From acf29bdbdcdc6ad8c2d9d27e8a47500981b605cd Mon Sep 17 00:00:00 2001 From: Alberto Griggio Date: Thu, 9 Jun 2005 17:19:17 +0000 Subject: [PATCH] prima implementazione di demodulate, superposition_left e superposition_right con gli "indici"... --- helm/ocaml/paramodulation/indexing.ml | 401 ++++++++++++++++++++++++-- 1 file changed, 375 insertions(+), 26 deletions(-) diff --git a/helm/ocaml/paramodulation/indexing.ml b/helm/ocaml/paramodulation/indexing.ml index 8ed8f49a1..85821097d 100644 --- a/helm/ocaml/paramodulation/indexing.ml +++ b/helm/ocaml/paramodulation/indexing.ml @@ -2,39 +2,388 @@ (Cic.term * ((bool * Inference.equality) list)) list ;; *) -type pos = Left | Right -;; +type pos = Left | Right ;; -let head_of_term = - function - | Cic.Appl hd::tl -> hd - | t -> t +let head_of_term = function + | Cic.Appl (hd::tl) -> hd + | t -> t ;; -let index table eq = - let (_,(_,l,r,ordering),_,_) = eq in + +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,eq)::x_entry in - (match ordering with - | Utils.Gt -> - index hl Left - | Utils.Lt -> - index hr Right - | _ -> index hl Left; - index hr Right); + let x_entry = try Hashtbl.find table x with Not_found -> [] in + Hashtbl.replace table x ((pos, sign, eq)::x_entry) + 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 ;; -let demodulate_term env table cmp term = + +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 + in + remove_index hl Left; + remove_index hr Right; + table +;; + + +let rec find_matches metasenv context ugraph lift_amount term = + 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 + | [] -> 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 = + let subst', metasenv', ugraph' = + Inference.matching (metasenv @ metas) context term + (S.lift lift_amount c) ugraph + in + Some (C.Rel (1 + lift_amount), subst', metasenv', ugraph', + (proof, ty, c, other, 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 + in + if o <> U.Incomparable then + try do_match c other eq_URI + with e -> find_matches metasenv context ugraph lift_amount term 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 +;; + + +let rec demodulate_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 = Hashtbl.find table hd_term in - - - - - + let candidates = try Hashtbl.find table hd_term with Not_found -> [] in + match term with + | C.Meta _ -> None + | term -> + let res = + find_matches metasenv context ugraph lift_amount term 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 = + demodulate_term 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, info) -> + Some (C.Appl ll, subst, menv, ug, info) + ) + | C.Prod (nn, s, t) -> + let r1 = + demodulate_term metasenv context ugraph table lift_amount s in ( + match r1 with + | None -> + let r2 = + demodulate_term 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 (C.Prod (nn, (S.lift 1 s), t'), + subst, menv, ug, info) + ) + | Some (s', subst, menv, ug, info) -> + Some (C.Prod (nn, s', (S.lift 1 t)), subst, menv, ug, info) + ) + | 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 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 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]) + 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']) + 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) + in + newmeta, newtarget + 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 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 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 + in + [], C.Meta (i, 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, info) -> + C.Prod (nn, t, lifted_t), s, m, ug, info) l1 + and l2' = + List.map + (fun (t, s, m, ug, info) -> + C.Prod (nn, lifted_s, t), s, m, ug, info) l2 in + l1' @ l2', C.Prod (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, info) -> a::lifted_tl, s, m, ug, info) + arg_res + in + (l1 @ + (List.map + (fun (r, s, m, ug, info) -> lifted_arg::r, s, m, ug, info) + res), + lifted_arg::lifted_tl) + ) l ([], []) + in + (List.map (fun (l, s, m, ug, info) -> (C.Appl l, s, m, ug, info)) 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 +;; + + +let superposition_left (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 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 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']) + 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']) + 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 + in + (newproof, (eq_ty, left, right, ordering), [], []) + in + List.map build_new expansions +;; + + +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 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 = M.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, (proof', ty, what, other, eq_URI)) = + 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']) + 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']) + 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), [], []) + in + maxmeta := newmeta; + 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 + (!maxmeta, + (List.filter ok (new1 @ new2))) +;; -- 2.39.2