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,
389 false (* not in normal form *)
391 let small_delta_step (_,_,t1,_ as m1) (_,_,t2,_ as m2) =
392 let h1 = height_of t1 in
393 let h2 = height_of t2 in
395 if flexible [t1] then max 0 (h2 - 1) else
396 if flexible [t2] then max 0 (h1 - 1) else
397 if h1 = h2 then max 0 (h1 -1) else min h1 h2
399 pp (lazy("DELTA STEP TO: " ^ string_of_int delta));
400 let m1' = NCicReduction.reduce_machine ~delta ~subst context m1 in
401 let m2' = NCicReduction.reduce_machine ~delta ~subst context m2 in
402 if (m1' == m1 && m2' == m2 && delta > 0) then
403 (* if we have as heads a Fix of height n>m>0 and another term of height
404 * m, we set delta = m. The Fix may or may not reduce, depending on its
405 * rec argument. if no reduction was performed we decrease delta to m-1
406 * to reduce the other term *)
407 let delta = delta - 1 in
408 pp (lazy("DELTA STEP TO: " ^ string_of_int delta));
409 let m1' = NCicReduction.reduce_machine ~delta ~subst context m1 in
410 let m2' = NCicReduction.reduce_machine ~delta ~subst context m2 in
411 m1', m2', (m1 == m1' && m2 == m2') || delta = 0
412 else m1', m2', delta = 0
414 let rec unif_machines metasenv subst =
416 | ((k1,e1,t1,s1 as m1),(k2,e2,t2,s2 as m2),are_normal) ->
417 (* (*D*) inside 'M'; try let rc = *)
419 pp (lazy((if are_normal then "*" else " ") ^ " " ^
420 NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m1) ^
422 NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m2)));
424 let relevance = [] (* TO BE UNDERSTOOD
426 | C.Const r -> NCicEnvironment.get_relevance r
428 let unif_from_stack t1 t2 b metasenv subst =
430 let t1 = NCicReduction.from_stack t1 in
431 let t2 = NCicReduction.from_stack t2 in
432 unif_machines metasenv subst (put_in_whd t1 t2)
433 with UnificationFailure _ | Uncertain _ when not b ->
436 let rec check_stack l1 l2 r (metasenv, subst) =
438 | x1::tl1, x2::tl2, r::tr ->
439 check_stack tl1 tl2 tr
440 (unif_from_stack x1 x2 r metasenv subst)
441 | x1::tl1, x2::tl2, [] ->
442 check_stack tl1 tl2 []
443 (unif_from_stack x1 x2 true metasenv subst)
445 fo_unif test_eq_only metasenv subst
446 (NCicReduction.unwind (k1,e1,t1,List.rev l1))
447 (NCicReduction.unwind (k2,e2,t2,List.rev l2))
449 try check_stack (List.rev s1) (List.rev s2) relevance (metasenv,subst)
450 with UnificationFailure _ | Uncertain _ when not are_normal ->
451 unif_machines metasenv subst (small_delta_step m1 m2)
452 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
454 try fo_unif test_eq_only metasenv subst t1 t2
455 with UnificationFailure msg | Uncertain msg as exn ->
457 unif_machines metasenv subst
458 (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
460 | UnificationFailure _ -> raise (UnificationFailure msg)
461 | Uncertain _ -> raise exn
462 (* (*D*) in outside(); rc with exn -> outside (); raise exn *)
475 exception UnificationFailure of string Lazy.t;;
476 exception Uncertain of string Lazy.t;;
477 exception AssertFailure of string Lazy.t;;
479 let verbose = false;;
480 let debug_print = fun _ -> ()
482 let profiler_toa = HExtlib.profile "fo_unif_subst.type_of_aux'"
483 let profiler_beta_expand = HExtlib.profile "fo_unif_subst.beta_expand"
484 let profiler_deref = HExtlib.profile "fo_unif_subst.deref'"
485 let profiler_are_convertible = HExtlib.profile "fo_unif_subst.are_convertible"
487 let profile = HExtlib.profile "U/CicTypeChecker.type_of_aux'"
489 let type_of_aux' metasenv subst context term ugraph =
492 profile.HExtlib.profile
493 (CicTypeChecker.type_of_aux' ~subst metasenv context term) ugraph
495 CicTypeChecker.TypeCheckerFailure msg ->
499 "Kernel Type checking error:
500 %s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
501 (CicMetaSubst.ppterm ~metasenv subst term)
502 (CicMetaSubst.ppterm ~metasenv [] term)
503 (CicMetaSubst.ppcontext ~metasenv subst context)
504 (CicMetaSubst.ppmetasenv subst metasenv)
505 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
506 raise (AssertFailure msg)
507 | CicTypeChecker.AssertFailure msg ->
510 "Kernel Type checking assertion failure:
511 %s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
512 (CicMetaSubst.ppterm ~metasenv subst term)
513 (CicMetaSubst.ppterm ~metasenv [] term)
514 (CicMetaSubst.ppcontext ~metasenv subst context)
515 (CicMetaSubst.ppmetasenv subst metasenv)
516 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)) in
517 raise (AssertFailure msg)
518 in profiler_toa.HExtlib.profile foo ()
521 let exists_a_meta l =
525 | Cic.Appl (Cic.Meta _::_) -> true
528 let rec deref subst t =
529 let snd (_,a,_) = a in
534 (CicSubstitution.subst_meta
535 l (snd (CicUtil.lookup_subst n subst)))
537 CicUtil.Subst_not_found _ -> t)
538 | Cic.Appl(Cic.Meta(n,l)::args) ->
539 (match deref subst (Cic.Meta(n,l)) with
540 | Cic.Lambda _ as t ->
541 deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
542 | r -> Cic.Appl(r::args))
543 | Cic.Appl(((Cic.Lambda _) as t)::args) ->
544 deref subst (CicReduction.head_beta_reduce (Cic.Appl(t::args)))
549 let foo () = deref subst t
550 in profiler_deref.HExtlib.profile foo ()
552 exception WrongShape;;
553 let eta_reduce after_beta_expansion after_beta_expansion_body
554 before_beta_expansion
557 match before_beta_expansion,after_beta_expansion_body with
558 Cic.Appl l, Cic.Appl l' ->
559 let rec all_but_last check_last =
563 | [_] -> if check_last then raise WrongShape else []
564 | he::tl -> he::(all_but_last check_last tl)
566 let all_but_last check_last l =
567 match all_but_last check_last l with
572 let t = CicSubstitution.subst (Cic.Rel (-1)) (all_but_last true l') in
573 let all_but_last = all_but_last false l in
574 (* here we should test alpha-equivalence; however we know by
575 construction that here alpha_equivalence is equivalent to = *)
576 if t = all_but_last then
580 | _,_ -> after_beta_expansion
582 WrongShape -> after_beta_expansion
584 let rec beta_expand num test_equality_only metasenv subst context t arg ugraph =
585 let module S = CicSubstitution in
586 let module C = Cic in
588 let rec aux metasenv subst n context t' ugraph =
591 let subst,metasenv,ugraph1 =
592 fo_unif_subst test_equality_only subst context metasenv
593 (CicSubstitution.lift n arg) t' ugraph
596 subst,metasenv,C.Rel (1 + n),ugraph1
599 | UnificationFailure _ ->
601 | C.Rel m -> subst,metasenv,
602 (if m <= n then C.Rel m else C.Rel (m+1)),ugraph
603 | C.Var (uri,exp_named_subst) ->
604 let subst,metasenv,exp_named_subst',ugraph1 =
605 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
607 subst,metasenv,C.Var (uri,exp_named_subst'),ugraph1
609 (* andrea: in general, beta_expand can create badly typed
610 terms. This happens quite seldom in practice, UNLESS we
611 iterate on the local context. For this reason, we renounce
612 to iterate and just lift *)
616 Some t -> Some (CicSubstitution.lift 1 t)
618 subst, metasenv, C.Meta (i,l), ugraph
620 | C.Implicit _ as t -> subst,metasenv,t,ugraph
622 let subst,metasenv,te',ugraph1 =
623 aux metasenv subst n context te ugraph in
624 let subst,metasenv,ty',ugraph2 =
625 aux metasenv subst n context ty ugraph1 in
626 (* TASSI: sure this is in serial? *)
627 subst,metasenv,(C.Cast (te', ty')),ugraph2
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
635 (* TASSI: sure this is in serial? *)
636 subst,metasenv,(C.Prod (nn, s', t')),ugraph2
637 | C.Lambda (nn,s,t) ->
638 let subst,metasenv,s',ugraph1 =
639 aux metasenv subst n context s ugraph in
640 let subst,metasenv,t',ugraph2 =
641 aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t ugraph1
643 (* TASSI: sure this is in serial? *)
644 subst,metasenv,(C.Lambda (nn, s', t')),ugraph2
645 | C.LetIn (nn,s,ty,t) ->
646 let subst,metasenv,s',ugraph1 =
647 aux metasenv subst n context s ugraph in
648 let subst,metasenv,ty',ugraph1 =
649 aux metasenv subst n context ty ugraph in
650 let subst,metasenv,t',ugraph2 =
651 aux metasenv subst (n+1) ((Some (nn, C.Def (s,ty)))::context) t
654 (* TASSI: sure this is in serial? *)
655 subst,metasenv,(C.LetIn (nn, s', ty', t')),ugraph2
657 let subst,metasenv,revl',ugraph1 =
659 (fun (subst,metasenv,appl,ugraph) t ->
660 let subst,metasenv,t',ugraph1 =
661 aux metasenv subst n context t ugraph in
662 subst,metasenv,(t'::appl),ugraph1
663 ) (subst,metasenv,[],ugraph) l
665 subst,metasenv,(C.Appl (List.rev revl')),ugraph1
666 | C.Const (uri,exp_named_subst) ->
667 let subst,metasenv,exp_named_subst',ugraph1 =
668 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
670 subst,metasenv,(C.Const (uri,exp_named_subst')),ugraph1
671 | C.MutInd (uri,i,exp_named_subst) ->
672 let subst,metasenv,exp_named_subst',ugraph1 =
673 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
675 subst,metasenv,(C.MutInd (uri,i,exp_named_subst')),ugraph1
676 | C.MutConstruct (uri,i,j,exp_named_subst) ->
677 let subst,metasenv,exp_named_subst',ugraph1 =
678 aux_exp_named_subst metasenv subst n context exp_named_subst ugraph
680 subst,metasenv,(C.MutConstruct (uri,i,j,exp_named_subst')),ugraph1
681 | C.MutCase (sp,i,outt,t,pl) ->
682 let subst,metasenv,outt',ugraph1 =
683 aux metasenv subst n context outt ugraph in
684 let subst,metasenv,t',ugraph2 =
685 aux metasenv subst n context t ugraph1 in
686 let subst,metasenv,revpl',ugraph3 =
688 (fun (subst,metasenv,pl,ugraph) t ->
689 let subst,metasenv,t',ugraph1 =
690 aux metasenv subst n context t ugraph in
691 subst,metasenv,(t'::pl),ugraph1
692 ) (subst,metasenv,[],ugraph2) pl
694 subst,metasenv,(C.MutCase (sp,i,outt', t', List.rev revpl')),ugraph3
695 (* TASSI: not sure this is serial *)
697 (*CSC: not implemented
698 let tylen = List.length fl in
701 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
704 C.Fix (i, substitutedfl)
706 subst,metasenv,(CicSubstitution.lift 1 t' ),ugraph
708 (*CSC: not implemented
709 let tylen = List.length fl in
712 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
715 C.CoFix (i, substitutedfl)
718 subst,metasenv,(CicSubstitution.lift 1 t'), ugraph
720 and aux_exp_named_subst metasenv subst n context ens ugraph =
722 (fun (uri,t) (subst,metasenv,l,ugraph) ->
723 let subst,metasenv,t',ugraph1 = aux metasenv subst n context t ugraph in
724 subst,metasenv,((uri,t')::l),ugraph1) ens (subst,metasenv,[],ugraph)
726 let argty,ugraph1 = type_of_aux' metasenv subst context arg ugraph in
728 FreshNamesGenerator.mk_fresh_name ~subst
729 metasenv context (Cic.Name ("Hbeta" ^ string_of_int num)) ~typ:argty
731 let subst,metasenv,t',ugraph2 = aux metasenv subst 0 context t ugraph1 in
732 let t'' = eta_reduce (C.Lambda (fresh_name,argty,t')) t' t in
733 subst, metasenv, t'', ugraph2
734 in profiler_beta_expand.HExtlib.profile foo ()
737 and beta_expand_many test_equality_only metasenv subst context t args ugraph =
738 let _,subst,metasenv,hd,ugraph =
740 (fun arg (num,subst,metasenv,t,ugraph) ->
741 let subst,metasenv,t,ugraph1 =
742 beta_expand num test_equality_only
743 metasenv subst context t arg ugraph
745 num+1,subst,metasenv,t,ugraph1
746 ) args (1,subst,metasenv,t,ugraph)
748 subst,metasenv,hd,ugraph
750 and warn_if_not_unique xxx to1 to2 carr car1 car2 =
753 | (m2,_,c2,c2')::_ ->
754 let m1,c1,c1' = carr,to1,to2 in
756 function Some (_,t) -> CicPp.ppterm t
760 ("There are two minimal joins of "^ CoercDb.string_of_carr car1^" and "^
761 CoercDb.string_of_carr car2^": " ^
762 CoercDb.string_of_carr m1^" via "^unopt c1^" + "^
763 unopt c1'^" and "^ CoercDb.string_of_carr m2^" via "^
764 unopt c2^" + "^unopt c2')
766 (* NUOVA UNIFICAZIONE *)
767 (* A substitution is a (int * Cic.term) list that associates a
768 metavariable i with its body.
769 A metaenv is a (int * Cic.term) list that associate a metavariable
771 fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
772 a new substitution which is _NOT_ unwinded. It must be unwinded before
775 and fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph =
776 let module C = Cic in
777 let module R = CicReduction in
778 let module S = CicSubstitution in
779 let t1 = deref subst t1 in
780 let t2 = deref subst t2 in
781 let (&&&) a b = (a && b) || ((not a) && (not b)) in
782 (* let bef = Sys.time () in *)
784 if not (CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t1) &&& CicUtil.is_meta_closed (CicMetaSubst.apply_subst subst t2)) then
788 R.are_convertible ~subst ~metasenv context t1 t2 ugraph
789 in profiler_are_convertible.HExtlib.profile foo ()
791 (* let aft = Sys.time () in
792 if (aft -. bef > 2.0) then prerr_endline ("LEEEENTO: " ^
793 CicMetaSubst.ppterm_in_context subst ~metasenv t1 context ^ " <===> " ^
794 CicMetaSubst.ppterm_in_context subst ~metasenv t2 context); *)
796 subst, metasenv, ugraph
799 | (C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
800 let _,subst,metasenv,ugraph1 =
803 (fun (j,subst,metasenv,ugraph) t1 t2 ->
806 | _,None -> j+1,subst,metasenv,ugraph
807 | Some t1', Some t2' ->
808 (* First possibility: restriction *)
809 (* Second possibility: unification *)
810 (* Third possibility: convertibility *)
813 ~subst ~metasenv context t1' t2' ugraph
816 j+1,subst,metasenv, ugraph1
819 let subst,metasenv,ugraph2 =
822 subst context metasenv t1' t2' ugraph
824 j+1,subst,metasenv,ugraph2
827 | UnificationFailure _ ->
828 debug_print (lazy ("restringo Meta n." ^ (string_of_int n) ^ "on variable n." ^ (string_of_int j)));
829 let metasenv, subst =
830 CicMetaSubst.restrict
831 subst [(n,j)] metasenv in
832 j+1,subst,metasenv,ugraph1)
833 ) (1,subst,metasenv,ugraph) ln lm
837 (UnificationFailure (lazy "1"))
840 "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."
841 (CicMetaSubst.ppterm ~metasenv subst t1)
842 (CicMetaSubst.ppterm ~metasenv subst t2))) *)
843 | Invalid_argument _ ->
845 (UnificationFailure (lazy "2")))
848 "Error trying to unify %s with %s: the lengths of the two local contexts do not match."
849 (CicMetaSubst.ppterm ~metasenv subst t1)
850 (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
851 in subst,metasenv,ugraph1
852 | (C.Meta (n,_), C.Meta (m,_)) when n>m ->
853 fo_unif_subst test_equality_only subst context metasenv t2 t1 ugraph
855 | (t, C.Meta (n,l)) ->
858 C.Meta (n,_), C.Meta (m,_) when n < m -> false
859 | _, C.Meta _ -> false
862 let lower = fun x y -> if swap then y else x in
863 let upper = fun x y -> if swap then x else y in
864 let fo_unif_subst_ordered
865 test_equality_only subst context metasenv m1 m2 ugraph =
866 fo_unif_subst test_equality_only subst context metasenv
867 (lower m1 m2) (upper m1 m2) ugraph
870 let subst,metasenv,ugraph1 =
871 let (_,_,meta_type) = CicUtil.lookup_meta n metasenv in
874 type_of_aux' metasenv subst context t ugraph
878 subst context metasenv tyt (S.subst_meta l meta_type) ugraph1
880 UnificationFailure _ as e -> raise e
881 | Uncertain msg -> raise (UnificationFailure msg)
883 debug_print (lazy "siamo allo huge hack");
884 (* TODO huge hack!!!!
885 * we keep on unifying/refining in the hope that
886 * the problem will be eventually solved.
887 * In the meantime we're breaking a big invariant:
888 * the terms that we are unifying are no longer well
889 * typed in the current context (in the worst case
890 * we could even diverge) *)
891 (subst, metasenv,ugraph)) in
892 let t',metasenv,subst =
894 CicMetaSubst.delift n subst context metasenv l t
896 (CicMetaSubst.MetaSubstFailure msg)->
897 raise (UnificationFailure msg)
898 | (CicMetaSubst.Uncertain msg) -> raise (Uncertain msg)
902 C.Sort (C.Type u) when not test_equality_only ->
903 let u' = CicUniv.fresh () in
904 let s = C.Sort (C.Type u') in
907 CicUniv.add_ge (upper u u') (lower u u') ugraph1
911 CicUniv.UniverseInconsistency msg ->
912 raise (UnificationFailure msg))
915 (* Unifying the types may have already instantiated n. Let's check *)
917 let (_, oldt,_) = CicUtil.lookup_subst n subst in
918 let lifted_oldt = S.subst_meta l oldt in
919 fo_unif_subst_ordered
920 test_equality_only subst context metasenv t lifted_oldt ugraph2
922 CicUtil.Subst_not_found _ ->
923 let (_, context, ty) = CicUtil.lookup_meta n metasenv in
924 let subst = (n, (context, t'',ty)) :: subst in
926 List.filter (fun (m,_,_) -> not (n = m)) metasenv in
927 subst, metasenv, ugraph2
929 | (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
930 | (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
931 if UriManager.eq uri1 uri2 then
932 fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
933 exp_named_subst1 exp_named_subst2 ugraph
935 raise (UnificationFailure (lazy
937 "Can't unify %s with %s due to different constants"
938 (CicMetaSubst.ppterm ~metasenv subst t1)
939 (CicMetaSubst.ppterm ~metasenv subst t2))))
940 | C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
941 if UriManager.eq uri1 uri2 && i1 = i2 then
942 fo_unif_subst_exp_named_subst
944 subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
946 raise (UnificationFailure
949 "Can't unify %s with %s due to different inductive principles"
950 (CicMetaSubst.ppterm ~metasenv subst t1)
951 (CicMetaSubst.ppterm ~metasenv subst t2))))
952 | C.MutConstruct (uri1,i1,j1,exp_named_subst1),
953 C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
954 if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
955 fo_unif_subst_exp_named_subst
957 subst context metasenv exp_named_subst1 exp_named_subst2 ugraph
959 raise (UnificationFailure
962 "Can't unify %s with %s due to different inductive constructors"
963 (CicMetaSubst.ppterm ~metasenv subst t1)
964 (CicMetaSubst.ppterm ~metasenv subst t2))))
965 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
966 | (C.Cast (te,ty), t2) -> fo_unif_subst test_equality_only
967 subst context metasenv te t2 ugraph
968 | (t1, C.Cast (te,ty)) -> fo_unif_subst test_equality_only
969 subst context metasenv t1 te ugraph
970 | (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
971 let subst',metasenv',ugraph1 =
972 fo_unif_subst test_equality_only subst context metasenv s1 s2 ugraph
974 fo_unif_subst test_equality_only
975 subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
976 | (C.LetIn (_,s1,ty1,t1), t2)
977 | (t2, C.LetIn (_,s1,ty1,t1)) ->
979 test_equality_only subst context metasenv t2 (S.subst s1 t1) ugraph
980 | (C.Appl l1, C.Appl l2) ->
981 (* andrea: this case should be probably rewritten in the
984 | C.Meta (i,_)::args1, C.Meta (j,_)::args2 when i = j ->
987 (fun (subst,metasenv,ugraph) t1 t2 ->
989 test_equality_only subst context metasenv t1 t2 ugraph)
990 (subst,metasenv,ugraph) l1 l2
991 with (Invalid_argument msg) ->
992 raise (UnificationFailure (lazy msg)))
993 | C.Meta (i,l)::args, _ when not(exists_a_meta args) ->
994 (* we verify that none of the args is a Meta,
995 since beta expanding with respoect to a metavariable
999 let (_,t,_) = CicUtil.lookup_subst i subst in
1000 let lifted = S.subst_meta l t in
1001 let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
1004 subst context metasenv reduced t2 ugraph
1005 with CicUtil.Subst_not_found _ -> *)
1006 let subst,metasenv,beta_expanded,ugraph1 =
1008 test_equality_only metasenv subst context t2 args ugraph
1010 fo_unif_subst test_equality_only subst context metasenv
1011 (C.Meta (i,l)) beta_expanded ugraph1
1012 | _, C.Meta (i,l)::args when not(exists_a_meta args) ->
1014 let (_,t,_) = CicUtil.lookup_subst i subst in
1015 let lifted = S.subst_meta l t in
1016 let reduced = CicReduction.head_beta_reduce (Cic.Appl (lifted::args)) in
1019 subst context metasenv t1 reduced ugraph
1020 with CicUtil.Subst_not_found _ -> *)
1021 let subst,metasenv,beta_expanded,ugraph1 =
1024 metasenv subst context t1 args ugraph
1026 fo_unif_subst test_equality_only subst context metasenv
1027 (C.Meta (i,l)) beta_expanded ugraph1
1029 let lr1 = List.rev l1 in
1030 let lr2 = List.rev l2 in
1032 fo_unif_l test_equality_only subst metasenv (l1,l2) ugraph =
1035 | _,[] -> assert false
1038 test_equality_only subst context metasenv h1 h2 ugraph
1041 fo_unif_subst test_equality_only subst context metasenv
1042 h (C.Appl (List.rev l)) ugraph
1043 | ((h1::l1),(h2::l2)) ->
1044 let subst', metasenv',ugraph1 =
1047 subst context metasenv h1 h2 ugraph
1050 test_equality_only subst' metasenv' (l1,l2) ugraph1
1054 test_equality_only subst metasenv (lr1, lr2) ugraph
1056 | UnificationFailure s
1057 | Uncertain s as exn ->
1060 | (((Cic.Const (uri1, ens1)) as cc1) :: tl1),
1061 (((Cic.Const (uri2, ens2)) as cc2) :: tl2) when
1062 CoercDb.is_a_coercion cc1 <> None &&
1063 CoercDb.is_a_coercion cc2 <> None &&
1064 not (UriManager.eq uri1 uri2) ->
1066 prerr_endline ("<<<< " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^ " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
1068 let inner_coerced t =
1069 let t = CicMetaSubst.apply_subst subst t in
1073 (match CoercGraph.coerced_arg l with
1075 | Some (t,_) -> aux (List.hd l) t t)
1078 aux (Cic.Implicit None) (Cic.Implicit None) t
1080 let c1,last_tl1 = inner_coerced (Cic.Appl l1) in
1081 let c2,last_tl2 = inner_coerced (Cic.Appl l2) in
1084 CoercDb.is_a_coercion c1, CoercDb.is_a_coercion c2
1086 | Some (s1,_,_,_,_), Some (s2,_,_,_,_) -> s1, s2
1089 let head1_c, head2_c =
1091 CoercDb.is_a_coercion cc1, CoercDb.is_a_coercion cc2
1093 | Some (_,t1,_,_,_), Some (_,t2,_,_,_) -> t1, t2
1096 let unfold uri ens args =
1098 CicEnvironment.get_obj CicUniv.oblivion_ugraph uri
1102 | Cic.Constant (_,Some bo,_,_,_) ->
1103 CicReduction.head_beta_reduce ~delta:false
1104 (Cic.Appl (bo::args))
1107 let conclude subst metasenv ugraph last_tl1' last_tl2' =
1108 let subst',metasenv,ugraph =
1111 ("OK " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl1' context ^
1112 " <==> " ^ CicMetaSubst.ppterm_in_context ~metasenv subst last_tl2' context);
1114 fo_unif_subst test_equality_only subst context
1115 metasenv last_tl1' last_tl2' ugraph
1117 if subst = subst' then raise exn
1120 let subst,metasenv,ugrph as res =
1122 fo_unif_subst test_equality_only subst' context
1123 metasenv (C.Appl l1) (C.Appl l2) ugraph
1127 (">>>> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l1) context ^
1128 " <==> "^CicMetaSubst.ppterm_in_context ~metasenv subst (C.Appl l2) context);
1132 if CoercDb.eq_carr car1 car2 then
1133 match last_tl1,last_tl2 with
1134 | C.Meta (i1,_),C.Meta(i2,_) when i1 = i2 -> raise exn
1137 let subst,metasenv,ugraph =
1138 fo_unif_subst test_equality_only subst context
1139 metasenv last_tl1 last_tl2 ugraph
1141 fo_unif_subst test_equality_only subst context
1142 metasenv (Cic.Appl l1) (Cic.Appl l2) ugraph
1143 | _ when CoercDb.eq_carr head1_c head2_c ->
1144 (* composite VS composition + metas avoiding
1145 * coercions not only in coerced position *)
1146 if c1 <> cc1 && c2 <> cc2 then
1147 conclude subst metasenv ugraph
1152 unfold uri1 ens1 tl1, Cic.Appl (cc2::tl2)
1154 Cic.Appl (cc1::tl1), unfold uri2 ens2 tl2
1156 fo_unif_subst test_equality_only subst context
1157 metasenv l1 l2 ugraph
1161 match last_tl1 with Cic.Meta _ -> true | _ -> false in
1163 match last_tl2 with Cic.Meta _ -> true | _ -> false in
1164 if not (grow1 || grow2) then
1165 (* no flexible terminals -> no pullback, but
1166 * we still unify them, in some cases it helps *)
1167 conclude subst metasenv ugraph last_tl1 last_tl2
1171 metasenv subst context (grow1,car1) (grow2,car2)
1175 | (carr,metasenv,to1,to2)::xxx ->
1176 warn_if_not_unique xxx to1 to2 carr car1 car2;
1177 let last_tl1',(subst,metasenv,ugraph) =
1178 match grow1,to1 with
1179 | true,Some (last,coerced) ->
1181 fo_unif_subst test_equality_only subst context
1182 metasenv coerced last_tl1 ugraph
1183 | _ -> last_tl1,(subst,metasenv,ugraph)
1185 let last_tl2',(subst,metasenv,ugraph) =
1186 match grow2,to2 with
1187 | true,Some (last,coerced) ->
1189 fo_unif_subst test_equality_only subst context
1190 metasenv coerced last_tl2 ugraph
1191 | _ -> last_tl2,(subst,metasenv,ugraph)
1193 conclude subst metasenv ugraph last_tl1' last_tl2')
1195 (* {{{ CSC: This is necessary because of the "elim H" tactic
1196 where the type of H is only reducible to an
1197 inductive type. This could be extended from inductive
1198 types to any rigid term. However, the code is
1199 duplicated in two places: inside applications and
1200 outside them. Probably it would be better to
1201 work with lambda-bar terms instead. *)
1202 | (Cic.MutInd _::_, Cic.MutInd _::_) -> raise exn
1203 | (_, Cic.MutInd _::_) ->
1204 let t1' = R.whd ~subst context t1 in
1206 C.Appl (C.MutInd _::_) ->
1207 fo_unif_subst test_equality_only
1208 subst context metasenv t1' t2 ugraph
1209 | _ -> raise (UnificationFailure (lazy "88")))
1210 | (Cic.MutInd _::_,_) ->
1211 let t2' = R.whd ~subst context t2 in
1213 C.Appl (C.MutInd _::_) ->
1214 fo_unif_subst test_equality_only
1215 subst context metasenv t1 t2' ugraph
1218 (lazy ("not a mutind :"^
1219 CicMetaSubst.ppterm ~metasenv subst t2 ))))
1222 | (C.MutCase (_,_,outt1,t1',pl1), C.MutCase (_,_,outt2,t2',pl2))->
1223 let subst', metasenv',ugraph1 =
1224 fo_unif_subst test_equality_only subst context metasenv outt1 outt2
1226 let subst'',metasenv'',ugraph2 =
1227 fo_unif_subst test_equality_only subst' context metasenv' t1' t2'
1231 (fun (subst,metasenv,ugraph) t1 t2 ->
1233 test_equality_only subst context metasenv t1 t2 ugraph
1234 ) (subst'',metasenv'',ugraph2) pl1 pl2
1236 Invalid_argument _ ->
1237 raise (UnificationFailure (lazy "6.1")))
1239 "Error trying to unify %s with %s: the number of branches is not the same."
1240 (CicMetaSubst.ppterm ~metasenv subst t1)
1241 (CicMetaSubst.ppterm ~metasenv subst t2)))) *)
1242 | (C.Rel _, _) | (_, C.Rel _) ->
1244 subst, metasenv,ugraph
1246 raise (UnificationFailure (lazy
1248 "Can't unify %s with %s because they are not convertible"
1249 (CicMetaSubst.ppterm ~metasenv subst t1)
1250 (CicMetaSubst.ppterm ~metasenv subst t2))))
1251 | (C.Appl (C.Meta(i,l)::args),t2) when not(exists_a_meta args) ->
1252 let subst,metasenv,beta_expanded,ugraph1 =
1254 test_equality_only metasenv subst context t2 args ugraph
1256 fo_unif_subst test_equality_only subst context metasenv
1257 (C.Meta (i,l)) beta_expanded ugraph1
1258 | (t1,C.Appl (C.Meta(i,l)::args)) when not(exists_a_meta args) ->
1259 let subst,metasenv,beta_expanded,ugraph1 =
1261 test_equality_only metasenv subst context t1 args ugraph
1263 fo_unif_subst test_equality_only subst context metasenv
1264 beta_expanded (C.Meta (i,l)) ugraph1
1265 (* Works iff there are no arguments applied to it; similar to the
1267 | (_, C.MutInd _) ->
1268 let t1' = R.whd ~subst context t1 in
1271 fo_unif_subst test_equality_only
1272 subst context metasenv t1' t2 ugraph
1273 | _ -> raise (UnificationFailure (lazy "8")))
1275 | (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
1276 let subst',metasenv',ugraph1 =
1277 fo_unif_subst true subst context metasenv s1 s2 ugraph
1279 fo_unif_subst test_equality_only
1280 subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2 ugraph1
1282 (match CicReduction.whd ~subst context t2 with
1284 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1285 | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t2^"Not a product"))))
1287 (match CicReduction.whd ~subst context t1 with
1289 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1290 | _ -> raise (UnificationFailure (lazy (CicMetaSubst.ppterm ~metasenv subst t1^"Not a product"))))
1292 (* delta-beta reduction should almost never be a problem for
1294 1. long computations require iota reduction
1295 2. it is extremely rare that a close term t1 (that could be unified
1296 to t2) beta-delta reduces to t1' while t2 does not beta-delta
1297 reduces in the same way. This happens only if one meta of t2
1298 occurs in head position during beta reduction. In this unluky
1299 case too much reduction will be performed on t1 and unification
1300 will surely fail. *)
1301 let t1' = CicReduction.head_beta_reduce ~delta:true t1 in
1302 let t2' = CicReduction.head_beta_reduce ~delta:true t2 in
1303 if t1 = t1' && t2 = t2' then
1304 raise (UnificationFailure
1307 "Can't unify %s with %s because they are not convertible"
1308 (CicMetaSubst.ppterm ~metasenv subst t1)
1309 (CicMetaSubst.ppterm ~metasenv subst t2))))
1312 fo_unif_subst test_equality_only subst context metasenv t1' t2' ugraph
1314 UnificationFailure _
1316 raise (UnificationFailure
1319 "Can't unify %s with %s because they are not convertible"
1320 (CicMetaSubst.ppterm ~metasenv subst t1)
1321 (CicMetaSubst.ppterm ~metasenv subst t2))))
1323 and fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
1324 exp_named_subst1 exp_named_subst2 ugraph
1328 (fun (subst,metasenv,ugraph) (uri1,t1) (uri2,t2) ->
1329 assert (uri1=uri2) ;
1330 fo_unif_subst test_equality_only subst context metasenv t1 t2 ugraph
1331 ) (subst,metasenv,ugraph) exp_named_subst1 exp_named_subst2
1333 Invalid_argument _ ->
1338 UriManager.string_of_uri uri ^ " := " ^ (CicMetaSubst.ppterm ~metasenv subst t)
1341 raise (UnificationFailure (lazy (sprintf
1342 "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))))
1344 (* A substitution is a (int * Cic.term) list that associates a *)
1345 (* metavariable i with its body. *)
1346 (* metasenv is of type Cic.metasenv *)
1347 (* fo_unif takes a metasenv, a context, two terms t1 and t2 and gives back *)
1348 (* a new substitution which is already unwinded and ready to be applied and *)
1349 (* a new metasenv in which some hypothesis in the contexts of the *)
1350 (* metavariables may have been restricted. *)
1351 let fo_unif metasenv context t1 t2 ugraph =
1352 fo_unif_subst false [] context metasenv t1 t2 ugraph ;;
1354 let enrich_msg msg subst context metasenv t1 t2 ugraph =
1357 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"
1358 (CicMetaSubst.ppterm ~metasenv subst t1)
1360 let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
1363 | UnificationFailure s
1365 | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
1366 (CicMetaSubst.ppterm ~metasenv subst t2)
1368 let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
1371 | UnificationFailure s
1373 | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
1374 (CicMetaSubst.ppcontext ~metasenv subst context)
1375 (CicMetaSubst.ppmetasenv subst metasenv)
1376 (CicMetaSubst.ppsubst ~metasenv subst) (Lazy.force msg)
1378 sprintf "Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nbecause %s"
1379 (CicMetaSubst.ppterm_in_context ~metasenv subst t1 context)
1381 let ty_t1,_ = type_of_aux' metasenv subst context t1 ugraph in
1382 CicMetaSubst.ppterm_in_context ~metasenv subst ty_t1 context
1384 | UnificationFailure s
1386 | AssertFailure s -> sprintf "MALFORMED(t1): \n<BEGIN>%s\n<END>" (Lazy.force s))
1387 (CicMetaSubst.ppterm_in_context ~metasenv subst t2 context)
1389 let ty_t2,_ = type_of_aux' metasenv subst context t2 ugraph in
1390 CicMetaSubst.ppterm_in_context ~metasenv subst ty_t2 context
1392 | UnificationFailure s
1394 | AssertFailure s -> sprintf "MALFORMED(t2): \n<BEGIN>%s\n<END>" (Lazy.force s))
1395 (CicMetaSubst.ppcontext ~metasenv subst context)
1396 (CicMetaSubst.ppmetasenv subst metasenv)
1400 let fo_unif_subst subst context metasenv t1 t2 ugraph =
1402 fo_unif_subst false subst context metasenv t1 t2 ugraph
1404 | AssertFailure msg ->
1405 raise (AssertFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))
1406 | UnificationFailure msg ->
1407 raise (UnificationFailure (enrich_msg msg subst context metasenv t1 t2 ugraph))