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 = (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_equality ?env eq =
81 let w, _, (ty, left, right, o), _ , id = open_equality eq in
82 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s"
83 id w (CicPp.ppterm ty)
85 (Utils.string_of_comparison o) (CicPp.ppterm right)
86 | Some (_, context, _) ->
87 let names = Utils.names_of_context context in
88 let w, _, (ty, left, right, o), _ , id = open_equality eq in
89 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s"
90 id w (CicPp.pp ty names)
91 (CicPp.pp left names) (Utils.string_of_comparison o)
92 (CicPp.pp right names)
95 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
96 Pervasives.compare s1 s2
101 let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
104 Not_found -> assert false
107 let string_of_proof ?(names=[]) p gp =
108 let str_of_rule = function
109 | SuperpositionRight -> "SupR"
110 | SuperpositionLeft -> "SupL"
111 | Demodulation -> "Demod"
113 let str_of_pos = function
114 | Utils.Left -> "left"
115 | Utils.Right -> "right"
117 let fst3 (x,_,_) = x in
118 let rec aux margin name =
119 let prefix = String.make margin ' ' ^ name ^ ": " in function
121 Printf.sprintf "%sExact (%s)\n"
122 prefix (CicPp.pp t names)
123 | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
124 Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
125 prefix (str_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
126 (CicPp.pp pred names)^
127 aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^
128 aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2))
135 "GOAL: %s %d %s %s\n"
136 (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
137 aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
141 let rec depend eq id =
142 let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
143 if id = ideq then true else
146 | Step (_,(_,id1,(_,id2),_)) ->
147 let eq1 = Hashtbl.find id_to_eq id1 in
148 let eq2 = Hashtbl.find id_to_eq id2 in
149 depend eq1 id || depend eq2 id
152 let ppsubst = Subst.ppsubst ~names:[];;
154 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
155 let build_ens uri termlist =
156 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
158 | Cic.Constant (_, _, _, uris, _) ->
159 assert (List.length uris <= List.length termlist);
160 let rec aux = function
162 | (uri::uris), (term::tl) ->
163 let ens, args = aux (uris, tl) in
164 (uri, term)::ens, args
165 | _, _ -> assert false
171 let mk_sym uri ty t1 t2 p =
172 let ens, args = build_ens uri [ty;t1;t2;p] in
173 Cic.Appl (Cic.Const(uri, ens) :: args)
176 let mk_trans uri ty t1 t2 t3 p12 p23 =
177 let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
178 Cic.Appl (Cic.Const (uri, ens) :: args)
181 let mk_eq_ind uri ty what pred p1 other p2 =
182 Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
185 let p_of_sym ens tl =
186 let args = List.map snd ens @ tl in
192 let open_trans ens tl =
193 let args = List.map snd ens @ tl in
195 | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
199 let open_eq_ind args =
201 | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
207 | Cic.Lambda (_,ty,(Cic.Appl [Cic.MutInd (uri, 0,_);_;l;r]))
208 when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
209 | _ -> prerr_endline (CicPp.ppterm pred); assert false
213 CicSubstitution.subst (Cic.Implicit None) t <>
214 CicSubstitution.subst (Cic.Rel 1) t
219 let rec remove_refl t =
221 | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
222 when LibraryObjects.is_trans_eq_URI uri_trans ->
223 let ty,l,m,r,p1,p2 = open_trans ens tl in
225 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
227 | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
229 | _ -> Cic.Appl (List.map remove_refl args))
230 | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
231 | Cic.LetIn (name,bo,rest) ->
232 Cic.LetIn (name,remove_refl bo,remove_refl rest)
235 let rec canonical t =
237 | Cic.LetIn(name,bo,rest) -> Cic.LetIn(name,canonical bo,canonical rest)
238 | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
239 when LibraryObjects.is_sym_eq_URI uri_sym ->
240 (match p_of_sym ens tl with
241 | Cic.Appl ((Cic.Const(uri,ens))::tl)
242 when LibraryObjects.is_sym_eq_URI uri ->
243 canonical (p_of_sym ens tl)
244 | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
245 when LibraryObjects.is_trans_eq_URI uri_trans ->
246 let ty,l,m,r,p1,p2 = open_trans ens tl in
247 mk_trans uri_trans ty r m l
248 (canonical (mk_sym uri_sym ty m r p2))
249 (canonical (mk_sym uri_sym ty l m p1))
250 | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl)
251 when LibraryObjects.is_eq_ind_URI uri_ind ||
252 LibraryObjects.is_eq_ind_r_URI uri_ind ->
253 let ty, what, pred, p1, other, p2 =
255 | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
260 | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
261 when LibraryObjects.is_eq_URI uri ->
263 (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
265 prerr_endline (CicPp.ppterm pred);
268 let l = CicSubstitution.subst what l in
269 let r = CicSubstitution.subst what r in
272 canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
273 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
274 when LibraryObjects.is_eq_URI uri -> t
275 | _ -> Cic.Appl (List.map canonical args))
276 | Cic.Appl l -> Cic.Appl (List.map canonical l)
279 remove_refl (canonical t)
282 let ty_of_lambda = function
283 | Cic.Lambda (_,ty,_) -> ty
287 let compose_contexts ctx1 ctx2 =
288 ProofEngineReduction.replace_lifting
289 ~equality:(=) ~what:[Cic.Rel 1] ~with_what:[ctx2] ~where:ctx1
292 let put_in_ctx ctx t =
293 ProofEngineReduction.replace_lifting
294 ~equality:(=) ~what:[Cic.Rel 1] ~with_what:[t] ~where:ctx
297 let mk_eq uri ty l r =
298 Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r]
301 let mk_refl uri ty t =
302 Cic.Appl [Cic.MutConstruct(uri,0,1,[]);ty;t]
305 let open_eq = function
306 | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
311 let contextualize uri ty left right t =
312 (* aux [uri] [ty] [left] [right] [ctx] [t]
314 * the parameters validate this invariant
315 * t: eq(uri) ty left right
316 * that is used only by the base case
318 * ctx is a term with an open (Rel 1). (Rel 1) is the empty context
320 let rec aux uri ty left right ctx_d = function
321 | Cic.LetIn (name,body,rest) ->
322 (* we should go in body *)
323 Cic.LetIn (name,body,aux uri ty left right ctx_d rest)
324 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
325 when LibraryObjects.is_eq_ind_URI uri_ind ||
326 LibraryObjects.is_eq_ind_r_URI uri_ind ->
327 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
328 let ty2,eq,lp,rp = open_pred pred in
329 let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
330 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
331 let is_not_fixed_lp = is_not_fixed lp in
332 let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
333 (* extract the context and the fixed term from the predicate *)
335 let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
336 (* they were under a lambda *)
337 let m = CicSubstitution.subst (Cic.Implicit None) m in
338 let ctx_c = CicSubstitution.subst (Cic.Rel 1) ctx_c in
341 (* create the compound context and put the terms under it *)
342 let ctx_dc = compose_contexts ctx_d ctx_c in
343 let dc_what = put_in_ctx ctx_dc what in
344 let dc_other = put_in_ctx ctx_dc other in
345 (* m is already in ctx_c so it is put in ctx_d only *)
346 let d_m = put_in_ctx ctx_d m in
347 (* we also need what in ctx_c *)
348 let c_what = put_in_ctx ctx_c what in
349 (* now put the proofs in the compound context *)
350 let p1 = (* p1: dc_what = d_m *)
351 if is_not_fixed_lp then
352 aux uri ty1 c_what m ctx_d p1
354 mk_sym uri_sym ty d_m dc_what
355 (aux uri ty1 m c_what ctx_d p1)
357 let p2 = (* p2: dc_other = dc_what *)
359 mk_sym uri_sym ty dc_what dc_other
360 (aux uri ty1 what other ctx_dc p2)
362 aux uri ty1 other what ctx_dc p2
364 (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
365 if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
366 let a,b,c,paeqb,pbeqc =
367 if is_not_fixed_lp then
368 dc_other,dc_what,d_m,p2,p1
370 d_m,dc_what,dc_other,
371 (mk_sym uri_sym ty dc_what d_m p1),
372 (mk_sym uri_sym ty dc_other dc_what p2)
374 mk_trans uri_trans ty a b c paeqb pbeqc
376 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
377 let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in
379 (* ctx_d will go under a lambda, but put_in_ctx substitutes Rel 1 *)
380 let ctx_d = CicSubstitution.lift_from 2 1 ctx_d in (* bleah *)
381 let r = put_in_ctx ctx_d (CicSubstitution.lift 1 left) in
383 let lty = CicSubstitution.lift 1 ty in
384 Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r))
386 let d_left = put_in_ctx ctx_d left in
387 let d_right = put_in_ctx ctx_d right in
388 let refl_eq = mk_refl uri ty d_left in
389 mk_sym uri_sym ty d_right d_left
390 (mk_eq_ind uri_ind ty left pred refl_eq right t)
392 let empty_context = Cic.Rel 1 in
393 aux uri ty left right empty_context t
396 let contextualize_rewrites t ty =
397 let eq,ty,l,r = open_eq ty in
398 contextualize eq ty l r t
401 let build_proof_step lift subst p1 p2 pos l r pred =
402 let p1 = Subst.apply_subst_lift lift subst p1 in
403 let p2 = Subst.apply_subst_lift lift subst p2 in
404 let l = CicSubstitution.lift lift l in
405 let l = Subst.apply_subst_lift lift subst l in
406 let r = CicSubstitution.lift lift r in
407 let r = Subst.apply_subst_lift lift subst r in
408 let pred = CicSubstitution.lift lift pred in
409 let pred = Subst.apply_subst_lift lift subst pred in
412 | Cic.Lambda (_,ty,body) -> ty,body
416 if pos = Utils.Left then l,r else r,l
420 mk_eq_ind (Utils.eq_ind_URI ()) ty what pred p1 other p2
422 mk_eq_ind (Utils.eq_ind_r_URI ()) ty what pred p1 other p2
425 let parametrize_proof p ty =
426 let parameters = CicUtil.metas_of_term p in (* ?if they are under a lambda? *)
428 HExtlib.list_uniq (List.sort Pervasives.compare parameters)
430 let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
431 let with_what, lift_no =
432 List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
434 let p = CicSubstitution.lift (lift_no-1) p in
436 ProofEngineReduction.replace_lifting
437 ~equality:(=) ~what ~with_what ~where:p
439 let ty_of_m _ = ty (*function
440 | Cic.Meta (i,_) -> List.assoc i menv
441 | _ -> assert false *)
445 (fun (instance,p,n) m ->
448 (Cic.Name ("x"^string_of_int n),
449 CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
455 let instance = match args with | [x] -> x | _ -> Cic.Appl args in
459 let wfo goalproof proof =
461 let p,_,_ = proof_of_id id in
463 | Exact _ -> if (List.mem id acc) then acc else id :: acc
464 | Step (_,(_,id1, (_,id2), _)) ->
465 let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
466 let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
472 | Step (_,(_,id1, (_,id2), _)) -> aux (aux [] id1) id2
474 List.fold_left (fun acc (_,id,_,_) -> aux acc id) acc goalproof
477 let string_of_id names id =
479 let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
482 Printf.sprintf "%d = %s: %s = %s" id
483 (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
484 | Step (_,(step,id1, (_,id2), _) ) ->
485 Printf.sprintf "%6d: %s %6d %6d %s = %s" id
486 (if step = SuperpositionRight then "SupR" else "Demo")
487 id1 id2 (CicPp.pp l names) (CicPp.pp r names)
489 Not_found -> assert false
491 let pp_proof names goalproof proof =
492 String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof)) ^
493 "\ngoal is demodulated with " ^
495 ((List.map (fun (_,i,_,_) -> string_of_int i) goalproof)))
498 (* returns the list of ids that should be factorized *)
499 let get_duplicate_step_in_wfo l p =
500 let ol = List.rev l in
501 let h = Hashtbl.create 13 in
503 let p,_,_ = proof_of_id i in
507 try let (pos,no) = Hashtbl.find h i in Hashtbl.replace h i (pos,no+1)
508 with Not_found -> Hashtbl.add h i (n,1)
510 let rec aux n = function
512 | Step (_,(_,i1,(_,i2),_)) ->
514 max (aux (n+1) (let p,_,_ = proof_of_id i1 in p))
515 (aux (n+1) (let p,_,_ = proof_of_id i2 in p))
520 (fun acc (_,id,_,_) -> aux acc (let p,_,_ = proof_of_id id in p))
523 (* now h is complete *)
524 let proofs = Hashtbl.fold (fun k (pos,count) acc->(k,pos,count)::acc) h [] in
525 let proofs = List.filter (fun (_,_,c) -> c > 1) proofs in
527 List.sort (fun (_,c1,_) (_,c2,_) -> Pervasives.compare c2 c1) proofs
529 List.map (fun (i,_,_) -> i) proofs
532 let build_proof_term h lift proof =
533 let proof_of_id aux id =
534 let p,l,r = proof_of_id id in
535 try List.assoc id h,l,r with Not_found -> aux p, l, r
537 let rec aux = function
538 | Exact term -> CicSubstitution.lift lift term
539 | Step (subst,(_, id1, (pos,id2), pred)) ->
540 if Subst.is_in_subst 9 subst then
541 prerr_endline (Printf.sprintf "ID %d-%d has: %s\n" id1 id2 (Subst.ppsubst
543 let p1,_,_ = proof_of_id aux id1 in
544 let p2,l,r = proof_of_id aux id2 in
545 build_proof_step lift subst p1 p2 pos l r pred
550 let build_goal_proof l initial ty se =
551 let se = List.map (fun i -> Cic.Meta (i,[])) se in
552 let lets = get_duplicate_step_in_wfo l initial in
553 let letsno = List.length lets in
554 let _,mty,_,_ = open_eq ty in
555 let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l
560 let p,_,_ = proof_of_id id in
561 let cic = build_proof_term h n p in
562 let real_cic,instance =
563 parametrize_proof cic (CicSubstitution.lift n mty)
565 let h = (id, instance)::lift_list h in
566 acc@[id,real_cic],n+1,h)
570 let rec aux se current_proof = function
571 | [] -> current_proof,se
572 | (pos,id,subst,pred)::tl ->
573 let p,l,r = proof_of_id id in
574 let p = build_proof_term h letsno p in
575 let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
577 build_proof_step letsno subst current_proof p pos l r pred
579 let proof,se = aux se proof tl in
580 Subst.apply_subst_lift letsno subst proof,
581 List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
583 aux se (build_proof_term h letsno initial) l
586 let initial = proof in
588 (fun (id,cic) (n,p) ->
591 Cic.Name ("H"^string_of_int id),
593 lets (letsno-1,initial)
595 canonical (contextualize_rewrites proof (CicSubstitution.lift letsno ty)), se
598 let refl_proof ty term =
601 (LibraryObjects.eq_URI (), 0, 1, []);
605 let metas_of_proof p =
606 let p = build_proof_term [] 0 p in
607 Utils.metas_of_term p
610 let relocate newmeta menv =
611 let subst, metasenv, newmeta =
613 (fun (i, context, ty) (subst, menv, maxmeta) ->
615 CicMkImplicit.identity_relocation_list_for_metavariable context *)
617 let newsubst = Subst.buildsubst i context (Cic.Meta(maxmeta,irl)) ty subst in
618 let newmeta = maxmeta, context, ty in
619 newsubst, newmeta::menv, maxmeta+1)
620 menv (Subst.empty_subst, [], newmeta+1)
622 let metasenv = Subst.apply_subst_metasenv subst metasenv in
623 let subst = Subst.flatten_subst subst in
624 subst, metasenv, newmeta
627 let fix_metas newmeta eq =
628 let w, p, (ty, left, right, o), menv,_ = open_equality eq in
629 let subst, metasenv, newmeta = relocate newmeta menv in
630 let ty = Subst.apply_subst subst ty in
631 let left = Subst.apply_subst subst left in
632 let right = Subst.apply_subst subst right in
633 let fix_proof = function
634 | Exact p -> Exact (Subst.apply_subst subst p)
635 | Step (s,(r,id1,(pos,id2),pred)) ->
636 Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
638 let p = fix_proof p in
639 let eq = mk_equality (w, p, (ty, left, right, o), metasenv) in
642 exception NotMetaConvertible;;
644 let meta_convertibility_aux table t1 t2 =
645 let module C = Cic in
646 let rec aux ((table_l, table_r) as table) t1 t2 =
648 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
649 let m1_binding, table_l =
650 try List.assoc m1 table_l, table_l
651 with Not_found -> m2, (m1, m2)::table_l
652 and m2_binding, table_r =
653 try List.assoc m2 table_r, table_r
654 with Not_found -> m1, (m2, m1)::table_r
656 if (m1_binding <> m2) || (m2_binding <> m1) then
657 raise NotMetaConvertible
663 | None, Some _ | Some _, None -> raise NotMetaConvertible
665 | Some t1, Some t2 -> (aux res t1 t2))
666 (table_l, table_r) tl1 tl2
667 with Invalid_argument _ ->
668 raise NotMetaConvertible
670 | C.Var (u1, ens1), C.Var (u2, ens2)
671 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
672 aux_ens table ens1 ens2
673 | C.Cast (s1, t1), C.Cast (s2, t2)
674 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
675 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
676 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
677 let table = aux table s1 s2 in
679 | C.Appl l1, C.Appl l2 -> (
680 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
681 with Invalid_argument _ -> raise NotMetaConvertible
683 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
684 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
685 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
686 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
687 aux_ens table ens1 ens2
688 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
689 when (UriManager.eq u1 u2) && i1 = i2 ->
690 let table = aux table s1 s2 in
691 let table = aux table t1 t2 in (
692 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
693 with Invalid_argument _ -> raise NotMetaConvertible
695 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
698 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
699 if i1 <> i2 then raise NotMetaConvertible
701 let res = (aux res s1 s2) in aux res t1 t2)
703 with Invalid_argument _ -> raise NotMetaConvertible
705 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
708 (fun res (n1, s1, t1) (n2, s2, t2) ->
709 let res = aux res s1 s2 in aux res t1 t2)
711 with Invalid_argument _ -> raise NotMetaConvertible
713 | t1, t2 when t1 = t2 -> table
714 | _, _ -> raise NotMetaConvertible
716 and aux_ens table ens1 ens2 =
717 let cmp (u1, t1) (u2, t2) =
718 Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
720 let ens1 = List.sort cmp ens1
721 and ens2 = List.sort cmp ens2 in
724 (fun res (u1, t1) (u2, t2) ->
725 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
728 with Invalid_argument _ -> raise NotMetaConvertible
734 let meta_convertibility_eq eq1 eq2 =
735 let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
736 let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
739 else if (left = left') && (right = right') then
741 else if (left = right') && (right = left') then
745 let table = meta_convertibility_aux ([], []) left left' in
746 let _ = meta_convertibility_aux table right right' in
748 with NotMetaConvertible ->
750 let table = meta_convertibility_aux ([], []) left right' in
751 let _ = meta_convertibility_aux table right left' in
753 with NotMetaConvertible ->
758 let meta_convertibility t1 t2 =
763 ignore(meta_convertibility_aux ([], []) t1 t2);
765 with NotMetaConvertible ->
769 exception TermIsNotAnEquality;;
771 let term_is_equality term =
772 let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in
774 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
778 let equality_of_term proof term =
779 let eq_uri = LibraryObjects.eq_URI () in
780 let iseq uri = UriManager.eq uri eq_uri in
782 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
783 let o = !Utils.compare_terms t1 t2 in
784 let stat = (ty,t1,t2,o) in
785 let w = Utils.compute_equality_weight stat in
786 let e = mk_equality (w, Exact proof, stat,[]) in
789 raise TermIsNotAnEquality
792 let is_weak_identity eq =
793 let _,_,(_,left, right,_),_,_ = open_equality eq in
794 left = right || meta_convertibility left right
797 let is_identity (_, context, ugraph) eq =
798 let _,_,(ty,left,right,_),menv,_ = open_equality eq in
800 (* (meta_convertibility left right)) *)
801 fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
805 let term_of_equality equality =
806 let _, _, (ty, left, right, _), menv, _= open_equality equality in
807 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
808 let argsno = List.length menv in
810 CicSubstitution.lift argsno
811 (Cic.Appl [Cic.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right])
815 (fun (i,_,ty) (n, t) ->
816 let name = Cic.Name ("X" ^ (string_of_int n)) in
817 let ty = CicSubstitution.lift (n-1) ty in
819 ProofEngineReduction.replace
820 ~equality:eq ~what:[i]
821 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
823 (n-1, Cic.Prod (name, ty, t)))