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
49 type goal = goal_proof * Cic.metasenv * Cic.term
53 let id_to_eq = Hashtbl.create 1024;;
61 Hashtbl.clear id_to_eq
64 let uncomparable = fun _ -> 0
66 let mk_equality (weight,p,(ty,l,r,o),m) =
67 let id = freshid () in
68 let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
69 Hashtbl.add id_to_eq id eq;
74 let mk_tmp_equality (weight,(ty,l,r,o),m) =
76 uncomparable,weight,Exact (Cic.Implicit None),(ty,l,r,o),m,id
80 let open_equality (_,weight,proof,(ty,l,r,o),m,id) =
81 (weight,proof,(ty,l,r,o),m,id)
83 let string_of_rule = function
84 | SuperpositionRight -> "SupR"
85 | SuperpositionLeft -> "SupL"
86 | Demodulation -> "Demod"
89 let string_of_equality ?env eq =
92 let w, _, (ty, left, right, o), m , id = open_equality eq in
93 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
94 id w (CicPp.ppterm ty)
96 (Utils.string_of_comparison o) (CicPp.ppterm right)
97 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
98 | Some (_, context, _) ->
99 let names = Utils.names_of_context context in
100 let w, _, (ty, left, right, o), m , id = open_equality eq in
101 Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]"
102 id w (CicPp.pp ty names)
103 (CicPp.pp left names) (Utils.string_of_comparison o)
104 (CicPp.pp right names)
105 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
108 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
109 Pervasives.compare s1 s2
112 let rec max_weight_in_proof current =
115 | Step (_, (_,id1,(_,id2),_)) ->
116 let eq1 = Hashtbl.find id_to_eq id1 in
117 let eq2 = Hashtbl.find id_to_eq id2 in
118 let (w1,p1,(_,_,_,_),_,_) = open_equality eq1 in
119 let (w2,p2,(_,_,_,_),_,_) = open_equality eq2 in
120 let current = max current w1 in
121 let current = max_weight_in_proof current p1 in
122 let current = max current w2 in
123 max_weight_in_proof current p2
125 let max_weight_in_goal_proof =
127 (fun current (_,_,id,_,_) ->
128 let eq = Hashtbl.find id_to_eq id in
129 let (w,p,(_,_,_,_),_,_) = open_equality eq in
130 let current = max current w in
131 max_weight_in_proof current p)
133 let max_weight goal_proof proof =
134 let current = max_weight_in_proof 0 proof in
135 max_weight_in_goal_proof current goal_proof
139 let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
142 Not_found -> assert false
145 let string_of_proof ?(names=[]) p gp =
146 let str_of_pos = function
147 | Utils.Left -> "left"
148 | Utils.Right -> "right"
150 let fst3 (x,_,_) = x in
151 let rec aux margin name =
152 let prefix = String.make margin ' ' ^ name ^ ": " in function
154 Printf.sprintf "%sExact (%s)\n"
155 prefix (CicPp.pp t names)
156 | Step (subst,(rule,eq1,(pos,eq2),pred)) ->
157 Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
158 prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos)
159 (CicPp.pp pred names)^
160 aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^
161 aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2))
166 (fun (r,pos,i,s,t) ->
168 "GOAL: %s %s %d %s %s\n" (string_of_rule r)
169 (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^
170 aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
174 let rec depend eq id seen =
175 let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
176 if List.mem ideq seen then
183 | Exact _ -> false,seen
184 | Step (_,(_,id1,(_,id2),_)) ->
185 let seen = ideq::seen in
186 let eq1 = Hashtbl.find id_to_eq id1 in
187 let eq2 = Hashtbl.find id_to_eq id2 in
188 let b1,seen = depend eq1 id seen in
189 if b1 then b1,seen else depend eq2 id seen
192 let depend eq id = fst (depend eq id []);;
194 let ppsubst = Subst.ppsubst ~names:[];;
196 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
197 let build_ens uri termlist =
198 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
200 | Cic.Constant (_, _, _, uris, _) ->
201 assert (List.length uris <= List.length termlist);
202 let rec aux = function
204 | (uri::uris), (term::tl) ->
205 let ens, args = aux (uris, tl) in
206 (uri, term)::ens, args
207 | _, _ -> assert false
213 let mk_sym uri ty t1 t2 p =
214 let ens, args = build_ens uri [ty;t1;t2;p] in
215 Cic.Appl (Cic.Const(uri, ens) :: args)
218 let mk_trans uri ty t1 t2 t3 p12 p23 =
219 let ens, args = build_ens uri [ty;t1;t2;t3;p12;p23] in
220 Cic.Appl (Cic.Const (uri, ens) :: args)
223 let mk_eq_ind uri ty what pred p1 other p2 =
224 Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
227 let p_of_sym ens tl =
228 let args = List.map snd ens @ tl in
234 let open_trans ens tl =
235 let args = List.map snd ens @ tl in
237 | [ty;l;m;r;p1;p2] -> ty,l,m,r,p1,p2
241 let open_sym ens tl =
242 let args = List.map snd ens @ tl in
244 | [ty;l;r;p] -> ty,l,r,p
248 let open_eq_ind args =
250 | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
256 | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]))
257 when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
258 | _ -> prerr_endline (CicPp.ppterm pred); assert false
262 CicSubstitution.subst (Cic.Implicit None) t <>
263 CicSubstitution.subst (Cic.Rel 1) t
266 let head_of_apply = function | Cic.Appl (hd::_) -> hd | t -> t;;
267 let tail_of_apply = function | Cic.Appl (_::tl) -> tl | t -> [];;
268 let count_args t = List.length (tail_of_apply t);;
270 let u = UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind" in
272 | 0 -> Cic.MutConstruct(u,0,1,[])
274 Cic.Appl [Cic.MutConstruct(u,0,2,[]);build_nat (n-1)]
276 let tyof context menv t =
278 fst(CicTypeChecker.type_of_aux' menv context t CicUniv.empty_ugraph)
280 | CicTypeChecker.TypeCheckerFailure _
281 | CicTypeChecker.AssertFailure _ -> assert false
283 let rec lambdaof left context = function
284 | Cic.Prod (n,s,t) ->
285 Cic.Lambda (n,s,lambdaof left context t)
286 | Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r]
287 when LibraryObjects.is_eq_URI uri -> if left then l else r
289 let names = Utils.names_of_context context in
290 prerr_endline ("lambdaof: " ^ (CicPp.pp t names));
294 let canonical t context menv =
295 let rec remove_refl t =
297 | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
298 when LibraryObjects.is_trans_eq_URI uri_trans ->
299 let ty,l,m,r,p1,p2 = open_trans ens tl in
301 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_],p2 ->
303 | p1,Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] ->
305 | _ -> Cic.Appl (List.map remove_refl args))
306 | Cic.Appl l -> Cic.Appl (List.map remove_refl l)
307 | Cic.LetIn (name,bo,rest) ->
308 Cic.LetIn (name,remove_refl bo,remove_refl rest)
311 let rec canonical context t =
313 | Cic.LetIn(name,bo,rest) ->
314 let context' = (Some (name,Cic.Def (bo,None)))::context in
315 Cic.LetIn(name,canonical context bo,canonical context' rest)
316 | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
317 when LibraryObjects.is_sym_eq_URI uri_sym ->
318 (match p_of_sym ens tl with
319 | Cic.Appl ((Cic.Const(uri,ens))::tl)
320 when LibraryObjects.is_sym_eq_URI uri ->
321 canonical context (p_of_sym ens tl)
322 | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
323 when LibraryObjects.is_trans_eq_URI uri_trans ->
324 let ty,l,m,r,p1,p2 = open_trans ens tl in
325 mk_trans uri_trans ty r m l
326 (canonical context (mk_sym uri_sym ty m r p2))
327 (canonical context (mk_sym uri_sym ty l m p1))
328 | Cic.Appl (([Cic.Const(uri_feq,ens);ty1;ty2;f;x;y;p])) ->
331 Cic.Const (UriManager.uri_of_string
332 "cic:/matita/logic/equality/eq_f1.con",[])
334 Cic.Appl (([eq_f_sym;ty1;ty2;f;x;y;p]))
337 let sym_eq = Cic.Const(uri_sym,ens) in
338 let eq_f = Cic.Const(uri_feq,[]) in
339 let b = Cic.MutConstruct (UriManager.uri_of_string
340 "cic:/matita/datatypes/bool/bool.ind",0,1,[])
344 let n = build_nat (count_args p) in
345 let h = head_of_apply p in
346 let predl = lambdaof true context (tyof context menv h) in
347 let predr = lambdaof false context (tyof context menv h) in
348 let args = tail_of_apply p in
351 ([Cic.Const(UriManager.uri_of_string
352 "cic:/matita/paramodulation/rewrite.con",[]);
353 eq; sym_eq; eq_f; b; u; ctx; n; predl; predr; h] @
359 | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl)
360 when LibraryObjects.is_eq_ind_URI uri_ind ||
361 LibraryObjects.is_eq_ind_r_URI uri_ind ->
362 let ty, what, pred, p1, other, p2 =
364 | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
369 | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
370 when LibraryObjects.is_eq_URI uri ->
372 (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
374 prerr_endline (CicPp.ppterm pred);
377 let l = CicSubstitution.subst what l in
378 let r = CicSubstitution.subst what r in
381 canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
383 | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
384 when LibraryObjects.is_eq_URI uri -> t
385 | _ -> Cic.Appl (List.map (canonical context) args))
386 | Cic.Appl l -> Cic.Appl (List.map (canonical context) l)
389 remove_refl (canonical context t)
392 let ty_of_lambda = function
393 | Cic.Lambda (_,ty,_) -> ty
397 let compose_contexts ctx1 ctx2 =
398 ProofEngineReduction.replace_lifting
399 ~equality:(=) ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
402 let put_in_ctx ctx t =
403 ProofEngineReduction.replace_lifting
404 ~equality:(=) ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
407 let mk_eq uri ty l r =
408 Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r]
411 let mk_refl uri ty t =
412 Cic.Appl [Cic.MutConstruct(uri,0,1,[]);ty;t]
415 let open_eq = function
416 | Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r] when LibraryObjects.is_eq_URI uri ->
421 let mk_feq uri_feq ty ty1 left pred right t =
422 Cic.Appl [Cic.Const(uri_feq,[]);ty;ty1;pred;left;right;t]
425 let rec look_ahead aux = function
426 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) as t
427 when LibraryObjects.is_eq_ind_URI uri_ind ||
428 LibraryObjects.is_eq_ind_r_URI uri_ind ->
429 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
430 let ty2,eq,lp,rp = open_pred pred in
431 let hole = Cic.Implicit (Some `Hole) in
432 let ty2 = CicSubstitution.subst hole ty2 in
433 aux ty1 (CicSubstitution.subst other lp) (CicSubstitution.subst other rp) hole ty2 t
434 | Cic.Lambda (n,s,t) -> Cic.Lambda (n,s,look_ahead aux t)
438 let contextualize uri ty left right t =
439 let hole = Cic.Implicit (Some `Hole) in
440 (* aux [uri] [ty] [left] [right] [ctx] [ctx_ty] [t]
442 * the parameters validate this invariant
443 * t: eq(uri) ty left right
444 * that is used only by the base case
446 * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
447 * ctx_ty is the type of ctx
449 let rec aux uri ty left right ctx_d ctx_ty = function
450 | Cic.Appl ((Cic.Const(uri_sym,ens))::tl)
451 when LibraryObjects.is_sym_eq_URI uri_sym ->
452 let ty,l,r,p = open_sym ens tl in
453 mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
454 | Cic.LetIn (name,body,rest) ->
455 Cic.LetIn (name,look_ahead (aux uri) body, aux uri ty left right ctx_d ctx_ty rest)
456 | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
457 when LibraryObjects.is_eq_ind_URI uri_ind ||
458 LibraryObjects.is_eq_ind_r_URI uri_ind ->
459 let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
460 let ty2,eq,lp,rp = open_pred pred in
461 let uri_trans = LibraryObjects.trans_eq_URI ~eq:uri in
462 let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
463 let is_not_fixed_lp = is_not_fixed lp in
464 let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
465 (* extract the context and the fixed term from the predicate *)
467 let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
468 (* they were under a lambda *)
469 let m = CicSubstitution.subst hole m in
470 let ctx_c = CicSubstitution.subst hole ctx_c in
471 let ty2 = CicSubstitution.subst hole ty2 in
474 (* create the compound context and put the terms under it *)
475 let ctx_dc = compose_contexts ctx_d ctx_c in
476 let dc_what = put_in_ctx ctx_dc what in
477 let dc_other = put_in_ctx ctx_dc other in
478 (* m is already in ctx_c so it is put in ctx_d only *)
479 let d_m = put_in_ctx ctx_d m in
480 (* we also need what in ctx_c *)
481 let c_what = put_in_ctx ctx_c what in
482 (* now put the proofs in the compound context *)
483 let p1 = (* p1: dc_what = d_m *)
484 if is_not_fixed_lp then
485 aux uri ty2 c_what m ctx_d ctx_ty p1
487 mk_sym uri_sym ctx_ty d_m dc_what
488 (aux uri ty2 m c_what ctx_d ctx_ty p1)
490 let p2 = (* p2: dc_other = dc_what *)
492 mk_sym uri_sym ctx_ty dc_what dc_other
493 (aux uri ty1 what other ctx_dc ctx_ty p2)
495 aux uri ty1 other what ctx_dc ctx_ty p2
497 (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
498 if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
499 let a,b,c,paeqb,pbeqc =
500 if is_not_fixed_lp then
501 dc_other,dc_what,d_m,p2,p1
503 d_m,dc_what,dc_other,
504 (mk_sym uri_sym ctx_ty dc_what d_m p1),
505 (mk_sym uri_sym ctx_ty dc_other dc_what p2)
507 mk_trans uri_trans ctx_ty a b c paeqb pbeqc
508 | t when ctx_d = hole -> t
510 (* let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in *)
511 (* let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in *)
513 UriManager.uri_of_string "cic:/matita/logic/equality/eq_f.con"
516 (* let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in *)
518 let ctx_d = CicSubstitution.lift 1 ctx_d in
519 put_in_ctx ctx_d (Cic.Rel 1)
521 (* let lty = CicSubstitution.lift 1 ctx_ty in *)
522 (* Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r)) *)
523 Cic.Lambda (Cic.Name "foo",ty,l)
525 (* let d_left = put_in_ctx ctx_d left in *)
526 (* let d_right = put_in_ctx ctx_d right in *)
527 (* let refl_eq = mk_refl uri ctx_ty d_left in *)
528 (* mk_sym uri_sym ctx_ty d_right d_left *)
529 (* (mk_eq_ind uri_ind ty left pred refl_eq right t) *)
530 (mk_feq uri_feq ty ctx_ty left pred right t)
532 aux uri ty left right hole ty t
535 let contextualize_rewrites t ty =
536 let eq,ty,l,r = open_eq ty in
537 contextualize eq ty l r t
540 let add_subst subst =
542 | Exact t -> Exact (Subst.apply_subst subst t)
543 | Step (s,(rule, id1, (pos,id2), pred)) ->
544 Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
547 let build_proof_step eq lift subst p1 p2 pos l r pred =
548 let p1 = Subst.apply_subst_lift lift subst p1 in
549 let p2 = Subst.apply_subst_lift lift subst p2 in
550 let l = CicSubstitution.lift lift l in
551 let l = Subst.apply_subst_lift lift subst l in
552 let r = CicSubstitution.lift lift r in
553 let r = Subst.apply_subst_lift lift subst r in
554 let pred = CicSubstitution.lift lift pred in
555 let pred = Subst.apply_subst_lift lift subst pred in
558 | Cic.Lambda (_,ty,body) -> ty,body
562 if pos = Utils.Left then l,r else r,l
567 mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
569 mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
574 let parametrize_proof p l r ty =
575 let uniq l = HExtlib.list_uniq (List.sort Pervasives.compare l) in
576 let mot = CicUtil.metas_of_term_set in
577 let parameters = uniq ((*mot p @*) mot l @ mot r) in
578 (* ?if they are under a lambda? *)
580 HExtlib.list_uniq (List.sort Pervasives.compare parameters)
582 let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in
583 let with_what, lift_no =
584 List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1)
586 let p = CicSubstitution.lift (lift_no-1) p in
588 ProofEngineReduction.replace_lifting
589 ~equality:(fun t1 t2 ->
590 match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false)
591 ~what ~with_what ~where:p
593 let ty_of_m _ = ty (*function
594 | Cic.Meta (i,_) -> List.assoc i menv
595 | _ -> assert false *)
599 (fun (instance,p,n) m ->
602 (Cic.Name ("x"^string_of_int n),
603 CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
609 let instance = match args with | [x] -> x | _ -> Cic.Appl args in
613 let wfo goalproof proof id =
615 let p,_,_ = proof_of_id id in
617 | Exact _ -> if (List.mem id acc) then acc else id :: acc
618 | Step (_,(_,id1, (_,id2), _)) ->
619 let acc = if not (List.mem id1 acc) then aux acc id1 else acc in
620 let acc = if not (List.mem id2 acc) then aux acc id2 else acc in
626 | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
628 List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
631 let string_of_id names id =
632 if id = 0 then "" else
634 let (_,p,(_,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
637 Printf.sprintf "%d = %s: %s = %s [%s]" id
638 (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
639 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
640 | Step (_,(step,id1, (_,id2), _) ) ->
641 Printf.sprintf "%6d: %s %6d %6d %s = %s [%s]" id
642 (string_of_rule step)
643 id1 id2 (CicPp.pp l names) (CicPp.pp r names)
644 (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m))
646 Not_found -> assert false
648 let pp_proof names goalproof proof subst id initial_goal =
649 String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof id)) ^
652 (fst (List.fold_right
653 (fun (r,pos,i,s,pred) (acc,g) ->
654 let _,_,left,right = open_eq g in
657 | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
658 | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
660 let ty = Subst.apply_subst s ty in
661 ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
662 ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
663 "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
669 let compare = Pervasives.compare
672 module M = Map.Make(OT)
674 let rec find_deps m i =
677 let p,_,_ = proof_of_id i in
679 | Exact _ -> M.add i [] m
680 | Step (_,(_,id1,(_,id2),_)) ->
681 let m = find_deps m id1 in
682 let m = find_deps m id2 in
683 (* without the uniq there is a stack overflow doing concatenation *)
684 let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in
685 let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
689 let topological_sort l =
690 (* build the partial order relation *)
691 let m = List.fold_left (fun m i -> find_deps m i) M.empty l in
692 let m = (* keep only deps inside l *)
695 M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m')
698 let m = M.map (fun x -> Some x) m in
700 let keys m = M.fold (fun i _ acc -> i::acc) m [] in
701 let split l m = List.filter (fun i -> M.find i m = Some []) l in
704 (fun k v -> if List.mem k l then None else
707 | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll))
712 let ok = split keys m in
713 let m = purge ok m in
714 let res = ok @ res in
715 if ok = [] then res else aux m res
717 let rc = List.rev (aux m []) in
722 (* returns the list of ids that should be factorized *)
723 let get_duplicate_step_in_wfo l p =
724 let ol = List.rev l in
725 let h = Hashtbl.create 13 in
726 (* NOTE: here the n parameter is an approximation of the dependency
727 between equations. To do things seriously we should maintain a
728 dependency graph. This approximation is not perfect. *)
730 let p,_,_ = proof_of_id i in
735 let no = Hashtbl.find h i in
736 Hashtbl.replace h i (no+1);
738 with Not_found -> Hashtbl.add h i 1;true
740 let rec aux = function
742 | Step (_,(_,i1,(_,i2),_)) ->
743 let go_on_1 = add i1 in
744 let go_on_2 = add i2 in
745 if go_on_1 then aux (let p,_,_ = proof_of_id i1 in p);
746 if go_on_2 then aux (let p,_,_ = proof_of_id i2 in p)
750 (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id id in p))
752 (* now h is complete *)
753 let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
754 let proofs = List.filter (fun (_,c) -> c > 1) proofs in
755 let res = topological_sort (List.map (fun (i,_) -> i) proofs) in
759 let build_proof_term eq h lift proof =
760 let proof_of_id aux id =
761 let p,l,r = proof_of_id id in
762 try List.assoc id h,l,r with Not_found -> aux p, l, r
764 let rec aux = function
766 CicSubstitution.lift lift term
767 | Step (subst,(rule, id1, (pos,id2), pred)) ->
768 let p1,_,_ = proof_of_id aux id1 in
769 let p2,l,r = proof_of_id aux id2 in
772 | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos)
773 | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
778 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
781 let p = build_proof_step eq lift subst p1 p2 pos l r pred in
782 (* let cond = (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
784 prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
791 let build_goal_proof eq l initial ty se context menv =
792 let se = List.map (fun i -> Cic.Meta (i,[])) se in
793 let lets = get_duplicate_step_in_wfo l initial in
794 let letsno = List.length lets in
795 let _,mty,_,_ = open_eq ty in
796 let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l in
800 let p,l,r = proof_of_id id in
801 let cic = build_proof_term eq h n p in
802 let real_cic,instance =
803 parametrize_proof cic l r (CicSubstitution.lift n mty)
805 let h = (id, instance)::lift_list h in
806 acc@[id,real_cic],n+1,h)
810 let rec aux se current_proof = function
811 | [] -> current_proof,se
812 | (rule,pos,id,subst,pred)::tl ->
813 let p,l,r = proof_of_id id in
814 let p = build_proof_term eq h letsno p in
815 let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
818 | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos)
819 | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
824 | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
828 build_proof_step eq letsno subst current_proof p pos l r pred
830 let proof,se = aux se proof tl in
831 Subst.apply_subst_lift letsno subst proof,
832 List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
834 aux se (build_proof_term eq h letsno initial) l
837 let initial = proof in
839 (fun (id,cic) (n,p) ->
842 Cic.Name ("H"^string_of_int id),
844 lets (letsno-1,initial)
847 (contextualize_rewrites proof (CicSubstitution.lift letsno ty))
852 let refl_proof eq_uri ty term =
853 Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
856 let metas_of_proof p =
858 match LibraryObjects.eq_URI () with
862 (ProofEngineTypes.Fail
863 (lazy "No default equality defined when calling metas_of_proof"))
865 let p = build_proof_term eq [] 0 p in
866 Utils.metas_of_term p
869 let remove_local_context eq =
870 let w, p, (ty, left, right, o), menv,id = open_equality eq in
871 let p = Utils.remove_local_context p in
872 let ty = Utils.remove_local_context ty in
873 let left = Utils.remove_local_context left in
874 let right = Utils.remove_local_context right in
875 w, p, (ty, left, right, o), menv, id
878 let relocate newmeta menv to_be_relocated =
879 let subst, newmetasenv, newmeta =
881 (fun i (subst, metasenv, maxmeta) ->
882 let _,context,ty = CicUtil.lookup_meta i menv in
884 let newmeta = Cic.Meta(maxmeta,irl) in
885 let newsubst = Subst.buildsubst i context newmeta ty subst in
886 newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1)
887 to_be_relocated (Subst.empty_subst, [], newmeta+1)
889 let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
892 let fix_metas_goal newmeta goal =
893 let (proof, menv, ty) = goal in
894 let to_be_relocated =
895 HExtlib.list_uniq (List.sort Pervasives.compare (Utils.metas_of_term ty))
897 let subst, menv, newmeta = relocate newmeta menv to_be_relocated in
898 let ty = Subst.apply_subst subst ty in
901 | [] -> assert false (* is a nonsense to relocate the initial goal *)
902 | (r,pos,id,s,p) :: tl -> (r,pos,id,Subst.concat subst s,p) :: tl
904 newmeta+1,(proof, menv, ty)
907 let fix_metas newmeta eq =
908 let w, p, (ty, left, right, o), menv,_ = open_equality eq in
909 let to_be_relocated =
910 (* List.map (fun i ,_,_ -> i) menv *)
912 (List.sort Pervasives.compare
913 (Utils.metas_of_term left @ Utils.metas_of_term right))
915 let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
916 let ty = Subst.apply_subst subst ty in
917 let left = Subst.apply_subst subst left in
918 let right = Subst.apply_subst subst right in
919 let fix_proof = function
920 | Exact p -> Exact (Subst.apply_subst subst p)
921 | Step (s,(r,id1,(pos,id2),pred)) ->
922 Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
924 let p = fix_proof p in
925 let eq' = mk_equality (w, p, (ty, left, right, o), metasenv) in
928 exception NotMetaConvertible;;
930 let meta_convertibility_aux table t1 t2 =
931 let module C = Cic in
932 let rec aux ((table_l, table_r) as table) t1 t2 =
934 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
935 let tl1, tl2 = [],[] in
936 let m1_binding, table_l =
937 try List.assoc m1 table_l, table_l
938 with Not_found -> m2, (m1, m2)::table_l
939 and m2_binding, table_r =
940 try List.assoc m2 table_r, table_r
941 with Not_found -> m1, (m2, m1)::table_r
943 if (m1_binding <> m2) || (m2_binding <> m1) then
944 raise NotMetaConvertible
950 | None, Some _ | Some _, None -> raise NotMetaConvertible
952 | Some t1, Some t2 -> (aux res t1 t2))
953 (table_l, table_r) tl1 tl2
954 with Invalid_argument _ ->
955 raise NotMetaConvertible
957 | C.Var (u1, ens1), C.Var (u2, ens2)
958 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
959 aux_ens table ens1 ens2
960 | C.Cast (s1, t1), C.Cast (s2, t2)
961 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
962 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
963 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
964 let table = aux table s1 s2 in
966 | C.Appl l1, C.Appl l2 -> (
967 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
968 with Invalid_argument _ -> raise NotMetaConvertible
970 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
971 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
972 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
973 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
974 aux_ens table ens1 ens2
975 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
976 when (UriManager.eq u1 u2) && i1 = i2 ->
977 let table = aux table s1 s2 in
978 let table = aux table t1 t2 in (
979 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
980 with Invalid_argument _ -> raise NotMetaConvertible
982 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
985 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
986 if i1 <> i2 then raise NotMetaConvertible
988 let res = (aux res s1 s2) in aux res t1 t2)
990 with Invalid_argument _ -> raise NotMetaConvertible
992 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
995 (fun res (n1, s1, t1) (n2, s2, t2) ->
996 let res = aux res s1 s2 in aux res t1 t2)
998 with Invalid_argument _ -> raise NotMetaConvertible
1000 | t1, t2 when t1 = t2 -> table
1001 | _, _ -> raise NotMetaConvertible
1003 and aux_ens table ens1 ens2 =
1004 let cmp (u1, t1) (u2, t2) =
1005 Pervasives.compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
1007 let ens1 = List.sort cmp ens1
1008 and ens2 = List.sort cmp ens2 in
1011 (fun res (u1, t1) (u2, t2) ->
1012 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
1015 with Invalid_argument _ -> raise NotMetaConvertible
1021 let meta_convertibility_eq eq1 eq2 =
1022 let _, _, (ty, left, right, _), _,_ = open_equality eq1 in
1023 let _, _, (ty', left', right', _), _,_ = open_equality eq2 in
1026 else if (left = left') && (right = right') then
1028 else if (left = right') && (right = left') then
1032 let table = meta_convertibility_aux ([], []) left left' in
1033 let _ = meta_convertibility_aux table right right' in
1035 with NotMetaConvertible ->
1037 let table = meta_convertibility_aux ([], []) left right' in
1038 let _ = meta_convertibility_aux table right left' in
1040 with NotMetaConvertible ->
1045 let meta_convertibility t1 t2 =
1050 ignore(meta_convertibility_aux ([], []) t1 t2);
1052 with NotMetaConvertible ->
1056 exception TermIsNotAnEquality;;
1058 let term_is_equality term =
1060 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _]
1061 when LibraryObjects.is_eq_URI uri -> true
1065 let equality_of_term proof term =
1067 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2]
1068 when LibraryObjects.is_eq_URI uri ->
1069 let o = !Utils.compare_terms t1 t2 in
1070 let stat = (ty,t1,t2,o) in
1071 let w = Utils.compute_equality_weight stat in
1072 let e = mk_equality (w, Exact proof, stat,[]) in
1075 raise TermIsNotAnEquality
1078 let is_weak_identity eq =
1079 let _,_,(_,left, right,_),_,_ = open_equality eq in
1080 left = right || meta_convertibility left right
1083 let is_identity (_, context, ugraph) eq =
1084 let _,_,(ty,left,right,_),menv,_ = open_equality eq in
1086 (* (meta_convertibility left right)) *)
1087 fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
1091 let term_of_equality eq_uri equality =
1092 let _, _, (ty, left, right, _), menv, _= open_equality equality in
1093 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
1094 let argsno = List.length menv in
1096 CicSubstitution.lift argsno
1097 (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
1101 (fun (i,_,ty) (n, t) ->
1102 let name = Cic.Name ("X" ^ (string_of_int n)) in
1103 let ty = CicSubstitution.lift (n-1) ty in
1105 ProofEngineReduction.replace
1106 ~equality:eq ~what:[i]
1107 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
1109 (n-1, Cic.Prod (name, ty, t)))
1113 let symmetric eq_ty l id uri m =
1114 let eq = Cic.MutInd(uri,0,[]) in
1116 Cic.Lambda (Cic.Name "Sym",eq_ty,
1117 Cic.Appl [CicSubstitution.lift 1 eq ;
1118 CicSubstitution.lift 1 eq_ty;
1119 Cic.Rel 1;CicSubstitution.lift 1 l])
1123 [Cic.MutConstruct(uri,0,1,[]);eq_ty;l])
1126 let eq = mk_equality (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
1127 let (_,_,_,_,id) = open_equality eq in
1130 Step(Subst.empty_subst,
1131 (Demodulation,id1,(Utils.Left,id),pred))
1134 module IntOT = struct
1136 let compare = Pervasives.compare
1139 module IntSet = Set.Make(IntOT);;
1141 let n_purged = ref 0;;
1143 let collect alive1 alive2 alive3 =
1144 let _ = <:start<collect>> in
1146 let p,_,_ = proof_of_id id in
1148 | Exact _ -> IntSet.empty
1149 | Step (_,(_,id1,(_,id2),_)) ->
1150 IntSet.add id1 (IntSet.add id2 IntSet.empty)
1153 let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
1154 if IntSet.equal news s then s else close news
1156 let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
1157 let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
1158 let closed_alive_set = close alive_set in
1162 if not (IntSet.mem k closed_alive_set) then
1163 k::s else s) id_to_eq []
1165 n_purged := !n_purged + List.length to_purge;
1166 List.iter (Hashtbl.remove id_to_eq) to_purge;
1167 let _ = <:stop<collect>> in ()
1171 let _,_,_,_,id = open_equality e in id
1175 <:show<Equality.>> ^
1176 "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"