(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)))
+;;
projects / helm.git / commitdiff