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 let debug = ref false;;
19 prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
24 let time1 = Unix.gettimeofday () in
25 indent := !indent ^ String.make 1 c;
26 times := time1 :: !times;
27 prerr_endline ("{{{" ^ !indent ^ " ")
33 let time2 = Unix.gettimeofday () in
35 match !times with time1::tl -> times := tl; time1 | [] -> assert false in
36 prerr_endline ("}}} " ^ string_of_float (time2 -. time1));
38 | Some e -> prerr_endline ("exception raised: " ^ Printexc.to_string e)
41 indent := String.sub !indent 0 (String.length !indent -1)
43 Invalid_argument _ -> indent := "??"; ()
47 exception MetaSubstFailure of string Lazy.t
48 exception Uncertain of string Lazy.t
51 let maxmeta = ref 0 in
52 (fun () -> incr maxmeta; !maxmeta),
56 exception NotFound of [`NotInTheList | `NotWellTyped];;
58 let position to_skip n (shift, lc) =
60 | NCic.Irl len when n <= shift + to_skip || n > shift + len ->
61 raise (NotFound `NotInTheList)
62 | NCic.Irl _ -> n - shift
64 let rec aux to_skip k = function
65 | [] -> raise (NotFound `NotInTheList)
66 | _ :: tl when to_skip > 0 -> aux (to_skip - 1) (k+1) tl
67 | (NCic.Rel m)::_ when m + shift = n -> k
68 | _::tl -> aux to_skip (k+1) tl
74 let rec are_contiguous k = function
76 | (NCic.Rel j) :: tl when j = k+1 -> are_contiguous j tl
80 | _, NCic.Ctx [] -> 0, NCic.Irl 0
81 | shift, NCic.Ctx (NCic.Rel k::tl as l) when are_contiguous k tl ->
82 shift+k-1, NCic.Irl (List.length l)
88 let mk_perforated_irl shift len restrictions =
91 if List.mem (n+shift) restrictions then aux (n-1)
92 else (NCic.Rel n) :: aux (n-1)
94 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
99 let purge_restricted restrictions more_restrictions l =
100 if more_restrictions = [] then l
103 pp (lazy ("TO BE RESTRICTED: " ^
104 (String.concat "," (List.map string_of_int restrictions))));
105 pp (lazy ("MORE RESTRICTIONS: " ^
106 (String.concat "," (List.map string_of_int more_restrictions))));
108 let lc = NCicUtils.expand_local_context lc in
112 | _ when List.mem n restrictions -> aux (n+1) lc
113 | _::tl when List.mem n more_restrictions -> aux (n+1) tl
114 | he::tl -> he::aux (n+1) tl
116 pack_lc (shift, NCic.Ctx (aux 1 lc))
120 let rec force_does_not_occur status metasenv subst restrictions t =
121 let rec aux k ms = function
122 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
123 | NCic.Rel r as orig ->
125 List.length (List.filter (fun x -> x < r - k) restrictions)
127 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
128 | NCic.Meta (n, (shift,lc as l)) as orig ->
130 let _,_,bo,_ = NCicUtils.lookup_subst n subst in
131 aux k ms (NCicSubstitution.subst_meta status l bo)
133 NCicUtils.Subst_not_found _ ->
134 (* we ignore the subst since restrict will take care of already
135 * instantiated/restricted metavariabels *)
136 let l = NCicUtils.expand_local_context lc in
137 let sl = List.map (NCicSubstitution.lift status shift) l in
138 let (metasenv,subst as ms), _, restrictions_for_n, l' =
140 (fun t (ms, i, restrictions_for_n, l) ->
142 (*pp (lazy ("L'ORLO DELLA FOSSA: k= " ^ string_of_int k ^ " shift=" ^
143 string_of_int shift ^ " t=" ^ status#ppterm ~metasenv ~subst ~context:[] t));*)
144 let ms, t = aux k ms t in
145 (*pp (lazy ("LA FOSSA: " ^ status#ppterm ~metasenv ~subst ~context:[] t));*)
146 ms, i-1, restrictions_for_n, t::l
148 ms, i-1, i::restrictions_for_n, l)
149 sl (ms, List.length l, [], [])
151 if restrictions_for_n = [] then
152 ms, if sl = l' then orig else (
153 (*pp (lazy ("FINITO: " ^ status#ppterm ~metasenv:[] ~subst:[]
154 ~context:[] (NCic.Meta (n,pack_lc (0, NCic.Ctx l')))));*)
155 NCic.Meta (n, pack_lc (0, NCic.Ctx l'))
158 let l' = pack_lc (0, NCic.Ctx l') in
159 let _ = pp (lazy ("restrictions for n are:" ^ String.concat "," (List.map string_of_int restrictions_for_n))) in
160 let metasenv, subst, newmeta, more_restricted =
161 restrict status metasenv subst n restrictions_for_n in
162 let _ = pp (lazy ("more restricted: " ^String.concat "," (List.map string_of_int more_restricted))) in
163 let l' = purge_restricted restrictions more_restricted l' in
164 (metasenv, subst), NCic.Meta (newmeta, l'))
165 | t -> NCicUntrusted.map_term_fold_a status (fun _ k -> k+1) k aux ms t
167 aux 0 (metasenv,subst) t
169 and force_does_not_occur_in_context status metasenv subst restrictions = function
170 | name, NCic.Decl t as orig ->
171 (* pp (lazy ("CCC: hd is" ^ status#ppterm ~metasenv:[] ~subst:[] ~context:[] t ^
172 "\nCCC: restrictions are:" ^ String.concat "," (List.map string_of_int restrictions)));*)
173 let (metasenv, subst), t' =
174 force_does_not_occur status metasenv subst restrictions t in
175 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
176 | name, NCic.Def (bo, ty) as orig ->
177 let (metasenv, subst), bo' =
178 force_does_not_occur status metasenv subst restrictions bo in
179 let (metasenv, subst), ty' =
180 force_does_not_occur status metasenv subst restrictions ty in
182 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
184 and erase_in_context status metasenv subst pos restrictions = function
185 | [] -> metasenv, subst, restrictions, []
187 let metasenv, subst, restricted, tl' =
188 erase_in_context status metasenv subst (pos+1) restrictions tl in
189 if List.mem pos restricted then
190 metasenv, subst, restricted, tl'
193 let metasenv, subst, hd' =
194 let delifted_restricted =
195 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
196 force_does_not_occur_in_context
197 status metasenv subst delifted_restricted hd
199 metasenv, subst, restricted,
200 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
202 metasenv, subst, (pos :: restricted), tl'
204 and restrict status metasenv subst i (restrictions as orig) =
205 assert (restrictions <> []);
207 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
209 let metasenv, subst, restrictions, newctx =
210 erase_in_context status metasenv subst 1 restrictions ctx in
211 let (metasenv, subst), newty =
212 force_does_not_occur status metasenv subst restrictions ty in
213 let (metasenv, subst), newbo =
214 force_does_not_occur status metasenv subst restrictions bo in
215 let j = newmeta () in
216 let subst_entry_j = j, (name, newctx, newbo, newty) in
217 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
218 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
220 subst_entry_j :: List.map
221 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst
223 let diff = List.filter (fun x -> not (List.mem x orig)) restrictions in
224 metasenv, new_subst, j, diff
225 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
226 ("Cannot restrict the context of the metavariable ?%d over "^^
227 "the hypotheses %s since ?%d is already instantiated "^^
228 "with %s and at least one of the hypotheses occurs in "^^
229 "the substituted term") i (String.concat ", "
230 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
231 (status#ppterm ~metasenv ~subst ~context:ctx bo))))
232 with NCicUtils.Subst_not_found _ ->
234 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
236 let metasenv, subst, restrictions, newctx =
237 erase_in_context status metasenv subst 1 restrictions ctx in
238 let (metasenv, subst), newty =
239 force_does_not_occur status metasenv subst restrictions ty in
240 let j = newmeta () in
241 let metasenv_entry = j, (name, newctx, newty) in
243 mk_perforated_irl 0 (List.length ctx) restrictions in
244 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
245 (* pp (lazy ("BBB: dopo1 \n" ^ NCicPp.ppsubst ~metasenv [subst_entry]));
246 pp (lazy ("BBB: dopo2 \n" ^ NCicPp.ppsubst ~metasenv (subst_entry::subst)));
247 pp (lazy ("BBB: dopo metasenv\n" ^ NCicPp.ppmetasenv ~subst [metasenv_entry]));*)
248 let diff = List.filter (fun x -> not (List.mem x orig)) restrictions in
250 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
252 subst_entry :: subst, j, diff
253 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
254 ("Cannot restrict the context of the metavariable ?%d "^^
255 "over the hypotheses %s since metavariable's type depends "^^
256 "on at least one of them") i (String.concat ", "
257 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
259 | NCicUtils.Meta_not_found _ -> assert false
262 let rec is_flexible status context ~subst = function
263 | NCic.Meta (i,lc) ->
265 let _,_,t,_ = NCicUtils.lookup_subst i subst in
266 let t = NCicSubstitution.subst_meta status lc t in
267 is_flexible status context ~subst t
268 with NCicUtils.Subst_not_found _ -> true)
269 | NCic.Appl (NCic.Meta (i,lc) :: args)->
271 let _,_,t,_ = NCicUtils.lookup_subst i subst in
272 let t = NCicSubstitution.subst_meta status lc t in
273 is_flexible status context ~subst
274 (NCicReduction.head_beta_reduce status ~delta:max_int
275 (NCic.Appl (t :: args)))
276 with NCicUtils.Subst_not_found _ -> true)
277 (* this is a cheap whd, it only performs zeta-reduction.
279 * it works when the **omissis** disambiguation algorithm
280 * is run on `let x := K a b in t`, K is substituted for a
281 * ? and thus in t metavariables have a flexible Rel
285 match List.nth context (i-1)
287 | _,NCic.Def (bo,_) ->
288 is_flexible status context ~subst
289 (NCicSubstitution.lift status i bo)
293 prerr_endline (Printf.sprintf "Rel %d inside context:\n%s" i
294 (status#ppcontext ~subst ~metasenv:[] context));
296 | Invalid_argument _ -> assert false)
300 let is_out_scope = function `OutScope _ -> true | _ -> false;;
301 let is_out_scope_tag = List.exists is_out_scope;;
302 let int_of_out_scope_tag tag =
303 match List.filter is_out_scope tag with [`OutScope n] -> n | _ -> assert false
308 exception TypeNotGood;;
310 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
311 otherwise the occur check does not make sense in case of unification
313 let delift status ~unify metasenv subst context n l t =
314 (*D*) inside 'D'; try let rc =
315 let is_in_scope_meta subst = function
318 let tag, _, _, _ = NCicUtils.lookup_subst i subst in
319 List.mem `InScope tag
320 with NCicUtils.Subst_not_found _ -> false)
323 let contains_in_scope subst t =
324 let rec aux _ () = function
325 | NCic.Meta _ as t ->
326 if is_in_scope_meta subst t then raise Found
329 if is_in_scope_meta subst t then raise Found
330 else NCicUtils.fold (fun _ () -> ()) () aux () t
332 try aux () () t; false with Found -> true
334 let unify_list in_scope =
336 | _, NCic.Irl _ -> fun _ _ _ _ _ -> None
337 | shift, NCic.Ctx l -> fun metasenv subst context k t ->
338 if is_flexible status context ~subst t || contains_in_scope subst t then None else
341 let t = NCicSubstitution.lift status (k+shift) t in
342 t, is_flexible status context ~subst t)
346 (fun (li,flexible) i ->
347 if flexible || i < in_scope then None else
348 match unify metasenv subst context li t with
349 | Some (metasenv,subst) ->
350 Some ((metasenv, subst), NCic.Rel (i+1+k))
354 let rec aux (context,k,in_scope) (metasenv, subst as ms) t =
355 match unify_list in_scope metasenv subst context k t with
359 | NCic.Rel n as t when n <= k -> ms, t
362 match List.nth context (n-1) with
363 | _,NCic.Def (bo,_) ->
364 (try ms, NCic.Rel ((position in_scope (n-k) l) + k)
365 with (NotFound `NotInTheList) ->
366 (* CSC: This bit of reduction hurts performances since it is
367 * possible to have an exponential explosion of the size of the
368 * proof. required for nat/nth_prime.ma *)
369 aux (context,k,in_scope) ms (NCicSubstitution.lift status n bo))
370 | _,NCic.Decl _ -> ms, NCic.Rel ((position in_scope (n-k) l) + k)
371 with Failure _ -> assert false) (*Unbound variable found in delift*)
372 | NCic.Meta (i,_) when i=n ->
373 raise (MetaSubstFailure (lazy (Printf.sprintf (
374 "Cannot unify the metavariable ?%d with a term that has "^^
375 "as subterm %s in which the same metavariable "^^
376 "occurs (occur check)") i
377 (status#ppterm ~context ~metasenv ~subst t))))
378 | NCic.Meta (i,l1) as orig ->
380 let tag,c,t,ty = NCicUtils.lookup_subst i subst in
381 let in_scope, clear =
382 if List.mem `InScope tag then 0, true
383 else if is_out_scope_tag tag then int_of_out_scope_tag tag,true
390 (i,([],c,t,ty)) :: List.filter (fun j,_ -> i <> j) subst
392 aux (context,k,in_scope) ms (NCicSubstitution.subst_meta status l1 t)
393 with NCicUtils.Subst_not_found _ ->
394 if snd l1 = NCic.Irl 0 || snd l1 = NCic.Ctx [] then ms, orig
396 let shift1,lc1 = l1 in
398 let shift = shift + k in
400 | NCic.Irl len, NCic.Irl len1
401 when shift1 + len1 < shift || shift1 > shift + len ->
402 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
403 let metasenv, subst, newmeta, more_restricted =
404 restrict status metasenv subst i restrictions in
405 let l' = (0,NCic.Irl (max 0 (k-shift1))) in
406 let l' = purge_restricted restrictions more_restricted l' in
407 (metasenv, subst),NCic.Meta (newmeta,l')
408 | NCic.Irl len, NCic.Irl len1 ->
409 let low_restrictions, new_shift =
410 if k <= shift1 && shift1 < shift then
411 HExtlib.list_seq 1 (shift - shift1 + 1), k
412 else if shift1 < k (* <= shift *) then
413 let save_below = k - shift1 in
414 HExtlib.list_seq (save_below + 1) (shift - shift1 + 1),
416 else [], shift1 - shift + k
418 let high_restrictions =
419 let last = shift + len in
420 let last1 = shift1 + len1 in
422 let high_gap = last1 - last in
423 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
426 let restrictions = low_restrictions @ high_restrictions in
427 if restrictions = [] then
428 if shift = k then ms, orig
429 else ms, NCic.Meta (i, (new_shift, lc1))
431 let metasenv, subst, newmeta, more_restricted =
432 restrict status metasenv subst i restrictions in
433 let newlc_len = len1 - List.length restrictions in
434 let l' = new_shift, NCic.Irl newlc_len in
435 let l' = purge_restricted restrictions more_restricted l' in
436 (metasenv, subst),NCic.Meta(newmeta,l')
439 let lc1 = NCicUtils.expand_local_context lc1 in
440 let lc1 = List.map (NCicSubstitution.lift status shift1) lc1 in
441 let rec deliftl tbr j ms = function
444 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
446 let ms, t = aux (context,k,in_scope) ms t in
449 | (NotFound `NotInTheList) | MetaSubstFailure _ -> ms, j::tbr, tl
451 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
452 pp (lazy ("TO BE RESTRICTED: " ^
453 (String.concat "," (List.map string_of_int to_be_r))));
454 let l1 = pack_lc (0, NCic.Ctx lc1') in
455 pp (lazy ("newmeta:" ^ status#ppterm
456 ~metasenv ~subst ~context (NCic.Meta (999,l1))));
457 pp (lazy (status#ppmetasenv ~subst metasenv));
460 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
462 let metasenv, subst, newmeta, more_restricted =
463 restrict status metasenv subst i to_be_r in
464 let l1 = purge_restricted to_be_r more_restricted l1 in
465 (metasenv, subst), NCic.Meta(newmeta,l1))
468 NCicUntrusted.map_term_fold_a status
469 (fun e (c,k,s) -> (e::c,k+1,s)) (context,k,in_scope) aux ms t
473 "DELIFTO " ^ status#ppterm ~metasenv ~subst ~context t ^ " w.r.t. " ^
474 status#ppterm ~metasenv ~subst ~context (NCic.Meta(n,l)) ^ " i.e. " ^
475 String.concat ", " (List.map (status#ppterm ~metasenv ~subst ~context) (
477 (List.map (NCicSubstitution.lift status shift)
478 (NCicUtils.expand_local_context lc))
482 (*assert (try n = -1 or (ignore(NCicUtils.lookup_meta n metasenv); true) with NCicUtils.Meta_not_found _ -> false);*)
483 let ((metasenv,subst),t) as res = aux (context,0,0) (metasenv,subst) t in
484 if (try n <> -1 && (ignore(NCicUtils.lookup_meta n metasenv); false)
485 with NCicUtils.Meta_not_found _ -> true)
487 let _,context,bo,_ = NCicUtils.lookup_subst n subst in
488 match unify metasenv subst context bo t with
489 None -> raise (NotFound `NotWellTyped)
490 | Some (metasenv,subst) -> (metasenv,subst),t
493 let _,context,ty = NCicUtils.lookup_meta n metasenv in
496 NCic.Sort _ -> (* could be algebraic *) NCic.Implicit `Closed
497 | _ -> NCicTypeChecker.typeof status ~subst ~metasenv context t in
501 NCic.Sort _ | NCic.Meta _ | NCic.Implicit _ -> res
502 | _ -> raise TypeNotGood)
503 | _,NCic.Implicit _ ->
505 NCic.Sort _ | NCic.Meta _ | NCic.Implicit _ -> res
506 | _ -> raise TypeNotGood)
509 NCicReduction.are_convertible status ~metasenv ~subst context ty' ty
515 NCicUtils.Meta_not_found _ ->
516 (* Fake metavariable used in NTacStatus and NCicRefiner :-( *)
518 | NCicTypeChecker.TypeCheckerFailure msg ->
519 HLog.error "----------- Problem with Dependent Types ----------";
520 HLog.error (Lazy.force msg) ;
521 HLog.error "---------------------------------------------------";
522 raise (NotFound `NotWellTyped)
524 | NCicTypeChecker.AssertFailure _
525 | NCicReduction.AssertFailure _
526 | NCicTypeChecker.TypeCheckerFailure _ ->
527 raise (NotFound `NotWellTyped))
528 with NotFound reason ->
529 (* This is the case where we fail even first order unification. *)
530 (* The reason is that our delift function is weaker than first *)
531 (* order (in the sense of alpha-conversion). See comment above *)
532 (* related to the delift function. *)
535 `NotInTheList -> "some variable cannot be delifted"
536 | `NotWellTyped -> "the unifier found is not well typed" in
537 let msg = (lazy (Printf.sprintf
538 ("Error trying to abstract %s over [%s]: %s")
539 (status#ppterm ~metasenv ~subst
540 ~context t) (String.concat "; " (List.map (status#ppterm ~metasenv
541 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
542 status shift) (NCicUtils.expand_local_context lc)))) reason))
545 let lc = NCicUtils.expand_local_context lc in
546 let l = List.map (NCicSubstitution.lift status shift) lc in
548 List.exists (fun t-> NCicUntrusted.metas_of_term status subst context t <> [])l
550 raise (Uncertain msg)
552 raise (MetaSubstFailure msg)
553 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
556 let mk_meta ?(attrs=[]) metasenv context ?with_type kind =
557 assert(kind <> `IsSort || context = []);
558 let n = newmeta () in
559 let ty= match with_type with None-> NCic.Implicit (`Typeof n)| Some x ->x in
560 let len = List.length context in
561 let attrs = NCicUntrusted.set_kind kind attrs in
562 let menv_entry = (n, (attrs, context, ty)) in
563 menv_entry :: metasenv, n, NCic.Meta (n, (0,NCic.Irl len)), ty
566 let extend_meta metasenv n =
568 let attrs,cc,ty = NCicUtils.lookup_meta n metasenv in
570 | NCic.Implicit (`Typeof _) ->
571 let mk_meta context kind =
572 let metasenv, _, ty, _ = mk_meta metasenv context kind in
573 (n, (attrs, cc, ty)) :: List.filter (fun x,_ -> x <> n) metasenv, ty
575 (match NCicUntrusted.kind_of_meta attrs with
577 | `IsType -> mk_meta [] `IsSort
578 | `IsTerm -> mk_meta cc `IsType)
579 | ty -> metasenv, ty)
580 with NCicUtils.Meta_not_found _ -> assert false
583 let saturate status ?(delta=0) metasenv subst context ty goal_arity =
584 assert (goal_arity >= 0);
585 let rec aux metasenv = function
586 | NCic.Prod (name,s,t) as ty ->
587 let metasenv1, _, arg,_ =
588 mk_meta ~attrs:[`Name name] metasenv context ~with_type:s `IsTerm in
589 let t, metasenv1, args, pno =
590 aux metasenv1 (NCicSubstitution.subst status arg t)
592 if pno + 1 = goal_arity then
593 ty, metasenv, [], goal_arity+1
595 t, metasenv1, arg::args, pno+1
597 match NCicReduction.whd status ~subst context ty ~delta with
598 | NCic.Prod _ as ty -> aux metasenv ty
599 | ty -> ty, metasenv, [], 0
601 let res, newmetasenv, arguments, _ = aux metasenv ty in
602 res, newmetasenv, arguments