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
50 let newmeta,maxmeta,pushmaxmeta,popmaxmeta =
51 let maxmeta = ref 0 in
52 let pushedmetas = ref [] in
53 (fun () -> incr maxmeta; !maxmeta),
55 (fun () -> pushedmetas := !maxmeta::!pushedmetas; maxmeta := 0),
56 (fun () -> match !pushedmetas with [] -> assert false | hd::tl -> pushedmetas := tl)
59 exception NotFound of [`NotInTheList | `NotWellTyped];;
61 let position to_skip n (shift, lc) =
63 | NCic.Irl len when n <= shift + to_skip || n > shift + len ->
64 raise (NotFound `NotInTheList)
65 | NCic.Irl _ -> n - shift
67 let rec aux to_skip k = function
68 | [] -> raise (NotFound `NotInTheList)
69 | _ :: tl when to_skip > 0 -> aux (to_skip - 1) (k+1) tl
70 | (NCic.Rel m)::_ when m + shift = n -> k
71 | _::tl -> aux to_skip (k+1) tl
77 let rec are_contiguous k = function
79 | (NCic.Rel j) :: tl when j = k+1 -> are_contiguous j tl
83 | _, NCic.Ctx [] -> 0, NCic.Irl 0
84 | shift, NCic.Ctx (NCic.Rel k::tl as l) when are_contiguous k tl ->
85 shift+k-1, NCic.Irl (List.length l)
91 let mk_perforated_irl shift len restrictions =
94 if List.mem (n+shift) restrictions then aux (n-1)
95 else (NCic.Rel n) :: aux (n-1)
97 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
102 let purge_restricted restrictions more_restrictions l =
103 if more_restrictions = [] then l
106 pp (lazy ("TO BE RESTRICTED: " ^
107 (String.concat "," (List.map string_of_int restrictions))));
108 pp (lazy ("MORE RESTRICTIONS: " ^
109 (String.concat "," (List.map string_of_int more_restrictions))));
111 let lc = NCicUtils.expand_local_context lc in
115 | _ when List.mem n restrictions -> aux (n+1) lc
116 | _::tl when List.mem n more_restrictions -> aux (n+1) tl
117 | he::tl -> he::aux (n+1) tl
119 pack_lc (shift, NCic.Ctx (aux 1 lc))
123 let rec force_does_not_occur status metasenv subst restrictions t =
124 let rec aux k ms = function
125 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
126 | NCic.Rel r as orig ->
128 List.length (List.filter (fun x -> x < r - k) restrictions)
130 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
131 | NCic.Meta (n, (shift,lc as l)) as orig ->
133 let _,_,bo,_ = NCicUtils.lookup_subst n subst in
134 aux k ms (NCicSubstitution.subst_meta status l bo)
136 NCicUtils.Subst_not_found _ ->
137 (* we ignore the subst since restrict will take care of already
138 * instantiated/restricted metavariabels *)
139 let l = NCicUtils.expand_local_context lc in
140 let sl = List.map (NCicSubstitution.lift status shift) l in
141 let (metasenv,subst as ms), _, restrictions_for_n, l' =
143 (fun t (ms, i, restrictions_for_n, l) ->
145 (*pp (lazy ("L'ORLO DELLA FOSSA: k= " ^ string_of_int k ^ " shift=" ^
146 string_of_int shift ^ " t=" ^ status#ppterm ~metasenv ~subst ~context:[] t));*)
147 let ms, t = aux k ms t in
148 (*pp (lazy ("LA FOSSA: " ^ status#ppterm ~metasenv ~subst ~context:[] t));*)
149 ms, i-1, restrictions_for_n, t::l
151 ms, i-1, i::restrictions_for_n, l)
152 sl (ms, List.length l, [], [])
154 if restrictions_for_n = [] then
155 ms, if sl = l' then orig else (
156 (*pp (lazy ("FINITO: " ^ status#ppterm ~metasenv:[] ~subst:[]
157 ~context:[] (NCic.Meta (n,pack_lc (0, NCic.Ctx l')))));*)
158 NCic.Meta (n, pack_lc (0, NCic.Ctx l'))
161 let l' = pack_lc (0, NCic.Ctx l') in
162 let _ = pp (lazy ("restrictions for n are:" ^ String.concat "," (List.map string_of_int restrictions_for_n))) in
163 let metasenv, subst, newmeta, more_restricted =
164 restrict status metasenv subst n restrictions_for_n in
165 let _ = pp (lazy ("more restricted: " ^String.concat "," (List.map string_of_int more_restricted))) in
166 let l' = purge_restricted restrictions more_restricted l' in
167 (metasenv, subst), NCic.Meta (newmeta, l'))
168 | t -> NCicUntrusted.map_term_fold_a status (fun _ k -> k+1) k aux ms t
170 aux 0 (metasenv,subst) t
172 and force_does_not_occur_in_context status metasenv subst restrictions = function
173 | name, NCic.Decl t as orig ->
174 (* pp (lazy ("CCC: hd is" ^ status#ppterm ~metasenv:[] ~subst:[] ~context:[] t ^
175 "\nCCC: restrictions are:" ^ String.concat "," (List.map string_of_int restrictions)));*)
176 let (metasenv, subst), t' =
177 force_does_not_occur status metasenv subst restrictions t in
178 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
179 | name, NCic.Def (bo, ty) as orig ->
180 let (metasenv, subst), bo' =
181 force_does_not_occur status metasenv subst restrictions bo in
182 let (metasenv, subst), ty' =
183 force_does_not_occur status metasenv subst restrictions ty in
185 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
187 and erase_in_context status metasenv subst pos restrictions = function
188 | [] -> metasenv, subst, restrictions, []
190 let metasenv, subst, restricted, tl' =
191 erase_in_context status metasenv subst (pos+1) restrictions tl in
192 if List.mem pos restricted then
193 metasenv, subst, restricted, tl'
196 let metasenv, subst, hd' =
197 let delifted_restricted =
198 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
199 force_does_not_occur_in_context
200 status metasenv subst delifted_restricted hd
202 metasenv, subst, restricted,
203 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
205 metasenv, subst, (pos :: restricted), tl'
207 and restrict status metasenv subst i (restrictions as orig) =
208 assert (restrictions <> []);
210 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
212 let metasenv, subst, restrictions, newctx =
213 erase_in_context status metasenv subst 1 restrictions ctx in
214 let (metasenv, subst), newty =
215 force_does_not_occur status metasenv subst restrictions ty in
216 let (metasenv, subst), newbo =
217 force_does_not_occur status metasenv subst restrictions bo in
218 let j = newmeta () in
219 let subst_entry_j = j, (name, newctx, newbo, newty) in
220 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
221 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
223 subst_entry_j :: List.map
224 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst
226 let diff = List.filter (fun x -> not (List.mem x orig)) restrictions in
227 metasenv, new_subst, j, diff
228 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
229 ("Cannot restrict the context of the metavariable ?%d over "^^
230 "the hypotheses %s since ?%d is already instantiated "^^
231 "with %s and at least one of the hypotheses occurs in "^^
232 "the substituted term") i (String.concat ", "
233 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
234 (status#ppterm ~metasenv ~subst ~context:ctx bo))))
235 with NCicUtils.Subst_not_found _ ->
237 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
239 let metasenv, subst, restrictions, newctx =
240 erase_in_context status metasenv subst 1 restrictions ctx in
241 let (metasenv, subst), newty =
242 force_does_not_occur status metasenv subst restrictions ty in
243 let j = newmeta () in
244 let metasenv_entry = j, (name, newctx, newty) in
246 mk_perforated_irl 0 (List.length ctx) restrictions in
247 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
248 (* pp (lazy ("BBB: dopo1 \n" ^ NCicPp.ppsubst ~metasenv [subst_entry]));
249 pp (lazy ("BBB: dopo2 \n" ^ NCicPp.ppsubst ~metasenv (subst_entry::subst)));
250 pp (lazy ("BBB: dopo metasenv\n" ^ NCicPp.ppmetasenv ~subst [metasenv_entry]));*)
251 let diff = List.filter (fun x -> not (List.mem x orig)) restrictions in
253 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
255 subst_entry :: subst, j, diff
256 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
257 ("Cannot restrict the context of the metavariable ?%d "^^
258 "over the hypotheses %s since metavariable's type depends "^^
259 "on at least one of them") i (String.concat ", "
260 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
262 | NCicUtils.Meta_not_found _ -> assert false
265 let rec is_flexible status context ~subst = function
266 | NCic.Meta (i,lc) ->
268 let _,_,t,_ = NCicUtils.lookup_subst i subst in
269 let t = NCicSubstitution.subst_meta status lc t in
270 is_flexible status context ~subst t
271 with NCicUtils.Subst_not_found _ -> true)
272 | NCic.Appl (NCic.Meta (i,lc) :: args)->
274 let _,_,t,_ = NCicUtils.lookup_subst i subst in
275 let t = NCicSubstitution.subst_meta status lc t in
276 is_flexible status context ~subst
277 (NCicReduction.head_beta_reduce status ~delta:max_int
278 (NCic.Appl (t :: args)))
279 with NCicUtils.Subst_not_found _ -> true)
280 (* this is a cheap whd, it only performs zeta-reduction.
282 * it works when the **omissis** disambiguation algorithm
283 * is run on `let x := K a b in t`, K is substituted for a
284 * ? and thus in t metavariables have a flexible Rel
288 match List.nth context (i-1)
290 | _,NCic.Def (bo,_) ->
291 is_flexible status context ~subst
292 (NCicSubstitution.lift status i bo)
296 prerr_endline (Printf.sprintf "Rel %d inside context:\n%s" i
297 (status#ppcontext ~subst ~metasenv:[] context));
299 | Invalid_argument _ -> assert false)
303 let is_out_scope = function `OutScope _ -> true | _ -> false;;
304 let is_out_scope_tag = List.exists is_out_scope;;
305 let int_of_out_scope_tag tag =
306 match List.filter is_out_scope tag with [`OutScope n] -> n | _ -> assert false
311 exception TypeNotGood;;
313 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
314 otherwise the occur check does not make sense in case of unification
316 let delift status ~unify metasenv subst context n l t =
317 (*D*) inside 'D'; try let rc =
318 let is_in_scope_meta subst = function
321 let tag, _, _, _ = NCicUtils.lookup_subst i subst in
322 List.mem `InScope tag
323 with NCicUtils.Subst_not_found _ -> false)
326 let contains_in_scope subst t =
327 let rec aux _ () = function
328 | NCic.Meta _ as t ->
329 if is_in_scope_meta subst t then raise Found
332 if is_in_scope_meta subst t then raise Found
333 else NCicUtils.fold (fun _ () -> ()) () aux () t
335 try aux () () t; false with Found -> true
337 let unify_list in_scope =
339 | _, NCic.Irl _ -> fun _ _ _ _ _ -> None
340 | shift, NCic.Ctx l -> fun metasenv subst context k t ->
341 if is_flexible status context ~subst t || contains_in_scope subst t then None else
344 let t = NCicSubstitution.lift status (k+shift) t in
345 t, is_flexible status context ~subst t)
349 (fun (li,flexible) i ->
350 if flexible || i < in_scope then None else
351 match unify metasenv subst context li t with
352 | Some (metasenv,subst) ->
353 Some ((metasenv, subst), NCic.Rel (i+1+k))
357 let rec aux (context,k,in_scope) (metasenv, subst as ms) t =
358 match unify_list in_scope metasenv subst context k t with
362 | NCic.Rel n as t when n <= k -> ms, t
365 match List.nth context (n-1) with
366 | _,NCic.Def (bo,_) ->
367 (try ms, NCic.Rel ((position in_scope (n-k) l) + k)
368 with (NotFound `NotInTheList) ->
369 (* CSC: This bit of reduction hurts performances since it is
370 * possible to have an exponential explosion of the size of the
371 * proof. required for nat/nth_prime.ma *)
372 aux (context,k,in_scope) ms (NCicSubstitution.lift status n bo))
373 | _,NCic.Decl _ -> ms, NCic.Rel ((position in_scope (n-k) l) + k)
374 with Failure _ -> assert false) (*Unbound variable found in delift*)
375 | NCic.Meta (i,_) when i=n ->
376 raise (MetaSubstFailure (lazy (Printf.sprintf (
377 "Cannot unify the metavariable ?%d with a term that has "^^
378 "as subterm %s in which the same metavariable "^^
379 "occurs (occur check)") i
380 (status#ppterm ~context ~metasenv ~subst t))))
381 | NCic.Meta (i,l1) as orig ->
383 let tag,c,t,ty = NCicUtils.lookup_subst i subst in
384 let in_scope, clear =
385 if List.mem `InScope tag then 0, true
386 else if is_out_scope_tag tag then int_of_out_scope_tag tag,true
393 (i,([],c,t,ty)) :: List.filter (fun j,_ -> i <> j) subst
395 aux (context,k,in_scope) ms (NCicSubstitution.subst_meta status l1 t)
396 with NCicUtils.Subst_not_found _ ->
397 if snd l1 = NCic.Irl 0 || snd l1 = NCic.Ctx [] then ms, orig
399 let shift1,lc1 = l1 in
401 let shift = shift + k in
403 | NCic.Irl len, NCic.Irl len1
404 when shift1 + len1 < shift || shift1 > shift + len ->
405 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
406 let metasenv, subst, newmeta, more_restricted =
407 restrict status metasenv subst i restrictions in
408 let l' = (0,NCic.Irl (max 0 (k-shift1))) in
409 let l' = purge_restricted restrictions more_restricted l' in
410 (metasenv, subst),NCic.Meta (newmeta,l')
411 | NCic.Irl len, NCic.Irl len1 ->
412 let low_restrictions, new_shift =
413 if k <= shift1 && shift1 < shift then
414 HExtlib.list_seq 1 (shift - shift1 + 1), k
415 else if shift1 < k (* <= shift *) then
416 let save_below = k - shift1 in
417 HExtlib.list_seq (save_below + 1) (shift - shift1 + 1),
419 else [], shift1 - shift + k
421 let high_restrictions =
422 let last = shift + len in
423 let last1 = shift1 + len1 in
425 let high_gap = last1 - last in
426 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
429 let restrictions = low_restrictions @ high_restrictions in
430 if restrictions = [] then
431 if shift = k then ms, orig
432 else ms, NCic.Meta (i, (new_shift, lc1))
434 let metasenv, subst, newmeta, more_restricted =
435 restrict status metasenv subst i restrictions in
436 let newlc_len = len1 - List.length restrictions in
437 let l' = new_shift, NCic.Irl newlc_len in
438 let l' = purge_restricted restrictions more_restricted l' in
439 (metasenv, subst),NCic.Meta(newmeta,l')
442 let lc1 = NCicUtils.expand_local_context lc1 in
443 let lc1 = List.map (NCicSubstitution.lift status shift1) lc1 in
444 let rec deliftl tbr j ms = function
447 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
449 let ms, t = aux (context,k,in_scope) ms t in
452 | (NotFound `NotInTheList) | MetaSubstFailure _ -> ms, j::tbr, tl
454 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
455 pp (lazy ("TO BE RESTRICTED: " ^
456 (String.concat "," (List.map string_of_int to_be_r))));
457 let l1 = pack_lc (0, NCic.Ctx lc1') in
458 pp (lazy ("newmeta:" ^ status#ppterm
459 ~metasenv ~subst ~context (NCic.Meta (999,l1))));
460 pp (lazy (status#ppmetasenv ~subst metasenv));
463 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
465 let metasenv, subst, newmeta, more_restricted =
466 restrict status metasenv subst i to_be_r in
467 let l1 = purge_restricted to_be_r more_restricted l1 in
468 (metasenv, subst), NCic.Meta(newmeta,l1))
471 NCicUntrusted.map_term_fold_a status
472 (fun e (c,k,s) -> (e::c,k+1,s)) (context,k,in_scope) aux ms t
476 "DELIFTO " ^ status#ppterm ~metasenv ~subst ~context t ^ " w.r.t. " ^
477 status#ppterm ~metasenv ~subst ~context (NCic.Meta(n,l)) ^ " i.e. " ^
478 String.concat ", " (List.map (status#ppterm ~metasenv ~subst ~context) (
480 (List.map (NCicSubstitution.lift status shift)
481 (NCicUtils.expand_local_context lc))
485 (*assert (try n = -1 or (ignore(NCicUtils.lookup_meta n metasenv); true) with NCicUtils.Meta_not_found _ -> false);*)
486 let ((metasenv,subst),t) as res = aux (context,0,0) (metasenv,subst) t in
487 if (try n <> -1 && (ignore(NCicUtils.lookup_meta n metasenv); false)
488 with NCicUtils.Meta_not_found _ -> true)
490 let _,context,bo,_ = NCicUtils.lookup_subst n subst in
491 match unify metasenv subst context bo t with
492 None -> raise (NotFound `NotWellTyped)
493 | Some (metasenv,subst) -> (metasenv,subst),t
496 let _,context,ty = NCicUtils.lookup_meta n metasenv in
499 NCic.Sort _ -> (* could be algebraic *) NCic.Implicit `Closed
500 | _ -> NCicTypeChecker.typeof status ~subst ~metasenv context t in
504 NCic.Sort _ | NCic.Meta _ | NCic.Implicit _ -> res
505 | _ -> raise TypeNotGood)
506 | _,NCic.Implicit _ ->
508 NCic.Sort _ | NCic.Meta _ | NCic.Implicit _ -> res
509 | _ -> raise TypeNotGood)
512 NCicReduction.are_convertible status ~metasenv ~subst context ty' ty
518 NCicUtils.Meta_not_found _ ->
519 (* Fake metavariable used in NTacStatus and NCicRefiner :-( *)
521 | NCicTypeChecker.TypeCheckerFailure msg ->
522 HLog.error "----------- Problem with Dependent Types ----------";
523 HLog.error (Lazy.force msg) ;
524 HLog.error "---------------------------------------------------";
525 raise (NotFound `NotWellTyped)
527 | NCicTypeChecker.AssertFailure _
528 | NCicReduction.AssertFailure _
529 | NCicTypeChecker.TypeCheckerFailure _ ->
530 raise (NotFound `NotWellTyped))
531 with NotFound reason ->
532 (* This is the case where we fail even first order unification. *)
533 (* The reason is that our delift function is weaker than first *)
534 (* order (in the sense of alpha-conversion). See comment above *)
535 (* related to the delift function. *)
538 `NotInTheList -> "some variable cannot be delifted"
539 | `NotWellTyped -> "the unifier found is not well typed" in
540 let msg = (lazy (Printf.sprintf
541 ("Error trying to abstract %s over [%s]: %s")
542 (status#ppterm ~metasenv ~subst
543 ~context t) (String.concat "; " (List.map (status#ppterm ~metasenv
544 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
545 status shift) (NCicUtils.expand_local_context lc)))) reason))
548 let lc = NCicUtils.expand_local_context lc in
549 let l = List.map (NCicSubstitution.lift status shift) lc in
551 List.exists (fun t-> NCicUntrusted.metas_of_term status subst context t <> [])l
553 raise (Uncertain msg)
555 raise (MetaSubstFailure msg)
556 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
559 let mk_meta ?(attrs=[]) metasenv context ?with_type kind =
560 assert(kind <> `IsSort || context = []);
561 let n = newmeta () in
562 let ty= match with_type with None-> NCic.Implicit (`Typeof n)| Some x ->x in
563 let len = List.length context in
564 let attrs = NCicUntrusted.set_kind kind attrs in
565 let menv_entry = (n, (attrs, context, ty)) in
566 menv_entry :: metasenv, n, NCic.Meta (n, (0,NCic.Irl len)), ty
569 let extend_meta metasenv n =
571 let attrs,cc,ty = NCicUtils.lookup_meta n metasenv in
573 | NCic.Implicit (`Typeof _) ->
574 let mk_meta context kind =
575 let metasenv, _, ty, _ = mk_meta metasenv context kind in
576 (n, (attrs, cc, ty)) :: List.filter (fun x,_ -> x <> n) metasenv, ty
578 (match NCicUntrusted.kind_of_meta attrs with
580 | `IsType -> mk_meta [] `IsSort
581 | `IsTerm -> mk_meta cc `IsType)
582 | ty -> metasenv, ty)
583 with NCicUtils.Meta_not_found _ -> assert false
586 let saturate status ?(delta=0) metasenv subst context ty goal_arity =
587 assert (goal_arity >= 0);
588 let rec aux metasenv = function
589 | NCic.Prod (name,s,t) as ty ->
590 let metasenv1, _, arg,_ =
591 mk_meta ~attrs:[`Name name] metasenv context ~with_type:s `IsTerm in
592 let t, metasenv1, args, pno =
593 aux metasenv1 (NCicSubstitution.subst status arg t)
595 if pno + 1 = goal_arity then
596 ty, metasenv, [], goal_arity+1
598 t, metasenv1, arg::args, pno+1
600 match NCicReduction.whd status ~subst context ty ~delta with
601 | NCic.Prod _ as ty -> aux metasenv ty
602 | ty -> ty, metasenv, [], 0
604 let res, newmetasenv, arguments, _ = aux metasenv ty in
605 res, newmetasenv, arguments