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)
183 let mk_perforated_irl shift len restrictions =
185 if n = 0 then [] else
186 if List.mem (n+shift) restrictions then aux (n-1)
187 else (NCic.Rel n) :: aux (n-1)
189 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
194 let rec force_does_not_occur metasenv subst restrictions t =
195 let rec aux k ms = function
196 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
197 | NCic.Rel r as orig ->
199 List.length (List.filter (fun x -> x < r - k) restrictions)
201 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
202 | NCic.Meta (n, (shift,lc as l)) as orig ->
203 (* we ignore the subst since restrict will take care of already
204 * instantiated/restricted metavariabels *)
205 let (metasenv,subst as ms), restrictions_for_n, l' =
206 let l = NCicUtils.expand_local_context lc in
208 let ms, _, restrictions_for_n, l =
210 (fun t (ms, i, restrictions_for_n, l) ->
212 let ms, t = aux (k-shift) ms t in
213 ms, i-1, restrictions_for_n, t::l
215 ms, i-1, i::restrictions_for_n, l)
216 l (ms, List.length l, [], [])
219 ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
221 if restrictions_for_n = [] then
222 ms, if l = l' then orig else NCic.Meta (n, l')
224 let metasenv, subst, newmeta =
225 restrict metasenv subst n restrictions_for_n
227 (metasenv, subst), NCic.Meta (newmeta, l')
228 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
230 aux 0 (metasenv,subst) t
232 and force_does_not_occur_in_context metasenv subst restrictions = function
233 | name, NCic.Decl t as orig ->
234 let (metasenv, subst), t' =
235 force_does_not_occur metasenv subst restrictions t in
236 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
237 | name, NCic.Def (bo, ty) as orig ->
238 let (metasenv, subst), bo' =
239 force_does_not_occur metasenv subst restrictions bo in
240 let (metasenv, subst), ty' =
241 force_does_not_occur metasenv subst restrictions ty in
243 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
245 and erase_in_context metasenv subst pos restrictions = function
246 | [] -> metasenv, subst, restrictions, []
248 let metasenv, subst, restricted, tl' =
249 erase_in_context metasenv subst (pos+1) restrictions tl in
250 if List.mem pos restricted then
251 metasenv, subst, restricted, tl'
254 let metasenv, subst, hd' =
255 let delifted_restricted =
256 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
257 force_does_not_occur_in_context
258 metasenv subst delifted_restricted hd
260 metasenv, subst, restricted,
261 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
263 metasenv, subst, (pos :: restricted), tl'
265 and restrict metasenv subst i restrictions =
266 assert (restrictions <> []);
268 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
270 let metasenv, subst, restrictions, newctx =
271 erase_in_context metasenv subst 1 restrictions ctx in
272 let (metasenv, subst), newty =
273 force_does_not_occur metasenv subst restrictions ty in
274 let (metasenv, subst), newbo =
275 force_does_not_occur metasenv subst restrictions bo in
276 let j = newmeta () in
277 let subst_entry_j = j, (name, newctx, newbo, newty) in
278 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
279 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
281 subst_entry_j :: List.map
282 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst
285 prerr_endline ("restringo nella subst: " ^string_of_int i ^ " -> " ^
286 string_of_int j ^ "\n" ^
287 NCicPp.ppsubst ~metasenv [subst_entry_j] ^ "\n\n" ^
288 NCicPp.ppsubst ~metasenv [subst_entry_i] ^ "\n" ^
289 NCicPp.ppterm ~metasenv ~subst ~context:ctx bo ^ " ---- " ^
290 NCicPp.ppterm ~metasenv ~subst ~context:newctx newbo
293 metasenv, new_subst, j
294 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
295 ("Cannot restrict the context of the metavariable ?%d over "^^
296 "the hypotheses %s since ?%d is already instantiated "^^
297 "with %s and at least one of the hypotheses occurs in "^^
298 "the substituted term") i (String.concat ", "
299 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
300 (NCicPp.ppterm ~metasenv ~subst ~context:ctx bo))))
301 with NCicUtils.Subst_not_found _ ->
303 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
305 let metasenv, subst, restrictions, newctx =
306 erase_in_context metasenv subst 1 restrictions ctx in
307 let (metasenv, subst), newty =
308 force_does_not_occur metasenv subst restrictions ty in
309 let j = newmeta () in
310 let metasenv_entry = j, (name, newctx, newty) in
312 mk_perforated_irl 0 (List.length ctx) restrictions in
313 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
315 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
317 subst_entry :: subst, j
318 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
319 ("Cannot restrict the context of the metavariable ?%d "^^
320 "over the hypotheses %s since metavariable's type depends "^^
321 "on at least one of them") i (String.concat ", "
322 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
324 | NCicUtils.Meta_not_found _ -> assert false
327 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
328 otherwise the occur check does not make sense in case of unification
330 let delift metasenv subst context n l t =
331 let rec aux k (metasenv, subst as ms) = function
332 | NCic.Rel n as t when n <= k -> ms, t
335 match List.nth context (n-k-1) with
336 | _,NCic.Def (bo,_) ->
337 (try ms, NCic.Rel ((position (n-k) l) + k)
339 (* CSC: This bit of reduction hurts performances since it is
340 * possible to have an exponential explosion of the size of the
341 * proof. required for nat/nth_prime.ma *)
342 aux k ms (NCicSubstitution.lift n bo))
343 | _,NCic.Decl _ -> ms, NCic.Rel ((position (n-k) l) + k)
344 with Failure _ -> assert false) (*Unbound variable found in delift*)
345 | NCic.Meta (_,(_,(NCic.Irl 0| NCic.Ctx []))) as orig -> ms, orig
346 | NCic.Meta (i,l1) as orig ->
348 let _,_,t,_ = NCicUtils.lookup_subst i subst in
349 aux k ms (NCicSubstitution.subst_meta l1 t)
350 with NCicUtils.Subst_not_found _ ->
351 (* see the top level invariant *)
353 raise (MetaSubstFailure (lazy (Printf.sprintf (
354 "Cannot unify the metavariable ?%d with a term that has "^^
355 "as subterm %s in which the same metavariable "^^
356 "occurs (occur check)") i
357 (NCicPp.ppterm ~context ~metasenv ~subst t))))
359 let shift1,lc1 = l1 in
361 let shift = shift + k in
363 | NCic.Irl len, NCic.Irl len1
364 when shift1 + len1 < shift || shift1 > shift + len ->
365 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
366 let metasenv, subst, newmeta =
367 restrict metasenv subst i restrictions
370 NCic.Meta (newmeta, (0,NCic.Irl (max 0 (k-shift1))))
371 | NCic.Irl len, NCic.Irl len1
372 when shift1 < shift || len1 + shift1 > len + shift ->
373 (* C. Hoare. Premature optimization is the root of all evil*)
374 let stop = shift + len in
375 let stop1 = shift1 + len1 in
376 let low_gap = max 0 (shift - shift1) in
377 let high_gap = max 0 (stop1 - stop) in
379 HExtlib.list_seq (*max 1 (k+1-shift1)*) (k+1) (low_gap + 1) @
380 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
382 let metasenv, subst, newmeta =
383 restrict metasenv subst i restrictions
386 prerr_endline ("RESTRICTIONS FOR: " ^
387 NCicPp.ppterm ~metasenv ~subst ~context:[]
388 (NCic.Meta (i,l1))^" that was part of a term unified with "
389 ^ NCicPp.ppterm ~metasenv ~subst ~context:[] (NCic.Meta
390 (n,l)) ^ " ====> " ^ String.concat "," (List.map
391 string_of_int restrictions) ^ "\nMENV:\n" ^
392 NCicPp.ppmetasenv ~subst metasenv ^ "\nSUBST:\n" ^
393 NCicPp.ppsubst subst ~metasenv);
396 len1 - low_gap - high_gap + max 0 (k - shift1) in
397 assert (if shift1 > k then
398 shift1 + low_gap - shift = 0 else true);
400 NCic.Meta(newmeta,(shift1 + low_gap - shift,
403 let _, cctx, _ = NCicUtils.lookup_meta newmeta metasenv in
404 assert (List.length cctx = newlc_len);
405 (metasenv, subst), meta
407 | NCic.Irl _, NCic.Irl _ when shift = k -> ms, orig
408 | NCic.Irl _, NCic.Irl _ ->
409 ms, NCic.Meta (i, (max 0 (shift1 - shift + k), lc1))
411 let lc1 = NCicUtils.expand_local_context lc1 in
412 let lc1 = List.map (NCicSubstitution.lift shift1) lc1 in
413 let rec deliftl tbr j ms = function
416 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
418 let ms, t = aux k ms t in
421 | NotInTheList | MetaSubstFailure _ -> ms, j::tbr, tl
423 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
425 prerr_endline ("TO BE RESTRICTED: " ^
426 (String.concat "," (List.map string_of_int to_be_r)));
428 let l1 = pack_lc (0, NCic.Ctx lc1') in
430 prerr_endline ("newmeta:" ^ NCicPp.ppterm
431 ~metasenv ~subst ~context (NCic.Meta (999,l1)));
435 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
437 let metasenv, subst, newmeta =
438 restrict metasenv subst i to_be_r in
439 (metasenv, subst), NCic.Meta(newmeta,l1))
441 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
443 try aux 0 (metasenv,subst) t
445 (* This is the case where we fail even first order unification. *)
446 (* The reason is that our delift function is weaker than first *)
447 (* order (in the sense of alpha-conversion). See comment above *)
448 (* related to the delift function. *)
449 let msg = (lazy (Printf.sprintf
450 ("Error trying to abstract %s over [%s]: the algorithm only tried to "^^
451 "abstract over bound variables") (NCicPp.ppterm ~metasenv ~subst
452 ~context t) (String.concat "; " (List.map (NCicPp.ppterm ~metasenv
453 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
454 shift) (NCicUtils.expand_local_context lc))))))
457 let lc = NCicUtils.expand_local_context lc in
458 let l = List.map (NCicSubstitution.lift shift) lc in
462 NCicUntrusted.metas_of_term subst context t = [])
465 raise (Uncertain msg)
467 raise (MetaSubstFailure msg)
470 let mk_meta ?name metasenv context ty =
473 let n = newmeta () in
474 let ty = NCic.Implicit (`Typeof n) in
475 let menv_entry = (n, (name, context, ty)) in
476 menv_entry :: metasenv,NCic.Meta (n, (0,NCic.Irl (List.length context))), ty
479 let context_for_ty = if ty = `Type then [] else context in
480 let n = newmeta () in
481 let ty_menv_entry = (n, (name,context_for_ty, NCic.Implicit (`Typeof n))) in
482 let m = newmeta () in
483 let ty = NCic.Meta (n, (0,NCic.Irl (List.length context_for_ty))) in
484 let menv_entry = (m, (name, context, ty)) in
485 menv_entry :: ty_menv_entry :: metasenv,
486 NCic.Meta (m, (0,NCic.Irl (List.length context))), ty
488 let n = newmeta () in
489 let len = List.length context in
490 let menv_entry = (n, (name, context, ty)) in
491 menv_entry :: metasenv, NCic.Meta (n, (0,NCic.Irl len)), ty
494 let saturate ?(delta=0) metasenv context ty goal_arity =
495 assert (goal_arity >= 0);
496 let rec aux metasenv = function
497 | NCic.Prod (name,s,t) ->
498 let metasenv1, arg,_ =
499 mk_meta ~name:name metasenv context (`WithType s) in
500 let t, metasenv1, args, pno =
501 aux metasenv1 (NCicSubstitution.subst arg t)
503 if pno + 1 = goal_arity then
504 ty, metasenv, [], goal_arity+1
506 t, metasenv1, arg::args, pno+1
508 match NCicReduction.whd context ty ~delta with
509 | NCic.Prod _ as ty -> aux metasenv ty
510 | ty -> ty, metasenv, [], 0
512 let res, newmetasenv, arguments, _ = aux metasenv ty in
513 res, newmetasenv, arguments