1 (* Copyright (C) 2000, 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 exception UnificationFailed;;
28 exception OccurCheck;;
29 exception RelToHiddenHypothesis;;
34 (* the delift function takes in input an ordered list of optional terms *)
35 (* [t1,...,tn] and a term t, and substitutes every tk = Some (rel(nk)) with *)
36 (* rel(k). Typically, the list of optional terms is the explicit substitution *)(* that is applied to a metavariable occurrence and the result of the delift *)
37 (* function is a term the implicit variable can be substituted with to make *)
38 (* the term [t] unifiable with the metavariable occurrence. *)
39 (* In general, the problem is undecidable if we consider equivalence in place *)
40 (* of alpha convertibility. Our implementation, though, is even weaker than *)
41 (* alpha convertibility, since it replace the term [tk] if and only if [tk] *)
42 (* is a Rel (missing all the other cases). Does this matter in practice? *)
44 exception NotInTheList;;
49 [] -> raise NotInTheList
50 | (Some (Cic.Rel m))::_ when m=n -> k
51 | _::tl -> aux (k+1) tl in
55 (*CSC: this restriction function is utterly wrong, since it does not check *)
56 (*CSC: that the variable that is going to be restricted does not occur free *)
57 (*CSC: in a part of the sequent that is not going to be restricted. *)
58 (*CSC: In particular, the whole approach is wrong; if restriction can fail *)
59 (*CSC: (as indeed it is the case), we can not collect all the restrictions *)
60 (*CSC: and restrict everything at the end ;-( *)
61 let restrict to_be_restricted =
65 | _::tl when List.mem (n,i) to_be_restricted ->
66 None::(erase (i+1) n tl)
67 | he::tl -> he::(erase (i+1) n tl) in
71 | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
76 (*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
77 let delift context metasenv l t =
78 let module S = CicSubstitution in
79 let to_be_restricted = ref [] in
85 C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
86 (*CSC: deliftato la regola per il LetIn *)
87 (*CSC: FALSO! La regola per il LetIn non lo fa *)
89 (match List.nth context (m-k-1) with
90 Some (_,C.Def (t,_)) ->
91 (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
92 (*CSC: first order unification. Does it help or does it harm? *)
93 deliftaux k (S.lift m t)
94 | Some (_,C.Decl t) ->
95 (*CSC: The following check seems to be wrong! *)
96 (*CSC: B:Set |- ?2 : Set *)
97 (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x *)
98 (*CSC: Why should I restrict ?2 over B? The instantiation *)
99 (*CSC: ?1 := A is perfectly reasonable and well-typed. *)
100 (*CSC: Thus I comment out the following two lines that *)
101 (*CSC: are the incriminated ones. *)
102 (*(* It may augment to_be_restricted *)
103 ignore (deliftaux k (S.lift m t)) ;*)
104 (*CSC: end of bug commented out *)
105 C.Rel ((position (m-k) l) + k)
106 | None -> raise RelToHiddenHypothesis)
107 | C.Var (uri,exp_named_subst) ->
108 let exp_named_subst' =
109 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
111 C.Var (uri,exp_named_subst')
112 | C.Meta (i, l1) as t ->
116 | None::tl -> None::(deliftl (j+1) tl)
118 let l1' = (deliftl (j+1) tl) in
120 Some (deliftaux k t)::l1'
122 RelToHiddenHypothesis
124 to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
126 let l' = deliftl 1 l1 in
129 | C.Implicit as t -> t
130 | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
131 | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
132 | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
133 | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
134 | C.Appl l -> C.Appl (List.map (deliftaux k) l)
135 | C.Const (uri,exp_named_subst) ->
136 let exp_named_subst' =
137 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
139 C.Const (uri,exp_named_subst')
140 | C.MutInd (uri,typeno,exp_named_subst) ->
141 let exp_named_subst' =
142 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
144 C.MutInd (uri,typeno,exp_named_subst')
145 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
146 let exp_named_subst' =
147 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
149 C.MutConstruct (uri,typeno,consno,exp_named_subst')
150 | C.MutCase (sp,i,outty,t,pl) ->
151 C.MutCase (sp, i, deliftaux k outty, deliftaux k t,
152 List.map (deliftaux k) pl)
154 let len = List.length fl in
157 (fun (name, i, ty, bo) ->
158 (name, i, deliftaux k ty, deliftaux (k+len) bo))
163 let len = List.length fl in
166 (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
169 C.CoFix (i, liftedfl)
176 (* This is the case where we fail even first order unification. *)
177 (* The reason is that our delift function is weaker than first *)
178 (* order (in the sense of alpha-conversion). See comment above *)
179 (* related to the delift function. *)
180 prerr_endline "!!!!!!!!!!! First Order UnificationFailed, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
181 raise UnificationFailed
183 res, restrict !to_be_restricted metasenv
186 (**** END OF DELIFT ****)
188 type substitution = (int * Cic.term) list
190 (* NUOVA UNIFICAZIONE *)
191 (* A substitution is a (int * Cic.term) list that associates a
192 metavariable i with its body.
193 A metaenv is a (int * Cic.term) list that associate a metavariable
195 fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
196 a new substitution which is _NOT_ unwinded. It must be unwinded before
199 let rec fo_unif_subst subst context metasenv t1 t2 =
200 let module C = Cic in
201 let module R = CicReduction in
202 let module S = CicSubstitution in
204 (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
212 | Some t1', Some t2' ->
213 (* First possibility: restriction *)
214 (* Second possibility: unification *)
215 (* Third possibility: convertibility *)
216 R.are_convertible context t1' t2'
219 if ok then subst,metasenv else raise UnificationFailed
220 | (C.Meta (n,l), C.Meta (m,_)) when n>m ->
221 fo_unif_subst subst context metasenv t2 t1
223 | (t, C.Meta (n,l)) ->
224 let subst',metasenv' =
226 let oldt = (List.assoc n subst) in
227 let lifted_oldt = S.lift_meta l oldt in
228 fo_unif_subst subst context metasenv lifted_oldt t
230 let t',metasenv' = delift context metasenv l t in
231 (n, t')::subst, metasenv'
233 let (_,_,meta_type) =
234 List.find (function (m,_,_) -> m=n) metasenv' in
235 let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
236 fo_unif_subst subst' context metasenv' (S.lift_meta l meta_type) tyt
237 | (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
238 | (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
239 if UriManager.eq uri1 uri2 then
240 fo_unif_subst_exp_named_subst subst context metasenv
241 exp_named_subst1 exp_named_subst2
243 raise UnificationFailed
244 | C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
245 if UriManager.eq uri1 uri2 && i1 = i2 then
246 fo_unif_subst_exp_named_subst subst context metasenv
247 exp_named_subst1 exp_named_subst2
249 raise UnificationFailed
250 | C.MutConstruct (uri1,i1,j1,exp_named_subst1),
251 C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
252 if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
253 fo_unif_subst_exp_named_subst subst context metasenv
254 exp_named_subst1 exp_named_subst2
256 raise UnificationFailed
263 if R.are_convertible context t1 t2 then
266 raise UnificationFailed
267 | (C.Cast (te,ty), t2) -> fo_unif_subst subst context metasenv te t2
268 | (t1, C.Cast (te,ty)) -> fo_unif_subst subst context metasenv t1 te
269 | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
270 let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
271 fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
272 | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
273 let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
274 fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
275 | (C.LetIn (_,s1,t1), t2)
276 | (t2, C.LetIn (_,s1,t1)) ->
277 fo_unif_subst subst context metasenv t2 (S.subst s1 t1)
278 | (C.Appl l1, C.Appl l2) ->
279 let lr1 = List.rev l1 in
280 let lr2 = List.rev l2 in
281 let rec fo_unif_l subst metasenv =
284 | _,[] -> assert false
286 fo_unif_subst subst context metasenv h1 h2
289 fo_unif_subst subst context metasenv h (C.Appl (List.rev l))
290 | ((h1::l1),(h2::l2)) ->
291 let subst', metasenv' =
292 fo_unif_subst subst context metasenv h1 h2
294 fo_unif_l subst' metasenv' (l1,l2)
296 fo_unif_l subst metasenv (lr1, lr2)
301 | (C.MutConstruct _, _)
302 | (_, C.MutConstruct _) ->
303 if R.are_convertible context t1 t2 then
306 raise UnificationFailed
307 | (C.MutCase (_,_,outt1,t1,pl1), C.MutCase (_,_,outt2,t2,pl2))->
308 let subst', metasenv' =
309 fo_unif_subst subst context metasenv outt1 outt2 in
310 let subst'',metasenv'' =
311 fo_unif_subst subst' context metasenv' t1 t2 in
313 (function (subst,metasenv) ->
314 fo_unif_subst subst context metasenv
315 ) (subst'',metasenv'') pl1 pl2
320 if R.are_convertible context t1 t2 then
323 raise UnificationFailed
325 if R.are_convertible context t1 t2 then
328 raise UnificationFailed
330 and fo_unif_subst_exp_named_subst subst context metasenv
331 exp_named_subst1 exp_named_subst2
335 (fun (subst,metasenv) (uri1,t1) (uri2,t2) ->
337 fo_unif_subst subst context metasenv t1 t2
338 ) (subst,metasenv) exp_named_subst1 exp_named_subst2
341 let uri = UriManager.uri_of_string "cic:/dummy.var" in
342 prerr_endline ("@@@: " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst1)) ^
343 " <==> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst2))) ; raise e
346 let unwind metasenv subst unwinded t =
347 let unwinded = ref unwinded in
348 let frozen = ref [] in
349 let rec um_aux metasenv =
350 let module C = Cic in
351 let module S = CicSubstitution in
353 C.Rel _ as t -> t,metasenv
354 | C.Var _ as t -> t,metasenv
357 S.lift_meta l (List.assoc i !unwinded), metasenv
359 if List.mem i !frozen then raise OccurCheck
361 let saved_frozen = !frozen in
362 frozen := i::!frozen ;
365 let t = List.assoc i subst in
366 let t',metasenv' = um_aux metasenv t in
368 let (_,canonical_context,_) =
369 List.find (function (m,_,_) -> m=i) metasenv
371 delift canonical_context metasenv' l t'
373 unwinded := (i,t')::!unwinded ;
374 S.lift_meta l t', metasenv'
377 (* not constrained variable, i.e. free in subst*)
380 (fun t (tl,metasenv) ->
382 None -> None::tl,metasenv
384 let t',metasenv' = um_aux metasenv t in
385 (Some t')::tl, metasenv'
388 C.Meta (i,l'), metasenv'
390 frozen := saved_frozen ;
394 | C.Implicit as t -> t,metasenv
396 let te',metasenv' = um_aux metasenv te in
397 let ty',metasenv'' = um_aux metasenv' ty in
398 C.Cast (te',ty'),metasenv''
400 let s',metasenv' = um_aux metasenv s in
401 let t',metasenv'' = um_aux metasenv' t in
402 C.Prod (n, s', t'), metasenv''
403 | C.Lambda (n,s,t) ->
404 let s',metasenv' = um_aux metasenv s in
405 let t',metasenv'' = um_aux metasenv' t in
406 C.Lambda (n, s', t'), metasenv''
408 let s',metasenv' = um_aux metasenv s in
409 let t',metasenv'' = um_aux metasenv' t in
410 C.LetIn (n, s', t'), metasenv''
414 (fun t (tl,metasenv) ->
415 let t',metasenv' = um_aux metasenv t in
420 match um_aux metasenv' he with
421 (C.Appl l, metasenv'') -> C.Appl (l@tl'),metasenv''
422 | (he', metasenv'') -> C.Appl (he'::tl'),metasenv''
424 | C.Appl _ -> assert false
425 | C.Const (uri,exp_named_subst) ->
426 let exp_named_subst', metasenv' =
428 (fun (uri,t) (tl,metasenv) ->
429 let t',metasenv' = um_aux metasenv t in
430 (uri,t')::tl, metasenv'
431 ) exp_named_subst ([],metasenv)
433 C.Const (uri,exp_named_subst'),metasenv'
434 | C.MutInd (uri,typeno,exp_named_subst) ->
435 let exp_named_subst', metasenv' =
437 (fun (uri,t) (tl,metasenv) ->
438 let t',metasenv' = um_aux metasenv t in
439 (uri,t')::tl, metasenv'
440 ) exp_named_subst ([],metasenv)
442 C.MutInd (uri,typeno,exp_named_subst'),metasenv'
443 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
444 let exp_named_subst', metasenv' =
446 (fun (uri,t) (tl,metasenv) ->
447 let t',metasenv' = um_aux metasenv t in
448 (uri,t')::tl, metasenv'
449 ) exp_named_subst ([],metasenv)
451 C.MutConstruct (uri,typeno,consno,exp_named_subst'),metasenv'
452 | C.MutCase (sp,i,outty,t,pl) ->
453 let outty',metasenv' = um_aux metasenv outty in
454 let t',metasenv'' = um_aux metasenv' t in
455 let pl',metasenv''' =
457 (fun p (pl,metasenv) ->
458 let p',metasenv' = um_aux metasenv p in
462 C.MutCase (sp, i, outty', t', pl'),metasenv'''
464 let len = List.length fl in
465 let liftedfl,metasenv' =
467 (fun (name, i, ty, bo) (fl,metasenv) ->
468 let ty',metasenv' = um_aux metasenv ty in
469 let bo',metasenv'' = um_aux metasenv' bo in
470 (name, i, ty', bo')::fl,metasenv''
473 C.Fix (i, liftedfl),metasenv'
475 let len = List.length fl in
476 let liftedfl,metasenv' =
478 (fun (name, ty, bo) (fl,metasenv) ->
479 let ty',metasenv' = um_aux metasenv ty in
480 let bo',metasenv'' = um_aux metasenv' bo in
481 (name, ty', bo')::fl,metasenv''
484 C.CoFix (i, liftedfl),metasenv'
486 let t',metasenv' = um_aux metasenv t in
487 t',metasenv',!unwinded
490 (* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
491 (* performs as (apply_subst subst t) until it finds an application of *)
492 (* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
493 (* a new beta-redex; in this case up to [reductions_no] consecutive *)
494 (* beta-reductions are performed. *)
495 (* Hint: this function is usually called when [reductions_no] *)
496 (* eta-expansions have been performed and the head of the new *)
497 (* application has been unified with (META [meta_to_reduce]): *)
498 (* during the unwinding the eta-expansions are undone. *)
500 let apply_subst_reducing subst meta_to_reduce t =
501 let unwinded = ref subst in
503 let module C = Cic in
504 let module S = CicSubstitution in
508 | C.Meta (i,l) as t ->
510 S.lift_meta l (List.assoc i !unwinded)
514 | C.Implicit as t -> t
515 | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
516 | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
517 | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
518 | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
520 let tl' = List.map um_aux tl in
523 C.Appl l -> C.Appl (l@tl')
524 | _ as he' -> C.Appl (he'::tl')
527 match meta_to_reduce,he with
528 Some (mtr,reductions_no), C.Meta (m,_) when m = mtr ->
529 let rec beta_reduce =
531 (n,(C.Appl (C.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
532 let he'' = CicSubstitution.subst he' t in
536 beta_reduce (n-1,C.Appl(he''::tl'))
539 beta_reduce (reductions_no,t')
542 | C.Appl _ -> assert false
543 | C.Const (uri,exp_named_subst) ->
544 let exp_named_subst' =
545 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
547 C.Const (uri,exp_named_subst')
548 | C.MutInd (uri,typeno,exp_named_subst) ->
549 let exp_named_subst' =
550 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
552 C.MutInd (uri,typeno,exp_named_subst')
553 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
554 let exp_named_subst' =
555 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
557 C.MutConstruct (uri,typeno,consno,exp_named_subst')
558 | C.MutCase (sp,i,outty,t,pl) ->
559 C.MutCase (sp, i, um_aux outty, um_aux t,
562 let len = List.length fl in
565 (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo))
570 let len = List.length fl in
573 (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo))
576 C.CoFix (i, liftedfl)
581 (* UNWIND THE MGU INSIDE THE MGU *)
582 let unwind_subst metasenv subst =
583 let identity_relocation_list_for_metavariable i =
584 let (_,canonical_context,_) =
585 List.find (function (m,_,_) -> m=i) metasenv
587 let canonical_context_length = List.length canonical_context in
590 n when n > canonical_context_length -> []
591 | n -> (Some (Cic.Rel n))::(aux (n+1))
596 (fun (unwinded,metasenv) (i,_) ->
597 let identity_relocation_list =
598 identity_relocation_list_for_metavariable i
600 let (_,metasenv',subst') =
601 unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
604 ) ([],metasenv) subst
607 let apply_subst subst t =
608 (* metasenv will not be used nor modified. So, let's use a dummy empty one *)
610 let (t',_,_) = unwind metasenv [] subst t in
614 (* A substitution is a (int * Cic.term) list that associates a *)
615 (* metavariable i with its body. *)
616 (* metasenv is of type Cic.metasenv *)
617 (* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
618 (* a new substitution which is already unwinded and ready to be applied and *)
619 (* a new metasenv in which some hypothesis in the contexts of the *)
620 (* metavariables may have been restricted. *)
621 let fo_unif metasenv context t1 t2 =
622 let subst_to_unwind,metasenv' = fo_unif_subst [] context metasenv t1 t2 in
623 unwind_subst metasenv' subst_to_unwind