4 exception AssertFailure of string
5 exception MetaSubstFailure of string
7 let debug_print = prerr_endline
9 type substitution = (int * Cic.term) list
14 (fun (idx, term) -> Printf.sprintf "?%d := %s" idx (CicPp.ppterm term))
18 (* the delift function takes in input a metavariable index, an ordered list of
19 * optional terms [t1,...,tn] and a term t, and substitutes every tk = Some
20 * (rel(nk)) with rel(k). Typically, the list of optional terms is the explicit
21 * substitution that is applied to a metavariable occurrence and the result of
22 * the delift function is a term the implicit variable can be substituted with
23 * to make the term [t] unifiable with the metavariable occurrence. In general,
24 * the problem is undecidable if we consider equivalence in place of alpha
25 * convertibility. Our implementation, though, is even weaker than alpha
26 * convertibility, since it replace the term [tk] if and only if [tk] is a Rel
27 * (missing all the other cases). Does this matter in practice?
28 * The metavariable index is the index of the metavariable that must not occur
29 * in the term (for occur check).
32 exception NotInTheList;;
37 [] -> raise NotInTheList
38 | (Some (Cic.Rel m))::_ when m=n -> k
39 | _::tl -> aux (k+1) tl in
45 let rec force_does_not_occur subst to_be_restricted t =
47 let more_to_be_restricted = ref [] in
48 let rec aux k = function
49 C.Rel r when List.mem (r+k) to_be_restricted -> raise Occur
52 | C.Implicit -> assert false
54 (* we do not retrieve the term associated to ?n in subst since *)
55 (* in this way we can restrict if something goes wrong *)
67 prerr_endline (Printf.sprintf "RESTRINGO (%d,%d)" n !i) ;
68 more_to_be_restricted := (n,!i) :: !more_to_be_restricted;
73 | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
74 | C.Prod (name,so,dest) -> C.Prod (name, aux k so, aux (k+1) dest)
75 | C.Lambda (name,so,dest) -> C.Lambda (name, aux k so, aux (k+1) dest)
76 | C.LetIn (name,so,dest) -> C.LetIn (name, aux k so, aux (k+1) dest)
77 | C.Appl l -> C.Appl (List.map (aux k) l)
78 | C.Var (uri,exp_named_subst) ->
79 let exp_named_subst' =
80 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
82 C.Var (uri, exp_named_subst')
83 | C.Const (uri, exp_named_subst) ->
84 let exp_named_subst' =
85 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
87 C.Const (uri, exp_named_subst')
88 | C.MutInd (uri,tyno,exp_named_subst) ->
89 let exp_named_subst' =
90 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
92 C.MutInd (uri, tyno, exp_named_subst')
93 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
94 let exp_named_subst' =
95 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
97 C.MutConstruct (uri, tyno, consno, exp_named_subst')
98 | C.MutCase (uri,tyno,out,te,pl) ->
99 C.MutCase (uri, tyno, aux k out, aux k te, List.map (aux k) pl)
101 let len = List.length fl in
102 let k_plus_len = k + len in
105 (fun (name,j,ty,bo) -> (name, j, aux k ty, aux k_plus_len bo)) fl
109 let len = List.length fl in
110 let k_plus_len = k + len in
113 (fun (name,ty,bo) -> (name, aux k ty, aux k_plus_len bo)) fl
118 (!more_to_be_restricted, res)
120 let rec restrict subst to_be_restricted metasenv =
121 let names_of_context_indexes context indexes =
125 match List.nth context i with
126 | None -> assert false
127 | Some (n, _) -> CicPp.ppname n)
130 let force_does_not_occur_in_context to_be_restricted = function
132 | Some (name, Cic.Decl t) ->
133 let (more_to_be_restricted, t') =
134 force_does_not_occur subst to_be_restricted t
136 more_to_be_restricted, Some (name, Cic.Decl t)
137 | Some (name, Cic.Def (bo, ty)) ->
138 let (more_to_be_restricted, bo') =
139 force_does_not_occur subst to_be_restricted bo
141 let more_to_be_restricted, ty' =
143 | None -> more_to_be_restricted, None
145 let more_to_be_restricted', ty' =
146 force_does_not_occur subst to_be_restricted ty
148 more_to_be_restricted @ more_to_be_restricted',
151 more_to_be_restricted, Some (name, Cic.Def (bo', ty'))
153 let rec erase i to_be_restricted n = function
154 | [] -> [], to_be_restricted, []
156 let restrict_me = List.mem i to_be_restricted in
158 let more_to_be_restricted, restricted, new_tl =
159 erase (i+1) (i :: to_be_restricted) n tl
161 more_to_be_restricted, restricted, None :: new_tl
164 let more_to_be_restricted, hd' =
165 force_does_not_occur_in_context to_be_restricted hd
167 let more_to_be_restricted', restricted, tl' =
168 erase (i+1) to_be_restricted n tl
170 more_to_be_restricted @ more_to_be_restricted',
171 restricted, hd' :: tl'
173 let more_to_be_restricted, restricted, tl' =
174 erase (i+1) (i :: to_be_restricted) n tl
176 more_to_be_restricted, restricted, None :: tl')
178 let (more_to_be_restricted, metasenv, subst) =
180 (fun (n, context, t) (more, metasenv, subst) ->
181 let to_be_restricted =
182 List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
184 let (more_to_be_restricted, restricted, context') =
185 erase 1 to_be_restricted n context
188 let more_to_be_restricted', t' =
189 force_does_not_occur subst restricted t
191 let metasenv' = (n, context', t') :: metasenv in
193 let s = List.assoc n subst in
195 let more_to_be_restricted'', s' =
196 force_does_not_occur subst restricted s
198 let subst' = (n, s') :: (List.remove_assoc n subst) in
200 more @ more_to_be_restricted @ more_to_be_restricted' @
201 more_to_be_restricted''
203 (more, metasenv', subst')
205 raise (MetaSubstFailure (sprintf
206 "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since ?%d is already instantiated with %s and at least one of the hypotheses occurs in the substituted term"
207 n (names_of_context_indexes context to_be_restricted) n
209 with Not_found -> (more @ more_to_be_restricted @ more_to_be_restricted', metasenv', subst))
211 raise (MetaSubstFailure (sprintf
212 "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since metavariable's type depends on at least one of them"
213 n (names_of_context_indexes context to_be_restricted))))
214 metasenv ([], [], subst)
216 match more_to_be_restricted with
217 | [] -> (metasenv, subst)
218 | _ -> restrict subst more_to_be_restricted metasenv
221 (*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
222 let delift n subst context metasenv l t =
223 let module S = CicSubstitution in
224 let to_be_restricted = ref [] in
225 let rec deliftaux k =
226 let module C = Cic in
230 C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
231 (*CSC: deliftato la regola per il LetIn *)
232 (*CSC: FALSO! La regola per il LetIn non lo fa *)
234 (match List.nth context (m-k-1) with
235 Some (_,C.Def (t,_)) ->
236 (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
237 (*CSC: first order unification. Does it help or does it harm? *)
238 deliftaux k (S.lift m t)
239 | Some (_,C.Decl t) ->
240 (*CSC: The following check seems to be wrong! *)
241 (*CSC: B:Set |- ?2 : Set *)
242 (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x *)
243 (*CSC: Why should I restrict ?2 over B? The instantiation *)
244 (*CSC: ?1 := A is perfectly reasonable and well-typed. *)
245 (*CSC: Thus I comment out the following two lines that *)
246 (*CSC: are the incriminated ones. *)
247 (*(* It may augment to_be_restricted *)
248 ignore (deliftaux k (S.lift m t)) ;*)
249 (*CSC: end of bug commented out *)
250 C.Rel ((position (m-k) l) + k)
251 | None -> raise (MetaSubstFailure "RelToHiddenHypothesis"))
252 | C.Var (uri,exp_named_subst) ->
253 let exp_named_subst' =
254 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
256 C.Var (uri,exp_named_subst')
257 | C.Meta (i, l1) as t ->
259 raise (MetaSubstFailure (sprintf
260 "Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
263 (* I do not consider the term associated to ?i in subst since *)
264 (* in this way I can restrict if something goes wrong. *)
268 | None::tl -> None::(deliftl (j+1) tl)
270 let l1' = (deliftl (j+1) tl) in
272 Some (deliftaux k t)::l1'
275 | MetaSubstFailure _ ->
276 to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
278 let l' = deliftl 1 l1 in
281 | C.Implicit as t -> t
282 | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
283 | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
284 | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
285 | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
286 | C.Appl l -> C.Appl (List.map (deliftaux k) l)
287 | C.Const (uri,exp_named_subst) ->
288 let exp_named_subst' =
289 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
291 C.Const (uri,exp_named_subst')
292 | C.MutInd (uri,typeno,exp_named_subst) ->
293 let exp_named_subst' =
294 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
296 C.MutInd (uri,typeno,exp_named_subst')
297 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
298 let exp_named_subst' =
299 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
301 C.MutConstruct (uri,typeno,consno,exp_named_subst')
302 | C.MutCase (sp,i,outty,t,pl) ->
303 C.MutCase (sp, i, deliftaux k outty, deliftaux k t,
304 List.map (deliftaux k) pl)
306 let len = List.length fl in
309 (fun (name, i, ty, bo) ->
310 (name, i, deliftaux k ty, deliftaux (k+len) bo))
315 let len = List.length fl in
318 (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
321 C.CoFix (i, liftedfl)
328 (* This is the case where we fail even first order unification. *)
329 (* The reason is that our delift function is weaker than first *)
330 (* order (in the sense of alpha-conversion). See comment above *)
331 (* related to the delift function. *)
332 debug_print "!!!!!!!!!!! First Order UnificationFailure, but maybe it could have been successful even in a first order setting (no conversion, only alpha convertibility)! Please, implement a better delift function !!!!!!!!!!!!!!!!" ;
333 raise (MetaSubstFailure (sprintf
334 "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
338 (function Some t -> CicPp.ppterm t | None -> "_")
341 let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
345 (**** END OF DELIFT ****)
347 let apply_subst_gen ~appl_fun subst term =
349 let module C = Cic in
350 let module S = CicSubstitution in
356 let t = List.assoc i subst in
357 um_aux (S.lift_meta l t)
358 with Not_found -> (* not constrained variable, i.e. free in subst*)
360 List.map (function None -> None | Some t -> Some (um_aux t)) l
364 | C.Implicit -> assert false
365 | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
366 | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
367 | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
368 | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
369 | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
370 | C.Appl _ -> assert false
371 | C.Const (uri,exp_named_subst) ->
372 let exp_named_subst' =
373 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
375 C.Const (uri, exp_named_subst')
376 | C.MutInd (uri,typeno,exp_named_subst) ->
377 let exp_named_subst' =
378 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
380 C.MutInd (uri,typeno,exp_named_subst')
381 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
382 let exp_named_subst' =
383 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
385 C.MutConstruct (uri,typeno,consno,exp_named_subst')
386 | C.MutCase (sp,i,outty,t,pl) ->
387 let pl' = List.map um_aux pl in
388 C.MutCase (sp, i, um_aux outty, um_aux t, pl')
391 List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
396 List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
403 let appl_fun um_aux he tl =
404 let tl' = List.map um_aux tl in
407 Cic.Appl l -> Cic.Appl (l@tl')
408 | he' -> Cic.Appl (he'::tl')
411 apply_subst_gen ~appl_fun
413 let ppterm subst term = CicPp.ppterm (apply_subst subst term)
415 (* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
416 (* performs as (apply_subst subst t) until it finds an application of *)
417 (* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
418 (* a new beta-redex; in this case up to [reductions_no] consecutive *)
419 (* beta-reductions are performed. *)
420 (* Hint: this function is usually called when [reductions_no] *)
421 (* eta-expansions have been performed and the head of the new *)
422 (* application has been unified with (META [meta_to_reduce]): *)
423 (* during the unwinding the eta-expansions are undone. *)
425 let apply_subst_reducing meta_to_reduce =
426 let appl_fun um_aux he tl =
427 let tl' = List.map um_aux tl in
430 Cic.Appl l -> Cic.Appl (l@tl')
431 | he' -> Cic.Appl (he'::tl')
434 match meta_to_reduce, he with
435 Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
436 let rec beta_reduce =
438 (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
439 let he'' = CicSubstitution.subst he' t in
443 beta_reduce (n-1,Cic.Appl(he''::tl'))
446 beta_reduce (reductions_no,t')
450 apply_subst_gen ~appl_fun
452 let rec apply_subst_context subst context =
456 | Some (n, Cic.Decl t) ->
457 let t' = apply_subst subst t in
458 Some (n, Cic.Decl t') :: context
459 | Some (n, Cic.Def (t, ty)) ->
463 | Some ty -> Some (apply_subst subst ty)
465 let t' = apply_subst subst t in
466 Some (n, Cic.Def (t', ty')) :: context
467 | None -> None :: context)
470 let apply_subst_metasenv subst metasenv =
472 (fun (n, context, ty) ->
473 (n, apply_subst_context subst context, apply_subst subst ty))
475 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
478 let ppterm subst term = CicPp.ppterm (apply_subst subst term)
480 let ppcontext ?(sep = "\n") subst context =
482 (List.rev_map (function
483 | Some (n, Cic.Decl t) ->
484 sprintf "%s : %s" (CicPp.ppname n) (ppterm subst t)
485 | Some (n, Cic.Def (t, ty)) ->
486 sprintf "%s : %s := %s"
488 (match ty with None -> "_" | Some ty -> ppterm subst ty)
493 let ppmetasenv ?(sep = "\n") metasenv subst =
497 sprintf "%s |- ?%d: %s" (ppcontext ~sep:"; " subst c) i
500 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
503 (* UNWIND THE MGU INSIDE THE MGU *)
505 let unwind_subst metasenv subst =
507 (fun (unwinded,metasenv) (i,_) ->
508 let (_,canonical_context,_) = CicUtil.lookup_meta i metasenv in
509 let identity_relocation_list =
510 CicMkImplicit.identity_relocation_list_for_metavariable canonical_context
512 let (_,metasenv',subst') =
513 unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
516 ) ([],metasenv) subst
519 (* From now on we recreate a kernel abstraction where substitutions are part of
522 let lift subst n term =
523 let term = apply_subst subst term in
525 CicSubstitution.lift n term
527 raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
529 let subst subst t1 t2 =
530 let t1 = apply_subst subst t1 in
531 let t2 = apply_subst subst t2 in
533 CicSubstitution.subst t1 t2
535 raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
537 let whd subst context term =
538 let term = apply_subst subst term in
539 let context = apply_subst_context subst context in
541 CicReduction.whd context term
543 raise (MetaSubstFailure ("Weak head reduction failure: " ^
544 Printexc.to_string e))
546 let are_convertible subst context t1 t2 =
547 let context = apply_subst_context subst context in
548 let t1 = apply_subst subst t1 in
549 let t2 = apply_subst subst t2 in
550 CicReduction.are_convertible context t1 t2
552 let type_of_aux' metasenv subst context term =
553 let term = apply_subst subst term in
554 let context = apply_subst_context subst context in
557 (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
559 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
563 CicTypeChecker.type_of_aux' metasenv context term
564 with CicTypeChecker.TypeCheckerFailure msg ->
565 raise (MetaSubstFailure ("Type checker failure: " ^ msg))