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 k 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 more_to_be_restricted := (n,!i) :: !more_to_be_restricted;
72 | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty)
73 | C.Prod (name,so,dest) -> C.Prod (name, aux k so, aux (k+1) dest)
74 | C.Lambda (name,so,dest) -> C.Lambda (name, aux k so, aux (k+1) dest)
75 | C.LetIn (name,so,dest) -> C.LetIn (name, aux k so, aux (k+1) dest)
76 | C.Appl l -> C.Appl (List.map (aux k) l)
77 | C.Var (uri,exp_named_subst) ->
78 let exp_named_subst' =
79 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
81 C.Var (uri, exp_named_subst')
82 | C.Const (uri, exp_named_subst) ->
83 let exp_named_subst' =
84 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
86 C.Const (uri, exp_named_subst')
87 | C.MutInd (uri,tyno,exp_named_subst) ->
88 let exp_named_subst' =
89 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
91 C.MutInd (uri, tyno, exp_named_subst')
92 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
93 let exp_named_subst' =
94 List.map (fun (uri,t) -> (uri, aux k t)) exp_named_subst
96 C.MutConstruct (uri, tyno, consno, exp_named_subst')
97 | C.MutCase (uri,tyno,out,te,pl) ->
98 C.MutCase (uri, tyno, aux k out, aux k te, List.map (aux k) pl)
100 let len = List.length fl in
101 let k_plus_len = k + len in
104 (fun (name,j,ty,bo) -> (name, j, aux k ty, aux k_plus_len bo)) fl
108 let len = List.length fl in
109 let k_plus_len = k + len in
112 (fun (name,ty,bo) -> (name, aux k ty, aux k_plus_len bo)) fl
117 (!more_to_be_restricted, res)
119 let rec restrict subst to_be_restricted metasenv =
120 let names_of_context_indexes context indexes =
124 match List.nth context i with
125 | None -> assert false
126 | Some (n, _) -> CicPp.ppname n)
129 let force_does_not_occur_in_context k to_be_restricted = function
131 | Some (name, Cic.Decl t) ->
132 let (more_to_be_restricted, t') =
133 force_does_not_occur k subst to_be_restricted t
135 more_to_be_restricted, Some (name, Cic.Decl t')
136 | Some (name, Cic.Def (bo, ty)) ->
137 let (more_to_be_restricted, bo') =
138 force_does_not_occur k subst to_be_restricted bo
140 let more_to_be_restricted, ty' =
142 | None -> more_to_be_restricted, None
144 let more_to_be_restricted', ty' =
145 force_does_not_occur k subst to_be_restricted ty
147 more_to_be_restricted @ more_to_be_restricted',
150 more_to_be_restricted, Some (name, Cic.Def (bo', ty'))
152 let rec erase i to_be_restricted n = function
153 | [] -> [], to_be_restricted, []
155 let more_to_be_restricted,restricted,tl' =
156 erase (i+1) to_be_restricted n tl
158 let restrict_me = List.mem i restricted in
160 more_to_be_restricted, restricted, None:: tl'
163 let more_to_be_restricted', hd' =
164 force_does_not_occur_in_context i restricted hd
166 more_to_be_restricted @ more_to_be_restricted',
167 restricted, hd' :: tl'
169 more_to_be_restricted, (i :: restricted), None :: tl')
171 let (more_to_be_restricted, metasenv, subst) =
173 (fun (n, context, t) (more, metasenv, subst) ->
174 let to_be_restricted =
175 List.map snd (List.filter (fun (m, _) -> m = n) to_be_restricted)
177 let (more_to_be_restricted, restricted, context') =
178 (* just an optimization *)
179 if to_be_restricted = [] then
182 erase 1 to_be_restricted n context
185 let more_to_be_restricted', t' =
186 force_does_not_occur 0 subst restricted t
188 let metasenv' = (n, context', t') :: metasenv in
190 let s = List.assoc n subst in
192 let more_to_be_restricted'', s' =
193 force_does_not_occur 0 subst restricted s
195 let subst' = (n, s') :: (List.remove_assoc n subst) in
197 more @ more_to_be_restricted @ more_to_be_restricted' @
198 more_to_be_restricted''
200 (more, metasenv', subst')
202 raise (MetaSubstFailure (sprintf
203 "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"
204 n (names_of_context_indexes context to_be_restricted) n
206 with Not_found -> (more @ more_to_be_restricted @ more_to_be_restricted', metasenv', subst))
208 raise (MetaSubstFailure (sprintf
209 "Cannot restrict the context of the metavariable ?%d over the hypotheses %s since metavariable's type depends on at least one of them"
210 n (names_of_context_indexes context to_be_restricted))))
211 metasenv ([], [], subst)
213 match more_to_be_restricted with
214 | [] -> (metasenv, subst)
215 | _ -> restrict subst more_to_be_restricted metasenv
218 (*CSC: maybe we should rename delift in abstract, as I did in my dissertation *)
219 let delift n subst context metasenv l t =
220 let module S = CicSubstitution in
221 (* THIS CODE SHOULD NOT BE USEFUL AT ALL
223 let (_, canonical_context, _) = CicUtil.lookup_meta n metasenv in
224 List.map2 (fun ct lt ->
231 let to_be_restricted = ref [] in
232 let rec deliftaux k =
233 let module C = Cic in
237 C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
238 (*CSC: deliftato la regola per il LetIn *)
239 (*CSC: FALSO! La regola per il LetIn non lo fa *)
241 (match List.nth context (m-k-1) with
242 Some (_,C.Def (t,_)) ->
243 (*CSC: Hmmm. This bit of reduction is not in the spirit of *)
244 (*CSC: first order unification. Does it help or does it harm? *)
245 deliftaux k (S.lift m t)
246 | Some (_,C.Decl t) ->
247 (*CSC: The following check seems to be wrong! *)
248 (*CSC: B:Set |- ?2 : Set *)
249 (*CSC: A:Set ; x:?2[A/B] |- ?1[x/A] =?= x *)
250 (*CSC: Why should I restrict ?2 over B? The instantiation *)
251 (*CSC: ?1 := A is perfectly reasonable and well-typed. *)
252 (*CSC: Thus I comment out the following two lines that *)
253 (*CSC: are the incriminated ones. *)
254 (*(* It may augment to_be_restricted *)
255 ignore (deliftaux k (S.lift m t)) ;*)
256 (*CSC: end of bug commented out *)
257 C.Rel ((position (m-k) l) + k)
258 | None -> raise (MetaSubstFailure "RelToHiddenHypothesis"))
259 | C.Var (uri,exp_named_subst) ->
260 let exp_named_subst' =
261 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
263 C.Var (uri,exp_named_subst')
264 | C.Meta (i, l1) as t ->
266 raise (MetaSubstFailure (sprintf
267 "Cannot unify the metavariable ?%d with a term that has as subterm %s in which the same metavariable occurs (occur check)"
270 (* I do not consider the term associated to ?i in subst since *)
271 (* in this way I can restrict if something goes wrong. *)
275 | None::tl -> None::(deliftl (j+1) tl)
277 let l1' = (deliftl (j+1) tl) in
279 Some (deliftaux k t)::l1'
282 | MetaSubstFailure _ ->
283 to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
285 let l' = deliftl 1 l1 in
288 | C.Implicit as t -> t
289 | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
290 | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
291 | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
292 | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
293 | C.Appl l -> C.Appl (List.map (deliftaux k) l)
294 | C.Const (uri,exp_named_subst) ->
295 let exp_named_subst' =
296 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
298 C.Const (uri,exp_named_subst')
299 | C.MutInd (uri,typeno,exp_named_subst) ->
300 let exp_named_subst' =
301 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
303 C.MutInd (uri,typeno,exp_named_subst')
304 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
305 let exp_named_subst' =
306 List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
308 C.MutConstruct (uri,typeno,consno,exp_named_subst')
309 | C.MutCase (sp,i,outty,t,pl) ->
310 C.MutCase (sp, i, deliftaux k outty, deliftaux k t,
311 List.map (deliftaux k) pl)
313 let len = List.length fl in
316 (fun (name, i, ty, bo) ->
317 (name, i, deliftaux k ty, deliftaux (k+len) bo))
322 let len = List.length fl in
325 (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
328 C.CoFix (i, liftedfl)
335 (* This is the case where we fail even first order unification. *)
336 (* The reason is that our delift function is weaker than first *)
337 (* order (in the sense of alpha-conversion). See comment above *)
338 (* related to the delift function. *)
339 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 !!!!!!!!!!!!!!!!" ;
340 raise (MetaSubstFailure (sprintf
341 "Error trying to abstract %s over [%s]: the algorithm only tried to abstract over bound variables"
345 (function Some t -> CicPp.ppterm t | None -> "_")
348 let (metasenv, subst) = restrict subst !to_be_restricted metasenv in
352 (**** END OF DELIFT ****)
354 let apply_subst_gen ~appl_fun subst term =
356 let module C = Cic in
357 let module S = CicSubstitution in
363 let t = List.assoc i subst in
364 um_aux (S.lift_meta l t)
365 with Not_found -> (* not constrained variable, i.e. free in subst*)
367 List.map (function None -> None | Some t -> Some (um_aux t)) l
371 | C.Implicit -> assert false
372 | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
373 | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
374 | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
375 | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
376 | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
377 | C.Appl _ -> assert false
378 | C.Const (uri,exp_named_subst) ->
379 let exp_named_subst' =
380 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
382 C.Const (uri, exp_named_subst')
383 | C.MutInd (uri,typeno,exp_named_subst) ->
384 let exp_named_subst' =
385 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
387 C.MutInd (uri,typeno,exp_named_subst')
388 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
389 let exp_named_subst' =
390 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
392 C.MutConstruct (uri,typeno,consno,exp_named_subst')
393 | C.MutCase (sp,i,outty,t,pl) ->
394 let pl' = List.map um_aux pl in
395 C.MutCase (sp, i, um_aux outty, um_aux t, pl')
398 List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
403 List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
410 let appl_fun um_aux he tl =
411 let tl' = List.map um_aux tl in
414 Cic.Appl l -> Cic.Appl (l@tl')
415 | he' -> Cic.Appl (he'::tl')
418 apply_subst_gen ~appl_fun
420 let ppterm subst term = CicPp.ppterm (apply_subst subst term)
422 (* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
423 (* performs as (apply_subst subst t) until it finds an application of *)
424 (* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
425 (* a new beta-redex; in this case up to [reductions_no] consecutive *)
426 (* beta-reductions are performed. *)
427 (* Hint: this function is usually called when [reductions_no] *)
428 (* eta-expansions have been performed and the head of the new *)
429 (* application has been unified with (META [meta_to_reduce]): *)
430 (* during the unwinding the eta-expansions are undone. *)
432 let apply_subst_reducing meta_to_reduce =
433 let appl_fun um_aux he tl =
434 let tl' = List.map um_aux tl in
437 Cic.Appl l -> Cic.Appl (l@tl')
438 | he' -> Cic.Appl (he'::tl')
441 match meta_to_reduce, he with
442 Some (mtr,reductions_no), Cic.Meta (m,_) when m = mtr ->
443 let rec beta_reduce =
445 (n,(Cic.Appl (Cic.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
446 let he'' = CicSubstitution.subst he' t in
450 beta_reduce (n-1,Cic.Appl(he''::tl'))
453 beta_reduce (reductions_no,t')
457 apply_subst_gen ~appl_fun
459 let rec apply_subst_context subst context =
463 | Some (n, Cic.Decl t) ->
464 let t' = apply_subst subst t in
465 Some (n, Cic.Decl t') :: context
466 | Some (n, Cic.Def (t, ty)) ->
470 | Some ty -> Some (apply_subst subst ty)
472 let t' = apply_subst subst t in
473 Some (n, Cic.Def (t', ty')) :: context
474 | None -> None :: context)
477 let apply_subst_metasenv subst metasenv =
479 (fun (n, context, ty) ->
480 (n, apply_subst_context subst context, apply_subst subst ty))
482 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
485 let ppterm subst term = CicPp.ppterm (apply_subst subst term)
487 let ppterm_in_context subst term name_context =
488 CicPp.pp (apply_subst subst term) name_context
490 let ppcontext' ?(sep = "\n") subst context =
491 let separate s = if s = "" then "" else s ^ sep in
493 (fun context_entry (i,name_context) ->
494 match context_entry with
495 Some (n,Cic.Decl t) ->
496 sprintf "%s%s : %s" (separate i) (CicPp.ppname n)
497 (ppterm_in_context subst t name_context), (Some n)::name_context
498 | Some (n,Cic.Def (bo,ty)) ->
499 sprintf "%s%s : %s := %s" (separate i) (CicPp.ppname n)
502 | Some ty -> ppterm_in_context subst ty name_context)
503 (ppterm_in_context subst bo name_context), (Some n)::name_context
505 sprintf "%s_ :? _" (separate i), None::name_context
508 let ppcontext ?sep subst context = fst (ppcontext' ?sep subst context)
510 let ppmetasenv ?(sep = "\n") metasenv subst =
514 let context,name_context = ppcontext' ~sep:"; " subst c in
515 sprintf "%s |- ?%d: %s" context i
516 (ppterm_in_context subst t name_context))
518 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
521 (* UNWIND THE MGU INSIDE THE MGU *)
523 let unwind_subst metasenv subst =
525 (fun (unwinded,metasenv) (i,_) ->
526 let (_,canonical_context,_) = CicUtil.lookup_meta i metasenv in
527 let identity_relocation_list =
528 CicMkImplicit.identity_relocation_list_for_metavariable canonical_context
530 let (_,metasenv',subst') =
531 unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
534 ) ([],metasenv) subst
537 (* From now on we recreate a kernel abstraction where substitutions are part of
540 let lift subst n term =
541 let term = apply_subst subst term in
543 CicSubstitution.lift n term
545 raise (MetaSubstFailure ("Lift failure: " ^ Printexc.to_string e))
547 let subst subst t1 t2 =
548 let t1 = apply_subst subst t1 in
549 let t2 = apply_subst subst t2 in
551 CicSubstitution.subst t1 t2
553 raise (MetaSubstFailure ("Subst failure: " ^ Printexc.to_string e))
555 let whd subst context term =
556 let term = apply_subst subst term in
557 let context = apply_subst_context subst context in
559 CicReduction.whd context term
561 raise (MetaSubstFailure ("Weak head reduction failure: " ^
562 Printexc.to_string e))
564 let are_convertible subst context t1 t2 =
565 let context = apply_subst_context subst context in
566 let t1 = apply_subst subst t1 in
567 let t2 = apply_subst subst t2 in
568 CicReduction.are_convertible context t1 t2
570 let tempi_type_of_aux_subst = ref 0.0;;
571 let tempi_type_of_aux = ref 0.0;;
573 let type_of_aux' metasenv subst context term =
574 let time1 = Unix.gettimeofday () in
575 let term = apply_subst subst term in
576 let context = apply_subst_context subst context in
579 (fun (i, c, t) -> (i, apply_subst_context subst c, apply_subst subst t))
581 (fun (i, _, _) -> not (List.exists (fun (j, _) -> (j = i)) subst))
584 let time2 = Unix.gettimeofday () in
587 CicTypeChecker.type_of_aux' metasenv context term
588 with CicTypeChecker.TypeCheckerFailure msg ->
589 raise (MetaSubstFailure ("Type checker failure: " ^ msg))
591 let time3 = Unix.gettimeofday () in
592 tempi_type_of_aux_subst := !tempi_type_of_aux_subst +. time3 -. time1 ;
593 tempi_type_of_aux := !tempi_type_of_aux +. time2 -. time1 ;