2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
14 exception MetaSubstFailure of string Lazy.t
15 exception Uncertain of string Lazy.t
18 (*** Functions to apply a substitution ***)
20 let apply_subst_gen ~appl_fun subst term =
23 let module S = CicSubstitution in
26 | C.Var (uri,exp_named_subst) ->
27 let exp_named_subst' =
28 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
30 C.Var (uri, exp_named_subst')
33 let (_, t,_) = lookup_subst i subst in
34 um_aux (S.subst_meta l t)
35 with CicUtil.Subst_not_found _ ->
36 (* unconstrained variable, i.e. free in subst*)
38 List.map (function None -> None | Some t -> Some (um_aux t)) l
42 | C.Implicit _ as t -> t
43 | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
44 | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
45 | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
46 | C.LetIn (n,s,ty,t) -> C.LetIn (n, um_aux s, um_aux ty, um_aux t)
47 | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
48 | C.Appl _ -> assert false
49 | C.Const (uri,exp_named_subst) ->
50 let exp_named_subst' =
51 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
53 C.Const (uri, exp_named_subst')
54 | C.MutInd (uri,typeno,exp_named_subst) ->
55 let exp_named_subst' =
56 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
58 C.MutInd (uri,typeno,exp_named_subst')
59 | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
60 let exp_named_subst' =
61 List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
63 C.MutConstruct (uri,typeno,consno,exp_named_subst')
64 | C.MutCase (sp,i,outty,t,pl) ->
65 let pl' = List.map um_aux pl in
66 C.MutCase (sp, i, um_aux outty, um_aux t, pl')
69 List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
74 List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
82 let appl_fun um_aux he tl =
83 let tl' = List.map um_aux tl in
86 Cic.Appl l -> Cic.Appl (l@tl')
87 | he' -> Cic.Appl (he'::tl')
91 Cic.Meta (m,_) -> CicReduction.head_beta_reduce t'
96 (* incr apply_subst_counter; *)
99 | _ -> apply_subst_gen ~appl_fun subst t
102 let profiler = HExtlib.profile "U/CicMetaSubst.apply_subst"
103 let apply_subst s t =
104 profiler.HExtlib.profile (apply_subst s) t
107 let apply_subst_context subst context =
112 incr apply_subst_context_counter;
113 context_length := !context_length + List.length context;
118 | Some (n, Cic.Decl t) ->
119 let t' = apply_subst subst t in
120 Some (n, Cic.Decl t') :: context
121 | Some (n, Cic.Def (t, ty)) ->
122 let ty' = apply_subst subst ty in
123 let t' = apply_subst subst t in
124 Some (n, Cic.Def (t', ty')) :: context
125 | None -> None :: context)
128 let apply_subst_metasenv subst metasenv =
130 incr apply_subst_metasenv_counter;
131 metasenv_length := !metasenv_length + List.length metasenv;
137 (fun (n, context, ty) ->
138 (n, apply_subst_context subst context, apply_subst subst ty))
140 (fun (i, _, _) -> not (List.mem_assoc i subst))
143 let tempi_type_of_aux_subst = ref 0.0;;
144 let tempi_subst = ref 0.0;;
145 let tempi_type_of_aux = ref 0.0;;
149 let maxmeta = ref 0 in
150 fun () -> incr maxmeta; !maxmeta
153 exception NotInTheList;;
155 let position n (shift, lc) =
157 | NCic.Irl len when n <= shift || n > shift + len -> raise NotInTheList
158 | NCic.Irl _ -> n - shift
160 let rec aux k = function
161 | [] -> raise NotInTheList
162 | (NCic.Rel m)::_ when m + shift = n -> k
163 | _::tl -> aux (k+1) tl
169 let rec are_contiguous k = function
171 | (NCic.Rel j) :: tl when j = k+1 -> are_contiguous j tl
175 | _, NCic.Ctx [] -> 0, NCic.Irl 0
176 | shift, NCic.Ctx (NCic.Rel k::tl as l) when are_contiguous k tl ->
177 shift+k-1, NCic.Irl (List.length l)
182 let mk_restricted_irl shift len restrictions =
185 if List.mem (n+shift) restrictions then aux (n-1)
188 pack_lc (shift, NCic.Irl (aux len))
192 let mk_perforated_irl shift len restrictions =
194 if n = 0 then [] else
195 if List.mem (n+shift) restrictions then aux (n-1)
196 else (NCic.Rel n) :: aux (n-1)
198 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
203 let rec force_does_not_occur metasenv subst restrictions t =
204 let rec aux k ms = function
205 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
206 | NCic.Rel r as orig ->
208 List.length (List.filter (fun x -> x < r - k) restrictions)
210 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
211 | NCic.Meta (n, l) as orig ->
212 (* we ignore the subst since restrict will take care of already
213 * instantiated/restricted metavariabels *)
214 let (metasenv,subst as ms), restrictions_for_n, l' =
216 | shift, NCic.Irl len ->
219 (fun i -> i > shift && i <= shift + len) restrictions in
220 ms, restrictions, mk_restricted_irl shift len restrictions
221 | shift, NCic.Ctx l ->
222 let ms, _, restrictions_for_n, l =
224 (fun t (ms, i, restrictions_for_n, l) ->
226 let ms, t = aux (k-shift) ms t in
227 ms, i-1, restrictions_for_n, t::l
229 ms, i-1, i::restrictions_for_n, l)
230 l (ms, List.length l, [], [])
232 ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
234 if restrictions_for_n = [] then
235 ms, if l = l' then orig else NCic.Meta (n, l')
237 let metasenv, subst, newmeta =
238 restrict metasenv subst n restrictions_for_n
240 (metasenv, subst), NCic.Meta (newmeta, l')
241 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
243 aux 0 (metasenv,subst) t
245 and force_does_not_occur_in_context metasenv subst restrictions = function
246 | name, NCic.Decl t as orig ->
247 let (metasenv, subst), t' =
248 force_does_not_occur metasenv subst restrictions t in
249 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
250 | name, NCic.Def (bo, ty) as orig ->
251 let (metasenv, subst), bo' =
252 force_does_not_occur metasenv subst restrictions bo in
253 let (metasenv, subst), ty' =
254 force_does_not_occur metasenv subst restrictions ty in
256 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
258 and erase_in_context metasenv subst pos restrictions = function
259 | [] -> metasenv, subst, restrictions, []
261 let metasenv, subst, restricted, tl' =
262 erase_in_context metasenv subst (pos+1) restrictions tl in
263 if List.mem pos restricted then
264 metasenv, subst, restricted, tl'
267 let metasenv, subst, hd' =
268 let delifted_restricted =
269 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
270 force_does_not_occur_in_context
271 metasenv subst delifted_restricted hd
273 metasenv, subst, restricted,
274 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
276 metasenv, subst, (pos :: restricted), tl'
278 and restrict metasenv subst i restrictions =
279 assert (restrictions <> []);
281 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
283 let metasenv, subst, restrictions, newctx =
284 erase_in_context metasenv subst 1 restrictions ctx in
285 let (metasenv, subst), newty =
286 force_does_not_occur metasenv subst restrictions ty in
287 let (metasenv, subst), newbo =
288 force_does_not_occur metasenv subst restrictions bo in
289 let j = newmeta () in
290 let subst_entry_j = j, (name, newctx, newty, newbo) in
291 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
292 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
294 subst_entry_j :: List.map
295 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst,
297 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
298 ("Cannot restrict the context of the metavariable ?%d over "^^
299 "the hypotheses %s since ?%d is already instantiated "^^
300 "with %s and at least one of the hypotheses occurs in "^^
301 "the substituted term") i (String.concat ", "
302 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
303 (NCicPp.ppterm ~metasenv ~subst ~context:ctx bo))))
304 with NCicUtils.Subst_not_found _ ->
306 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
308 let metasenv, subst, restrictions, newctx =
309 erase_in_context metasenv subst 1 restrictions ctx in
310 let (metasenv, subst), newty =
311 force_does_not_occur metasenv subst restrictions ty in
312 let j = newmeta () in
313 let metasenv_entry = j, (name, newctx, newty) in
315 mk_perforated_irl 0 (List.length ctx) restrictions in
316 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
318 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
320 subst_entry :: subst, j
321 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
322 ("Cannot restrict the context of the metavariable ?%d "^^
323 "over the hypotheses %s since metavariable's type depends "^^
324 "on at least one of them") i (String.concat ", "
325 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
327 | NCicUtils.Meta_not_found _ -> assert false
330 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
331 otherwise the occur check does not make sense in case of unification
333 let delift metasenv subst context n l t =
334 let rec aux k (metasenv, subst as ms) = function
335 | NCic.Rel n as t when n <= k -> ms, t
338 match List.nth context (n-k-1) with
339 | _,NCic.Def (bo,_) ->
340 (try ms, NCic.Rel ((position (n-k) l) + k)
342 (* CSC: This bit of reduction hurts performances since it is
343 * possible to have an exponential explosion of the size of the
344 * proof. required for nat/nth_prime.ma *)
345 aux k ms (NCicSubstitution.lift n bo))
346 | _,NCic.Decl _ -> ms, NCic.Rel ((position (n-k) l) + k)
347 with Failure _ -> assert false) (*Unbound variable found in delift*)
348 | NCic.Meta (_,(_,(NCic.Irl 0| NCic.Ctx []))) as orig -> ms, orig
349 | NCic.Meta (i,l1) as orig ->
351 let _,_,t,_ = NCicUtils.lookup_subst i subst in
352 aux k ms (NCicSubstitution.subst_meta l1 t)
353 with NCicUtils.Subst_not_found _ ->
354 (* see the top level invariant *)
356 raise (MetaSubstFailure (lazy (Printf.sprintf (
357 "Cannot unify the metavariable ?%d with a term that has "^^
358 "as subterm %s in which the same metavariable "^^
359 "occurs (occur check)") i
360 (NCicPp.ppterm ~context ~metasenv ~subst t))))
362 let shift1,lc1 = l1 in
364 let shift = shift + k in
365 let _ = prerr_endline ("XXX restringo " ^ string_of_int i) in
367 | NCic.Irl len, NCic.Irl len1
368 when shift1 + len1 < shift || shift1 > shift + len ->
369 prerr_endline "WWW 1";
370 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
371 let metasenv, subst, newmeta =
372 restrict metasenv subst i restrictions
375 NCic.Meta (newmeta, (0,NCic.Irl (max 0 (k-shift1))))
376 | NCic.Irl len, NCic.Irl len1
377 when shift1 < shift || len1 + shift1 > len + shift ->
378 (* C. Hoare. Premature optimization is the root of all evil*)
379 prerr_endline ("WWW 2 : " ^ string_of_int i);
380 let stop = shift + len in
381 let stop1 = shift1 + len1 in
382 let low_gap = max 0 (shift - shift1) in
383 let high_gap = max 0 (stop1 - stop) in
385 HExtlib.list_seq (k+1-shift1) (low_gap + 1) @
386 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
388 let metasenv, subst, newmeta =
389 restrict metasenv subst i restrictions
391 prerr_endline ("RESTRICTIONS FOR: " ^
392 NCicPp.ppterm ~metasenv ~subst ~context:[]
394 " that was part of a term unified with " ^
395 NCicPp.ppterm ~metasenv ~subst ~context:[]
396 (NCic.Meta (n,l)) ^ " ====> " ^
397 String.concat "," (List.map string_of_int restrictions)
398 ^ "\nMENV:\n" ^ NCicPp.ppmetasenv ~subst metasenv
399 ^ "\nSUBST:\n" ^ NCicPp.ppsubst subst ~metasenv
402 assert (if shift1 > k then shift1 + low_gap - shift = 0 else
404 NCic.Irl (len1 - low_gap - high_gap + max 0 (k - shift1)) in
406 NCic.Meta(newmeta,(shift1 + low_gap - shift, newlc))
408 (metasenv, subst), meta
410 | NCic.Irl _, NCic.Irl _ when shift = 0 -> ms, orig
411 | NCic.Irl _, NCic.Irl _ ->
412 ms, NCic.Meta (i, (max 0 (shift1 - shift), lc1))
414 let lc1 = NCicUtils.expand_local_context lc1 in
415 let rec deliftl tbr j ms = function
418 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
420 let ms, t = aux (k-shift1) ms t in
423 | NotInTheList | MetaSubstFailure _ -> ms, j::tbr, tl
425 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
427 prerr_endline ("TO BE RESTRICTED: " ^
428 (String.concat "," (List.map string_of_int to_be_r)));
430 let l1 = pack_lc (shift, NCic.Ctx lc1') in
433 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
435 let metasenv, subst, newmeta =
436 restrict metasenv subst i to_be_r in
437 (metasenv, subst), NCic.Meta(newmeta,l1))
438 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
440 try aux 0 (metasenv,subst) t
442 (* This is the case where we fail even first order unification. *)
443 (* The reason is that our delift function is weaker than first *)
444 (* order (in the sense of alpha-conversion). See comment above *)
445 (* related to the delift function. *)
446 let msg = (lazy (Printf.sprintf
447 ("Error trying to abstract %s over [%s]: the algorithm only tried to "^^
448 "abstract over bound variables") (NCicPp.ppterm ~metasenv ~subst
449 ~context t) (String.concat "; " (List.map (NCicPp.ppterm ~metasenv
450 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
451 shift) (NCicUtils.expand_local_context lc))))))
454 let lc = NCicUtils.expand_local_context lc in
455 let l = List.map (NCicSubstitution.lift shift) lc in
458 (fun t -> NCicUntrusted.metas_of_term subst context t = [])
461 raise (Uncertain msg)
463 raise (MetaSubstFailure msg)
467 (* delifts a term t of n levels strating from k, that is changes (Rel m)
468 * to (Rel (m - n)) when m > (k + n). if k <= m < k + n delift fails
470 let delift_rels_from subst metasenv k n =
471 let rec liftaux subst metasenv k =
472 let module C = Cic in
477 else if m < k + n then
478 raise DeliftingARelWouldCaptureAFreeVariable
480 C.Rel (m - n), subst, metasenv
481 | C.Var (uri,exp_named_subst) ->
482 let exp_named_subst',subst,metasenv =
484 (fun (uri,t) (l,subst,metasenv) ->
485 let t',subst,metasenv = liftaux subst metasenv k t in
486 (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
488 C.Var (uri,exp_named_subst'),subst,metasenv
491 let (_, t,_) = lookup_subst i subst in
492 liftaux subst metasenv k (CicSubstitution.subst_meta l t)
493 with CicUtil.Subst_not_found _ ->
494 let l',to_be_restricted,subst,metasenv =
495 let rec aux con l subst metasenv =
497 [] -> [],[],subst,metasenv
499 let tl',to_be_restricted,subst,metasenv =
500 aux (con + 1) tl subst metasenv in
501 let he',more_to_be_restricted,subst,metasenv =
503 None -> None,[],subst,metasenv
506 let t',subst,metasenv = liftaux subst metasenv k t in
507 Some t',[],subst,metasenv
509 DeliftingARelWouldCaptureAFreeVariable ->
510 None,[i,con],subst,metasenv
512 he'::tl',more_to_be_restricted@to_be_restricted,subst,metasenv
514 aux 1 l subst metasenv in
515 let metasenv,subst = restrict subst to_be_restricted metasenv in
516 C.Meta(i,l'),subst,metasenv)
517 | C.Sort _ as t -> t,subst,metasenv
518 | C.Implicit _ as t -> t,subst,metasenv
520 let te',subst,metasenv = liftaux subst metasenv k te in
521 let ty',subst,metasenv = liftaux subst metasenv k ty in
522 C.Cast (te',ty'),subst,metasenv
524 let s',subst,metasenv = liftaux subst metasenv k s in
525 let t',subst,metasenv = liftaux subst metasenv (k+1) t in
526 C.Prod (n,s',t'),subst,metasenv
527 | C.Lambda (n,s,t) ->
528 let s',subst,metasenv = liftaux subst metasenv k s in
529 let t',subst,metasenv = liftaux subst metasenv (k+1) t in
530 C.Lambda (n,s',t'),subst,metasenv
531 | C.LetIn (n,s,ty,t) ->
532 let s',subst,metasenv = liftaux subst metasenv k s in
533 let ty',subst,metasenv = liftaux subst metasenv k ty in
534 let t',subst,metasenv = liftaux subst metasenv (k+1) t in
535 C.LetIn (n,s',ty',t'),subst,metasenv
537 let l',subst,metasenv =
539 (fun t (l,subst,metasenv) ->
540 let t',subst,metasenv = liftaux subst metasenv k t in
541 t'::l,subst,metasenv) l ([],subst,metasenv) in
542 C.Appl l',subst,metasenv
543 | C.Const (uri,exp_named_subst) ->
544 let exp_named_subst',subst,metasenv =
546 (fun (uri,t) (l,subst,metasenv) ->
547 let t',subst,metasenv = liftaux subst metasenv k t in
548 (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
550 C.Const (uri,exp_named_subst'),subst,metasenv
551 | C.MutInd (uri,tyno,exp_named_subst) ->
552 let exp_named_subst',subst,metasenv =
554 (fun (uri,t) (l,subst,metasenv) ->
555 let t',subst,metasenv = liftaux subst metasenv k t in
556 (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
558 C.MutInd (uri,tyno,exp_named_subst'),subst,metasenv
559 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
560 let exp_named_subst',subst,metasenv =
562 (fun (uri,t) (l,subst,metasenv) ->
563 let t',subst,metasenv = liftaux subst metasenv k t in
564 (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
566 C.MutConstruct (uri,tyno,consno,exp_named_subst'),subst,metasenv
567 | C.MutCase (sp,i,outty,t,pl) ->
568 let outty',subst,metasenv = liftaux subst metasenv k outty in
569 let t',subst,metasenv = liftaux subst metasenv k t in
570 let pl',subst,metasenv =
572 (fun t (l,subst,metasenv) ->
573 let t',subst,metasenv = liftaux subst metasenv k t in
574 t'::l,subst,metasenv) pl ([],subst,metasenv)
576 C.MutCase (sp,i,outty',t',pl'),subst,metasenv
578 let len = List.length fl in
579 let liftedfl,subst,metasenv =
581 (fun (name, i, ty, bo) (l,subst,metasenv) ->
582 let ty',subst,metasenv = liftaux subst metasenv k ty in
583 let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
584 (name,i,ty',bo')::l,subst,metasenv
585 ) fl ([],subst,metasenv)
587 C.Fix (i, liftedfl),subst,metasenv
589 let len = List.length fl in
590 let liftedfl,subst,metasenv =
592 (fun (name, ty, bo) (l,subst,metasenv) ->
593 let ty',subst,metasenv = liftaux subst metasenv k ty in
594 let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
595 (name,ty',bo')::l,subst,metasenv
596 ) fl ([],subst,metasenv)
598 C.CoFix (i, liftedfl),subst,metasenv
600 liftaux subst metasenv k
602 let delift_rels subst metasenv n t =
603 delift_rels_from subst metasenv 1 n t
606 let mk_meta ?name metasenv context ty =
609 let n = newmeta () in
610 let ty = NCic.Implicit (`Typeof n) in
611 let menv_entry = (n, (name, context, ty)) in
612 menv_entry :: metasenv,NCic.Meta (n, (0,NCic.Irl (List.length context))), ty
615 let context_for_ty = if ty = `Type then [] else context in
616 let n = newmeta () in
617 let ty_menv_entry = (n, (name,context_for_ty, NCic.Implicit (`Typeof n))) in
618 let m = newmeta () in
619 let ty = NCic.Meta (n, (0,NCic.Irl (List.length context_for_ty))) in
620 let menv_entry = (m, (name, context, ty)) in
621 menv_entry :: ty_menv_entry :: metasenv,
622 NCic.Meta (m, (0,NCic.Irl (List.length context))), ty
624 let n = newmeta () in
625 let len = List.length context in
626 let menv_entry = (n, (name, context, ty)) in
627 menv_entry :: metasenv, NCic.Meta (n, (0,NCic.Irl len)), ty
630 let saturate ?(delta=0) metasenv context ty goal_arity =
631 assert (goal_arity >= 0);
632 let rec aux metasenv = function
633 | NCic.Prod (name,s,t) ->
634 let metasenv1, arg,_ =
635 mk_meta ~name:name metasenv context (`WithType s) in
636 let t, metasenv1, args, pno =
637 aux metasenv1 (NCicSubstitution.subst arg t)
639 if pno + 1 = goal_arity then
640 ty, metasenv, [], goal_arity+1
642 t, metasenv1, arg::args, pno+1
644 match NCicReduction.whd context ty ~delta with
645 | NCic.Prod _ as ty -> aux metasenv ty
646 | ty -> ty, metasenv, [], 0
648 let res, newmetasenv, arguments, _ = aux metasenv ty in
649 res, newmetasenv, arguments