, (newproof, (eq_ty, left, right, ordering), newmetasenv, newargs) + 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 - newmeta, newtarget + 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 = demodulate_term metasenv context ugraph table 0 left in - match res with - | Some t -> - let newmeta, newtarget = build_newtarget true t in - if Inference.is_identity (metasenv, context, ugraph) newtarget then - newmeta, newtarget - else - demodulate newmeta env table newtarget - | None -> - let res = demodulate_term 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 then - newmeta, newtarget - else - demodulate newmeta env table newtarget - | None -> - newmeta, target + 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 hd_term = head_of_term term in - let candidates = try Hashtbl.find table hd_term with Not_found -> [] in + let candidates = get_candidates Unification table term in let res, lifted_term = match term with | C.Meta (i, l) -> - let l = - List.map (function - | Some t -> Some (S.lift lift_amount t) - | None -> None) 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 - [], C.Meta (i, l) + e, C.Meta (i, lifted_l) | C.Rel m -> [], if m <= lift_amount then C.Rel m else C.Rel (m+1) @@ -242,14 +665,30 @@ let rec betaexpand_term metasenv context ugraph table lift_amount term = table (lift_amount+1) t in let l1' = List.map - (fun (t, s, m, ug, info) -> - C.Prod (nn, t, lifted_t), s, m, ug, info) l1 + (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, info) -> - C.Prod (nn, lifted_s, t), s, m, ug, info) l2 in + (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 @@ -259,72 +698,144 @@ let rec betaexpand_term metasenv context ugraph table lift_amount term = in let l1 = List.map - (fun (a, s, m, ug, info) -> a::lifted_tl, s, m, ug, info) + (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, info) -> lifted_arg::r, s, m, ug, info) + (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, info) -> (C.Appl l, s, m, ug, info)) l', + (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 _ -> res, lifted_term - | _ -> - match - find_matches metasenv context ugraph lift_amount term candidates - with - | None -> res, lifted_term - | Some r -> r::res, lifted_term + | 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 superposition_left (metasenv, context, ugraph) table target = +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 proof, (eq_ty, left, right, ordering), _, _ = target 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 build_new (bo, s, m, ug, (proof', ty, what, other, eq_URI)) = + 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' = S.subst (M.apply_subst s other) bo in - let bo'' = - C.Appl ( - [C.MutInd (HL.Logic.eq_URI, 0, []); - S.lift 1 eq_ty] @ - if ordering = U.Gt then [bo'; S.lift 1 right] - else [S.lift 1 left; bo']) + 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 - let t' = C.Lambda (C.Anonymous, ty, bo'') in - S.subst (M.apply_subst s other) bo, - M.apply_subst s - (C.Appl [C.Const (eq_URI, []); ty; what; t'; - proof; other; proof']) + (bo', + Inference.ProofGoalBlock (Inference.BasicProof refl, target_proof)) in - let left, right, newordering = - if ordering = U.Gt then - newgoal, right, !Utils.compare_terms newgoal right - else - left, newgoal, !Utils.compare_terms left newgoal + 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 - (newproof, (eq_ty, left, right, ordering), [], []) + res in - List.map build_new expansions + !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 @@ -332,58 +843,209 @@ let superposition_right newmeta (metasenv, context, ugraph) table target = 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 _, 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) + | 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 = M.apply_subst subst in + 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)) + (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, (proof', ty, what, other, eq_URI)) = + 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' = S.subst (M.apply_subst s other) bo in + 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'' = - C.Appl ( - [C.MutInd (HL.Logic.eq_URI, 0, []); - S.lift 1 eq_ty] @ - if ordering = U.Gt then [bo'; S.lift 1 right] - else [S.lift 1 left; 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 - let t' = C.Lambda (C.Anonymous, ty, bo'') in - S.subst (M.apply_subst s other) bo, - M.apply_subst s - (C.Appl [C.Const (eq_URI, []); ty; what; t'; - eqproof; other; proof']) + bo', + Inference.ProofBlock (s, eq_URI, (name, ty), bo'', eq_found, eqproof) in let newmeta, newequality = - let left, right, newordering = - if ordering = U.Gt then - newgoal, right, !Utils.compare_terms newgoal right - else - left, newgoal, !Utils.compare_terms left newgoal - in - Inference.fix_metas !maxmeta - (newproof, (eq_ty, left, right, ordering), [], []) + 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 = function - | _, (_, left, right, _), _, _ -> - not (fst (CR.are_convertible context left right ugraph)) - 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 +;;