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 let restrict to_be_restricted =
59 | _::tl when List.mem (n,i) to_be_restricted ->
60 None::(erase (i+1) n tl)
61 | he::tl -> he::(erase (i+1) n tl) in
65 | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
70 (*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
71 let delift context metasenv l t =
72 let module S = CicSubstitution in
73 let to_be_restricted = ref [] in
79 C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
80 (*CSC: deliftato la regola per il LetIn *)
81 (*CSC: FALSO! La regola per il LetIn non lo fa *)
83 (match List.nth context (m-k-1) with
84 Some (_,C.Def (t,_)) ->
85 (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
86 (*CSC: first order unification. Does it help or does it harm? *)
87 deliftaux k (S.lift m t)
88 | Some (_,C.Decl t) ->
89 (* It may augment to_be_restricted *)
90 (*CSC: Really? Even in the case of well-typed terms? *)
91 (*CSC: I am no longer sure of the usefulness of the check *)
92 ignore (deliftaux k (S.lift m t)) ;
93 C.Rel ((position (m-k) l) + k)
94 | None -> raise RelToHiddenHypothesis)
95 | C.Var (uri,exp_named_subst) ->
96 let exp_named_subst' =
97 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
99 C.Var (uri,exp_named_subst')
100 | C.Meta (i, l1) as t ->
104 | None::tl -> None::(deliftl (j+1) tl)
106 let l1' = (deliftl (j+1) tl) in
108 Some (deliftaux k t)::l1'
110 RelToHiddenHypothesis
112 to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
114 let l' = deliftl 1 l1 in
117 | C.Implicit as t -> t
118 | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
119 | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
120 | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
121 | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
122 | C.Appl l -> C.Appl (List.map (deliftaux k) l)
123 | C.Const (uri,exp_named_subst) ->
124 let exp_named_subst' =
125 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
127 C.Const (uri,exp_named_subst')
128 | C.MutInd (uri,typeno,exp_named_subst) ->
129 let exp_named_subst' =
130 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
132 C.MutInd (uri,typeno,exp_named_subst')
133 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
134 let exp_named_subst' =
135 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
137 C.MutConstruct (uri,typeno,consno,exp_named_subst')
138 | C.MutCase (sp,i,outty,t,pl) ->
139 C.MutCase (sp, i, deliftaux k outty, deliftaux k t,
140 List.map (deliftaux k) pl)
142 let len = List.length fl in
145 (fun (name, i, ty, bo) ->
146 (name, i, deliftaux k ty, deliftaux (k+len) bo))
151 let len = List.length fl in
154 (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
157 C.CoFix (i, liftedfl)
164 (* This is the case where we fail even first order unification. *)
165 (* The reason is that our delift function is weaker than first *)
166 (* order (in the sense of alpha-conversion). See comment above *)
167 (* related to the delift function. *)
168 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 !!!!!!!!!!!!!!!!" ;
169 raise UnificationFailed
171 res, restrict !to_be_restricted metasenv
174 (**** END OF DELIFT ****)
176 type substitution = (int * Cic.term) list
178 (* NUOVA UNIFICAZIONE *)
179 (* A substitution is a (int * Cic.term) list that associates a
180 metavariable i with its body.
181 A metaenv is a (int * Cic.term) list that associate a metavariable
183 fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
184 a new substitution which is _NOT_ unwinded. It must be unwinded before
187 let rec fo_unif_subst subst context metasenv t1 t2 =
188 let module C = Cic in
189 let module R = CicReduction in
190 let module S = CicSubstitution in
192 (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
200 | Some t1', Some t2' ->
201 (* First possibility: restriction *)
202 (* Second possibility: unification *)
203 (* Third possibility: convertibility *)
204 R.are_convertible context t1' t2'
207 if ok then subst,metasenv else raise UnificationFailed
208 | (C.Meta (n,l), C.Meta (m,_)) when n>m ->
209 fo_unif_subst subst context metasenv t2 t1
211 | (t, C.Meta (n,l)) ->
212 let subst',metasenv' =
214 let oldt = (List.assoc n subst) in
215 let lifted_oldt = S.lift_meta l oldt in
216 fo_unif_subst subst context metasenv lifted_oldt t
218 let t',metasenv' = delift context metasenv l t in
219 (n, t')::subst, metasenv'
221 let (_,_,meta_type) =
222 List.find (function (m,_,_) -> m=n) metasenv' in
223 let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
224 fo_unif_subst subst' context metasenv' (S.lift_meta l meta_type) tyt
225 | (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
226 | (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
227 if UriManager.eq uri1 uri2 then
228 fo_unif_subst_exp_named_subst subst context metasenv
229 exp_named_subst1 exp_named_subst2
231 raise UnificationFailed
232 | C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
233 if UriManager.eq uri1 uri2 && i1 = i2 then
234 fo_unif_subst_exp_named_subst subst context metasenv
235 exp_named_subst1 exp_named_subst2
237 raise UnificationFailed
238 | C.MutConstruct (uri1,i1,j1,exp_named_subst1),
239 C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
240 if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
241 fo_unif_subst_exp_named_subst subst context metasenv
242 exp_named_subst1 exp_named_subst2
244 raise UnificationFailed
251 if R.are_convertible context t1 t2 then
254 raise UnificationFailed
255 | (C.Cast (te,ty), t2) -> fo_unif_subst subst context metasenv te t2
256 | (t1, C.Cast (te,ty)) -> fo_unif_subst subst context metasenv t1 te
257 | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
258 let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
259 fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
260 | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
261 let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
262 fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
263 | (C.LetIn (_,s1,t1), t2)
264 | (t2, C.LetIn (_,s1,t1)) ->
265 fo_unif_subst subst context metasenv t2 (S.subst s1 t1)
266 | (C.Appl l1, C.Appl l2) ->
267 let lr1 = List.rev l1 in
268 let lr2 = List.rev l2 in
269 let rec fo_unif_l subst metasenv =
272 | _,[] -> assert false
274 fo_unif_subst subst context metasenv h1 h2
277 fo_unif_subst subst context metasenv h (C.Appl (List.rev l))
278 | ((h1::l1),(h2::l2)) ->
279 let subst', metasenv' =
280 fo_unif_subst subst context metasenv h1 h2
282 fo_unif_l subst' metasenv' (l1,l2)
284 fo_unif_l subst metasenv (lr1, lr2)
289 | (C.MutConstruct _, _)
290 | (_, C.MutConstruct _) ->
291 if R.are_convertible context t1 t2 then
294 raise UnificationFailed
295 | (C.MutCase (_,_,outt1,t1,pl1), C.MutCase (_,_,outt2,t2,pl2))->
296 let subst', metasenv' =
297 fo_unif_subst subst context metasenv outt1 outt2 in
298 let subst'',metasenv'' =
299 fo_unif_subst subst' context metasenv' t1 t2 in
301 (function (subst,metasenv) ->
302 fo_unif_subst subst context metasenv
303 ) (subst'',metasenv'') pl1 pl2
308 if R.are_convertible context t1 t2 then
311 raise UnificationFailed
313 if R.are_convertible context t1 t2 then
316 raise UnificationFailed
318 and fo_unif_subst_exp_named_subst subst context metasenv
319 exp_named_subst1 exp_named_subst2
323 (fun (subst,metasenv) (uri1,t1) (uri2,t2) ->
325 fo_unif_subst subst context metasenv t1 t2
326 ) (subst,metasenv) exp_named_subst1 exp_named_subst2
329 let uri = UriManager.uri_of_string "cic:/dummy.var" in
330 prerr_endline ("@@@: " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst1)) ^
331 " <==> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst2))) ; raise e
334 let unwind metasenv subst unwinded t =
335 let unwinded = ref unwinded in
336 let frozen = ref [] in
337 let rec um_aux metasenv =
338 let module C = Cic in
339 let module S = CicSubstitution in
341 C.Rel _ as t -> t,metasenv
342 | C.Var _ as t -> t,metasenv
345 S.lift_meta l (List.assoc i !unwinded), metasenv
347 if List.mem i !frozen then raise OccurCheck
349 let saved_frozen = !frozen in
350 frozen := i::!frozen ;
353 let t = List.assoc i subst in
354 let t',metasenv' = um_aux metasenv t in
356 let (_,canonical_context,_) =
357 List.find (function (m,_,_) -> m=i) metasenv
359 delift canonical_context metasenv' l t'
361 unwinded := (i,t')::!unwinded ;
362 S.lift_meta l t', metasenv'
365 (* not constrained variable, i.e. free in subst*)
368 (fun t (tl,metasenv) ->
370 None -> None::tl,metasenv
372 let t',metasenv' = um_aux metasenv t in
373 (Some t')::tl, metasenv'
376 C.Meta (i,l'), metasenv'
378 frozen := saved_frozen ;
382 | C.Implicit as t -> t,metasenv
384 let te',metasenv' = um_aux metasenv te in
385 let ty',metasenv'' = um_aux metasenv' ty in
386 C.Cast (te',ty'),metasenv''
388 let s',metasenv' = um_aux metasenv s in
389 let t',metasenv'' = um_aux metasenv' t in
390 C.Prod (n, s', t'), metasenv''
391 | C.Lambda (n,s,t) ->
392 let s',metasenv' = um_aux metasenv s in
393 let t',metasenv'' = um_aux metasenv' t in
394 C.Lambda (n, s', t'), metasenv''
396 let s',metasenv' = um_aux metasenv s in
397 let t',metasenv'' = um_aux metasenv' t in
398 C.LetIn (n, s', t'), metasenv''
402 (fun t (tl,metasenv) ->
403 let t',metasenv' = um_aux metasenv t in
408 match um_aux metasenv' he with
409 (C.Appl l, metasenv'') -> C.Appl (l@tl'),metasenv''
410 | (he', metasenv'') -> C.Appl (he'::tl'),metasenv''
412 | C.Appl _ -> assert false
413 | C.Const (uri,exp_named_subst) ->
414 let exp_named_subst', metasenv' =
416 (fun (uri,t) (tl,metasenv) ->
417 let t',metasenv' = um_aux metasenv t in
418 (uri,t')::tl, metasenv'
419 ) exp_named_subst ([],metasenv)
421 C.Const (uri,exp_named_subst'),metasenv'
422 | C.MutInd (uri,typeno,exp_named_subst) ->
423 let exp_named_subst', metasenv' =
425 (fun (uri,t) (tl,metasenv) ->
426 let t',metasenv' = um_aux metasenv t in
427 (uri,t')::tl, metasenv'
428 ) exp_named_subst ([],metasenv)
430 C.MutInd (uri,typeno,exp_named_subst'),metasenv'
431 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
432 let exp_named_subst', metasenv' =
434 (fun (uri,t) (tl,metasenv) ->
435 let t',metasenv' = um_aux metasenv t in
436 (uri,t')::tl, metasenv'
437 ) exp_named_subst ([],metasenv)
439 C.MutConstruct (uri,typeno,consno,exp_named_subst'),metasenv'
440 | C.MutCase (sp,i,outty,t,pl) ->
441 let outty',metasenv' = um_aux metasenv outty in
442 let t',metasenv'' = um_aux metasenv' t in
443 let pl',metasenv''' =
445 (fun p (pl,metasenv) ->
446 let p',metasenv' = um_aux metasenv p in
450 C.MutCase (sp, i, outty', t', pl'),metasenv'''
452 let len = List.length fl in
453 let liftedfl,metasenv' =
455 (fun (name, i, ty, bo) (fl,metasenv) ->
456 let ty',metasenv' = um_aux metasenv ty in
457 let bo',metasenv'' = um_aux metasenv' bo in
458 (name, i, ty', bo')::fl,metasenv''
461 C.Fix (i, liftedfl),metasenv'
463 let len = List.length fl in
464 let liftedfl,metasenv' =
466 (fun (name, ty, bo) (fl,metasenv) ->
467 let ty',metasenv' = um_aux metasenv ty in
468 let bo',metasenv'' = um_aux metasenv' bo in
469 (name, ty', bo')::fl,metasenv''
472 C.CoFix (i, liftedfl),metasenv'
474 let t',metasenv' = um_aux metasenv t in
475 t',metasenv',!unwinded
478 (* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
479 (* performs as (apply_subst subst t) until it finds an application of *)
480 (* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
481 (* a new beta-redex; in this case up to [reductions_no] consecutive *)
482 (* beta-reductions are performed. *)
483 (* Hint: this function is usually called when [reductions_no] *)
484 (* eta-expansions have been performed and the head of the new *)
485 (* application has been unified with (META [meta_to_reduce]): *)
486 (* during the unwinding the eta-expansions are undone. *)
488 let apply_subst_reducing subst meta_to_reduce t =
489 let unwinded = ref subst in
491 let module C = Cic in
492 let module S = CicSubstitution in
496 | C.Meta (i,l) as t ->
498 S.lift_meta l (List.assoc i !unwinded)
502 | C.Implicit as t -> t
503 | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
504 | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
505 | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
506 | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
508 let tl' = List.map um_aux tl in
511 C.Appl l -> C.Appl (l@tl')
512 | _ as he' -> C.Appl (he'::tl')
515 match meta_to_reduce,he with
516 Some (mtr,reductions_no), C.Meta (m,_) when m = mtr ->
517 let rec beta_reduce =
519 (n,(C.Appl (C.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
520 let he'' = CicSubstitution.subst he' t in
524 beta_reduce (n-1,C.Appl(he''::tl'))
527 beta_reduce (reductions_no,t')
530 | C.Appl _ -> assert false
531 | C.Const (uri,exp_named_subst) ->
532 let exp_named_subst' =
533 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
535 C.Const (uri,exp_named_subst')
536 | C.MutInd (uri,typeno,exp_named_subst) ->
537 let exp_named_subst' =
538 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
540 C.MutInd (uri,typeno,exp_named_subst')
541 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
542 let exp_named_subst' =
543 List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
545 C.MutConstruct (uri,typeno,consno,exp_named_subst')
546 | C.MutCase (sp,i,outty,t,pl) ->
547 C.MutCase (sp, i, um_aux outty, um_aux t,
550 let len = List.length fl in
553 (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo))
558 let len = List.length fl in
561 (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo))
564 C.CoFix (i, liftedfl)
569 (* UNWIND THE MGU INSIDE THE MGU *)
570 let unwind_subst metasenv subst =
571 let identity_relocation_list_for_metavariable i =
572 let (_,canonical_context,_) =
573 List.find (function (m,_,_) -> m=i) metasenv
575 let canonical_context_length = List.length canonical_context in
578 n when n > canonical_context_length -> []
579 | n -> (Some (Cic.Rel n))::(aux (n+1))
584 (fun (unwinded,metasenv) (i,_) ->
585 let identity_relocation_list =
586 identity_relocation_list_for_metavariable i
588 let (_,metasenv',subst') =
589 unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
592 ) ([],metasenv) subst
595 let apply_subst subst t =
596 (* metasenv will not be used nor modified. So, let's use a dummy empty one *)
598 let (t',_,_) = unwind metasenv [] subst t in
602 (* A substitution is a (int * Cic.term) list that associates a *)
603 (* metavariable i with its body. *)
604 (* metasenv is of type Cic.metasenv *)
605 (* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
606 (* a new substitution which is already unwinded and ready to be applied and *)
607 (* a new metasenv in which some hypothesis in the contexts of the *)
608 (* metavariables may have been restricted. *)
609 let fo_unif metasenv context t1 t2 =
610 let subst_to_unwind,metasenv' = fo_unif_subst [] context metasenv t1 t2 in
611 unwind_subst metasenv' subst_to_unwind