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 let maxmeta = ref 0 in
19 (fun () -> incr maxmeta; !maxmeta),
23 exception NotInTheList;;
25 let position to_skip n (shift, lc) =
27 | NCic.Irl _ when to_skip > 0 -> assert false (* unclear to me *)
28 | NCic.Irl len when n <= shift || n > shift + len -> raise NotInTheList
29 | NCic.Irl _ -> n - shift
31 let rec aux to_skip k = function
32 | [] -> raise NotInTheList
33 | _ :: tl when to_skip > 0 -> aux (to_skip - 1) (k+1) tl
34 | (NCic.Rel m)::_ when m + shift = n -> k
35 | _::tl -> aux to_skip (k+1) tl
41 let rec are_contiguous k = function
43 | (NCic.Rel j) :: tl when j = k+1 -> are_contiguous j tl
47 | _, NCic.Ctx [] -> 0, NCic.Irl 0
48 | shift, NCic.Ctx (NCic.Rel k::tl as l) when are_contiguous k tl ->
49 shift+k-1, NCic.Irl (List.length l)
55 let mk_perforated_irl shift len restrictions =
58 if List.mem (n+shift) restrictions then aux (n-1)
59 else (NCic.Rel n) :: aux (n-1)
61 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
66 let rec force_does_not_occur metasenv subst restrictions t =
67 let rec aux k ms = function
68 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
69 | NCic.Rel r as orig ->
71 List.length (List.filter (fun x -> x < r - k) restrictions)
73 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
74 | NCic.Meta (n, (shift,lc as l)) as orig ->
77 Some (NCicUtils.lookup_subst n subst)
79 NCicUtils.Subst_not_found _ -> None
81 (match meta_chain with
83 aux k ms (NCicSubstitution.subst_meta l bo)
85 (* we ignore the subst since restrict will take care of already
86 * instantiated/restricted metavariabels *)
87 let (metasenv,subst as ms), restrictions_for_n, l' =
88 let l = NCicUtils.expand_local_context lc in
90 let ms, _, restrictions_for_n, l =
92 (fun t (ms, i, restrictions_for_n, l) ->
94 let ms, t = aux (k-shift) ms t in
95 ms, i-1, restrictions_for_n, t::l
97 ms, i-1, i::restrictions_for_n, l)
98 l (ms, List.length l, [], [])
101 ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
103 if restrictions_for_n = [] then
104 ms, if l = l' then orig else NCic.Meta (n, l')
106 let metasenv, subst, newmeta =
107 restrict metasenv subst n restrictions_for_n
109 (metasenv, subst), NCic.Meta (newmeta, l'))
110 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
112 aux 0 (metasenv,subst) t
114 and force_does_not_occur_in_context metasenv subst restrictions = function
115 | name, NCic.Decl t as orig ->
116 let (metasenv, subst), t' =
117 force_does_not_occur metasenv subst restrictions t in
118 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
119 | name, NCic.Def (bo, ty) as orig ->
120 let (metasenv, subst), bo' =
121 force_does_not_occur metasenv subst restrictions bo in
122 let (metasenv, subst), ty' =
123 force_does_not_occur metasenv subst restrictions ty in
125 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
127 and erase_in_context metasenv subst pos restrictions = function
128 | [] -> metasenv, subst, restrictions, []
130 let metasenv, subst, restricted, tl' =
131 erase_in_context metasenv subst (pos+1) restrictions tl in
132 if List.mem pos restricted then
133 metasenv, subst, restricted, tl'
136 let metasenv, subst, hd' =
137 let delifted_restricted =
138 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
139 force_does_not_occur_in_context
140 metasenv subst delifted_restricted hd
142 metasenv, subst, restricted,
143 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
145 metasenv, subst, (pos :: restricted), tl'
147 and restrict metasenv subst i restrictions =
148 assert (restrictions <> []);
150 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
152 let metasenv, subst, restrictions, newctx =
153 erase_in_context metasenv subst 1 restrictions ctx in
154 let (metasenv, subst), newty =
155 force_does_not_occur metasenv subst restrictions ty in
156 let (metasenv, subst), newbo =
157 force_does_not_occur metasenv subst restrictions bo in
158 let j = newmeta () in
159 let subst_entry_j = j, (name, newctx, newbo, newty) in
160 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
161 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
163 subst_entry_j :: List.map
164 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst
167 prerr_endline ("restringo nella subst: " ^string_of_int i ^ " -> " ^
168 string_of_int j ^ "\n" ^
169 NCicPp.ppsubst ~metasenv [subst_entry_j] ^ "\n\n" ^
170 NCicPp.ppsubst ~metasenv [subst_entry_i] ^ "\n" ^
171 NCicPp.ppterm ~metasenv ~subst ~context:ctx bo ^ " ---- " ^
172 NCicPp.ppterm ~metasenv ~subst ~context:newctx newbo
175 metasenv, new_subst, j
176 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
177 ("Cannot restrict the context of the metavariable ?%d over "^^
178 "the hypotheses %s since ?%d is already instantiated "^^
179 "with %s and at least one of the hypotheses occurs in "^^
180 "the substituted term") i (String.concat ", "
181 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
182 (NCicPp.ppterm ~metasenv ~subst ~context:ctx bo))))
183 with NCicUtils.Subst_not_found _ ->
185 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
187 let metasenv, subst, restrictions, newctx =
188 erase_in_context metasenv subst 1 restrictions ctx in
189 let (metasenv, subst), newty =
190 force_does_not_occur metasenv subst restrictions ty in
191 let j = newmeta () in
192 let metasenv_entry = j, (name, newctx, newty) in
194 mk_perforated_irl 0 (List.length ctx) restrictions in
195 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
197 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
199 subst_entry :: subst, j
200 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
201 ("Cannot restrict the context of the metavariable ?%d "^^
202 "over the hypotheses %s since metavariable's type depends "^^
203 "on at least one of them") i (String.concat ", "
204 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
206 | NCicUtils.Meta_not_found _ -> assert false
209 let rec flexible_arg subst = function
210 | NCic.Meta (i,_) | NCic.Appl (NCic.Meta (i,_) :: _)->
212 let _,_,t,_ = List.assoc i subst in
214 with Not_found -> true)
218 let flexible subst l = List.exists (flexible_arg subst) l;;
220 let in_scope_tag = "tag:in_scope" ;;
221 let out_scope_tag_prefix = "tag:out_scope:"
222 let out_scope_tag n = out_scope_tag_prefix ^ string_of_int n ;;
223 let is_out_scope_tag tag =
224 String.length tag > String.length out_scope_tag_prefix &&
225 String.sub tag 0 (String.length out_scope_tag_prefix) = out_scope_tag_prefix
227 let int_of_out_scope_tag tag =
229 (String.sub tag (String.length out_scope_tag_prefix)
230 (String.length tag - (String.length out_scope_tag_prefix)))
236 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
237 otherwise the occur check does not make sense in case of unification
239 let delift ~unify metasenv subst context n l t =
240 let is_in_scope_meta subst = function
243 let tag, _, _, _ = NCicUtils.lookup_subst i subst in
244 tag = Some in_scope_tag
245 with NCicUtils.Subst_not_found _ -> false)
248 let contains_in_scope subst t =
249 let rec aux _ () = function
250 | NCic.Meta _ as t ->
251 if is_in_scope_meta subst t then raise Found
254 if is_in_scope_meta subst t then raise Found
255 else NCicUtils.fold (fun _ () -> ()) () aux () t
257 try aux () () t; false with Found -> true
259 let unify_list ~alpha in_scope =
261 | _, NCic.Irl _ -> fun _ _ _ _ _ -> None
262 | shift, NCic.Ctx l -> fun metasenv subst context k t ->
263 if flexible_arg subst t || contains_in_scope subst t then None else
264 let lb = List.map (fun t -> t, flexible_arg subst t) l in
266 (fun (li,flexible) i ->
267 if flexible || i < in_scope then None else
268 let li = NCicSubstitution.lift (k+shift) li in
270 if NCicReduction.alpha_eq metasenv subst context li t then
271 Some ((metasenv,subst), NCic.Rel (i+1+k))
275 match unify metasenv subst context li t with
276 | Some (metasenv,subst) ->
277 Some ((metasenv, subst), NCic.Rel (i+1+k))
281 let rec aux (context,k,in_scope) (metasenv, subst as ms) t =
282 match unify_list ~alpha:true in_scope metasenv subst context k t with
287 | NCic.Rel n as t when n <= k -> ms, t
290 match List.nth context (n-k-1) with
291 | _,NCic.Def (bo,_) ->
292 (try ms, NCic.Rel ((position in_scope (n-k) l) + k)
294 (* CSC: This bit of reduction hurts performances since it is
295 * possible to have an exponential explosion of the size of the
296 * proof. required for nat/nth_prime.ma *)
297 aux (context,k,in_scope) ms (NCicSubstitution.lift n bo))
298 | _,NCic.Decl _ -> ms, NCic.Rel ((position in_scope (n-k) l) + k)
299 with Failure _ -> assert false) (*Unbound variable found in delift*)
300 | NCic.Meta (i,_) when i=n ->
301 raise (MetaSubstFailure (lazy (Printf.sprintf (
302 "Cannot unify the metavariable ?%d with a term that has "^^
303 "as subterm %s in which the same metavariable "^^
304 "occurs (occur check)") i
305 (NCicPp.ppterm ~context ~metasenv ~subst t))))
306 | NCic.Meta (i,l1) as orig ->
308 let tag,c,t,ty = NCicUtils.lookup_subst i subst in
309 let in_scope, clear =
311 | Some tag when tag = in_scope_tag -> 0, true
312 | Some tag when is_out_scope_tag tag->int_of_out_scope_tag tag,true
313 | _ -> in_scope, false
319 (i,(None,c,t,ty)) :: List.filter (fun j,_ -> i <> j) subst
321 aux (context,k,in_scope) ms (NCicSubstitution.subst_meta l1 t)
322 with NCicUtils.Subst_not_found _ ->
323 if snd l1 = NCic.Irl 0 || snd l1 = NCic.Ctx [] then ms, orig
325 let shift1,lc1 = l1 in
327 let shift = shift + k in
329 | NCic.Irl len, NCic.Irl len1
330 when shift1 + len1 < shift || shift1 > shift + len ->
331 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
332 let metasenv, subst, newmeta =
333 restrict metasenv subst i restrictions
336 NCic.Meta (newmeta, (0,NCic.Irl (max 0 (k-shift1))))
337 | NCic.Irl len, NCic.Irl len1 ->
338 let low_restrictions, new_shift =
339 if k <= shift1 && shift1 < shift then
340 HExtlib.list_seq 1 (shift - shift1 + 1), k
341 else if shift1 < k (* <= shift *) then
342 let save_below = k - shift1 in
343 HExtlib.list_seq (save_below + 1) (shift - shift1 + 1),
345 else [], shift1 - shift + k
347 let high_restrictions =
348 let last = shift + len in
349 let last1 = shift1 + len1 in
351 let high_gap = last1 - last in
352 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
355 let restrictions = low_restrictions @ high_restrictions in
356 if restrictions = [] then
357 if shift = k then ms, orig
358 else ms, NCic.Meta (i, (new_shift, lc1))
360 let metasenv, subst, newmeta =
361 restrict metasenv subst i restrictions
364 prerr_endline ("RESTRICTIONS FOR: " ^
365 NCicPp.ppterm ~metasenv ~subst ~context:[]
366 (NCic.Meta (i,l1))^" that was part of a term unified with "
367 ^ NCicPp.ppterm ~metasenv ~subst ~context:[] (NCic.Meta
368 (n,l)) ^ " ====> " ^ String.concat "," (List.map
369 string_of_int restrictions) ^ "\nMENV:\n" ^
370 NCicPp.ppmetasenv ~subst metasenv ^ "\nSUBST:\n" ^
371 NCicPp.ppsubst subst ~metasenv);
373 let newlc_len = len1 - List.length restrictions in
375 NCic.Meta(newmeta,(new_shift, NCic.Irl newlc_len))
378 let _, cctx, _ = NCicUtils.lookup_meta newmeta metasenv in
379 List.length cctx = newlc_len);
380 (metasenv, subst), meta
383 let lc1 = NCicUtils.expand_local_context lc1 in
384 let lc1 = List.map (NCicSubstitution.lift shift1) lc1 in
385 let rec deliftl tbr j ms = function
388 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
390 let ms, t = aux (context,k,in_scope) ms t in
393 | NotInTheList | MetaSubstFailure _ -> ms, j::tbr, tl
395 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
397 prerr_endline ("TO BE RESTRICTED: " ^
398 (String.concat "," (List.map string_of_int to_be_r)));
400 let l1 = pack_lc (0, NCic.Ctx lc1') in
402 prerr_endline ("newmeta:" ^ NCicPp.ppterm
403 ~metasenv ~subst ~context (NCic.Meta (999,l1)));
407 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
409 let metasenv, subst, newmeta =
410 restrict metasenv subst i to_be_r in
411 (metasenv, subst), NCic.Meta(newmeta,l1))
414 NCicUntrusted.map_term_fold_a
415 (fun e (c,k,s) -> (e::c,k+1,s)) (context,k,in_scope) aux ms t
417 match unify_list ~alpha:false in_scope metasenv subst context k t with
419 | None -> raise NotInTheList
421 try aux (context,0,0) (metasenv,subst) t
423 (* This is the case where we fail even first order unification. *)
424 (* The reason is that our delift function is weaker than first *)
425 (* order (in the sense of alpha-conversion). See comment above *)
426 (* related to the delift function. *)
427 let msg = (lazy (Printf.sprintf
428 ("Error trying to abstract %s over [%s]: the algorithm only tried to "^^
429 "abstract over bound variables") (NCicPp.ppterm ~metasenv ~subst
430 ~context t) (String.concat "; " (List.map (NCicPp.ppterm ~metasenv
431 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
432 shift) (NCicUtils.expand_local_context lc))))))
435 let lc = NCicUtils.expand_local_context lc in
436 let l = List.map (NCicSubstitution.lift shift) lc in
438 List.exists (fun t-> NCicUntrusted.metas_of_term subst context t = []) l
440 raise (Uncertain msg)
442 raise (MetaSubstFailure msg)
445 let mk_meta ?name metasenv context ty =
446 let tyof = function Some s -> Some ("typeof_"^s) | None -> None in
447 let rec mk_meta name n metasenv context = function
449 let len = List.length context in
450 let menv_entry = (n, (name, context, ty)) in
451 menv_entry :: metasenv, n, NCic.Meta (n, (0,NCic.Irl len)), ty
453 let ty = NCic.Implicit (`Typeof n) in
454 mk_meta (tyof name) n metasenv [] (`WithType ty)
456 let metasenv, _, ty, _ =
457 mk_meta (tyof name) (newmeta ()) metasenv context `Sort in
458 mk_meta name n metasenv context (`WithType ty)
460 let metasenv, _, ty, _ =
461 mk_meta (tyof name) (newmeta ()) metasenv context `Type in
462 mk_meta name n metasenv context (`WithType ty)
464 mk_meta name (newmeta ()) metasenv context ty
467 let saturate ?(delta=0) metasenv subst context ty goal_arity =
468 assert (goal_arity >= 0);
469 let rec aux metasenv = function
470 | NCic.Prod (name,s,t) as ty ->
471 let metasenv1, _, arg,_ =
472 mk_meta ~name:name metasenv context (`WithType s) in
473 let t, metasenv1, args, pno =
474 aux metasenv1 (NCicSubstitution.subst arg t)
476 if pno + 1 = goal_arity then
477 ty, metasenv, [], goal_arity+1
479 t, metasenv1, arg::args, pno+1
481 match NCicReduction.whd ~subst context ty ~delta with
482 | NCic.Prod _ as ty -> aux metasenv ty
483 | ty -> ty, metasenv, [], 0
485 let res, newmetasenv, arguments, _ = aux metasenv ty in
486 res, newmetasenv, arguments