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
22 exception NotInTheList;;
24 let position to_skip n (shift, lc) =
26 | NCic.Irl _ when to_skip > 0 -> assert false (* unclear to me *)
27 | NCic.Irl len when n <= shift || n > shift + len -> raise NotInTheList
28 | NCic.Irl _ -> n - shift
30 let rec aux to_skip k = function
31 | [] -> raise NotInTheList
32 | _ :: tl when to_skip > 0 -> aux (to_skip - 1) (k+1) tl
33 | (NCic.Rel m)::_ when m + shift = n -> k
34 | _::tl -> aux to_skip (k+1) tl
40 let rec are_contiguous k = function
42 | (NCic.Rel j) :: tl when j = k+1 -> are_contiguous j tl
46 | _, NCic.Ctx [] -> 0, NCic.Irl 0
47 | shift, NCic.Ctx (NCic.Rel k::tl as l) when are_contiguous k tl ->
48 shift+k-1, NCic.Irl (List.length l)
54 let mk_perforated_irl shift len restrictions =
57 if List.mem (n+shift) restrictions then aux (n-1)
58 else (NCic.Rel n) :: aux (n-1)
60 pack_lc (shift, NCic.Ctx (List.rev (aux len)))
65 let rec force_does_not_occur metasenv subst restrictions t =
66 let rec aux k ms = function
67 | NCic.Rel r when List.mem (r - k) restrictions -> raise Occur
68 | NCic.Rel r as orig ->
70 List.length (List.filter (fun x -> x < r - k) restrictions)
72 if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
73 | NCic.Meta (n, (shift,lc as l)) as orig ->
74 (* we ignore the subst since restrict will take care of already
75 * instantiated/restricted metavariabels *)
76 let (metasenv,subst as ms), restrictions_for_n, l' =
77 let l = NCicUtils.expand_local_context lc in
79 let ms, _, restrictions_for_n, l =
81 (fun t (ms, i, restrictions_for_n, l) ->
83 let ms, t = aux (k-shift) ms t in
84 ms, i-1, restrictions_for_n, t::l
86 ms, i-1, i::restrictions_for_n, l)
87 l (ms, List.length l, [], [])
90 ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
92 if restrictions_for_n = [] then
93 ms, if l = l' then orig else NCic.Meta (n, l')
95 let metasenv, subst, newmeta =
96 restrict metasenv subst n restrictions_for_n
98 (metasenv, subst), NCic.Meta (newmeta, l')
99 | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
101 aux 0 (metasenv,subst) t
103 and force_does_not_occur_in_context metasenv subst restrictions = function
104 | name, NCic.Decl t as orig ->
105 let (metasenv, subst), t' =
106 force_does_not_occur metasenv subst restrictions t in
107 metasenv, subst, (if t == t' then orig else (name,NCic.Decl t'))
108 | name, NCic.Def (bo, ty) as orig ->
109 let (metasenv, subst), bo' =
110 force_does_not_occur metasenv subst restrictions bo in
111 let (metasenv, subst), ty' =
112 force_does_not_occur metasenv subst restrictions ty in
114 (if bo == bo' && ty == ty' then orig else (name, NCic.Def (bo', ty')))
116 and erase_in_context metasenv subst pos restrictions = function
117 | [] -> metasenv, subst, restrictions, []
119 let metasenv, subst, restricted, tl' =
120 erase_in_context metasenv subst (pos+1) restrictions tl in
121 if List.mem pos restricted then
122 metasenv, subst, restricted, tl'
125 let metasenv, subst, hd' =
126 let delifted_restricted =
127 List.map ((+) ~-pos) (List.filter ((<=) pos) restricted) in
128 force_does_not_occur_in_context
129 metasenv subst delifted_restricted hd
131 metasenv, subst, restricted,
132 (if hd' == hd && tl' == tl then orig else (hd' :: tl'))
134 metasenv, subst, (pos :: restricted), tl'
136 and restrict metasenv subst i restrictions =
137 assert (restrictions <> []);
139 let name, ctx, bo, ty = NCicUtils.lookup_subst i subst in
141 let metasenv, subst, restrictions, newctx =
142 erase_in_context metasenv subst 1 restrictions ctx in
143 let (metasenv, subst), newty =
144 force_does_not_occur metasenv subst restrictions ty in
145 let (metasenv, subst), newbo =
146 force_does_not_occur metasenv subst restrictions bo in
147 let j = newmeta () in
148 let subst_entry_j = j, (name, newctx, newbo, newty) in
149 let reloc_irl = mk_perforated_irl 0 (List.length ctx) restrictions in
150 let subst_entry_i = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
152 subst_entry_j :: List.map
153 (fun (n,_) as orig -> if i = n then subst_entry_i else orig) subst
156 prerr_endline ("restringo nella subst: " ^string_of_int i ^ " -> " ^
157 string_of_int j ^ "\n" ^
158 NCicPp.ppsubst ~metasenv [subst_entry_j] ^ "\n\n" ^
159 NCicPp.ppsubst ~metasenv [subst_entry_i] ^ "\n" ^
160 NCicPp.ppterm ~metasenv ~subst ~context:ctx bo ^ " ---- " ^
161 NCicPp.ppterm ~metasenv ~subst ~context:newctx newbo
164 metasenv, new_subst, j
165 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
166 ("Cannot restrict the context of the metavariable ?%d over "^^
167 "the hypotheses %s since ?%d is already instantiated "^^
168 "with %s and at least one of the hypotheses occurs in "^^
169 "the substituted term") i (String.concat ", "
170 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)) i
171 (NCicPp.ppterm ~metasenv ~subst ~context:ctx bo))))
172 with NCicUtils.Subst_not_found _ ->
174 let name, ctx, ty = NCicUtils.lookup_meta i metasenv in
176 let metasenv, subst, restrictions, newctx =
177 erase_in_context metasenv subst 1 restrictions ctx in
178 let (metasenv, subst), newty =
179 force_does_not_occur metasenv subst restrictions ty in
180 let j = newmeta () in
181 let metasenv_entry = j, (name, newctx, newty) in
183 mk_perforated_irl 0 (List.length ctx) restrictions in
184 let subst_entry = i, (name, ctx, NCic.Meta (j, reloc_irl), ty) in
186 (fun (n,_) as orig -> if i = n then metasenv_entry else orig)
188 subst_entry :: subst, j
189 with Occur -> raise (MetaSubstFailure (lazy (Printf.sprintf
190 ("Cannot restrict the context of the metavariable ?%d "^^
191 "over the hypotheses %s since metavariable's type depends "^^
192 "on at least one of them") i (String.concat ", "
193 (List.map (fun x -> fst (List.nth ctx (x-1))) restrictions)))))
195 | NCicUtils.Meta_not_found _ -> assert false
198 let rec flexible_arg subst = function
199 | NCic.Meta (i,_) | NCic.Appl (NCic.Meta (i,_) :: _)->
201 let _,_,t,_ = List.assoc i subst in
203 with Not_found -> true)
207 let flexible subst l = List.exists (flexible_arg subst) l;;
209 let in_scope_tag = "tag:in_scope" ;;
210 let out_scope_tag_prefix = "tag:out_scope:"
211 let out_scope_tag n = out_scope_tag_prefix ^ string_of_int n ;;
212 let is_out_scope_tag tag =
213 String.length tag > String.length out_scope_tag_prefix &&
214 String.sub tag 0 (String.length out_scope_tag_prefix) = out_scope_tag_prefix
216 let int_of_out_scope_tag tag =
218 (String.sub tag (String.length out_scope_tag_prefix)
219 (String.length tag - (String.length out_scope_tag_prefix)))
225 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_),
226 otherwise the occur check does not make sense in case of unification
228 let delift ~unify metasenv subst context n l t =
229 let is_in_scope_meta subst = function
232 let tag, _, _, _ = NCicUtils.lookup_subst i subst in
233 tag = Some in_scope_tag
234 with NCicUtils.Subst_not_found _ -> false)
237 let contains_in_scope subst t =
238 let rec aux _ () = function
239 | NCic.Meta _ as t ->
240 if is_in_scope_meta subst t then raise Found
243 if is_in_scope_meta subst t then raise Found
244 else NCicUtils.fold (fun _ () -> ()) () aux () t
246 try aux () () t; false with Found -> true
248 let unify_list in_scope =
250 | _, NCic.Irl _ -> fun _ _ _ _ _ -> None
251 | shift, NCic.Ctx l -> fun metasenv subst context k t ->
252 if flexible_arg subst t || contains_in_scope subst t then None else
253 let lb = List.map (fun t -> t, flexible_arg subst t) l in
255 (fun (li,flexible) i ->
256 if flexible || i < in_scope then None else
257 let li = NCicSubstitution.lift (k+shift) li in
258 match unify metasenv subst context li t with
259 | Some (metasenv,subst) ->
260 Some ((metasenv, subst), NCic.Rel (i+1+k))
264 let rec aux (context,k,in_scope) (metasenv, subst as ms) t =
265 match unify_list in_scope metasenv subst context k t with
269 | NCic.Rel n as t when n <= k -> ms, t
272 match List.nth context (n-k-1) with
273 | _,NCic.Def (bo,_) ->
274 (try ms, NCic.Rel ((position in_scope (n-k) l) + k)
276 (* CSC: This bit of reduction hurts performances since it is
277 * possible to have an exponential explosion of the size of the
278 * proof. required for nat/nth_prime.ma *)
279 aux (context,k,in_scope) ms (NCicSubstitution.lift n bo))
280 | _,NCic.Decl _ -> ms, NCic.Rel ((position in_scope (n-k) l) + k)
281 with Failure _ -> assert false) (*Unbound variable found in delift*)
282 | NCic.Meta (i,_) when i=n ->
283 raise (MetaSubstFailure (lazy (Printf.sprintf (
284 "Cannot unify the metavariable ?%d with a term that has "^^
285 "as subterm %s in which the same metavariable "^^
286 "occurs (occur check)") i
287 (NCicPp.ppterm ~context ~metasenv ~subst t))))
288 | NCic.Meta (i,l1) as orig ->
290 let tag,c,t,ty = NCicUtils.lookup_subst i subst in
291 let in_scope, clear =
293 | Some tag when tag = in_scope_tag -> 0, true
294 | Some tag when is_out_scope_tag tag->int_of_out_scope_tag tag,true
295 | _ -> in_scope, false
301 (i,(None,c,t,ty)) :: List.filter (fun j,_ -> i <> j) subst
303 aux (context,k,in_scope) ms (NCicSubstitution.subst_meta l1 t)
304 with NCicUtils.Subst_not_found _ ->
305 if snd l1 = NCic.Irl 0 || snd l1 = NCic.Ctx [] then ms, orig
307 let shift1,lc1 = l1 in
309 let shift = shift + k in
311 | NCic.Irl len, NCic.Irl len1
312 when shift1 + len1 < shift || shift1 > shift + len ->
313 let restrictions = HExtlib.list_seq 1 (len1 + 1) in
314 let metasenv, subst, newmeta =
315 restrict metasenv subst i restrictions
318 NCic.Meta (newmeta, (0,NCic.Irl (max 0 (k-shift1))))
319 | NCic.Irl len, NCic.Irl len1 ->
320 let low_restrictions, new_shift =
321 if k <= shift1 && shift1 < shift then
322 HExtlib.list_seq 1 (shift - shift1 + 1), k
323 else if shift1 < k (* <= shift *) then
324 let save_below = k - shift1 in
325 HExtlib.list_seq (save_below + 1) (shift - shift1 + 1),
327 else [], shift1 - shift + k
329 let high_restrictions =
330 let last = shift + len in
331 let last1 = shift1 + len1 in
333 let high_gap = last1 - last in
334 HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
337 let restrictions = low_restrictions @ high_restrictions in
338 if restrictions = [] then
339 if shift = k then ms, orig
340 else ms, NCic.Meta (i, (new_shift, lc1))
342 let metasenv, subst, newmeta =
343 restrict metasenv subst i restrictions
346 prerr_endline ("RESTRICTIONS FOR: " ^
347 NCicPp.ppterm ~metasenv ~subst ~context:[]
348 (NCic.Meta (i,l1))^" that was part of a term unified with "
349 ^ NCicPp.ppterm ~metasenv ~subst ~context:[] (NCic.Meta
350 (n,l)) ^ " ====> " ^ String.concat "," (List.map
351 string_of_int restrictions) ^ "\nMENV:\n" ^
352 NCicPp.ppmetasenv ~subst metasenv ^ "\nSUBST:\n" ^
353 NCicPp.ppsubst subst ~metasenv);
355 let newlc_len = len1 - List.length restrictions in
357 NCic.Meta(newmeta,(new_shift, NCic.Irl newlc_len))
360 let _, cctx, _ = NCicUtils.lookup_meta newmeta metasenv in
361 List.length cctx = newlc_len);
362 (metasenv, subst), meta
365 let lc1 = NCicUtils.expand_local_context lc1 in
366 let lc1 = List.map (NCicSubstitution.lift shift1) lc1 in
367 let rec deliftl tbr j ms = function
370 let ms, tbr, tl = deliftl tbr (j+1) ms tl in
372 let ms, t = aux (context,k,in_scope) ms t in
375 | NotInTheList | MetaSubstFailure _ -> ms, j::tbr, tl
377 let (metasenv, subst), to_be_r, lc1' = deliftl [] 1 ms lc1 in
379 prerr_endline ("TO BE RESTRICTED: " ^
380 (String.concat "," (List.map string_of_int to_be_r)));
382 let l1 = pack_lc (0, NCic.Ctx lc1') in
384 prerr_endline ("newmeta:" ^ NCicPp.ppterm
385 ~metasenv ~subst ~context (NCic.Meta (999,l1)));
389 (if lc1' = lc1 then orig else NCic.Meta (i,l1))
391 let metasenv, subst, newmeta =
392 restrict metasenv subst i to_be_r in
393 (metasenv, subst), NCic.Meta(newmeta,l1))
396 NCicUntrusted.map_term_fold_a
397 (fun e (c,k,s) -> (e::c,k+1,s)) (context,k,in_scope) aux ms t
399 try aux (context,0,0) (metasenv,subst) t
401 (* This is the case where we fail even first order unification. *)
402 (* The reason is that our delift function is weaker than first *)
403 (* order (in the sense of alpha-conversion). See comment above *)
404 (* related to the delift function. *)
405 let msg = (lazy (Printf.sprintf
406 ("Error trying to abstract %s over [%s]: the algorithm only tried to "^^
407 "abstract over bound variables") (NCicPp.ppterm ~metasenv ~subst
408 ~context t) (String.concat "; " (List.map (NCicPp.ppterm ~metasenv
409 ~subst ~context) (let shift, lc = l in List.map (NCicSubstitution.lift
410 shift) (NCicUtils.expand_local_context lc))))))
413 let lc = NCicUtils.expand_local_context lc in
414 let l = List.map (NCicSubstitution.lift shift) lc in
418 NCicUntrusted.metas_of_term subst context t = [])
421 raise (Uncertain msg)
423 raise (MetaSubstFailure msg)
426 let mk_meta ?name metasenv context ty =
427 let tyof = function Some s -> Some ("typeof_"^s) | None -> None in
428 let rec mk_meta name n metasenv context = function
430 let len = List.length context in
431 let menv_entry = (n, (name, context, ty)) in
432 menv_entry :: metasenv, n, NCic.Meta (n, (0,NCic.Irl len)), ty
434 let ty = NCic.Implicit (`Typeof n) in
435 mk_meta (tyof name) n metasenv [] (`WithType ty)
437 let metasenv, _, ty, _ =
438 mk_meta (tyof name) (newmeta ()) metasenv context `Sort in
439 mk_meta name n metasenv context (`WithType ty)
441 let metasenv, _, ty, _ =
442 mk_meta (tyof name) (newmeta ()) metasenv context `Type in
443 mk_meta name n metasenv context (`WithType ty)
445 mk_meta name (newmeta ()) metasenv context ty
448 let saturate ?(delta=0) metasenv subst context ty goal_arity =
449 assert (goal_arity >= 0);
450 let rec aux metasenv = function
451 | NCic.Prod (name,s,t) as ty ->
452 let metasenv1, _, arg,_ =
453 mk_meta ~name:name metasenv context (`WithType s) in
454 let t, metasenv1, args, pno =
455 aux metasenv1 (NCicSubstitution.subst arg t)
457 if pno + 1 = goal_arity then
458 ty, metasenv, [], goal_arity+1
460 t, metasenv1, arg::args, pno+1
462 match NCicReduction.whd ~subst context ty ~delta with
463 | NCic.Prod _ as ty -> aux metasenv ty
464 | ty -> ty, metasenv, [], 0
466 let res, newmetasenv, arguments, _ = aux metasenv ty in
467 res, newmetasenv, arguments