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;;
18 let (===) x y = Pervasives.compare x y = 0 ;;
20 let uncert_exc metasenv subst context t1 t2 =
22 "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
23 " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
26 let fail_exc metasenv subst context t1 t2 =
27 UnificationFailure (lazy (
28 "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
29 " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
34 | NCic.Appl l -> NCic.Appl (l@tl)
35 | _ -> NCic.Appl (hd :: tl)
42 | NCic.Appl (NCic.Meta _::_) -> true
46 exception WrongShape;;
49 let delift_if_not_occur body orig =
51 NCicSubstitution.psubst ~avoid_beta_redexes:true
52 (fun () -> raise WrongShape) [()] body
53 with WrongShape -> orig
56 | NCic.Lambda(_, _, NCic.Appl [hd; NCic.Rel 1]) as orig ->
57 delift_if_not_occur hd orig
58 | NCic.Lambda(_, _, NCic.Appl (hd :: l)) as orig
59 when HExtlib.list_last l = NCic.Rel 1 ->
61 let args, _ = HExtlib.split_nth (List.length l - 1) l in
64 delift_if_not_occur body orig
69 module Ref = NReference;;
72 let inside c = indent := !indent ^ String.make 1 c;;
73 let outside () = indent := String.sub !indent 0 (String.length !indent -1);;
77 prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
83 let rec beta_expand num test_eq_only swap metasenv subst context t arg =
84 let rec aux (n,context,test_eq_only as k) (metasenv, subst as acc) t' =
88 unify test_eq_only metasenv subst context t' (NCicSubstitution.lift n arg)
90 unify test_eq_only metasenv subst context (NCicSubstitution.lift n arg) t'
92 (metasenv, subst), NCic.Rel (1 + n)
93 with Uncertain _ | UnificationFailure _ ->
95 | NCic.Rel m as orig ->
96 (metasenv, subst), if m <= n then orig else NCic.Rel (m+1)
97 (* andrea: in general, beta_expand can create badly typed
98 terms. This happens quite seldom in practice, UNLESS we
99 iterate on the local context. For this reason, we renounce
100 to iterate and just lift *)
101 | NCic.Meta (i,(shift,lc)) ->
102 (metasenv,subst), NCic.Meta (i,(shift+1,lc))
103 | NCic.Prod (name, src, tgt) as orig ->
104 let (metasenv, subst), src1 = aux (n,context,true) acc src in
105 let k = n+1, (name, NCic.Decl src) :: context, test_eq_only in
106 let ms, tgt1 = aux k (metasenv, subst) tgt in
107 if src == src1 && tgt == tgt1 then ms, orig else
108 ms, NCic.Prod (name, src1, tgt1)
110 NCicUntrusted.map_term_fold_a
111 (fun e (n,ctx,teq) -> n+1,e::ctx,teq) k aux acc t
114 let argty = NCicTypeChecker.typeof ~metasenv ~subst context arg in
115 let fresh_name = "Hbeta" ^ string_of_int num in
116 let (metasenv,subst), t1 =
117 aux (0, context, test_eq_only) (metasenv, subst) t in
118 let t2 = eta_reduce (NCic.Lambda (fresh_name,argty,t1)) in
120 ignore(NCicTypeChecker.typeof ~metasenv ~subst context t2);
122 with NCicTypeChecker.TypeCheckerFailure _ ->
123 metasenv, subst, NCic.Lambda ("_", argty, NCicSubstitution.lift 1 arg)
125 and beta_expand_many test_equality_only swap metasenv subst context t args =
126 (* (*D*) inside 'B'; try let rc = *)
127 pp (lazy (String.concat ", "
128 (List.map (NCicPp.ppterm ~metasenv ~subst ~context)
129 args) ^ " ∈ " ^ NCicPp.ppterm ~metasenv ~subst ~context t));
130 let _, subst, metasenv, hd =
132 (fun arg (num,subst,metasenv,t) ->
133 let metasenv, subst, t =
134 beta_expand num test_equality_only swap metasenv subst context t arg
136 num+1,subst,metasenv,t)
137 args (1,subst,metasenv,t)
139 pp (lazy ("Head syntesized by b-exp: " ^
140 NCicPp.ppterm ~metasenv ~subst ~context hd));
142 (* (*D*) in outside (); rc with exn -> outside (); raise exn *)
144 and instantiate test_eq_only metasenv subst context n lc t swap =
145 (* (*D*) inside 'I'; try let rc = *)
146 let unify test_eq_only m s c t1 t2 =
147 if swap then unify test_eq_only m s c t2 t1
148 else unify test_eq_only m s c t1 t2
151 try NCicTypeChecker.typeof ~subst ~metasenv context t
152 with NCicTypeChecker.TypeCheckerFailure msg ->
153 prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context t);
154 prerr_endline (Lazy.force msg);
157 let name, ctx, ty = NCicUtils.lookup_meta n metasenv in
158 let lty = NCicSubstitution.subst_meta lc ty in
159 pp (lazy("On the types: " ^
160 NCicPp.ppterm ~metasenv ~subst ~context lty ^ " === "
161 ^ NCicPp.ppterm ~metasenv ~subst ~context ty_t));
162 let metasenv, subst = unify test_eq_only metasenv subst context lty ty_t in
163 let (metasenv, subst), t =
164 try NCicMetaSubst.delift metasenv subst context n lc t
165 with NCicMetaSubst.Uncertain msg -> raise (Uncertain msg)
166 | NCicMetaSubst.MetaSubstFailure msg -> raise (UnificationFailure msg)
168 (* Unifying the types may have already instantiated n. *)
170 let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
171 let oldt = NCicSubstitution.subst_meta lc oldt in
172 (* conjecture: always fail --> occur check *)
173 unify test_eq_only metasenv subst context oldt t
174 with NCicUtils.Subst_not_found _ ->
175 (* by cumulativity when unify(?,Type_i)
176 * we could ? := Type_j with j <= i... *)
177 let subst = (n, (name, ctx, t, ty)) :: subst in
178 pp (lazy ("?"^string_of_int n^" := "^NCicPp.ppterm
179 ~metasenv ~subst ~context:ctx (NCicSubstitution.subst_meta lc t)));
181 List.filter (fun (m,_) -> not (n = m)) metasenv
184 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
186 and unify test_eq_only metasenv subst context t1 t2 =
187 (* (*D*) inside 'U'; try let rc = *)
188 let fo_unif test_eq_only metasenv subst t1 t2 =
189 (* (*D*) inside 'F'; try let rc = *)
191 pp (lazy(" " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
192 NCicPp.ppterm ~metasenv ~subst ~context t2));
198 | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
199 if NCicEnvironment.universe_leq a b then metasenv, subst
200 else raise (fail_exc metasenv subst context t1 t2)
201 | (C.Sort (C.Type a), C.Sort (C.Type b)) ->
202 if NCicEnvironment.universe_eq a b then metasenv, subst
203 else raise (fail_exc metasenv subst context t1 t2)
204 | (C.Sort C.Prop,C.Sort (C.Type _)) ->
205 if (not test_eq_only) then metasenv, subst
206 else raise (fail_exc metasenv subst context t1 t2)
208 | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2))
209 | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
210 let metasenv, subst = unify true metasenv subst context s1 s2 in
211 unify test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
212 | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
213 let metasenv,subst=unify test_eq_only metasenv subst context ty1 ty2 in
214 let metasenv,subst=unify test_eq_only metasenv subst context s1 s2 in
215 let context = (name1, C.Def (s1,ty1))::context in
216 unify test_eq_only metasenv subst context t1 t2
218 | (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
220 let l1 = NCicUtils.expand_local_context l1 in
221 let l2 = NCicUtils.expand_local_context l2 in
222 let metasenv, subst, to_restrict, _ =
224 (fun t1 t2 (metasenv, subst, to_restrict, i) ->
226 let metasenv, subst =
227 unify test_eq_only metasenv subst context
228 (NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
230 metasenv, subst, to_restrict, i-1
231 with UnificationFailure _ | Uncertain _ ->
232 metasenv, subst, i::to_restrict, i-1)
233 l1 l2 (metasenv, subst, [], List.length l1)
235 let metasenv, subst, _ =
236 NCicMetaSubst.restrict metasenv subst n1 to_restrict
240 | Invalid_argument _ -> assert false
241 | NCicMetaSubst.MetaSubstFailure msg ->
243 let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
244 let term1 = NCicSubstitution.subst_meta lc1 term in
245 let term2 = NCicSubstitution.subst_meta lc2 term in
246 unify test_eq_only metasenv subst context term1 term2
247 with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
249 | C.Meta (n,lc), t ->
251 let _,_,term,_ = NCicUtils.lookup_subst n subst in
252 let term = NCicSubstitution.subst_meta lc term in
253 unify test_eq_only metasenv subst context term t
254 with NCicUtils.Subst_not_found _->
255 instantiate test_eq_only metasenv subst context n lc t false)
257 | t, C.Meta (n,lc) ->
259 let _,_,term,_ = NCicUtils.lookup_subst n subst in
260 let term = NCicSubstitution.subst_meta lc term in
261 unify test_eq_only metasenv subst context t term
262 with NCicUtils.Subst_not_found _->
263 instantiate test_eq_only metasenv subst context n lc t true)
265 | NCic.Appl (NCic.Meta (i,l)::args), _ when List.mem_assoc i subst ->
266 let _,_,term,_ = NCicUtils.lookup_subst i subst in
267 let term = NCicSubstitution.subst_meta l term in
268 unify test_eq_only metasenv subst context (mk_appl term args) t2
270 | _, NCic.Appl (NCic.Meta (i,l)::args) when List.mem_assoc i subst ->
271 let _,_,term,_ = NCicUtils.lookup_subst i subst in
272 let term = NCicSubstitution.subst_meta l term in
273 unify test_eq_only metasenv subst context t1 (mk_appl term args)
275 | NCic.Appl (NCic.Meta (i,_)::_ as l1),
276 NCic.Appl (NCic.Meta (j,_)::_ as l2) when i=j ->
279 (fun (metasenv, subst) t1 t2 ->
280 unify test_eq_only metasenv subst context t1 t2)
281 (metasenv,subst) l1 l2
282 with Invalid_argument _ ->
283 raise (fail_exc metasenv subst context t1 t2))
285 | NCic.Appl (NCic.Meta (i,l)::args), _ when not (flexible args) ->
286 (* we verify that none of the args is a Meta,
287 since beta expanding w.r.t a metavariable makes no sense *)
288 let metasenv, subst, beta_expanded =
291 metasenv subst context t2 args
293 unify test_eq_only metasenv subst context
294 (C.Meta (i,l)) beta_expanded
296 | _, NCic.Appl (NCic.Meta (i,l)::args) when not(flexible args) ->
297 let metasenv, subst, beta_expanded =
300 metasenv subst context t1 args
302 unify test_eq_only metasenv subst context
303 beta_expanded (C.Meta (i,l))
305 (* processing this case here we avoid a useless small delta step *)
306 | (C.Appl ((C.Const r1) as _hd1::tl1), C.Appl (C.Const r2::tl2))
308 let relevance = NCicEnvironment.get_relevance r1 in
309 let relevance = match r1 with
310 | Ref.Ref (_,Ref.Con (_,_,lno)) ->
311 let _,relevance = HExtlib.split_nth lno relevance in
312 HExtlib.mk_list false lno @ relevance
315 let metasenv, subst, _ =
318 (fun (metasenv, subst, relevance) t1 t2 ->
320 match relevance with b::tl -> b,tl | _ -> true, [] in
321 let metasenv, subst =
322 try unify test_eq_only metasenv subst context t1 t2
323 with UnificationFailure _ | Uncertain _ when not b ->
326 metasenv, subst, relevance)
327 (metasenv, subst, relevance) tl1 tl2
328 with Invalid_argument _ ->
329 raise (uncert_exc metasenv subst context t1 t2)
333 | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
334 C.Match (ref2,outtype2,term2,pl2)) ->
335 let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
336 let _,_,ty,_ = List.nth itl tyno in
337 let rec remove_prods ~subst context ty =
338 let ty = NCicReduction.whd ~subst context ty in
341 | C.Prod (name,so,ta) ->
342 remove_prods ~subst ((name,(C.Decl so))::context) ta
346 match remove_prods ~subst [] ty with
347 | C.Sort C.Prop -> true
350 let rec remove_prods ~subst context ty =
351 let ty = NCicReduction.whd ~subst context ty in
354 | C.Prod (name,so,ta) ->
355 remove_prods ~subst ((name,(C.Decl so))::context) ta
358 if not (Ref.eq ref1 ref2) then
359 raise (uncert_exc metasenv subst context t1 t2)
361 let metasenv, subst =
362 unify test_eq_only metasenv subst context outtype1 outtype2 in
363 let metasenv, subst =
364 try unify test_eq_only metasenv subst context term1 term2
365 with UnificationFailure _ | Uncertain _ when is_prop ->
370 (fun (metasenv,subst) ->
371 unify test_eq_only metasenv subst context)
372 (metasenv, subst) pl1 pl2
373 with Invalid_argument _ ->
374 raise (uncert_exc metasenv subst context t1 t2))
375 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
376 | _ -> raise (uncert_exc metasenv subst context t1 t2)
377 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
379 let height_of = function
380 | NCic.Const (Ref.Ref (_,Ref.Def h))
381 | NCic.Const (Ref.Ref (_,Ref.Fix (_,_,h)))
382 | NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Def h))::_)
383 | NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
386 let put_in_whd m1 m2 =
387 NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
388 NCicReduction.reduce_machine ~delta:max_int ~subst context m2
391 ((_,_,t1,_ as m1, norm1) as x1) ((_,_,t2,_ as m2, norm2) as x2)
393 assert (not (norm1 && norm2));
395 x1,NCicReduction.reduce_machine ~delta:(height_of t2 -1) ~subst context m2
397 NCicReduction.reduce_machine ~delta:(height_of t1 -1) ~subst context m1,x2
399 let h1 = height_of t1 in
400 let h2 = height_of t2 in
401 let delta = if h1 = h2 then max 0 (h1 -1) else min h1 h2 in
402 NCicReduction.reduce_machine ~delta ~subst context m1,
403 NCicReduction.reduce_machine ~delta ~subst context m2
405 let rec unif_machines metasenv subst =
407 | ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2),norm2 as m2) ->
408 (* (*D*) inside 'M'; try let rc = *)
410 pp (lazy((if are_normal then "*" else " ") ^ " " ^
411 NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m1) ^
413 NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m2)));
415 let relevance = [] (* TO BE UNDERSTOOD
417 | C.Const r -> NCicEnvironment.get_relevance r
419 let unif_from_stack t1 t2 b metasenv subst =
421 let t1 = NCicReduction.from_stack t1 in
422 let t2 = NCicReduction.from_stack t2 in
423 unif_machines metasenv subst (put_in_whd t1 t2)
424 with UnificationFailure _ | Uncertain _ when not b ->
427 let rec check_stack l1 l2 r (metasenv, subst) =
429 | x1::tl1, x2::tl2, r::tr ->
430 check_stack tl1 tl2 tr
431 (unif_from_stack x1 x2 r metasenv subst)
432 | x1::tl1, x2::tl2, [] ->
433 check_stack tl1 tl2 []
434 (unif_from_stack x1 x2 true metasenv subst)
436 fo_unif test_eq_only metasenv subst
437 (NCicReduction.unwind (k1,e1,t1,List.rev l1))
438 (NCicReduction.unwind (k2,e2,t2,List.rev l2))
440 try check_stack (List.rev s1) (List.rev s2) relevance (metasenv,subst)
441 with UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
442 unif_machines metasenv subst (small_delta_step m1 m2)
443 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
445 try fo_unif test_eq_only metasenv subst t1 t2
446 with UnificationFailure msg | Uncertain msg as exn ->
448 unif_machines metasenv subst
449 (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
451 | UnificationFailure _ -> raise (UnificationFailure msg)
452 | Uncertain _ -> raise exn
453 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
466 exception UnificationFailure of string Lazy.t;;
467 exception Uncertain of string Lazy.t;;
468 exception AssertFailure of string Lazy.t;;
470 let verbose = false;;
471 let debug_print = fun _ -> ()
473 let profiler_toa = HExtlib.profile "fo_unif_subst.type_of_aux'"
474 let profiler_beta_expand = HExtlib.profile "fo_unif_subst.beta_expand"
475 let profiler_deref = HExtlib.profile "fo_unif_subst.deref'"
476 let profiler_are_convertible = HExtlib.profile "fo_unif_subst.are_convertible"
478 let profile = HExtlib.profile "U/CicTypeChecker.type_of_aux'"
480 let type_of_aux' metasenv subst context term ugraph =
483 profile.HExtlib.profile
484 (CicTypeChecker.type_of_aux' ~subst metasenv context term) ugraph
486 CicTypeChecker.TypeCheckerFailure msg ->
490 "Kernel Type checking error:
491 %s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
492 (CicMetaSubst.ppterm ~metasenv subst term)
493 (CicMetaSubst.ppterm ~metasenv [] term)
494 (CicMetaSubst.ppcontext ~metasenv subst context)
495 (CicMetaSubst.ppmetasenv subst metasenv)
496 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
497 raise (AssertFailure msg)
498 | CicTypeChecker.AssertFailure msg ->
501 "Kernel Type checking assertion failure:
502 %s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
503 (CicMetaSubst.ppterm ~metasenv subst term)
504 (CicMetaSubst.ppterm ~metasenv [] term)
505 (CicMetaSubst.ppcontext ~metasenv subst context)
506 (CicMetaSubst.ppmetasenv subst metasenv)
507 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
508 raise (AssertFailure msg)
509 in profiler_toa.HExtlib.profile foo ()
512 let exists_a_meta l =
516 | Cic.Appl (Cic.Meta _::_) -> true
519 let rec deref subst t =
520 let snd (_,a,_) = a in
525 (CicSubstitution.subst_meta
526 l (snd (CicUtil.lookup_subst n subst)))
528 CicUtil.Subst_not_found _ -> t)
529 | Cic.Appl(Cic.Meta(n,l)::args) ->
530 (match deref subst (Cic.Meta(n,l)) with
531 | Cic.Lambda _ as t ->
532 deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
533 | r -> Cic.Appl(r::args))
534 | Cic.Appl(((Cic.Lambda _) as t)::args) ->
535 deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
540 let foo () = deref subst t
541 in profiler_deref.HExtlib.profile foo ()
543 exception WrongShape;;
544 let eta_reduce after_beta_expansion after_beta_expansion_body
545 before_beta_expansion
548 match before_beta_expansion,after_beta_expansion_body with
549 Cic.Appl l, Cic.Appl l' ->
550 let rec all_but_last check_last =
554 | [_] -> if check_last then raise WrongShape else []
555 | he::tl -> he::(all_but_last check_last tl)
557 let all_but_last check_last l =
558 match all_but_last check_last l with
563 let t = CicSubstitution.subst (Cic.Rel (-1)) (all_but_last true l') in
564 let all_but_last = all_but_last false l in
565 (* here we should test alpha-equivalence; however we know by
566 construction that here alpha_equivalence is equivalent to = *)
567 if t = all_but_last then
571 | _,_ -> after_beta_expansion
573 WrongShape -> after_beta_expansion
575 let rec beta_expand num test_equality_only metasenv subst context t arg ugraph =
576 let module S = CicSubstitution in
577 let module C = Cic in
579 let rec aux metasenv subst n context t' ugraph =
582 let subst,metasenv,ugraph1 =
583 fo_unif_subst test_equality_only subst context metasenv
584 (CicSubstitution.lift n arg) t' ugraph
587 subst,metasenv,C.Rel (1 + n),ugraph1
590 | UnificationFailure _ ->
592 | C.Rel m -> subst,metasenv,
593 (if m <= n then C.Rel m else C.Rel (m+1)),ugraph
594 | C.Var (uri,exp_named_subst) ->
595 let subst,metasenv,exp_named_subst',ugraph1 =
596 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
598 subst,metasenv,C.Var (uri,exp_named_subst'),ugraph1
600 (* andrea: in general, beta_expand can create badly typed
601 terms. This happens quite seldom in practice, UNLESS we
602 iterate on the local context. For this reason, we renounce
603 to iterate and just lift *)
607 Some t -> Some (CicSubstitution.lift 1 t)
609 subst, metasenv, C.Meta (i,l), ugraph
611 | C.Implicit _ as t -> subst,metasenv,t,ugraph
613 let subst,metasenv,te',ugraph1 =
614 aux metasenv subst n context te ugraph in
615 let subst,metasenv,ty',ugraph2 =
616 aux metasenv subst n context ty ugraph1 in
617 (* TASSI: sure this is in serial? *)
618 subst,metasenv,(C.Cast (te', ty')),ugraph2
620 let subst,metasenv,s',ugraph1 =
621 aux metasenv subst n context s ugraph in
622 let subst,metasenv,t',ugraph2 =
623 aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t
626 (* TASSI: sure this is in serial? *)
627 subst,metasenv,(C.Prod (nn, s', t')),ugraph2
628 | C.Lambda (nn,s,t) ->
629 let subst,metasenv,s',ugraph1 =
630 aux metasenv subst n context s ugraph in
631 let subst,metasenv,t',ugraph2 =
632 aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t ugraph1
634 (* TASSI: sure this is in serial? *)
635 subst,metasenv,(C.Lambda (nn, s', t')),ugraph2
636 | C.LetIn (nn,s,ty,t) ->
637 let subst,metasenv,s',ugraph1 =
638 aux metasenv subst n context s ugraph in
639 let subst,metasenv,ty',ugraph1 =
640 aux metasenv subst n context ty ugraph in
641 let subst,metasenv,t',ugraph2 =
642 aux metasenv subst (n+1) ((Some (nn, C.Def (s,ty)))::context) t
645 (* TASSI: sure this is in serial? *)
646 subst,metasenv,(C.LetIn (nn, s', ty', t')),ugraph2
648 let subst,metasenv,revl',ugraph1 =
650 (fun (subst,metasenv,appl,ugraph) t ->
651 let subst,metasenv,t',ugraph1 =
652 aux metasenv subst n context t ugraph in
653 subst,metasenv,(t'::appl),ugraph1
654 ) (subst,metasenv,[],ugraph) l
656 subst,metasenv,(C.Appl (List.rev revl')),ugraph1
657 | C.Const (uri,exp_named_subst) ->
658 let subst,metasenv,exp_named_subst',ugraph1 =
659 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
661 subst,metasenv,(C.Const (uri,exp_named_subst')),ugraph1
662 | C.MutInd (uri,i,exp_named_subst) ->
663 let subst,metasenv,exp_named_subst',ugraph1 =
664 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
666 subst,metasenv,(C.MutInd (uri,i,exp_named_subst')),ugraph1
667 | C.MutConstruct (uri,i,j,exp_named_subst) ->
668 let subst,metasenv,exp_named_subst',ugraph1 =
669 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
671 subst,metasenv,(C.MutConstruct (uri,i,j,exp_named_subst')),ugraph1
672 | C.MutCase (sp,i,outt,t,pl) ->
673 let subst,metasenv,outt',ugraph1 =
674 aux metasenv subst n context outt ugraph in
675 let subst,metasenv,t',ugraph2 =
676 aux metasenv subst n context t ugraph1 in
677 let subst,metasenv,revpl',ugraph3 =
679 (fun (subst,metasenv,pl,ugraph) t ->
680 let subst,metasenv,t',ugraph1 =
681 aux metasenv subst n context t ugraph in
682 subst,metasenv,(t'::pl),ugraph1
683 ) (subst,metasenv,[],ugraph2) pl
685 subst,metasenv,(C.MutCase (sp,i,outt', t', List.rev revpl')),ugraph3
686 (* TASSI: not sure this is serial *)
688 (*CSC: not implemented
689 let tylen = List.length fl in
692 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
695 C.Fix (i, substitutedfl)
697 subst,metasenv,(CicSubstitution.lift 1 t' ),ugraph
699 (*CSC: not implemented
700 let tylen = List.length fl in
703 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
706 C.CoFix (i, substitutedfl)
709 subst,metasenv,(CicSubstitution.lift 1 t'), ugraph
711 and aux_exp_named_subst metasenv subst n context ens ugraph =
713 (fun (uri,t) (subst,metasenv,l,ugraph) ->
714 let subst,metasenv,t',ugraph1 = aux metasenv subst n context t ugraph in
715 subst,metasenv,((uri,t')::l),ugraph1) ens (subst,metasenv,[],ugraph)
717 let argty,ugraph1 = type_of_aux' metasenv subst context arg ugraph in
719 FreshNamesGenerator.mk_fresh_name ~subst
720 metasenv context (Cic.Name ("Hbeta" ^ string_of_int num)) ~typ:argty
722 let subst,metasenv,t',ugraph2 = aux metasenv subst 0 context t ugraph1 in
723 let t'' = eta_reduce (C.Lambda (fresh_name,argty,t')) t' t in
724 subst, metasenv, t'', ugraph2
725 in profiler_beta_expand.HExtlib.profile foo ()
728 and beta_expand_many test_equality_only metasenv subst context t args ugraph =
729 let _,subst,metasenv,hd,ugraph =
731 (fun arg (num,subst,metasenv,t,ugraph) ->
732 let subst,metasenv,t,ugraph1 =
733 beta_expand num test_equality_only
734 metasenv subst context t arg ugraph
736 num+1,subst,metasenv,t,ugraph1
737 ) args (1,subst,metasenv,t,ugraph)
739 subst,metasenv,hd,ugraph
741 and warn_if_not_unique xxx to1 to2 carr car1 car2 =
744 | (m2,_,c2,c2')::_ ->
745 let m1,c1,c1' = carr,to1,to2 in
747 function Some (_,t) -> CicPp.ppterm t
751 ("There are two minimal joins of "^ CoercDb.string_of_carr car1^" and "^
752 CoercDb.string_of_carr car2^": " ^
753 CoercDb.string_of_carr m1^" via "^unopt c1^" + "^
754 unopt c1'^" and "^ CoercDb.string_of_carr m2^" via "^
755 unopt c2^" + "^unopt c2')
757 (* NUOVA UNIFICAZIONE *)
758 (* A substitution is a (int * Cic.term) list that associates a
759 metavariable i with its body.
760 A metaenv is a (int * Cic.term) list that associate a metavariable
762 fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
763 a new substitution which is _NOT_ unwinded. It must be unwinded before
766 and fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph =
767 let module C = Cic in
768 let module R = CicReduction in
769 let module S = CicSubstitution in
770 let t1 = deref subst t1 in
771 let t2 = deref subst t2 in
772 let (&&&) a b = (a && b) || ((not a) && (not b)) in
773 (* let bef = Sys.time () in *)
775 if not (CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t1) &&& CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t2)) then
779 R.are_convertible ~subst ~metasenv context t1 t2 ugraph
780 in profiler_are_convertible.HExtlib.profile foo ()
782 (* let aft = Sys.time () in
783 if (aft -. bef > 2.0) then prerr_endline ("LEEEENTO: " ^
784 CicMetaSubst.ppterm_in_context subst ~metasenv t1 context ^ " <===> " ^
785 CicMetaSubst.ppterm_in_context subst ~metasenv t2 context); *)
787 subst, metasenv, ugraph
790 | (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
791 let _,subst,metasenv,ugraph1 =
794 (fun (j,subst,metasenv,ugraph) t1 t2 ->
797 | _,None -> j+1,subst,metasenv,ugraph
798 | Some t1', Some t2' ->
799 (* First possibility: restriction *)
800 (* Second possibility: unification *)
801 (* Third possibility: convertibility *)
804 ~subst ~metasenv context t1' t2' ugraph
807 j+1,subst,metasenv, ugraph1
810 let subst,metasenv,ugraph2 =
813 subst context metasenv t1' t2' ugraph
815 j+1,subst,metasenv,ugraph2
818 | UnificationFailure _ ->
819 debug_print (lazy ("restringo Meta n." ^ (string_of_int n) ^ "on variable n." ^ (string_of_int j)));
820 let metasenv, subst =
821 CicMetaSubst.restrict
822 subst [(n,j)] metasenv in
823 j+1,subst,metasenv,ugraph1)
824 ) (1,subst,metasenv,ugraph) ln lm
828 (UnificationFailure (lazy "1"))
831 "Error trying to unify %s with %s: the algorithm tried to check whether the two substitutions are convertible; if they are not, it tried to unify the two substitutions. No restriction was attempted."
832 (CicMetaSubst.ppterm ~metasenv subst t1)
833 (CicMetaSubst.ppterm ~metasenv subst t2))) *)
834 | Invalid_argument _ ->
836 (UnificationFailure (lazy "2")))
839 "Error trying to unify %s with %s: the lengths of the two local contexts do not match."
840 (CicMetaSubst.ppterm ~metasenv subst t1)
841 (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
842 in subst,metasenv,ugraph1
843 | (C.Meta (n,_), C.Meta (m,_)) when n>m ->
844 fo_unif_subst test_equality_only subst context metasenv t2 t1 ugraph
846 | (t, C.Meta (n,l)) ->
849 C.Meta (n,_), C.Meta (m,_) when n < m -> false
850 | _, C.Meta _ -> false
853 let lower = fun x y -> if swap then y else x in
854 let upper = fun x y -> if swap then x else y in
855 let fo_unif_subst_ordered
856 test_equality_only subst context metasenv m1 m2 ugraph =
857 fo_unif_subst test_equality_only subst context metasenv
858 (lower m1 m2) (upper m1 m2) ugraph
861 let subst,metasenv,ugraph1 =
862 let (_,_,meta_type) = CicUtil.lookup_meta n metasenv in
865 type_of_aux' metasenv subst context t ugraph
869 subst context metasenv tyt (S.subst_meta l meta_type) ugraph1
871 UnificationFailure _ as e -> raise e
872 | Uncertain msg -> raise (UnificationFailure msg)
874 debug_print (lazy "siamo allo huge hack");
875 (* TODO huge hack!!!!
876 * we keep on unifying/refining in the hope that
877 * the problem will be eventually solved.
878 * In the meantime we're breaking a big invariant:
879 * the terms that we are unifying are no longer well
880 * typed in the current context (in the worst case
881 * we could even diverge) *)
882 (subst, metasenv,ugraph)) in
883 let t',metasenv,subst =
885 CicMetaSubst.delift n subst context metasenv l t
887 (CicMetaSubst.MetaSubstFailure msg)->
888 raise (UnificationFailure msg)
889 | (CicMetaSubst.Uncertain msg) -> raise (Uncertain msg)
893 C.Sort (C.Type u) when not test_equality_only ->
894 let u' = CicUniv.fresh () in
895 let s = C.Sort (C.Type u') in
898 CicUniv.add_ge (upper u u') (lower u u') ugraph1
902 CicUniv.UniverseInconsistency msg ->
903 raise (UnificationFailure msg))
906 (* Unifying the types may have already instantiated n. Let's check *)
908 let (_, oldt,_) = CicUtil.lookup_subst n subst in
909 let lifted_oldt = S.subst_meta l oldt in
910 fo_unif_subst_ordered
911 test_equality_only subst context metasenv t lifted_oldt ugraph2
913 CicUtil.Subst_not_found _ ->
914 let (_, context, ty) = CicUtil.lookup_meta n metasenv in
915 let subst = (n, (context, t'',ty)) :: subst in
917 List.filter (fun (m,_,_) -> not (n = m)) metasenv in
918 subst, metasenv, ugraph2
920 | (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
921 | (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
922 if UriManager.eq uri1 uri2 then
923 fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
924 exp_named_subst1 exp_named_subst2 ugraph
926 raise (UnificationFailure (lazy
928 "Can't unify %s with %s due to different constants"
929 (CicMetaSubst.ppterm ~metasenv subst t1)
930 (CicMetaSubst.ppterm ~metasenv subst t2))))
931 | C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
932 if UriManager.eq uri1 uri2 && i1 = i2 then
933 fo_unif_subst_exp_named_subst
935 subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
937 raise (UnificationFailure
940 "Can't unify %s with %s due to different inductive principles"
941 (CicMetaSubst.ppterm ~metasenv subst t1)
942 (CicMetaSubst.ppterm ~metasenv subst t2))))
943 | C.MutConstruct (uri1,i1,j1,exp_named_subst1),
944 C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
945 if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
946 fo_unif_subst_exp_named_subst
948 subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
950 raise (UnificationFailure
953 "Can't unify %s with %s due to different inductive constructors"
954 (CicMetaSubst.ppterm ~metasenv subst t1)
955 (CicMetaSubst.ppterm ~metasenv subst t2))))
956 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
957 | (C.Cast (te,ty), t2) -> fo_unif_subst test_equality_only
958 subst context metasenv te t2 ugraph
959 | (t1, C.Cast (te,ty)) -> fo_unif_subst test_equality_only
960 subst context metasenv t1 te ugraph
961 | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
962 let subst',metasenv',ugraph1 =
963 fo_unif_subst test_equality_only subst context metasenv s1 s2 ugraph
965 fo_unif_subst test_equality_only
966 subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
967 | (C.LetIn (_,s1,ty1,t1), t2)
968 | (t2, C.LetIn (_,s1,ty1,t1)) ->
970 test_equality_only subst context metasenv t2 (S.subst s1 t1) ugraph
971 | (C.Appl l1, C.Appl l2) ->
972 (* andrea: this case should be probably rewritten in the
975 | C.Meta (i,_)::args1, C.Meta (j,_)::args2 when i = j ->
978 (fun (subst,metasenv,ugraph) t1 t2 ->
980 test_equality_only subst context metasenv t1 t2 ugraph)
981 (subst,metasenv,ugraph) l1 l2
982 with (Invalid_argument msg) ->
983 raise (UnificationFailure (lazy msg)))
984 | C.Meta (i,l)::args, _ when not(exists_a_meta args) ->
985 (* we verify that none of the args is a Meta,
986 since beta expanding with respoect to a metavariable
990 let (_,t,_) = CicUtil.lookup_subst i subst in
991 let lifted = S.subst_meta l t in
992 let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
995 subst context metasenv reduced t2 ugraph
996 with CicUtil.Subst_not_found _ -> *)
997 let subst,metasenv,beta_expanded,ugraph1 =
999 test_equality_only metasenv subst context t2 args ugraph
1001 fo_unif_subst test_equality_only subst context metasenv
1002 (C.Meta (i,l)) beta_expanded ugraph1
1003 | _, C.Meta (i,l)::args when not(exists_a_meta args) ->
1005 let (_,t,_) = CicUtil.lookup_subst i subst in
1006 let lifted = S.subst_meta l t in
1007 let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
1010 subst context metasenv t1 reduced ugraph
1011 with CicUtil.Subst_not_found _ -> *)
1012 let subst,metasenv,beta_expanded,ugraph1 =
1015 metasenv subst context t1 args ugraph
1017 fo_unif_subst test_equality_only subst context metasenv
1018 (C.Meta (i,l)) beta_expanded ugraph1
1020 let lr1 = List.rev l1 in
1021 let lr2 = List.rev l2 in
1023 fo_unif_l test_equality_only subst metasenv (l1,l2) ugraph =
1026 | _,[] -> assert false
1029 test_equality_only subst context metasenv h1 h2 ugraph
1032 fo_unif_subst test_equality_only subst context metasenv
1033 h (C.Appl (List.rev l)) ugraph
1034 | ((h1::l1),(h2::l2)) ->
1035 let subst', metasenv',ugraph1 =
1038 subst context metasenv h1 h2 ugraph
1041 test_equality_only subst' metasenv' (l1,l2) ugraph1
1045 test_equality_only subst metasenv (lr1, lr2) ugraph
1047 | UnificationFailure s
1048 | Uncertain s as exn ->
1051 | (((Cic.Const (uri1, ens1)) as cc1) :: tl1),
1052 (((Cic.Const (uri2, ens2)) as cc2) :: tl2) when
1053 CoercDb.is_a_coercion cc1 <> None &&
1054 CoercDb.is_a_coercion cc2 <> None &&
1055 not (UriManager.eq uri1 uri2) ->
1057 prerr_endline ("<<<< " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^ " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
1059 let inner_coerced t =
1060 let t = CicMetaSubst.apply_subst subst t in
1064 (match CoercGraph.coerced_arg l with
1066 | Some (t,_) -> aux (List.hd l) t t)
1069 aux (Cic.Implicit None) (Cic.Implicit None) t
1071 let c1,last_tl1 = inner_coerced (Cic.Appl l1) in
1072 let c2,last_tl2 = inner_coerced (Cic.Appl l2) in
1075 CoercDb.is_a_coercion c1, CoercDb.is_a_coercion c2
1077 | Some (s1,_,_,_,_), Some (s2,_,_,_,_) -> s1, s2
1080 let head1_c, head2_c =
1082 CoercDb.is_a_coercion cc1, CoercDb.is_a_coercion cc2
1084 | Some (_,t1,_,_,_), Some (_,t2,_,_,_) -> t1, t2
1087 let unfold uri ens args =
1089 CicEnvironment.get_obj CicUniv.oblivion_ugraph uri
1093 | Cic.Constant (_,Some bo,_,_,_) ->
1094 CicReduction.head_beta_reduce ~delta:false
1095 (Cic.Appl (bo::args))
1098 let conclude subst metasenv ugraph last_tl1' last_tl2' =
1099 let subst',metasenv,ugraph =
1102 ("OK " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl1' context ^
1103 " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl2' context);
1105 fo_unif_subst test_equality_only subst context
1106 metasenv last_tl1' last_tl2' ugraph
1108 if subst = subst' then raise exn
1111 let subst,metasenv,ugrph as res =
1113 fo_unif_subst test_equality_only subst' context
1114 metasenv (C.Appl l1) (C.Appl l2) ugraph
1118 (">>>> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^
1119 " <==> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
1123 if CoercDb.eq_carr car1 car2 then
1124 match last_tl1,last_tl2 with
1125 | C.Meta (i1,_),C.Meta(i2,_) when i1 = i2 -> raise exn
1128 let subst,metasenv,ugraph =
1129 fo_unif_subst test_equality_only subst context
1130 metasenv last_tl1 last_tl2 ugraph
1132 fo_unif_subst test_equality_only subst context
1133 metasenv (Cic.Appl l1) (Cic.Appl l2) ugraph
1134 | _ when CoercDb.eq_carr head1_c head2_c ->
1135 (* composite VS composition + metas avoiding
1136 * coercions not only in coerced position *)
1137 if c1 <> cc1 && c2 <> cc2 then
1138 conclude subst metasenv ugraph
1143 unfold uri1 ens1 tl1, Cic.Appl (cc2::tl2)
1145 Cic.Appl (cc1::tl1), unfold uri2 ens2 tl2
1147 fo_unif_subst test_equality_only subst context
1148 metasenv l1 l2 ugraph
1152 match last_tl1 with Cic.Meta _ -> true | _ -> false in
1154 match last_tl2 with Cic.Meta _ -> true | _ -> false in
1155 if not (grow1 || grow2) then
1156 (* no flexible terminals -> no pullback, but
1157 * we still unify them, in some cases it helps *)
1158 conclude subst metasenv ugraph last_tl1 last_tl2
1162 metasenv subst context (grow1,car1) (grow2,car2)
1166 | (carr,metasenv,to1,to2)::xxx ->
1167 warn_if_not_unique xxx to1 to2 carr car1 car2;
1168 let last_tl1',(subst,metasenv,ugraph) =
1169 match grow1,to1 with
1170 | true,Some (last,coerced) ->
1172 fo_unif_subst test_equality_only subst context
1173 metasenv coerced last_tl1 ugraph
1174 | _ -> last_tl1,(subst,metasenv,ugraph)
1176 let last_tl2',(subst,metasenv,ugraph) =
1177 match grow2,to2 with
1178 | true,Some (last,coerced) ->
1180 fo_unif_subst test_equality_only subst context
1181 metasenv coerced last_tl2 ugraph
1182 | _ -> last_tl2,(subst,metasenv,ugraph)
1184 conclude subst metasenv ugraph last_tl1' last_tl2')
1186 (* {{{ CSC: This is necessary because of the "elim H" tactic
1187 where the type of H is only reducible to an
1188 inductive type. This could be extended from inductive
1189 types to any rigid term. However, the code is
1190 duplicated in two places: inside applications and
1191 outside them. Probably it would be better to
1192 work with lambda-bar terms instead. *)
1193 | (Cic.MutInd _::_, Cic.MutInd _::_) -> raise exn
1194 | (_, Cic.MutInd _::_) ->
1195 let t1' = R.whd ~subst context t1 in
1197 C.Appl (C.MutInd _::_) ->
1198 fo_unif_subst test_equality_only
1199 subst context metasenv t1' t2 ugraph
1200 | _ -> raise (UnificationFailure (lazy "88")))
1201 | (Cic.MutInd _::_,_) ->
1202 let t2' = R.whd ~subst context t2 in
1204 C.Appl (C.MutInd _::_) ->
1205 fo_unif_subst test_equality_only
1206 subst context metasenv t1 t2' ugraph
1209 (lazy ("not a mutind :"^
1210 CicMetaSubst.ppterm ~metasenv subst t2 ))))
1213 | (C.MutCase (_,_,outt1,t1',pl1), C.MutCase (_,_,outt2,t2',pl2))->
1214 let subst', metasenv',ugraph1 =
1215 fo_unif_subst test_equality_only subst context metasenv outt1 outt2
1217 let subst'',metasenv'',ugraph2 =
1218 fo_unif_subst test_equality_only subst' context metasenv' t1' t2'
1222 (fun (subst,metasenv,ugraph) t1 t2 ->
1224 test_equality_only subst context metasenv t1 t2 ugraph
1225 ) (subst'',metasenv'',ugraph2) pl1 pl2
1227 Invalid_argument _ ->
1228 raise (UnificationFailure (lazy "6.1")))
1230 "Error trying to unify %s with %s: the number of branches is not the same."
1231 (CicMetaSubst.ppterm ~metasenv subst t1)
1232 (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
1233 | (C.Rel _, _) | (_, C.Rel _) ->
1235 subst, metasenv,ugraph
1237 raise (UnificationFailure (lazy
1239 "Can't unify %s with %s because they are not convertible"
1240 (CicMetaSubst.ppterm ~metasenv subst t1)
1241 (CicMetaSubst.ppterm ~metasenv subst t2))))
1242 | (C.Appl (C.Meta(i,l)::args),t2) when not(exists_a_meta args) ->
1243 let subst,metasenv,beta_expanded,ugraph1 =
1245 test_equality_only metasenv subst context t2 args ugraph
1247 fo_unif_subst test_equality_only subst context metasenv
1248 (C.Meta (i,l)) beta_expanded ugraph1
1249 | (t1,C.Appl (C.Meta(i,l)::args)) when not(exists_a_meta args) ->
1250 let subst,metasenv,beta_expanded,ugraph1 =
1252 test_equality_only metasenv subst context t1 args ugraph
1254 fo_unif_subst test_equality_only subst context metasenv
1255 beta_expanded (C.Meta (i,l)) ugraph1
1256 (* Works iff there are no arguments applied to it; similar to the
1258 | (_, C.MutInd _) ->
1259 let t1' = R.whd ~subst context t1 in
1262 fo_unif_subst test_equality_only
1263 subst context metasenv t1' t2 ugraph
1264 | _ -> raise (UnificationFailure (lazy "8")))
1266 | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
1267 let subst',metasenv',ugraph1 =
1268 fo_unif_subst true subst context metasenv s1 s2 ugraph
1270 fo_unif_subst test_equality_only
1271 subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
1273 (match CicReduction.whd ~subst context t2 with
1275 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1276 | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t2^"Not a product"))))
1278 (match CicReduction.whd ~subst context t1 with
1280 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1281 | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t1^"Not a product"))))
1283 (* delta-beta reduction should almost never be a problem for
1285 1. long computations require iota reduction
1286 2. it is extremely rare that a close term t1 (that could be unified
1287 to t2) beta-delta reduces to t1' while t2 does not beta-delta
1288 reduces in the same way. This happens only if one meta of t2
1289 occurs in head position during beta reduction. In this unluky
1290 case too much reduction will be performed on t1 and unification
1291 will surely fail. *)
1292 let t1' = CicReduction.head_beta_reduce ~delta:true t1 in
1293 let t2' = CicReduction.head_beta_reduce ~delta:true t2 in
1294 if t1 = t1' && t2 = t2' then
1295 raise (UnificationFailure
1298 "Can't unify %s with %s because they are not convertible"
1299 (CicMetaSubst.ppterm ~metasenv subst t1)
1300 (CicMetaSubst.ppterm ~metasenv subst t2))))
1303 fo_unif_subst test_equality_only subst context metasenv t1' t2' ugraph
1305 UnificationFailure _
1307 raise (UnificationFailure
1310 "Can't unify %s with %s because they are not convertible"
1311 (CicMetaSubst.ppterm ~metasenv subst t1)
1312 (CicMetaSubst.ppterm ~metasenv subst t2))))
1314 and fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
1315 exp_named_subst1 exp_named_subst2 ugraph
1319 (fun (subst,metasenv,ugraph) (uri1,t1) (uri2,t2) ->
1320 assert (uri1=uri2) ;
1321 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1322 ) (subst,metasenv,ugraph) exp_named_subst1 exp_named_subst2
1324 Invalid_argument _ ->
1329 UriManager.string_of_uri uri ^ " := " ^ (CicMetaSubst.ppterm ~metasenv subst t)
1332 raise (UnificationFailure (lazy (sprintf
1333 "Error trying to unify the two explicit named substitutions (local contexts) %s and %s: their lengths is different." (print_ens exp_named_subst1) (print_ens exp_named_subst2))))
1335 (* A substitution is a (int * Cic.term) list that associates a *)
1336 (* metavariable i with its body. *)
1337 (* metasenv is of type Cic.metasenv *)
1338 (* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
1339 (* a new substitution which is already unwinded and ready to be applied and *)
1340 (* a new metasenv in which some hypothesis in the contexts of the *)
1341 (* metavariables may have been restricted. *)
1342 let fo_unif metasenv context t1 t2 ugraph =
1343 fo_unif_subst false [] context metasenv t1 t2 ugraph ;;
1345 let enrich_msg msg subst context metasenv t1 t2 ugraph =
1348 sprintf "[Verbose] Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nand substitution\n%s\nbecause %s"
1349 (CicMetaSubst.ppterm ~metasenv subst t1)
1351 let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
1354 | UnificationFailure s
1356 | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
1357 (CicMetaSubst.ppterm ~metasenv subst t2)
1359 let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
1362 | UnificationFailure s
1364 | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
1365 (CicMetaSubst.ppcontext ~metasenv subst context)
1366 (CicMetaSubst.ppmetasenv subst metasenv)
1367 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)
1369 sprintf "Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nbecause %s"
1370 (CicMetaSubst.ppterm_in_context ~metasenv subst t1 context)
1372 let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
1373 CicMetaSubst.ppterm_in_context ~metasenv subst ty_t1 context
1375 | UnificationFailure s
1377 | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
1378 (CicMetaSubst.ppterm_in_context ~metasenv subst t2 context)
1380 let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
1381 CicMetaSubst.ppterm_in_context ~metasenv subst ty_t2 context
1383 | UnificationFailure s
1385 | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
1386 (CicMetaSubst.ppcontext ~metasenv subst context)
1387 (CicMetaSubst.ppmetasenv subst metasenv)
1391 let fo_unif_subst subst context metasenv t1 t2 ugraph =
1393 fo_unif_subst false subst context metasenv t1 t2 ugraph
1395 | AssertFailure msg ->
1396 raise (AssertFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))
1397 | UnificationFailure msg ->
1398 raise (UnificationFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))