1 (* cOpyright (C) 2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 (* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
28 type rule = SuperpositionRight | SuperpositionLeft | Demodulation
29 type uncomparable = int -> int
31 uncomparable * (* trick to break structural equality *)
34 (Cic.term * (* type *)
35 Cic.term * (* left side *)
36 Cic.term * (* right side *)
37 Utils.comparison) * (* ordering *)
38 Cic.metasenv * (* environment for metas *)
42 | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
43 (* subst, (rule,eq1, eq2,predicate) *)
44 and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
49 let id_to_eq = Hashtbl.create 1024;;
57 Hashtbl.clear id_to_eq
60 let uncomparable = fun _ -> 0
62 let mk_equality (weight,p,(ty,l,r,o),m) =
63 let id = freshid () in
64 let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
65 Hashtbl.add id_to_eq id eq;
69 let mk_tmp_equality (weight,(ty,l,r,o),m) =
71 uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
75 let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
76 (weight,proof,(ty,l,r,o),m,id)
78 let string_of_rule = function
79 | SuperpositionRight -> "SupR"
80 | SuperpositionLeft -> "SupL"
81 | Demodulation -> "Demod"
84 let string_of_equality ?env eq =
87 let w, _, (ty, left, right, o), m , id = open_equality eq in
88 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
89 id w (CicPp.ppterm ty)
91 (Utils.string_of_comparison o) (CicPp.ppterm right)
92 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
93 | Some (_, context, _) ->
94 let names = Utils.names_of_context context in
95 let w, _, (ty, left, right, o), m , id = open_equality eq in
96 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
97 id w (CicPp.pp ty names)
98 (CicPp.pp left names) (Utils.string_of_comparison o)
99 (CicPp.pp right names)
100 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
103 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
104 Pervasives.compare s1 s2
109 let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
112 Not_found -> assert false
115 let string_of_proof ?(names=[]) p gp =
116 let str_of_pos = function
117 | Utils.Left -> "left"
118 | Utils.Right -> "right"
120 let fst3 (x,_,_) = x in
121 let rec aux margin name =
122 let prefix = String.make margin ' ' ^ name ^ ": " in function
124 Printf.sprintf "%sExact (%s)\n"
125 prefix (CicPp.pp t names)
126 | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
127 Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
128 prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
129 (CicPp.pp pred names)^
130 aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^
131 aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2))
136 (fun (r,pos,i,s,t) ->
138 "GOAL: %s %s %d %s %s\n" (string_of_rule r)
139 (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
140 aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
144 let rec depend eq id seen =
145 let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
146 if List.mem ideq seen then
153 | Exact _ -> false,seen
154 | Step (_,(_,id1,(_,id2),_)) ->
155 let seen = ideq::seen in
156 let eq1 = Hashtbl.find id_to_eq id1 in
157 let eq2 = Hashtbl.find id_to_eq id2 in
158 let b1,seen = depend eq1 id seen in
159 if b1 then b1,seen else depend eq2 id seen
162 let depend eq id = fst (depend eq id []);;
164 let ppsubst = Subst.ppsubst ~names:[];;
166 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
167 let build_ens uri termlist =
168 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
170 | Cic.Constant (_, _, _, uris, _) ->
171 assert (List.length uris <= List.length termlist);
172 let rec aux = function
174 | (uri::uris), (term::tl) ->
175 let ens, args = aux (uris, tl) in
176 (uri, term)::ens, args
177 | _, _ -> assert false
183 let mk_sym uri ty t1 t2 p =
184 let ens, args = build_ens uri [ty;t1;t2;p] in
185 Cic.Appl (Cic.Const(uri, ens) :: args)
188 let mk_trans uri ty t1 t2 t3 p12 p23 =
189 let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
190 Cic.Appl (Cic.Const (uri, ens) :: args)
193 let mk_eq_ind uri ty what pred p1 other p2 =
194 Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
197 let p_of_sym ens tl =
198 let args = List.map snd ens @ tl in
204 let open_trans ens tl =
205 let args = List.map snd ens @ tl in
207 | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
211 let open_sym ens tl =
212 let args = List.map snd ens @ tl in
214 | [ty;l;r;p] -> ty,l,r,p
218 let open_eq_ind args =
220 | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
226 | Cic.Lambda (_,ty,(Cic.Appl [Cic.MutInd (uri, 0,_);_;l;r]))
227 when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
228 | _ -> prerr_endline (CicPp.ppterm pred); assert false
232 CicSubstitution.subst (Cic.Implicit None) t <>
233 CicSubstitution.subst (Cic.Rel 1) t
238 let rec remove_refl t =
240 | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
241 when LibraryObjects.is_trans_eq_URI uri_trans ->
242 let ty,l,m,r,p1,p2 = open_trans ens tl in
244 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
246 | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
248 | _ -> Cic.Appl (List.map remove_refl args))
249 | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
250 | Cic.LetIn (name,bo,rest) ->
251 Cic.LetIn (name,remove_refl bo,remove_refl rest)
254 let rec canonical t =
256 | Cic.LetIn(name,bo,rest) -> Cic.LetIn(name,canonical bo,canonical rest)
257 | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
258 when LibraryObjects.is_sym_eq_URI uri_sym ->
259 (match p_of_sym ens tl with
260 | Cic.Appl ((Cic.Const(uri,ens))::tl)
261 when LibraryObjects.is_sym_eq_URI uri ->
262 canonical (p_of_sym ens tl)
263 | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
264 when LibraryObjects.is_trans_eq_URI uri_trans ->
265 let ty,l,m,r,p1,p2 = open_trans ens tl in
266 mk_trans uri_trans ty r m l
267 (canonical (mk_sym uri_sym ty m r p2))
268 (canonical (mk_sym uri_sym ty l m p1))
269 | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl)
270 when LibraryObjects.is_eq_ind_URI uri_ind ||
271 LibraryObjects.is_eq_ind_r_URI uri_ind ->
272 let ty, what, pred, p1, other, p2 =
274 | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
279 | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
280 when LibraryObjects.is_eq_URI uri ->
282 (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
284 prerr_endline (CicPp.ppterm pred);
287 let l = CicSubstitution.subst what l in
288 let r = CicSubstitution.subst what r in
291 canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
292 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
293 when LibraryObjects.is_eq_URI uri -> t
294 | _ -> Cic.Appl (List.map canonical args))
295 | Cic.Appl l -> Cic.Appl (List.map canonical l)
298 remove_refl (canonical t)
301 let ty_of_lambda = function
302 | Cic.Lambda (_,ty,_) -> ty
306 let compose_contexts ctx1 ctx2 =
307 ProofEngineReduction.replace_lifting
308 ~equality:(=) ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
311 let put_in_ctx ctx t =
312 ProofEngineReduction.replace_lifting
313 ~equality:(=) ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
316 let mk_eq uri ty l r =
317 Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r]
320 let mk_refl uri ty t =
321 Cic.Appl [Cic.MutConstruct(uri,0,1,[]);ty;t]
324 let open_eq = function
325 | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
330 let contextualize uri ty left right t =
331 let hole = Cic.Implicit (Some `Hole) in
332 (* aux [uri] [ty] [left] [right] [ctx] [t]
334 * the parameters validate this invariant
335 * t: eq(uri) ty left right
336 * that is used only by the base case
338 * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
340 let rec aux uri ty left right ctx_d = function
341 | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
342 when LibraryObjects.is_sym_eq_URI uri_sym ->
343 let ty,l,r,p = open_sym ens tl in
344 mk_sym uri_sym ty l r (aux uri ty l r ctx_d p)
345 | Cic.LetIn (name,body,rest) ->
346 (* we should go in body *)
347 Cic.LetIn (name,body,aux uri ty left right ctx_d rest)
348 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
349 when LibraryObjects.is_eq_ind_URI uri_ind ||
350 LibraryObjects.is_eq_ind_r_URI uri_ind ->
351 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
352 let ty2,eq,lp,rp = open_pred pred in
353 let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
354 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
355 let is_not_fixed_lp = is_not_fixed lp in
356 let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
357 (* extract the context and the fixed term from the predicate *)
359 let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
360 (* they were under a lambda *)
361 let m = CicSubstitution.subst (Cic.Implicit None) m in
362 let ctx_c = CicSubstitution.subst hole ctx_c in
365 (* create the compound context and put the terms under it *)
366 let ctx_dc = compose_contexts ctx_d ctx_c in
367 let dc_what = put_in_ctx ctx_dc what in
368 let dc_other = put_in_ctx ctx_dc other in
369 (* m is already in ctx_c so it is put in ctx_d only *)
370 let d_m = put_in_ctx ctx_d m in
371 (* we also need what in ctx_c *)
372 let c_what = put_in_ctx ctx_c what in
373 (* now put the proofs in the compound context *)
374 let p1 = (* p1: dc_what = d_m *)
375 if is_not_fixed_lp then
376 aux uri ty1 c_what m ctx_d p1
378 mk_sym uri_sym ty d_m dc_what
379 (aux uri ty1 m c_what ctx_d p1)
381 let p2 = (* p2: dc_other = dc_what *)
383 mk_sym uri_sym ty dc_what dc_other
384 (aux uri ty1 what other ctx_dc p2)
386 aux uri ty1 other what ctx_dc p2
388 (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
389 if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
390 let a,b,c,paeqb,pbeqc =
391 if is_not_fixed_lp then
392 dc_other,dc_what,d_m,p2,p1
394 d_m,dc_what,dc_other,
395 (mk_sym uri_sym ty dc_what d_m p1),
396 (mk_sym uri_sym ty dc_other dc_what p2)
398 mk_trans uri_trans ty a b c paeqb pbeqc
400 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
401 let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in
403 (* ctx_d will go under a lambda, but put_in_ctx substitutes Rel 1 *)
404 let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in
406 let ctx_d = CicSubstitution.lift 1 ctx_d in
407 put_in_ctx ctx_d (Cic.Rel 1)
409 let lty = CicSubstitution.lift 1 ty in
410 Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r))
412 let d_left = put_in_ctx ctx_d left in
413 let d_right = put_in_ctx ctx_d right in
414 let refl_eq = mk_refl uri ty d_left in
415 mk_sym uri_sym ty d_right d_left
416 (mk_eq_ind uri_ind ty left pred refl_eq right t)
418 aux uri ty left right hole t
421 let contextualize_rewrites t ty =
422 let eq,ty,l,r = open_eq ty in
423 contextualize eq ty l r t
426 let add_subst subst =
428 | Exact t -> Exact (Subst.apply_subst subst t)
429 | Step (s,(rule, id1, (pos,id2), pred)) ->
430 Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
433 let build_proof_step ?(sym=false) lift subst p1 p2 pos l r pred =
434 let p1 = Subst.apply_subst_lift lift subst p1 in
435 let p2 = Subst.apply_subst_lift lift subst p2 in
436 let l = CicSubstitution.lift lift l in
437 let l = Subst.apply_subst_lift lift subst l in
438 let r = CicSubstitution.lift lift r in
439 let r = Subst.apply_subst_lift lift subst r in
440 let pred = CicSubstitution.lift lift pred in
441 let pred = Subst.apply_subst_lift lift subst pred in
444 | Cic.Lambda (_,ty,body) -> ty,body
448 if pos = Utils.Left then l,r else r,l
453 mk_eq_ind (Utils.eq_ind_URI ()) ty what pred p1 other p2
455 mk_eq_ind (Utils.eq_ind_r_URI ()) ty what pred p1 other p2
459 let eq,_,pl,pr = open_eq body in
460 LibraryObjects.sym_eq_URI ~eq, pl, pr
462 let l = CicSubstitution.subst other pl in
463 let r = CicSubstitution.subst other pr in
469 let parametrize_proof p l r ty =
470 let parameters = CicUtil.metas_of_term p
471 @ CicUtil.metas_of_term l
472 @ CicUtil.metas_of_term r
473 in (* ?if they are under a lambda? *)
475 HExtlib.list_uniq (List.sort Pervasives.compare parameters)
477 let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
478 let with_what, lift_no =
479 List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
481 let p = CicSubstitution.lift (lift_no-1) p in
483 ProofEngineReduction.replace_lifting
484 ~equality:(fun t1 t2 ->
485 match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
486 ~what ~with_what ~where:p
488 let ty_of_m _ = ty (*function
489 | Cic.Meta (i,_) -> List.assoc i menv
490 | _ -> assert false *)
494 (fun (instance,p,n) m ->
497 (Cic.Name ("x"^string_of_int n),
498 CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
504 let instance = match args with | [x] -> x | _ -> Cic.Appl args in
508 let wfo goalproof proof id =
510 let p,_,_ = proof_of_id id in
512 | Exact _ -> if (List.mem id acc) then acc else id :: acc
513 | Step (_,(_,id1, (_,id2), _)) ->
514 let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
515 let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
521 | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
523 List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
526 let string_of_id names id =
527 if id = 0 then "" else
529 let (_,p,(_,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
532 Printf.sprintf "%d = %s: %s = %s [%s]" id
533 (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
534 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
535 | Step (_,(step,id1, (_,id2), _) ) ->
536 Printf.sprintf "%6d: %s %6d %6d %s = %s [%s]" id
537 (string_of_rule step)
538 id1 id2 (CicPp.pp l names) (CicPp.pp r names)
539 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
541 Not_found -> assert false
543 let pp_proof names goalproof proof subst id initial_goal =
544 String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof id)) ^
547 (fst (List.fold_right
548 (fun (r,pos,i,s,pred) (acc,g) ->
549 let _,_,left,right = open_eq g in
552 | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
553 | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
555 let ty = Subst.apply_subst s ty in
556 ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
557 ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
558 "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
564 let compare = Pervasives.compare
567 module M = Map.Make(OT)
569 let rec find_deps m i =
572 let p,_,_ = proof_of_id i in
574 | Exact _ -> M.add i [] m
575 | Step (_,(_,id1,(_,id2),_)) ->
576 let m = find_deps m id1 in
577 let m = find_deps m id2 in
578 M.add i (M.find id1 m @ M.find id2 m @ [id1;id2]) m
581 let topological_sort l =
582 (* build the partial order relation *)
584 List.fold_left (fun m i -> find_deps m i)
587 let m = M.map (fun x -> Some x) m in
589 let keys m = M.fold (fun i _ acc -> i::acc) m [] in
590 let split l m = List.filter (fun i -> M.find i m = Some []) l in
593 (fun k v -> if List.mem k l then None else
596 | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
601 let ok = split keys m in
602 let m = purge ok m in
603 ok @ (if ok = [] then [] else aux m)
609 (* returns the list of ids that should be factorized *)
610 let get_duplicate_step_in_wfo l p =
611 let ol = List.rev l in
612 let h = Hashtbl.create 13 in
613 (* NOTE: here the n parameter is an approximation of the dependency
614 between equations. To do things seriously we should maintain a
615 dependency graph. This approximation is not perfect. *)
617 let p,_,_ = proof_of_id i in
622 let no = Hashtbl.find h i in
623 Hashtbl.replace h i (no+1);
625 with Not_found -> Hashtbl.add h i 1;true
627 let rec aux = function
629 | Step (_,(_,i1,(_,i2),_)) ->
630 let go_on_1 = add i1 in
631 let go_on_2 = add i2 in
632 if go_on_1 then aux (let p,_,_ = proof_of_id i1 in p);
633 if go_on_2 then aux (let p,_,_ = proof_of_id i2 in p)
637 (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id id in p))
639 (* now h is complete *)
640 let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
641 let proofs = List.filter (fun (_,c) -> c > 1) proofs in
642 topological_sort (List.map (fun (i,_) -> i) proofs)
645 let build_proof_term h lift proof =
646 let proof_of_id aux id =
647 let p,l,r = proof_of_id id in
648 try List.assoc id h,l,r with Not_found -> aux p, l, r
650 let rec aux = function
651 | Exact term -> CicSubstitution.lift lift term
652 | Step (subst,(rule, id1, (pos,id2), pred)) ->
653 let p1,_,_ = proof_of_id aux id1 in
654 let p2,l,r = proof_of_id aux id2 in
657 | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
658 | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
663 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
666 let p = build_proof_step lift subst p1 p2 pos l r pred in
667 (* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
669 prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
676 let build_goal_proof l initial ty se =
677 let se = List.map (fun i -> Cic.Meta (i,[])) se in
678 let lets = get_duplicate_step_in_wfo l initial in
679 let letsno = List.length lets in
680 let _,mty,_,_ = open_eq ty in
681 let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l
686 let p,l,r = proof_of_id id in
687 let cic = build_proof_term h n p in
688 let real_cic,instance =
689 parametrize_proof cic l r (CicSubstitution.lift n mty)
691 let h = (id, instance)::lift_list h in
692 acc@[id,real_cic],n+1,h)
696 let rec aux se current_proof = function
697 | [] -> current_proof,se
698 | (rule,pos,id,subst,pred)::tl ->
699 let p,l,r = proof_of_id id in
700 let p = build_proof_term h letsno p in
701 let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
704 | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
705 | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
710 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
714 build_proof_step letsno subst current_proof p pos l r pred
716 let proof,se = aux se proof tl in
717 Subst.apply_subst_lift letsno subst proof,
718 List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
720 aux se (build_proof_term h letsno initial) l
723 let initial = proof in
725 (fun (id,cic) (n,p) ->
728 Cic.Name ("H"^string_of_int id),
730 lets (letsno-1,initial)
733 (* canonical (contextualize_rewrites proof (CicSubstitution.lift letsno ty)),
737 let refl_proof ty term =
740 (Utils.eq_URI (), 0, 1, []);
744 let metas_of_proof p =
745 let p = build_proof_term [] 0 p in
746 Utils.metas_of_term p
749 let relocate newmeta menv to_be_relocated =
750 let subst, newmetasenv, newmeta =
752 (fun i (subst, metasenv, maxmeta) ->
753 let _,context,ty = CicUtil.lookup_meta i menv in
755 let newmeta = Cic.Meta(maxmeta,irl) in
756 let newsubst = Subst.buildsubst i context newmeta ty subst in
757 newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1)
758 to_be_relocated (Subst.empty_subst, [], newmeta+1)
760 let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
764 let fix_metas newmeta eq =
765 let w, p, (ty, left, right, o), menv,_ = open_equality eq in
766 let to_be_relocated =
767 (* List.map (fun i ,_,_ -> i) menv *)
769 (List.sort Pervasives.compare
770 (Utils.metas_of_term left @ Utils.metas_of_term right))
772 let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
773 let ty = Subst.apply_subst subst ty in
774 let left = Subst.apply_subst subst left in
775 let right = Subst.apply_subst subst right in
776 let fix_proof = function
777 | Exact p -> Exact (Subst.apply_subst subst p)
778 | Step (s,(r,id1,(pos,id2),pred)) ->
779 Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
781 let p = fix_proof p in
782 let eq' = mk_equality (w, p, (ty, left, right, o), metasenv) in
785 exception NotMetaConvertible;;
787 let meta_convertibility_aux table t1 t2 =
788 let module C = Cic in
789 let rec aux ((table_l, table_r) as table) t1 t2 =
791 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
792 let m1_binding, table_l =
793 try List.assoc m1 table_l, table_l
794 with Not_found -> m2, (m1, m2)::table_l
795 and m2_binding, table_r =
796 try List.assoc m2 table_r, table_r
797 with Not_found -> m1, (m2, m1)::table_r
799 if (m1_binding <> m2) || (m2_binding <> m1) then
800 raise NotMetaConvertible
806 | None, Some _ | Some _, None -> raise NotMetaConvertible
808 | Some t1, Some t2 -> (aux res t1 t2))
809 (table_l, table_r) tl1 tl2
810 with Invalid_argument _ ->
811 raise NotMetaConvertible
813 | C.Var (u1, ens1), C.Var (u2, ens2)
814 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
815 aux_ens table ens1 ens2
816 | C.Cast (s1, t1), C.Cast (s2, t2)
817 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
818 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
819 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
820 let table = aux table s1 s2 in
822 | C.Appl l1, C.Appl l2 -> (
823 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
824 with Invalid_argument _ -> raise NotMetaConvertible
826 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
827 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
828 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
829 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
830 aux_ens table ens1 ens2
831 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
832 when (UriManager.eq u1 u2) && i1 = i2 ->
833 let table = aux table s1 s2 in
834 let table = aux table t1 t2 in (
835 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
836 with Invalid_argument _ -> raise NotMetaConvertible
838 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
841 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
842 if i1 <> i2 then raise NotMetaConvertible
844 let res = (aux res s1 s2) in aux res t1 t2)
846 with Invalid_argument _ -> raise NotMetaConvertible
848 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
851 (fun res (n1, s1, t1) (n2, s2, t2) ->
852 let res = aux res s1 s2 in aux res t1 t2)
854 with Invalid_argument _ -> raise NotMetaConvertible
856 | t1, t2 when t1 = t2 -> table
857 | _, _ -> raise NotMetaConvertible
859 and aux_ens table ens1 ens2 =
860 let cmp (u1, t1) (u2, t2) =
861 Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
863 let ens1 = List.sort cmp ens1
864 and ens2 = List.sort cmp ens2 in
867 (fun res (u1, t1) (u2, t2) ->
868 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
871 with Invalid_argument _ -> raise NotMetaConvertible
877 let meta_convertibility_eq eq1 eq2 =
878 let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
879 let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
882 else if (left = left') && (right = right') then
884 else if (left = right') && (right = left') then
888 let table = meta_convertibility_aux ([], []) left left' in
889 let _ = meta_convertibility_aux table right right' in
891 with NotMetaConvertible ->
893 let table = meta_convertibility_aux ([], []) left right' in
894 let _ = meta_convertibility_aux table right left' in
896 with NotMetaConvertible ->
901 let meta_convertibility t1 t2 =
906 ignore(meta_convertibility_aux ([], []) t1 t2);
908 with NotMetaConvertible ->
912 exception TermIsNotAnEquality;;
914 let term_is_equality term =
915 let iseq uri = UriManager.eq uri (Utils.eq_URI ()) in
917 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
921 let equality_of_term proof term =
922 let eq_uri = Utils.eq_URI () in
923 let iseq uri = UriManager.eq uri eq_uri in
925 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
926 let o = !Utils.compare_terms t1 t2 in
927 let stat = (ty,t1,t2,o) in
928 let w = Utils.compute_equality_weight stat in
929 let e = mk_equality (w, Exact proof, stat,[]) in
932 raise TermIsNotAnEquality
935 let is_weak_identity eq =
936 let _,_,(_,left, right,_),_,_ = open_equality eq in
937 left = right || meta_convertibility left right
940 let is_identity (_, context, ugraph) eq =
941 let _,_,(ty,left,right,_),menv,_ = open_equality eq in
943 (* (meta_convertibility left right)) *)
944 fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
948 let term_of_equality equality =
949 let _, _, (ty, left, right, _), menv, _= open_equality equality in
950 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
951 let argsno = List.length menv in
953 CicSubstitution.lift argsno
954 (Cic.Appl [Cic.MutInd (Utils.eq_URI (), 0, []); ty; left; right])
958 (fun (i,_,ty) (n, t) ->
959 let name = Cic.Name ("X" ^ (string_of_int n)) in
960 let ty = CicSubstitution.lift (n-1) ty in
962 ProofEngineReduction.replace
963 ~equality:eq ~what:[i]
964 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
966 (n-1, Cic.Prod (name, ty, t)))
970 let symmetric eq_ty l id uri m =
971 let eq = Cic.MutInd(uri,0,[]) in
973 Cic.Lambda (Cic.Name "Sym",eq_ty,
974 Cic.Appl [CicSubstitution.lift 1 eq ;
975 CicSubstitution.lift 1 eq_ty;
976 Cic.Rel 1;CicSubstitution.lift 1 l])
980 [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
983 let eq = mk_equality (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
984 let (_,_,_,_,id) = open_equality eq in
987 Step(Subst.empty_subst,
988 (Demodulation,id1,(Utils.Left,id),pred))