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 let _profiler = <:profiler<_profiler>>;;
28 (* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
30 type rule = SuperpositionRight | SuperpositionLeft | Demodulation
31 type uncomparable = int -> int
33 uncomparable * (* trick to break structural equality *)
36 (Cic.term * (* type *)
37 Cic.term * (* left side *)
38 Cic.term * (* right side *)
39 Utils.comparison) * (* ordering *)
40 Cic.metasenv * (* environment for metas *)
44 | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term)
45 (* subst, (rule,eq1, eq2,predicate) *)
46 and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
51 let id_to_eq = Hashtbl.create 1024;;
59 Hashtbl.clear id_to_eq
62 let uncomparable = fun _ -> 0
64 let mk_equality (weight,p,(ty,l,r,o),m) =
65 let id = freshid () in
66 let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
67 Hashtbl.add id_to_eq id eq;
71 let mk_tmp_equality (weight,(ty,l,r,o),m) =
73 uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
77 let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
78 (weight,proof,(ty,l,r,o),m,id)
80 let string_of_rule = function
81 | SuperpositionRight -> "SupR"
82 | SuperpositionLeft -> "SupL"
83 | Demodulation -> "Demod"
86 let string_of_equality ?env eq =
89 let w, _, (ty, left, right, o), m , id = open_equality eq in
90 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
91 id w (CicPp.ppterm ty)
93 (Utils.string_of_comparison o) (CicPp.ppterm right)
94 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
95 | Some (_, context, _) ->
96 let names = Utils.names_of_context context in
97 let w, _, (ty, left, right, o), m , id = open_equality eq in
98 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
99 id w (CicPp.pp ty names)
100 (CicPp.pp left names) (Utils.string_of_comparison o)
101 (CicPp.pp right names)
102 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
105 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
106 Pervasives.compare s1 s2
111 let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
114 Not_found -> assert false
117 let string_of_proof ?(names=[]) p gp =
118 let str_of_pos = function
119 | Utils.Left -> "left"
120 | Utils.Right -> "right"
122 let fst3 (x,_,_) = x in
123 let rec aux margin name =
124 let prefix = String.make margin ' ' ^ name ^ ": " in function
126 Printf.sprintf "%sExact (%s)\n"
127 prefix (CicPp.pp t names)
128 | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
129 Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
130 prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
131 (CicPp.pp pred names)^
132 aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^
133 aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2))
138 (fun (r,pos,i,s,t) ->
140 "GOAL: %s %s %d %s %s\n" (string_of_rule r)
141 (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
142 aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
146 let rec depend eq id seen =
147 let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
148 if List.mem ideq seen then
155 | Exact _ -> false,seen
156 | Step (_,(_,id1,(_,id2),_)) ->
157 let seen = ideq::seen in
158 let eq1 = Hashtbl.find id_to_eq id1 in
159 let eq2 = Hashtbl.find id_to_eq id2 in
160 let b1,seen = depend eq1 id seen in
161 if b1 then b1,seen else depend eq2 id seen
164 let depend eq id = fst (depend eq id []);;
166 let ppsubst = Subst.ppsubst ~names:[];;
168 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
169 let build_ens uri termlist =
170 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
172 | Cic.Constant (_, _, _, uris, _) ->
173 assert (List.length uris <= List.length termlist);
174 let rec aux = function
176 | (uri::uris), (term::tl) ->
177 let ens, args = aux (uris, tl) in
178 (uri, term)::ens, args
179 | _, _ -> assert false
185 let mk_sym uri ty t1 t2 p =
186 let ens, args = build_ens uri [ty;t1;t2;p] in
187 Cic.Appl (Cic.Const(uri, ens) :: args)
190 let mk_trans uri ty t1 t2 t3 p12 p23 =
191 let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
192 Cic.Appl (Cic.Const (uri, ens) :: args)
195 let mk_eq_ind uri ty what pred p1 other p2 =
196 Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
199 let p_of_sym ens tl =
200 let args = List.map snd ens @ tl in
206 let open_trans ens tl =
207 let args = List.map snd ens @ tl in
209 | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
213 let open_sym ens tl =
214 let args = List.map snd ens @ tl in
216 | [ty;l;r;p] -> ty,l,r,p
220 let open_eq_ind args =
222 | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
228 | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]))
229 when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
230 | _ -> prerr_endline (CicPp.ppterm pred); assert false
234 CicSubstitution.subst (Cic.Implicit None) t <>
235 CicSubstitution.subst (Cic.Rel 1) t
240 let rec remove_refl t =
242 | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
243 when LibraryObjects.is_trans_eq_URI uri_trans ->
244 let ty,l,m,r,p1,p2 = open_trans ens tl in
246 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
248 | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
250 | _ -> Cic.Appl (List.map remove_refl args))
251 | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
252 | Cic.LetIn (name,bo,rest) ->
253 Cic.LetIn (name,remove_refl bo,remove_refl rest)
256 let rec canonical t =
258 | Cic.LetIn(name,bo,rest) -> Cic.LetIn(name,canonical bo,canonical rest)
259 | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
260 when LibraryObjects.is_sym_eq_URI uri_sym ->
261 (match p_of_sym ens tl with
262 | Cic.Appl ((Cic.Const(uri,ens))::tl)
263 when LibraryObjects.is_sym_eq_URI uri ->
264 canonical (p_of_sym ens tl)
265 | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
266 when LibraryObjects.is_trans_eq_URI uri_trans ->
267 let ty,l,m,r,p1,p2 = open_trans ens tl in
268 mk_trans uri_trans ty r m l
269 (canonical (mk_sym uri_sym ty m r p2))
270 (canonical (mk_sym uri_sym ty l m p1))
271 | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl)
272 when LibraryObjects.is_eq_ind_URI uri_ind ||
273 LibraryObjects.is_eq_ind_r_URI uri_ind ->
274 let ty, what, pred, p1, other, p2 =
276 | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
281 | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
282 when LibraryObjects.is_eq_URI uri ->
284 (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
286 prerr_endline (CicPp.ppterm pred);
289 let l = CicSubstitution.subst what l in
290 let r = CicSubstitution.subst what r in
293 canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
294 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
295 when LibraryObjects.is_eq_URI uri -> t
296 | _ -> Cic.Appl (List.map canonical args))
297 | Cic.Appl l -> Cic.Appl (List.map canonical l)
300 remove_refl (canonical t)
303 let ty_of_lambda = function
304 | Cic.Lambda (_,ty,_) -> ty
308 let compose_contexts ctx1 ctx2 =
309 ProofEngineReduction.replace_lifting
310 ~equality:(=) ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
313 let put_in_ctx ctx t =
314 ProofEngineReduction.replace_lifting
315 ~equality:(=) ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
318 let mk_eq uri ty l r =
319 Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r]
322 let mk_refl uri ty t =
323 Cic.Appl [Cic.MutConstruct(uri,0,1,[]);ty;t]
326 let open_eq = function
327 | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
332 let contextualize uri ty left right t =
333 let hole = Cic.Implicit (Some `Hole) in
334 (* aux [uri] [ty] [left] [right] [ctx] [t]
336 * the parameters validate this invariant
337 * t: eq(uri) ty left right
338 * that is used only by the base case
340 * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
341 * ty_ctx is the type of ctx_d
343 let rec aux uri ty left right ctx_d ctx_ty = function
344 | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
345 when LibraryObjects.is_sym_eq_URI uri_sym ->
346 let ty,l,r,p = open_sym ens tl in
347 mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
348 | Cic.LetIn (name,body,rest) ->
349 (* we should go in body *)
350 Cic.LetIn (name,body,aux uri ty left right ctx_d ctx_ty rest)
351 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
352 when LibraryObjects.is_eq_ind_URI uri_ind ||
353 LibraryObjects.is_eq_ind_r_URI uri_ind ->
354 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
355 let ty2,eq,lp,rp = open_pred pred in
356 let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
357 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
358 let is_not_fixed_lp = is_not_fixed lp in
359 let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
360 (* extract the context and the fixed term from the predicate *)
362 let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
363 (* they were under a lambda *)
364 let m = CicSubstitution.subst hole m in
365 let ctx_c = CicSubstitution.subst hole ctx_c in
366 let ty2 = CicSubstitution.subst hole ty2 in
369 (* create the compound context and put the terms under it *)
370 let ctx_dc = compose_contexts ctx_d ctx_c in
371 let dc_what = put_in_ctx ctx_dc what in
372 let dc_other = put_in_ctx ctx_dc other in
373 (* m is already in ctx_c so it is put in ctx_d only *)
374 let d_m = put_in_ctx ctx_d m in
375 (* we also need what in ctx_c *)
376 let c_what = put_in_ctx ctx_c what in
377 (* now put the proofs in the compound context *)
378 let p1 = (* p1: dc_what = d_m *)
379 if is_not_fixed_lp then
380 aux uri ty2 c_what m ctx_d ctx_ty p1
382 mk_sym uri_sym ctx_ty d_m dc_what
383 (aux uri ty2 m c_what ctx_d ctx_ty p1)
385 let p2 = (* p2: dc_other = dc_what *)
387 mk_sym uri_sym ctx_ty dc_what dc_other
388 (aux uri ty1 what other ctx_dc ctx_ty p2)
390 aux uri ty1 other what ctx_dc ctx_ty p2
392 (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
393 if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
394 let a,b,c,paeqb,pbeqc =
395 if is_not_fixed_lp then
396 dc_other,dc_what,d_m,p2,p1
398 d_m,dc_what,dc_other,
399 (mk_sym uri_sym ctx_ty dc_what d_m p1),
400 (mk_sym uri_sym ctx_ty dc_other dc_what p2)
402 mk_trans uri_trans ctx_ty a b c paeqb pbeqc
403 | t when ctx_d = hole -> t
405 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
406 let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in
408 (* ctx_d will go under a lambda, but put_in_ctx substitutes Rel 1 *)
409 let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in
411 let ctx_d = CicSubstitution.lift 1 ctx_d in
412 put_in_ctx ctx_d (Cic.Rel 1)
414 let lty = CicSubstitution.lift 1 ctx_ty in
415 Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r))
417 let d_left = put_in_ctx ctx_d left in
418 let d_right = put_in_ctx ctx_d right in
419 let refl_eq = mk_refl uri ctx_ty d_left in
420 mk_sym uri_sym ctx_ty d_right d_left
421 (mk_eq_ind uri_ind ty left pred refl_eq right t)
423 aux uri ty left right hole ty t
426 let contextualize_rewrites t ty =
427 let eq,ty,l,r = open_eq ty in
428 contextualize eq ty l r t
431 let add_subst subst =
433 | Exact t -> Exact (Subst.apply_subst subst t)
434 | Step (s,(rule, id1, (pos,id2), pred)) ->
435 Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
438 let build_proof_step eq lift subst p1 p2 pos l r pred =
439 let p1 = Subst.apply_subst_lift lift subst p1 in
440 let p2 = Subst.apply_subst_lift lift subst p2 in
441 let l = CicSubstitution.lift lift l in
442 let l = Subst.apply_subst_lift lift subst l in
443 let r = CicSubstitution.lift lift r in
444 let r = Subst.apply_subst_lift lift subst r in
445 let pred = CicSubstitution.lift lift pred in
446 let pred = Subst.apply_subst_lift lift subst pred in
449 | Cic.Lambda (_,ty,body) -> ty,body
453 if pos = Utils.Left then l,r else r,l
458 mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
460 mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
465 let parametrize_proof p l r ty =
466 let uniq l = HExtlib.list_uniq (List.sort Pervasives.compare l) in
467 let mot = CicUtil.metas_of_term_set in
468 let parameters = uniq (mot p @ mot l @ mot r) in
469 (* ?if they are under a lambda? *)
471 HExtlib.list_uniq (List.sort Pervasives.compare parameters)
473 let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
474 let with_what, lift_no =
475 List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
477 let p = CicSubstitution.lift (lift_no-1) p in
479 ProofEngineReduction.replace_lifting
480 ~equality:(fun t1 t2 ->
481 match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
482 ~what ~with_what ~where:p
484 let ty_of_m _ = ty (*function
485 | Cic.Meta (i,_) -> List.assoc i menv
486 | _ -> assert false *)
490 (fun (instance,p,n) m ->
493 (Cic.Name ("x"^string_of_int n),
494 CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
500 let instance = match args with | [x] -> x | _ -> Cic.Appl args in
504 let wfo goalproof proof id =
506 let p,_,_ = proof_of_id id in
508 | Exact _ -> if (List.mem id acc) then acc else id :: acc
509 | Step (_,(_,id1, (_,id2), _)) ->
510 let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
511 let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
517 | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
519 List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
522 let string_of_id names id =
523 if id = 0 then "" else
525 let (_,p,(_,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
528 Printf.sprintf "%d = %s: %s = %s [%s]" id
529 (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
530 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
531 | Step (_,(step,id1, (_,id2), _) ) ->
532 Printf.sprintf "%6d: %s %6d %6d %s = %s [%s]" id
533 (string_of_rule step)
534 id1 id2 (CicPp.pp l names) (CicPp.pp r names)
535 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
537 Not_found -> assert false
539 let pp_proof names goalproof proof subst id initial_goal =
540 String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof id)) ^
543 (fst (List.fold_right
544 (fun (r,pos,i,s,pred) (acc,g) ->
545 let _,_,left,right = open_eq g in
548 | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
549 | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
551 let ty = Subst.apply_subst s ty in
552 ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
553 ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
554 "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
560 let compare = Pervasives.compare
563 module M = Map.Make(OT)
565 let rec find_deps m i =
568 let p,_,_ = proof_of_id i in
570 | Exact _ -> M.add i [] m
571 | Step (_,(_,id1,(_,id2),_)) ->
572 let m = find_deps m id1 in
573 let m = find_deps m id2 in
574 (* without the uniq there is a stack overflow doing concatenation *)
575 let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in
576 let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
580 let topological_sort l =
581 (* build the partial order relation *)
582 let m = List.fold_left (fun m i -> find_deps m i) M.empty l in
583 let m = (* keep only deps inside l *)
586 M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m')
589 let m = M.map (fun x -> Some x) m in
591 let keys m = M.fold (fun i _ acc -> i::acc) m [] in
592 let split l m = List.filter (fun i -> M.find i m = Some []) l in
595 (fun k v -> if List.mem k l then None else
598 | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
603 let ok = split keys m in
604 let m = purge ok m in
605 let res = ok @ res in
606 if ok = [] then res else aux m res
608 let rc = List.rev (aux m []) in
613 (* returns the list of ids that should be factorized *)
614 let get_duplicate_step_in_wfo l p =
615 let ol = List.rev l in
616 let h = Hashtbl.create 13 in
617 (* NOTE: here the n parameter is an approximation of the dependency
618 between equations. To do things seriously we should maintain a
619 dependency graph. This approximation is not perfect. *)
621 let p,_,_ = proof_of_id i in
626 let no = Hashtbl.find h i in
627 Hashtbl.replace h i (no+1);
629 with Not_found -> Hashtbl.add h i 1;true
631 let rec aux = function
633 | Step (_,(_,i1,(_,i2),_)) ->
634 let go_on_1 = add i1 in
635 let go_on_2 = add i2 in
636 if go_on_1 then aux (let p,_,_ = proof_of_id i1 in p);
637 if go_on_2 then aux (let p,_,_ = proof_of_id i2 in p)
641 (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id id in p))
643 (* now h is complete *)
644 let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
645 let proofs = List.filter (fun (_,c) -> c > 1) proofs in
646 let res = topological_sort (List.map (fun (i,_) -> i) proofs) in
650 let build_proof_term eq h lift proof =
651 let proof_of_id aux id =
652 let p,l,r = proof_of_id id in
653 try List.assoc id h,l,r with Not_found -> aux p, l, r
655 let rec aux = function
656 | Exact term -> CicSubstitution.lift lift term
657 | Step (subst,(rule, id1, (pos,id2), pred)) ->
658 let p1,_,_ = proof_of_id aux id1 in
659 let p2,l,r = proof_of_id aux id2 in
662 | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
663 | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
668 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
671 let p = build_proof_step eq lift subst p1 p2 pos l r pred in
672 (* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
674 prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
681 let build_goal_proof eq l initial ty se =
682 let se = List.map (fun i -> Cic.Meta (i,[])) se in
683 let lets = get_duplicate_step_in_wfo l initial in
684 let letsno = List.length lets in
685 let _,mty,_,_ = open_eq ty in
686 let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l in
690 let p,l,r = proof_of_id id in
691 let cic = build_proof_term eq h n p in
692 let real_cic,instance =
693 parametrize_proof cic l r (CicSubstitution.lift n mty)
695 let h = (id, instance)::lift_list h in
696 acc@[id,real_cic],n+1,h)
700 let rec aux se current_proof = function
701 | [] -> current_proof,se
702 | (rule,pos,id,subst,pred)::tl ->
703 let p,l,r = proof_of_id id in
704 let p = build_proof_term eq h letsno p in
705 let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
708 | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
709 | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
714 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
718 build_proof_step eq letsno subst current_proof p pos l r pred
720 let proof,se = aux se proof tl in
721 Subst.apply_subst_lift letsno subst proof,
722 List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
724 aux se (build_proof_term eq h letsno initial) l
727 let initial = proof in
729 (fun (id,cic) (n,p) ->
732 Cic.Name ("H"^string_of_int id),
734 lets (letsno-1,initial)
736 canonical (contextualize_rewrites proof (CicSubstitution.lift letsno ty)),
740 let refl_proof eq_uri ty term =
741 Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
744 let metas_of_proof p =
746 match LibraryObjects.eq_URI () with
750 (ProofEngineTypes.Fail
751 (lazy "No default equality defined when calling metas_of_proof"))
753 let p = build_proof_term eq [] 0 p in
754 Utils.metas_of_term p
757 let remove_local_context eq =
758 let w, p, (ty, left, right, o), menv,id = open_equality eq in
759 let p = Utils.remove_local_context p in
760 let ty = Utils.remove_local_context ty in
761 let left = Utils.remove_local_context left in
762 let right = Utils.remove_local_context right in
763 w, p, (ty, left, right, o), menv, id
766 let relocate newmeta menv to_be_relocated =
767 let subst, newmetasenv, newmeta =
769 (fun i (subst, metasenv, maxmeta) ->
770 let _,context,ty = CicUtil.lookup_meta i menv in
772 let newmeta = Cic.Meta(maxmeta,irl) in
773 let newsubst = Subst.buildsubst i context newmeta ty subst in
774 newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1)
775 to_be_relocated (Subst.empty_subst, [], newmeta+1)
777 let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
780 let fix_metas newmeta eq =
781 let w, p, (ty, left, right, o), menv,_ = open_equality eq in
782 let to_be_relocated =
783 (* List.map (fun i ,_,_ -> i) menv *)
785 (List.sort Pervasives.compare
786 (Utils.metas_of_term left @ Utils.metas_of_term right))
788 let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
789 let ty = Subst.apply_subst subst ty in
790 let left = Subst.apply_subst subst left in
791 let right = Subst.apply_subst subst right in
792 let fix_proof = function
793 | Exact p -> Exact (Subst.apply_subst subst p)
794 | Step (s,(r,id1,(pos,id2),pred)) ->
795 Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
797 let p = fix_proof p in
798 let eq' = mk_equality (w, p, (ty, left, right, o), metasenv) in
801 exception NotMetaConvertible;;
803 let meta_convertibility_aux table t1 t2 =
804 let module C = Cic in
805 let rec aux ((table_l, table_r) as table) t1 t2 =
807 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
808 let tl1, tl2 = [],[] in
809 let m1_binding, table_l =
810 try List.assoc m1 table_l, table_l
811 with Not_found -> m2, (m1, m2)::table_l
812 and m2_binding, table_r =
813 try List.assoc m2 table_r, table_r
814 with Not_found -> m1, (m2, m1)::table_r
816 if (m1_binding <> m2) || (m2_binding <> m1) then
817 raise NotMetaConvertible
823 | None, Some _ | Some _, None -> raise NotMetaConvertible
825 | Some t1, Some t2 -> (aux res t1 t2))
826 (table_l, table_r) tl1 tl2
827 with Invalid_argument _ ->
828 raise NotMetaConvertible
830 | C.Var (u1, ens1), C.Var (u2, ens2)
831 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
832 aux_ens table ens1 ens2
833 | C.Cast (s1, t1), C.Cast (s2, t2)
834 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
835 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
836 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
837 let table = aux table s1 s2 in
839 | C.Appl l1, C.Appl l2 -> (
840 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
841 with Invalid_argument _ -> raise NotMetaConvertible
843 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
844 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
845 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
846 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
847 aux_ens table ens1 ens2
848 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
849 when (UriManager.eq u1 u2) && i1 = i2 ->
850 let table = aux table s1 s2 in
851 let table = aux table t1 t2 in (
852 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
853 with Invalid_argument _ -> raise NotMetaConvertible
855 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
858 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
859 if i1 <> i2 then raise NotMetaConvertible
861 let res = (aux res s1 s2) in aux res t1 t2)
863 with Invalid_argument _ -> raise NotMetaConvertible
865 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
868 (fun res (n1, s1, t1) (n2, s2, t2) ->
869 let res = aux res s1 s2 in aux res t1 t2)
871 with Invalid_argument _ -> raise NotMetaConvertible
873 | t1, t2 when t1 = t2 -> table
874 | _, _ -> raise NotMetaConvertible
876 and aux_ens table ens1 ens2 =
877 let cmp (u1, t1) (u2, t2) =
878 Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
880 let ens1 = List.sort cmp ens1
881 and ens2 = List.sort cmp ens2 in
884 (fun res (u1, t1) (u2, t2) ->
885 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
888 with Invalid_argument _ -> raise NotMetaConvertible
894 let meta_convertibility_eq eq1 eq2 =
895 let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
896 let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
899 else if (left = left') && (right = right') then
901 else if (left = right') && (right = left') then
905 let table = meta_convertibility_aux ([], []) left left' in
906 let _ = meta_convertibility_aux table right right' in
908 with NotMetaConvertible ->
910 let table = meta_convertibility_aux ([], []) left right' in
911 let _ = meta_convertibility_aux table right left' in
913 with NotMetaConvertible ->
918 let meta_convertibility t1 t2 =
923 ignore(meta_convertibility_aux ([], []) t1 t2);
925 with NotMetaConvertible ->
929 exception TermIsNotAnEquality;;
931 let term_is_equality term =
933 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
934 when LibraryObjects.is_eq_URI uri -> true
938 let equality_of_term proof term =
940 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2]
941 when LibraryObjects.is_eq_URI uri ->
942 let o = !Utils.compare_terms t1 t2 in
943 let stat = (ty,t1,t2,o) in
944 let w = Utils.compute_equality_weight stat in
945 let e = mk_equality (w, Exact proof, stat,[]) in
948 raise TermIsNotAnEquality
951 let is_weak_identity eq =
952 let _,_,(_,left, right,_),_,_ = open_equality eq in
953 left = right || meta_convertibility left right
956 let is_identity (_, context, ugraph) eq =
957 let _,_,(ty,left,right,_),menv,_ = open_equality eq in
959 (* (meta_convertibility left right)) *)
960 fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
964 let term_of_equality eq_uri equality =
965 let _, _, (ty, left, right, _), menv, _= open_equality equality in
966 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
967 let argsno = List.length menv in
969 CicSubstitution.lift argsno
970 (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
974 (fun (i,_,ty) (n, t) ->
975 let name = Cic.Name ("X" ^ (string_of_int n)) in
976 let ty = CicSubstitution.lift (n-1) ty in
978 ProofEngineReduction.replace
979 ~equality:eq ~what:[i]
980 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
982 (n-1, Cic.Prod (name, ty, t)))
986 let symmetric eq_ty l id uri m =
987 let eq = Cic.MutInd(uri,0,[]) in
989 Cic.Lambda (Cic.Name "Sym",eq_ty,
990 Cic.Appl [CicSubstitution.lift 1 eq ;
991 CicSubstitution.lift 1 eq_ty;
992 Cic.Rel 1;CicSubstitution.lift 1 l])
996 [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
999 let eq = mk_equality (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
1000 let (_,_,_,_,id) = open_equality eq in
1003 Step(Subst.empty_subst,
1004 (Demodulation,id1,(Utils.Left,id),pred))
1007 module IntOT = struct
1009 let compare = Pervasives.compare
1012 module IntSet = Set.Make(IntOT);;
1014 let n_purged = ref 0;;
1016 let collect alive1 alive2 alive3 =
1017 let _ = <:start<collect>> in
1019 let p,_,_ = proof_of_id id in
1021 | Exact _ -> IntSet.empty
1022 | Step (_,(_,id1,(_,id2),_)) ->
1023 IntSet.add id1 (IntSet.add id2 IntSet.empty)
1026 let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
1027 if IntSet.equal news s then s else close news
1029 let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
1030 let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
1031 let closed_alive_set = close alive_set in
1035 if not (IntSet.mem k closed_alive_set) then
1036 k::s else s) id_to_eq []
1038 n_purged := !n_purged + List.length to_purge;
1039 List.iter (Hashtbl.remove id_to_eq) to_purge;
1040 let _ = <:stop<collect>> in ()
1044 let _,_,_,_,id = open_equality e in id
1048 <:show<Equality.>> ^
1049 "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"