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 UnificationFailure of string Lazy.t;;
15 exception Uncertain of string Lazy.t;;
16 exception AssertFailure of string Lazy.t;;
17 exception KeepReducing of string Lazy.t;;
18 exception KeepReducingThis of
19 string Lazy.t * (NCicReduction.machine * bool) *
20 (NCicReduction.machine * bool) ;;
22 let (===) x y = Pervasives.compare x y = 0 ;;
24 let mk_msg metasenv subst context t1 t2 =
26 "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
27 " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
29 let mk_appl ~upto hd tl =
30 NCicReduction.head_beta_reduce ~upto
32 | NCic.Appl l -> NCic.Appl (l@tl)
33 | _ -> NCic.Appl (hd :: tl))
36 exception WrongShape;;
38 let eta_reduce subst t =
39 let delift_if_not_occur body =
41 Some (NCicSubstitution.psubst ~avoid_beta_redexes:true
42 (fun () -> raise WrongShape) [()] body)
43 with WrongShape -> None
45 let rec eat_lambdas ctx = function
46 | NCic.Lambda (name, src, tgt) ->
47 eat_lambdas ((name, src) :: ctx) tgt
48 | NCic.Meta (i,lc) as t->
50 let _,_,t,_ = NCicUtils.lookup_subst i subst in
51 let t = NCicSubstitution.subst_meta lc t in
53 with Not_found -> ctx, t)
56 let context_body = eat_lambdas [] t in
57 let rec aux = function
59 | (name, src)::ctx, (NCic.Appl (hd::[NCic.Rel 1]) as bo) ->
60 (match delift_if_not_occur hd with
61 | None -> aux (ctx,NCic.Lambda(name,src, bo))
62 | Some bo -> aux (ctx,bo))
63 | (name, src)::ctx, (NCic.Appl args as bo)
64 when HExtlib.list_last args = NCic.Rel 1 ->
65 let args, _ = HExtlib.split_nth (List.length args - 1) args in
66 (match delift_if_not_occur (NCic.Appl args) with
67 | None -> aux (ctx,NCic.Lambda(name,src, bo))
68 | Some bo -> aux (ctx,bo))
69 | (name, src) :: ctx, t ->
70 aux (ctx,NCic.Lambda(name,src, t))
76 module Ref = NReference;;
78 let debug = ref false;;
83 prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
88 let time1 = Unix.gettimeofday () in
89 indent := !indent ^ String.make 1 c;
90 times := time1 :: !times;
91 prerr_endline ("{{{" ^ !indent ^ " ")
97 let time2 = Unix.gettimeofday () in
99 match !times with time1::tl -> times := tl; time1 | [] -> assert false in
100 prerr_endline ("}}} " ^ string_of_float (time2 -. time1));
102 | Some e -> prerr_endline ("exception raised: " ^ Printexc.to_string e)
105 indent := String.sub !indent 0 (String.length !indent -1)
107 Invalid_argument _ -> indent := "??"; ()
111 let ppcontext ~metasenv ~subst c =
112 "\nctx:\n"^ NCicPp.ppcontext ~metasenv ~subst c
114 let ppmetasenv ~subst m = "\nmenv:\n" ^ NCicPp.ppmetasenv ~subst m;;
116 let ppcontext ~metasenv:_metasenv ~subst:_subst _context = "";;
117 let ppmetasenv ~subst:_subst _metasenv = "";;
118 let ppterm ~metasenv ~subst ~context = NCicPp.ppterm ~metasenv ~subst ~context;;
119 (* let ppterm ~metasenv:_ ~subst:_ ~context:_ _ = "";; *)
121 let is_locked n subst =
123 match NCicUtils.lookup_subst n subst with
124 | tag, _,_,_ when NCicMetaSubst.is_out_scope_tag tag -> true
126 with NCicUtils.Subst_not_found _ -> false
129 let rec mk_irl stop base =
130 if base > stop then []
131 else (NCic.Rel base) :: mk_irl stop (base+1)
134 (* the argument must be a term in whd *)
135 let rec could_reduce =
138 | C.Appl (C.Const (Ref.Ref (_,Ref.Fix (_,recno,_)))::args)
139 when List.length args > recno -> could_reduce (List.nth args recno)
140 | C.Match (_,_,arg,_) -> could_reduce arg
141 | C.Appl (he::_) -> could_reduce he
142 | C.Sort _ | C.Rel _ | C.Prod _ | C.Lambda _ | C.Const _ -> false
143 | C.Appl [] | C.LetIn _ | C.Implicit _ -> assert false
146 let rec lambda_intros rdb metasenv subst context argsno ty =
147 pp (lazy ("LAMBDA INTROS: " ^ ppterm ~metasenv ~subst ~context ty));
150 let metasenv, _, bo, _ =
151 NCicMetaSubst.mk_meta metasenv context ~with_type:ty `IsTerm
155 (match NCicReduction.whd ~subst context ty with
158 lambda_intros rdb metasenv subst
159 ((n,C.Decl so)::context) (argsno - 1) ta
161 metasenv,C.Lambda (n,so,bo)
165 let unopt exc = function None -> raise exc | Some x -> x ;;
167 let fix metasenv subst is_sup test_eq_only exc t =
168 let rec aux test_eq_only metasenv = function
169 | NCic.Prod (n,so,ta) ->
170 let metasenv,so = aux true metasenv so in
171 let metasenv,ta = aux test_eq_only metasenv ta in
172 metasenv,NCic.Prod (n,so,ta)
173 | NCic.Sort (NCic.Type [(`CProp|`Type),_]) as orig when test_eq_only ->
175 | NCic.Sort (NCic.Type _) when test_eq_only -> raise exc
176 | NCic.Sort (NCic.Type u) when is_sup ->
177 metasenv, NCic.Sort (NCic.Type (unopt exc (NCicEnvironment.sup u)))
178 | NCic.Sort (NCic.Type u) ->
179 metasenv, NCic.Sort (NCic.Type
180 (unopt exc (NCicEnvironment.inf ~strict:false u)))
181 | NCic.Meta (n,_) as orig ->
183 let _,_,_,_ = NCicUtils.lookup_subst n subst in metasenv,orig
184 with NCicUtils.Subst_not_found _ ->
185 let metasenv, _ = NCicMetaSubst.extend_meta metasenv n in
188 NCicUntrusted.map_term_fold_a (fun _ x -> x) test_eq_only aux metasenv t
190 aux test_eq_only metasenv t
193 let rec sortfy exc metasenv subst = function
194 | NCic.Sort _ as orig -> metasenv, orig
195 | NCic.Meta (n,lc) ->
196 let attrs, context, ty = NCicUtils.lookup_meta n metasenv in
197 let kind = NCicUntrusted.kind_of_meta attrs in
198 kindfy exc metasenv subst context n lc ty kind `IsSort
199 | NCic.Implicit _ -> assert false
202 and kindfy exc metasenv subst context n lc ty kind kind2 =
203 match kind, ty, kind2 with
204 | `IsSort, _, _ -> assert(snd lc = NCic.Irl 0); metasenv, NCic.Meta(n,lc)
205 | k1, NCic.Implicit (`Typeof _), (`IsType|`IsTerm as k2) ->
206 let k = NCicUntrusted.max_kind k1 k2 in
208 NCicUntrusted.replace_in_metasenv n
209 (fun attrs,cc,ty -> NCicUntrusted.set_kind k attrs, cc, ty) metasenv
211 metasenv, NCic.Meta(n,lc)
212 | _, NCic.Implicit (`Typeof _), `IsSort ->
214 NCicUntrusted.replace_in_metasenv n
215 (fun attrs,_,ty-> NCicUntrusted.set_kind `IsSort attrs,[],ty) metasenv
217 metasenv, NCic.Meta (n,(0,NCic.Irl 0))
220 sortfy exc metasenv subst (NCicReduction.whd ~subst context ty)
223 NCicUntrusted.replace_in_metasenv n
224 (fun attrs,_,_-> NCicUntrusted.set_kind `IsSort attrs,[],ty) metasenv
226 metasenv, NCic.Meta (n,(0,NCic.Irl 0))
227 | k1, _, k2 when NCicUntrusted.max_kind k1 k2 = k1-> metasenv, NCic.Meta(n,lc)
228 | `IsTerm, ty, `IsType ->
230 sortfy exc metasenv subst (NCicReduction.whd ~subst context ty)
233 NCicUntrusted.replace_in_metasenv n
234 (fun attrs,cc,_-> NCicUntrusted.set_kind `IsType attrs,cc,ty) metasenv
236 metasenv, NCic.Meta (n,lc)
237 | _ -> assert false (* XXX *)
239 and instantiate rdb test_eq_only metasenv subst context n lc t swap =
240 (*D*) inside 'I'; try let rc =
241 pp (lazy(string_of_int n^" :=?= "^ppterm ~metasenv ~subst ~context t));
243 UnificationFailure (mk_msg metasenv subst context (NCic.Meta (n,lc)) t) in
244 let move_to_subst i attrs cc t ty metasenv subst =
245 let metasenv = List.remove_assoc i metasenv in
246 pp (lazy(string_of_int n ^ " :==> "^
247 ppterm ~metasenv ~subst ~context:cc t));
248 metasenv, (i,(attrs, cc, t, ty)) :: subst
250 let delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst =
251 pp (lazy(string_of_int n ^ " := 111 = "^
252 ppterm ~metasenv ~subst ~context t));
253 let (metasenv, subst), t =
256 ~unify:(fun m s c t1 t2 ->
259 try Some (unify rdb test_eq_only m s c t1 t2 )
260 with UnificationFailure _ | Uncertain _ -> None
263 metasenv subst context n lc t
264 with NCicMetaSubst.Uncertain msg ->
265 pp (lazy ("delift is uncertain: " ^ Lazy.force msg));
266 raise (Uncertain msg)
267 | NCicMetaSubst.MetaSubstFailure msg ->
268 pp (lazy ("delift fails: " ^ Lazy.force msg));
269 raise (UnificationFailure msg)
271 pp (lazy(string_of_int n ^ " := 222 = "^
272 ppterm ~metasenv ~subst ~context:cc t^ppmetasenv ~subst metasenv));
273 (* Unifying the types may have already instantiated n. *)
275 let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
276 let oldt = NCicSubstitution.subst_meta lc oldt in
277 let t = NCicSubstitution.subst_meta lc t in
278 (* conjecture: always fail --> occur check *)
279 unify rdb test_eq_only metasenv subst context t oldt
280 with NCicUtils.Subst_not_found _ ->
281 move_to_subst n attrs cc t ty metasenv subst
283 let attrs, cc, ty = NCicUtils.lookup_meta n metasenv in
284 match NCicUntrusted.kind_of_meta attrs, ty, t, swap with
285 | `IsSort, (NCic.Implicit (`Typeof _) as bot), NCic.Sort (NCic.Type u),false->
287 let u = NCicEnvironment.inf ~strict:false u in
288 let t = NCic.Sort (NCic.Type (unopt exc u)) in
289 move_to_subst n attrs cc t bot metasenv subst
290 | `IsSort, (NCic.Implicit (`Typeof _) as bot), NCic.Sort (NCic.Type u),true ->
292 let u = NCicEnvironment.sup u in
293 let t = NCic.Sort (NCic.Type (unopt exc u)) in
294 move_to_subst n attrs cc t bot metasenv subst
295 | `IsSort, (NCic.Sort(NCic.Type u1) as ty), NCic.Sort (NCic.Type u2), false ->
298 NCicEnvironment.inf ~strict:false (u1 @
299 unopt exc (NCicEnvironment.inf ~strict:true u2))
301 let t = NCic.Sort (NCic.Type (unopt exc u)) in
302 move_to_subst n attrs cc t ty metasenv subst
303 | `IsSort, (NCic.Sort(NCic.Type u1) as ty), NCic.Sort (NCic.Type u2), true ->
305 let u = unopt exc (NCicEnvironment.sup u2) in
306 if NCicEnvironment.universe_lt u u1 then
307 let t = NCic.Sort (NCic.Type u) in
308 move_to_subst n attrs cc t ty metasenv subst
310 | kind, ty, NCic.Meta(m,lcm), _ when List.mem_assoc m subst ->
311 let at,ccm,bo,tym = NCicUtils.lookup_subst m subst in
312 if NCicMetaSubst.is_out_scope_tag at then
314 (* Case meta vs out-scope *)
316 let ty_t, ccm, kindm =
317 NCicSubstitution.subst_meta lcm tym, ccm,
318 NCicUntrusted.kind_of_meta at in
319 let lty = NCicSubstitution.subst_meta lc ty in
320 pp (lazy ("On the types: " ^
321 ppterm ~metasenv ~subst ~context lty ^
322 (if test_eq_only then " === " else "=<=") ^
323 ppterm ~metasenv ~subst ~context ty_t));
324 let metasenv, subst =
325 unify rdb test_eq_only metasenv subst context ty_t lty in
326 (*CSC: here I should call kindfy, but it fails since the second
327 meta in in the susbt, not the metasenv! *)
328 (* let metasenv,t = kindfy exc metasenv subst ccm m lcm ty_t kindm kind in *)
329 delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst
332 let bo = NCicSubstitution.subst_meta lcm bo in
333 instantiate rdb test_eq_only metasenv subst context n lc bo swap
334 | kind, (NCic.Implicit (`Typeof _) as bot), NCic.Meta(m,lcm), _ ->
336 let attrsm, ccm, tym = NCicUtils.lookup_meta m metasenv in
337 let kindm = NCicUntrusted.kind_of_meta attrsm in
338 let metasenv, t = kindfy exc metasenv subst ccm m lcm tym kindm kind in
339 move_to_subst n attrs cc t bot metasenv subst
340 | kind, ty, (NCic.Meta(m,_) as t), _ when
341 let _, _, tym = NCicUtils.lookup_meta m metasenv in
342 (match tym with NCic.Implicit (`Typeof _) -> true | _ -> false) ->
344 let attrsm, _, _ = NCicUtils.lookup_meta m metasenv in
345 let kindm = NCicUntrusted.kind_of_meta attrsm in
346 let metasenv, _ = kindfy exc metasenv subst cc n lc ty kind kindm in
347 let attrs, cc, ty = NCicUtils.lookup_meta n metasenv in
348 let metasenv = NCicUntrusted.replace_in_metasenv m
349 (fun _,_,_ -> attrs,cc,ty) metasenv
351 (* XXX *)move_to_subst n attrs cc t ty metasenv subst
352 | kind, ty, NCic.Meta(m,lcm), _ ->
354 let ty_t, ccm, kindm =
355 let at, ccm, tym = NCicUtils.lookup_meta m metasenv in
356 NCicSubstitution.subst_meta lcm tym, ccm, NCicUntrusted.kind_of_meta at
358 let lty = NCicSubstitution.subst_meta lc ty in
359 pp (lazy ("On the types: " ^
360 ppterm ~metasenv ~subst ~context lty ^
361 (if test_eq_only then " === " else "=<=") ^
362 ppterm ~metasenv ~subst ~context ty_t));
363 let metasenv, subst =
364 unify rdb test_eq_only metasenv subst context ty_t lty
366 let metasenv, t = kindfy exc metasenv subst ccm m lcm ty_t kindm kind in
367 delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst
368 | _, (NCic.Implicit (`Typeof _) as bot), t, swap ->
370 let metasenv, t = fix metasenv subst swap test_eq_only exc t in
371 (* let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in *)
372 (* ty andrebbe deliftato *)
373 delift_to_subst test_eq_only n lc attrs cc t bot context metasenv subst
376 let lty = NCicSubstitution.subst_meta lc ty in
377 let metasenv, t = fix metasenv subst swap test_eq_only exc t in
378 let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in
379 pp (lazy ("On the types: " ^
380 ppterm ~metasenv ~subst ~context lty ^
381 (if test_eq_only then " === " else "=<=") ^
382 ppterm ~metasenv ~subst ~context ty_t));
383 let metasenv, subst =
384 unify rdb test_eq_only metasenv subst context ty_t lty
386 delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst
387 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
389 and unify rdb test_eq_only metasenv subst context t1 t2 =
390 (*D*) inside 'U'; try let rc =
391 let fo_unif test_eq_only metasenv subst (norm1,t1) (norm2,t2) =
392 (*D*) inside 'F'; try let rc =
393 pp (lazy(" " ^ ppterm ~metasenv ~subst ~context t1 ^ " ==?== " ^
394 ppterm ~metasenv ~subst ~context t2 ^ ppmetasenv
396 pp (lazy(" " ^ ppterm ~metasenv ~subst:[] ~context t1 ^ " ==??== " ^
397 ppterm ~metasenv ~subst:[] ~context t2 ^ ppmetasenv
401 (* CSC: To speed up Oliboni's stuff. Why is it necessary, anyway?
403 NCicUntrusted.metas_of_term subst context t1 = [] &&
404 NCicUntrusted.metas_of_term subst context t2 = []
406 if NCicReduction.are_convertible ~metasenv ~subst context t1 t2 then
409 raise (UnificationFailure (lazy "Closed terms not convertible"))
413 | C.Appl [_], _ | _, C.Appl [_] | C.Appl [], _ | _, C.Appl []
414 | C.Appl (C.Appl _::_), _ | _, C.Appl (C.Appl _::_) ->
415 prerr_endline "Appl [Appl _;_] or Appl [] or Appl [_] invariant";
417 | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
418 if NCicEnvironment.universe_leq a b then metasenv, subst
419 else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
420 | (C.Sort (C.Type a), C.Sort (C.Type b)) ->
421 if NCicEnvironment.universe_eq a b then metasenv, subst
422 else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
423 | (C.Sort C.Prop,C.Sort (C.Type _)) ->
424 if (not test_eq_only) then metasenv, subst
425 else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
427 | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2))
428 | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
429 let metasenv, subst = unify rdb true metasenv subst context s1 s2 in
430 unify rdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
431 | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
432 let metasenv,subst=unify rdb test_eq_only metasenv subst context ty1 ty2 in
433 let metasenv,subst=unify rdb test_eq_only metasenv subst context s1 s2 in
434 let context = (name1, C.Def (s1,ty1))::context in
435 unify rdb test_eq_only metasenv subst context t1 t2
437 | (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
439 let l1 = NCicUtils.expand_local_context l1 in
440 let l2 = NCicUtils.expand_local_context l2 in
441 let metasenv, subst, to_restrict, _ =
443 (fun t1 t2 (metasenv, subst, to_restrict, i) ->
445 let metasenv, subst =
446 unify rdb test_eq_only metasenv subst context
447 (NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
449 metasenv, subst, to_restrict, i-1
450 with UnificationFailure _ | Uncertain _ ->
451 metasenv, subst, i::to_restrict, i-1)
452 l1 l2 (metasenv, subst, [], List.length l1)
454 if to_restrict <> [] then
455 let metasenv, subst, _ =
456 NCicMetaSubst.restrict metasenv subst n1 to_restrict
461 | Invalid_argument _ -> assert false
462 | NCicMetaSubst.MetaSubstFailure msg ->
464 let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
465 let term1 = NCicSubstitution.subst_meta lc1 term in
466 let term2 = NCicSubstitution.subst_meta lc2 term in
467 unify rdb test_eq_only metasenv subst context term1 term2
468 with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
470 | NCic.Appl (NCic.Meta (i,_)::_ as l1),
471 NCic.Appl (NCic.Meta (j,_)::_ as l2) when i=j ->
474 (fun (metasenv, subst) t1 t2 ->
475 unify rdb test_eq_only metasenv subst context t1 t2)
476 (metasenv,subst) l1 l2
477 with Invalid_argument _ ->
478 raise (UnificationFailure (mk_msg metasenv subst context t1 t2)))
480 | _, NCic.Meta (n, _) when is_locked n subst ->
481 (let (metasenv, subst), i =
482 match NCicReduction.whd ~subst context t1 with
483 | NCic.Appl (NCic.Meta (i,l) as meta :: args) ->
484 let metasenv, lambda_Mj =
485 lambda_intros rdb metasenv subst context (List.length args)
486 (NCicTypeChecker.typeof ~metasenv ~subst context meta)
488 unify rdb test_eq_only metasenv subst context
489 (C.Meta (i,l)) lambda_Mj,
491 | NCic.Meta (i,_) -> (metasenv, subst), i
493 raise (UnificationFailure (lazy "Locked term vs non
494 flexible term; probably not saturated enough yet!"))
496 let t1 = NCicReduction.whd ~subst context t1 in
498 match t1 with NCic.Meta (j,l) -> j, l | _ -> assert false
500 let metasenv, subst =
501 instantiate rdb test_eq_only metasenv subst context j lj t2 true
503 (* We need to remove the out_scope_tags to avoid propagation of
504 them that triggers again the ad-hoc case *)
506 List.map (fun (i,(tag,ctx,bo,ty)) ->
509 (function `InScope | `OutScope _ -> false | _ -> true) tag
515 let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
516 let term = eta_reduce subst term in
517 let subst = List.filter (fun (j,_) -> j <> i) subst in
518 metasenv, ((i, (name, ctx, term, ty)) :: subst)
519 with Not_found -> assert false))
521 | C.Meta (n,lc), t when List.mem_assoc n subst ->
522 let _,_,term,_ = NCicUtils.lookup_subst n subst in
523 let term = NCicSubstitution.subst_meta lc term in
524 unify rdb test_eq_only metasenv subst context term t
526 | t, C.Meta (n,lc) when List.mem_assoc n subst ->
527 let _,_,term,_ = NCicUtils.lookup_subst n subst in
528 let term = NCicSubstitution.subst_meta lc term in
529 unify rdb test_eq_only metasenv subst context t term
531 | NCic.Appl (NCic.Meta (i,l)::args), _ when List.mem_assoc i subst ->
532 let _,_,term,_ = NCicUtils.lookup_subst i subst in
533 let term = NCicSubstitution.subst_meta l term in
534 unify rdb test_eq_only metasenv subst context
535 (mk_appl ~upto:(List.length args) term args) t2
537 | _, NCic.Appl (NCic.Meta (i,l)::args) when List.mem_assoc i subst ->
538 let _,_,term,_ = NCicUtils.lookup_subst i subst in
539 let term = NCicSubstitution.subst_meta l term in
540 unify rdb test_eq_only metasenv subst context t1
541 (mk_appl ~upto:(List.length args) term args)
543 | C.Meta (n,lc), t ->
544 instantiate rdb test_eq_only metasenv subst context n lc
545 (NCicReduction.head_beta_reduce ~subst t) false
547 | t, C.Meta (n,lc) ->
548 instantiate rdb test_eq_only metasenv subst context n lc
549 (NCicReduction.head_beta_reduce ~subst t) true
551 | NCic.Appl (NCic.Meta (i,l) as meta :: args), _ ->
552 let metasenv, lambda_Mj =
553 lambda_intros rdb metasenv subst context (List.length args)
554 (NCicTypeChecker.typeof ~metasenv ~subst context meta)
556 let metasenv, subst =
558 unify rdb test_eq_only metasenv subst context
559 (C.Meta (i,l)) lambda_Mj
560 with UnificationFailure msg | Uncertain msg when not norm2->
561 (* failure: let's try again argument vs argument *)
562 raise (KeepReducing msg)
564 let metasenv, subst =
565 unify rdb test_eq_only metasenv subst context t1 t2
568 let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
569 let term = eta_reduce subst term in
570 let subst = List.filter (fun (j,_) -> j <> i) subst in
571 metasenv, ((i, (name, ctx, term, ty)) :: subst)
572 with Not_found -> assert false)
574 | _, NCic.Appl (NCic.Meta (i,l) as meta :: args) ->
575 let metasenv, lambda_Mj =
576 lambda_intros rdb metasenv subst context (List.length args)
577 (NCicTypeChecker.typeof ~metasenv ~subst context meta)
579 let metasenv, subst =
581 unify rdb test_eq_only metasenv subst context
582 lambda_Mj (C.Meta (i,l))
583 with UnificationFailure msg | Uncertain msg when not norm1 ->
584 (* failure: let's try again argument vs argument *)
585 raise (KeepReducing msg)
587 let metasenv, subst =
588 unify rdb test_eq_only metasenv subst context t1 t2
591 let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
592 let term = eta_reduce subst term in
593 let subst = List.filter (fun (j,_) -> j <> i) subst in
594 metasenv, ((i, (name, ctx, term, ty)) :: subst)
595 with Not_found -> assert false)
597 (* processing this case here we avoid a useless small delta step *)
598 | (C.Appl ((C.Const r1) as _hd1::tl1), C.Appl (C.Const r2::tl2))
600 let relevance = NCicEnvironment.get_relevance r1 in
601 let metasenv, subst, _ =
604 (fun (metasenv, subst, relevance) t1 t2 ->
606 match relevance with b::tl -> b,tl | _ -> true, [] in
607 let metasenv, subst =
608 try unify rdb test_eq_only metasenv subst context t1 t2
609 with UnificationFailure _ | Uncertain _ when not b ->
612 metasenv, subst, relevance)
613 (metasenv, subst, relevance) tl1 tl2
615 Invalid_argument _ ->
616 raise (Uncertain (mk_msg metasenv subst context t1 t2))
617 | UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
618 raise (KeepReducing (mk_msg metasenv subst context t1 t2))
619 | KeepReducing _ | KeepReducingThis _ -> assert false
623 | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
624 C.Match (ref2,outtype2,term2,pl2)) ->
625 let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
626 let _,_,ty,_ = List.nth itl tyno in
627 let rec remove_prods ~subst context ty =
628 let ty = NCicReduction.whd ~subst context ty in
631 | C.Prod (name,so,ta) ->
632 remove_prods ~subst ((name,(C.Decl so))::context) ta
636 match remove_prods ~subst [] ty with
637 | C.Sort C.Prop -> true
640 if not (Ref.eq ref1 ref2) then
641 raise (Uncertain (mk_msg metasenv subst context t1 t2))
643 let metasenv, subst =
644 unify rdb test_eq_only metasenv subst context outtype1 outtype2 in
645 let metasenv, subst =
646 try unify rdb test_eq_only metasenv subst context term1 term2
647 with UnificationFailure _ | Uncertain _ when is_prop ->
652 (fun (metasenv,subst) ->
653 unify rdb test_eq_only metasenv subst context)
654 (metasenv, subst) pl1 pl2
655 with Invalid_argument _ -> assert false)
656 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
657 | _ when norm1 && norm2 ->
658 if (could_reduce t1 || could_reduce t2) then
659 raise (Uncertain (mk_msg metasenv subst context t1 t2))
661 raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
662 | _ -> raise (KeepReducing (mk_msg metasenv subst context t1 t2))
663 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
665 let try_hints metasenv subst (_,t1 as mt1) (_,t2 as mt2) (* exc*) =
666 (*D*) inside 'H'; try let rc =
667 pp(lazy ("\nProblema:\n" ^
668 ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
669 ppterm ~metasenv ~subst ~context t2));
671 NCicUnifHint.look_for_hint rdb metasenv subst context t1 t2
673 let rec cand_iter = function
674 | [] -> None (* raise exc *)
675 | (metasenv,(c1,c2),premises)::tl ->
676 pp (lazy ("\nProvo il candidato:\n" ^
680 ppterm ~metasenv ~subst ~context a ^ " =?= " ^
681 ppterm ~metasenv ~subst ~context b) premises) ^
682 "\n-------------------------------------------\n"^
683 ppterm ~metasenv ~subst ~context c1 ^ " = " ^
684 ppterm ~metasenv ~subst ~context c2));
686 (*D*) inside 'K'; try let rc =
688 fo_unif test_eq_only metasenv subst mt1 (false,c1) in
690 fo_unif test_eq_only metasenv subst (false,c2) mt2 in
693 (fun (metasenv, subst) (x,y) ->
694 unify rdb test_eq_only metasenv subst context x y)
695 (metasenv, subst) premises
697 pp(lazy("FUNZIONA!"));
698 Some (metasenv, subst)
699 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
701 KeepReducing _ | UnificationFailure _ | Uncertain _ -> cand_iter tl
702 | KeepReducingThis _ -> assert false
705 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
707 let put_in_whd m1 m2 =
708 NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
709 NCicReduction.reduce_machine ~delta:max_int ~subst context m2
711 let fo_unif_w_hints test_eq_only metasenv subst (_,t1 as m1) (_,t2 as m2) =
712 try fo_unif test_eq_only metasenv subst m1 m2
714 | UnificationFailure _ as exn -> raise exn
715 | KeepReducing _ | Uncertain _ as exn ->
716 let (t1,norm1 as tm1),(t2,norm2 as tm2) =
717 put_in_whd (0,[],t1,[]) (0,[],t2,[])
720 try_hints metasenv subst
721 (norm1,NCicReduction.unwind t1) (norm2,NCicReduction.unwind t2)
726 | KeepReducing msg -> raise (KeepReducingThis (msg,tm1,tm2))
727 | Uncertain _ as exn -> raise exn
730 let height_of = function
731 | NCic.Const (Ref.Ref (_,Ref.Def h))
732 | NCic.Const (Ref.Ref (_,Ref.Fix (_,_,h)))
733 | NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Def h))::_)
734 | NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
737 let small_delta_step ~subst
738 ((_,_,t1,_ as m1, norm1) as x1) ((_,_,t2,_ as m2, norm2) as x2)
740 assert (not (norm1 && norm2));
742 x1,NCicReduction.reduce_machine ~delta:0 ~subst context m2
744 NCicReduction.reduce_machine ~delta:0 ~subst context m1,x2
746 let h1 = height_of t1 in
747 let h2 = height_of t2 in
748 let delta = if h1 = h2 then max 0 (h1 -1) else min h1 h2 in
749 NCicReduction.reduce_machine ~delta ~subst context m1,
750 NCicReduction.reduce_machine ~delta ~subst context m2
752 let rec unif_machines metasenv subst =
754 | ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2),norm2 as m2) ->
755 (*D*) inside 'M'; try let rc =
757 ppterm ~metasenv ~subst ~context
758 (NCicReduction.unwind (k1,e1,t1,s1)) ^
760 ppterm ~metasenv ~subst ~context
761 (NCicReduction.unwind (k2,e2,t2,s2))));
762 pp (lazy (string_of_bool norm1 ^ " ?? " ^ string_of_bool norm2));
763 let relevance = [] (* TO BE UNDERSTOOD
765 | C.Const r -> NCicEnvironment.get_relevance r
767 let unif_from_stack t1 t2 b metasenv subst =
769 let t1 = NCicReduction.from_stack ~delta:max_int t1 in
770 let t2 = NCicReduction.from_stack ~delta:max_int t2 in
771 unif_machines metasenv subst (put_in_whd t1 t2)
772 with UnificationFailure _ | Uncertain _ when not b ->
775 let rec check_stack l1 l2 r todo =
777 | x1::tl1, x2::tl2, r::tr-> check_stack tl1 tl2 tr ((x1,x2,r)::todo)
778 | x1::tl1, x2::tl2, []-> check_stack tl1 tl2 [] ((x1,x2,true)::todo)
780 NCicReduction.unwind (k1,e1,t1,List.rev l1),
781 NCicReduction.unwind (k2,e2,t2,List.rev l2),
784 let hh1,hh2,todo=check_stack (List.rev s1) (List.rev s2) relevance [] in
787 fo_unif_w_hints test_eq_only metasenv subst (norm1,hh1) (norm2,hh2) in
789 (fun (metasenv,subst) (x1,x2,r) ->
790 unif_from_stack x1 x2 r metasenv subst
791 ) (metasenv,subst) todo
793 | KeepReducing _ -> assert false
794 | KeepReducingThis _ ->
795 assert (not (norm1 && norm2));
796 unif_machines metasenv subst (small_delta_step ~subst m1 m2)
797 | UnificationFailure _ | Uncertain _ when (not (norm1 && norm2))
798 -> unif_machines metasenv subst (small_delta_step ~subst m1 m2)
799 | UnificationFailure msg
800 when could_reduce (NCicReduction.unwind (fst m1))
801 || could_reduce (NCicReduction.unwind (fst m2))
802 -> raise (Uncertain msg)
803 (*D*) in outside None; rc with exn -> outside (Some exn); raise exn
805 try fo_unif_w_hints test_eq_only metasenv subst (false,t1) (false,t2)
807 | KeepReducingThis (msg,tm1,tm2) ->
809 unif_machines metasenv subst (tm1,tm2)
811 | UnificationFailure _ -> raise (UnificationFailure msg)
812 | Uncertain _ -> raise (Uncertain msg)
813 | KeepReducing _ -> assert false)
814 | KeepReducing _ -> assert false
816 (*D*) in outside None; rc with KeepReducing _ -> assert false | exn -> outside (Some exn); raise exn
818 and delift_type_wrt_terms rdb metasenv subst context t args =
819 let lc = List.rev args @ mk_irl (List.length context) (List.length args+1) in
820 let (metasenv, subst), t =
823 ~unify:(fun m s c t1 t2 ->
826 try Some (unify rdb false m s c t1 t2 )
827 with UnificationFailure _ | Uncertain _ -> None
830 metasenv subst context 0 (0,NCic.Ctx lc) t
832 NCicMetaSubst.MetaSubstFailure _
833 | NCicMetaSubst.Uncertain _ -> (metasenv, subst), t
839 let unify rdb ?(test_eq_only=false) =
841 unify rdb test_eq_only;;
844 fix m s true false (UnificationFailure (lazy "no sup"))