1 (* Copyright (C) 2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
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23 * http://cs.unibo.it/helm/.
32 (Cic.term * (* type *)
33 Cic.term * (* left side *)
34 Cic.term * (* right side *)
35 Utils.comparison) * (* ordering *)
36 Cic.metasenv * (* environment for metas *)
37 Cic.term list (* arguments *)
41 | BasicProof of Cic.term
43 Cic.substitution * UriManager.uri *
44 (Cic.name * Cic.term) * Cic.term * (Utils.pos * equality) * proof
45 | ProofGoalBlock of proof * proof
46 | ProofSymBlock of Cic.term list * proof
47 | SubProof of Cic.term * int * proof
51 let string_of_equality ?env =
55 | w, _, (ty, left, right, o), _, _ ->
56 Printf.sprintf "Weight: %d, {%s}: %s =(%s) %s" w (CicPp.ppterm ty)
57 (CicPp.ppterm left) (string_of_comparison o) (CicPp.ppterm right)
59 | Some (_, context, _) -> (
60 let names = names_of_context context in
62 | w, _, (ty, left, right, o), _, _ ->
63 Printf.sprintf "Weight: %d, {%s}: %s =(%s) %s" w (CicPp.pp ty names)
64 (CicPp.pp left names) (string_of_comparison o)
65 (CicPp.pp right names)
70 let rec string_of_proof = function
71 | NoProof -> "NoProof"
72 | BasicProof t -> "BasicProof " ^ (CicPp.ppterm t)
73 | SubProof (t, i, p) ->
74 Printf.sprintf "SubProof(%s, %s, %s)"
75 (CicPp.ppterm t) (string_of_int i) (string_of_proof p)
76 | ProofSymBlock _ -> "ProofSymBlock"
77 | ProofBlock _ -> "ProofBlock"
78 | ProofGoalBlock (p1, p2) ->
79 Printf.sprintf "ProofGoalBlock(%s, %s)"
80 (string_of_proof p1) (string_of_proof p2)
84 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
85 let build_ens_for_sym_eq sym_eq_URI termlist =
86 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph sym_eq_URI in
88 | Cic.Constant (_, _, _, uris, _) ->
89 assert (List.length uris <= List.length termlist);
90 let rec aux = function
92 | (uri::uris), (term::tl) ->
93 let ens, args = aux (uris, tl) in
94 (uri, term)::ens, args
95 | _, _ -> assert false
102 let build_proof_term proof =
103 let rec do_build_proof proof =
106 Printf.fprintf stderr "WARNING: no proof!\n";
108 | BasicProof term -> term
109 | ProofGoalBlock (proofbit, proof) ->
110 print_endline "found ProofGoalBlock, going up...";
111 do_build_goal_proof proofbit proof
112 | ProofSymBlock (termlist, proof) ->
113 let proof = do_build_proof proof in
114 let ens, args = build_ens_for_sym_eq (Utils.sym_eq_URI ()) termlist in
115 Cic.Appl ([Cic.Const (Utils.sym_eq_URI (), ens)] @ args @ [proof])
116 | ProofBlock (subst, eq_URI, (name, ty), bo, (pos, eq), eqproof) ->
117 let t' = Cic.Lambda (name, ty, bo) in
119 let _, proof', _, _, _ = eq in
120 do_build_proof proof'
122 let eqproof = do_build_proof eqproof in
123 let _, _, (ty, what, other, _), menv', args' = eq in
125 if pos = Utils.Left then what, other else other, what
127 CicMetaSubst.apply_subst subst
128 (Cic.Appl [Cic.Const (eq_URI, []); ty;
129 what; t'; eqproof; other; proof'])
130 | SubProof (term, meta_index, proof) ->
131 let proof = do_build_proof proof in
133 | Cic.Meta (j, _) -> i = j
136 ProofEngineReduction.replace
137 ~equality:eq ~what:[meta_index] ~with_what:[proof] ~where:term
139 and do_build_goal_proof proofbit proof =
141 | ProofGoalBlock (pb, p) ->
142 do_build_proof (ProofGoalBlock (replace_proof proofbit pb, p))
143 | _ -> do_build_proof (replace_proof proofbit proof)
145 and replace_proof newproof = function
146 | ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof) ->
147 let eqproof' = replace_proof newproof eqproof in
148 ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof')
149 | ProofGoalBlock (pb, p) ->
150 let pb' = replace_proof newproof pb in
151 ProofGoalBlock (pb', p)
152 | BasicProof _ -> newproof
153 | SubProof (term, meta_index, p) ->
154 SubProof (term, meta_index, replace_proof newproof p)
161 let rec metas_of_term = function
162 | Cic.Meta (i, c) -> [i]
165 | Cic.MutInd (_, _, ens)
166 | Cic.MutConstruct (_, _, _, ens) ->
167 List.flatten (List.map (fun (u, t) -> metas_of_term t) ens)
170 | Cic.Lambda (_, s, t)
171 | Cic.LetIn (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
172 | Cic.Appl l -> List.flatten (List.map metas_of_term l)
173 | Cic.MutCase (uri, i, s, t, l) ->
174 (metas_of_term s) @ (metas_of_term t) @
175 (List.flatten (List.map metas_of_term l))
178 (List.map (fun (s, i, t1, t2) ->
179 (metas_of_term t1) @ (metas_of_term t2)) il)
180 | Cic.CoFix (i, il) ->
182 (List.map (fun (s, t1, t2) ->
183 (metas_of_term t1) @ (metas_of_term t2)) il)
188 exception NotMetaConvertible;;
190 let meta_convertibility_aux table t1 t2 =
191 let module C = Cic in
195 (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
197 let rec aux ((table_l, table_r) as table) t1 t2 =
199 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
200 let m1_binding, table_l =
201 try List.assoc m1 table_l, table_l
202 with Not_found -> m2, (m1, m2)::table_l
203 and m2_binding, table_r =
204 try List.assoc m2 table_r, table_r
205 with Not_found -> m1, (m2, m1)::table_r
207 if (m1_binding <> m2) || (m2_binding <> m1) then
208 raise NotMetaConvertible
214 | None, Some _ | Some _, None -> raise NotMetaConvertible
216 | Some t1, Some t2 -> (aux res t1 t2))
217 (table_l, table_r) tl1 tl2
218 with Invalid_argument _ ->
219 raise NotMetaConvertible
221 | C.Var (u1, ens1), C.Var (u2, ens2)
222 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
223 aux_ens table ens1 ens2
224 | C.Cast (s1, t1), C.Cast (s2, t2)
225 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
226 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
227 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
228 let table = aux table s1 s2 in
230 | C.Appl l1, C.Appl l2 -> (
231 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
232 with Invalid_argument _ -> raise NotMetaConvertible
234 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
235 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
236 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
237 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
238 aux_ens table ens1 ens2
239 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
240 when (UriManager.eq u1 u2) && i1 = i2 ->
241 let table = aux table s1 s2 in
242 let table = aux table t1 t2 in (
243 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
244 with Invalid_argument _ -> raise NotMetaConvertible
246 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
249 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
250 if i1 <> i2 then raise NotMetaConvertible
252 let res = (aux res s1 s2) in aux res t1 t2)
254 with Invalid_argument _ -> raise NotMetaConvertible
256 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
259 (fun res (n1, s1, t1) (n2, s2, t2) ->
260 let res = aux res s1 s2 in aux res t1 t2)
262 with Invalid_argument _ -> raise NotMetaConvertible
264 | t1, t2 when t1 = t2 -> table
265 | _, _ -> raise NotMetaConvertible
267 and aux_ens table ens1 ens2 =
268 let cmp (u1, t1) (u2, t2) =
269 compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
271 let ens1 = List.sort cmp ens1
272 and ens2 = List.sort cmp ens2 in
275 (fun res (u1, t1) (u2, t2) ->
276 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
279 with Invalid_argument _ -> raise NotMetaConvertible
285 let meta_convertibility_eq eq1 eq2 =
286 let _, _, (ty, left, right, _), _, _ = eq1
287 and _, _, (ty', left', right', _), _, _ = eq2 in
290 else if (left = left') && (right = right') then
292 else if (left = right') && (right = left') then
296 let table = meta_convertibility_aux ([], []) left left' in
297 let _ = meta_convertibility_aux table right right' in
299 with NotMetaConvertible ->
301 let table = meta_convertibility_aux ([], []) left right' in
302 let _ = meta_convertibility_aux table right left' in
304 with NotMetaConvertible ->
309 let meta_convertibility t1 t2 =
313 (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
319 let l, r = meta_convertibility_aux ([], []) t1 t2 in
321 with NotMetaConvertible ->
326 let rec check_irl start = function
328 | None::tl -> check_irl (start+1) tl
329 | (Some (Cic.Rel x))::tl ->
330 if x = start then check_irl (start+1) tl else false
335 let rec is_simple_term = function
336 | Cic.Appl ((Cic.Meta _)::_) -> false
337 | Cic.Appl l -> List.for_all is_simple_term l
338 | Cic.Meta (i, l) -> check_irl 1 l
340 | Cic.Const _ -> true
341 | Cic.MutInd (_, _, []) -> true
342 | Cic.MutConstruct (_, _, _, []) -> true
347 let lookup_subst meta subst =
349 | Cic.Meta (i, _) -> (
350 try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
351 with Not_found -> meta
357 let unification_simple metasenv context t1 t2 ugraph =
358 let module C = Cic in
359 let module M = CicMetaSubst in
360 let module U = CicUnification in
361 let lookup = lookup_subst in
362 let rec occurs_check subst what where =
364 | t when what = t -> true
365 | C.Appl l -> List.exists (occurs_check subst what) l
367 let t = lookup where subst in
368 if t <> where then occurs_check subst what t else false
371 let rec unif subst menv s t =
372 let s = match s with C.Meta _ -> lookup s subst | _ -> s
373 and t = match t with C.Meta _ -> lookup t subst | _ -> t
376 | s, t when s = t -> subst, menv
377 | C.Meta (i, _), C.Meta (j, _) when i > j ->
379 | C.Meta _, t when occurs_check subst s t ->
381 (U.UnificationFailure (lazy "Inference.unification.unif"))
382 | C.Meta (i, l), t -> (
384 let _, _, ty = CicUtil.lookup_meta i menv in
386 if not (List.mem_assoc i subst) then (i, (context, t, ty))::subst
389 let menv = menv in (* List.filter (fun (m, _, _) -> i <> m) menv in *)
391 with CicUtil.Meta_not_found m ->
392 let names = names_of_context context in
395 (Printf.sprintf "Meta_not_found %d!: %s %s\n%s\n\n%s" m
396 (CicPp.pp t1 names) (CicPp.pp t2 names)
397 (print_metasenv menv) (print_metasenv metasenv)));
400 | _, C.Meta _ -> unif subst menv t s
401 | C.Appl (hds::_), C.Appl (hdt::_) when hds <> hdt ->
402 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
403 | C.Appl (hds::tls), C.Appl (hdt::tlt) -> (
406 (fun (subst', menv) s t -> unif subst' menv s t)
407 (subst, menv) tls tlt
408 with Invalid_argument _ ->
409 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
412 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
414 let subst, menv = unif [] metasenv t1 t2 in
418 try let _ = List.find (fun (i, _) -> m = i) subst in false
419 with Not_found -> true)
422 List.rev subst, menv, ugraph
426 let unification metasenv context t1 t2 ugraph =
427 let subst, menv, ug =
428 if not (is_simple_term t1) || not (is_simple_term t2) then (
431 (Printf.sprintf "NOT SIMPLE TERMS: %s %s"
432 (CicPp.ppterm t1) (CicPp.ppterm t2)));
433 CicUnification.fo_unif metasenv context t1 t2 ugraph
435 unification_simple metasenv context t1 t2 ugraph
437 let rec fix_term = function
438 | (Cic.Meta (i, l) as t) ->
439 let t' = lookup_subst t subst in
440 if t <> t' then fix_term t' else t
441 | Cic.Appl l -> Cic.Appl (List.map fix_term l)
444 let rec fix_subst = function
446 | (i, (c, t, ty))::tl -> (i, (c, fix_term t, fix_term ty))::(fix_subst tl)
448 fix_subst subst, menv, ug
452 let unification = CicUnification.fo_unif;;
454 exception MatchingFailure;;
458 let matching_simple metasenv context t1 t2 ugraph =
459 let module C = Cic in
460 let module M = CicMetaSubst in
461 let module U = CicUnification in
462 let lookup meta subst =
465 try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
466 with Not_found -> meta
470 let rec do_match subst menv s t =
472 | s, t when s = t -> subst, menv
473 | s, C.Meta (i, l) ->
474 let filter_menv i menv =
475 List.filter (fun (m, _, _) -> i <> m) menv
478 let value = lookup t subst in
480 | value when value = t ->
481 let _, _, ty = CicUtil.lookup_meta i menv in
482 (i, (context, s, ty))::subst, filter_menv i menv
483 | value when value <> s ->
484 raise MatchingFailure
485 | value -> do_match subst menv s value
488 | C.Appl ls, C.Appl lt -> (
491 (fun (subst, menv) s t -> do_match subst menv s t)
493 with Invalid_argument _ ->
494 raise MatchingFailure
497 raise MatchingFailure
499 let subst, menv = do_match [] metasenv t1 t2 in
505 let matching metasenv context t1 t2 ugraph =
507 let subst, metasenv, ugraph =
508 unification metasenv context t1 t2 ugraph
510 let t' = CicMetaSubst.apply_subst subst t1 in
511 if not (meta_convertibility t1 t') then
512 raise MatchingFailure
514 let metas = metas_of_term t1 in
515 let fix_subst = function
516 | (i, (c, Cic.Meta (j, lc), ty)) when List.mem i metas ->
517 (j, (c, Cic.Meta (i, lc), ty))
520 let subst = List.map fix_subst subst in
521 subst, metasenv, ugraph
523 | CicUnification.UnificationFailure _
524 | CicUnification.Uncertain _ ->
525 raise MatchingFailure
529 let find_equalities context proof =
530 let module C = Cic in
531 let module S = CicSubstitution in
532 let module T = CicTypeChecker in
533 let eq_uri = LibraryObjects.eq_URI () in
534 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
535 let ok_types ty menv =
536 List.for_all (fun (_, _, mt) -> mt = ty) menv
538 let rec aux index newmeta = function
540 | (Some (_, C.Decl (term)))::tl ->
541 let do_find context term =
543 | C.Prod (name, s, t) ->
544 let (head, newmetas, args, newmeta) =
545 ProofEngineHelpers.saturate_term newmeta []
546 context (S.lift index term) 0
549 if List.length args = 0 then
552 C.Appl ((C.Rel index)::args)
555 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
556 when (UriManager.eq uri eq_uri) && (ok_types ty newmetas) ->
559 (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
560 let o = !Utils.compare_terms t1 t2 in
561 let w = compute_equality_weight ty t1 t2 in
562 let proof = BasicProof p in
563 let e = (w, proof, (ty, t1, t2, o), newmetas, args) in
567 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
568 when UriManager.eq uri eq_uri ->
569 let t1 = S.lift index t1
570 and t2 = S.lift index t2 in
571 let o = !Utils.compare_terms t1 t2 in
572 let w = compute_equality_weight ty t1 t2 in
573 let e = (w, BasicProof (C.Rel index), (ty, t1, t2, o), [], []) in
577 match do_find context term with
579 let tl, newmeta' = (aux (index+1) newmeta tl) in
580 (index, p)::tl, max newmeta newmeta'
582 aux (index+1) newmeta tl
585 aux (index+1) newmeta tl
587 let il, maxm = aux 1 newmeta context in
588 let indexes, equalities = List.split il in
589 indexes, equalities, maxm
594 let equations_blacklist =
596 (fun s u -> UriManager.UriSet.add (UriManager.uri_of_string u) s)
597 UriManager.UriSet.empty [
598 "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)";
599 "cic:/Coq/Init/Logic/trans_eq.con";
600 "cic:/Coq/Init/Logic/f_equal.con";
601 "cic:/Coq/Init/Logic/f_equal2.con";
602 "cic:/Coq/Init/Logic/f_equal3.con";
603 "cic:/Coq/Init/Logic/f_equal4.con";
604 "cic:/Coq/Init/Logic/f_equal5.con";
605 "cic:/Coq/Init/Logic/sym_eq.con";
606 "cic:/Coq/Init/Logic/eq_ind.con";
607 "cic:/Coq/Init/Logic/eq_ind_r.con";
608 "cic:/Coq/Init/Logic/eq_rec.con";
609 "cic:/Coq/Init/Logic/eq_rec_r.con";
610 "cic:/Coq/Init/Logic/eq_rect.con";
611 "cic:/Coq/Init/Logic/eq_rect_r.con";
612 "cic:/Coq/Logic/Eqdep/UIP.con";
613 "cic:/Coq/Logic/Eqdep/UIP_refl.con";
614 "cic:/Coq/Logic/Eqdep_dec/eq2eqT.con";
615 "cic:/Coq/ZArith/Zcompare/rename.con";
616 (* ALB !!!! questo e` imbrogliare, ma x ora lo lasciamo cosi`...
617 perche' questo cacchio di teorema rompe le scatole :'( *)
618 "cic:/Rocq/SUBST/comparith/mult_n_2.con";
620 "cic:/matita/logic/equality/eq_f.con";
621 "cic:/matita/logic/equality/eq_f2.con";
622 "cic:/matita/logic/equality/eq_rec.con";
623 "cic:/matita/logic/equality/eq_rect.con";
627 let equations_blacklist = UriManager.UriSet.empty;;
630 let find_library_equalities dbd context status maxmeta =
631 let module C = Cic in
632 let module S = CicSubstitution in
633 let module T = CicTypeChecker in
636 (fun s u -> UriManager.UriSet.add u s)
638 [eq_XURI (); sym_eq_URI (); trans_eq_URI (); eq_ind_URI ();
644 let suri = UriManager.string_of_uri uri in
645 if UriManager.UriSet.mem uri blacklist then
648 let t = CicUtil.term_of_uri uri in
650 CicTypeChecker.type_of_aux' [] context t CicUniv.empty_ugraph
654 (let t1 = Unix.gettimeofday () in
655 let eqs = (MetadataQuery.equations_for_goal ~dbd status) in
656 let t2 = Unix.gettimeofday () in
659 (Printf.sprintf "Tempo di MetadataQuery.equations_for_goal: %.9f\n"
663 let eq_uri1 = eq_XURI ()
664 and eq_uri2 = LibraryObjects.eq_URI () in
666 (UriManager.eq uri eq_uri1) || (UriManager.eq uri eq_uri2)
668 let ok_types ty menv =
669 List.for_all (fun (_, _, mt) -> mt = ty) menv
671 let rec has_vars = function
672 | C.Meta _ | C.Rel _ | C.Const _ -> false
674 | C.Appl l -> List.exists has_vars l
675 | C.Prod (_, s, t) | C.Lambda (_, s, t)
676 | C.LetIn (_, s, t) | C.Cast (s, t) ->
677 (has_vars s) || (has_vars t)
680 let rec aux newmeta = function
682 | (uri, term, termty)::tl ->
685 (Printf.sprintf "Examining: %s (%s)"
686 (CicPp.ppterm term) (CicPp.ppterm termty)));
689 | C.Prod (name, s, t) when not (has_vars termty) ->
690 let head, newmetas, args, newmeta =
691 ProofEngineHelpers.saturate_term newmeta [] context termty 0
694 if List.length args = 0 then
700 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
701 when (iseq uri) && (ok_types ty newmetas) ->
704 (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
705 let o = !Utils.compare_terms t1 t2 in
706 let w = compute_equality_weight ty t1 t2 in
707 let proof = BasicProof p in
708 let e = (w, proof, (ty, t1, t2, o), newmetas, args) in
712 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
713 when iseq uri && not (has_vars termty) ->
714 let o = !Utils.compare_terms t1 t2 in
715 let w = compute_equality_weight ty t1 t2 in
716 let e = (w, BasicProof term, (ty, t1, t2, o), [], []) in
722 let tl, newmeta' = aux newmeta tl in
723 (uri, e)::tl, max newmeta newmeta'
727 let found, maxm = aux maxmeta candidates in
730 (fun (s, l) (u, e) ->
731 if List.exists (meta_convertibility_eq e) (List.map snd l) then (
734 (Printf.sprintf "NO!! %s already there!"
735 (string_of_equality e)));
736 (UriManager.UriSet.add u s, l)
737 ) else (UriManager.UriSet.add u s, (u, e)::l))
738 (UriManager.UriSet.empty, []) found)
744 let find_library_theorems dbd env status equalities_uris =
745 let module C = Cic in
746 let module S = CicSubstitution in
747 let module T = CicTypeChecker in
750 UriManager.uri_of_string "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)" in
752 UriManager.UriSet.remove refl_equal
753 (UriManager.UriSet.union equalities_uris equations_blacklist)
756 (fun s u -> UriManager.UriSet.add u s)
757 s [eq_XURI () ;sym_eq_URI (); trans_eq_URI (); eq_ind_URI ();
760 let metasenv, context, ugraph = env in
764 if UriManager.UriSet.mem uri blacklist then l
766 let t = CicUtil.term_of_uri uri in
767 let ty, _ = CicTypeChecker.type_of_aux' metasenv context t ugraph in
769 [] (MetadataQuery.signature_of_goal ~dbd status)
772 let u = eq_XURI () in
773 let t = CicUtil.term_of_uri u in
774 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
777 refl_equal::candidates
781 let find_context_hypotheses env equalities_indexes =
782 let metasenv, context, ugraph = env in
789 if List.mem n equalities_indexes then
794 CicTypeChecker.type_of_aux' metasenv context t ugraph in
795 (n+1, (t, ty, [])::l))
802 let fix_metas newmeta ((w, p, (ty, left, right, o), menv, args) as equality) =
803 let table = Hashtbl.create (List.length args) in
804 let newargs, newmeta =
806 (fun t (newargs, index) ->
809 if Hashtbl.mem table i then
810 let idx = Hashtbl.find table i in
811 ((Cic.Meta (idx, l))::newargs, index+1)
813 let _ = Hashtbl.add table i index in
814 ((Cic.Meta (index, l))::newargs, index+1)
819 ProofEngineReduction.replace ~equality:(=) ~what:args ~with_what:newargs
824 (fun (i, context, term) menv ->
826 let index = Hashtbl.find table i in
827 (index, context, term)::menv
829 (i, context, term)::menv)
834 and right = repl right in
835 let metas = (metas_of_term left) @ (metas_of_term right) in
836 let menv' = List.filter (fun (i, _, _) -> List.mem i metas) menv' in
839 (function Cic.Meta (i, _) -> List.mem i metas | _ -> assert false) newargs
842 if List.length metas > 0 then
843 let first = List.hd metas in
844 (* this new equality might have less variables than its parents: here
845 we fill the gap with a dummy arg. Example:
846 with (f X Y) = X we can simplify
849 So the new equation has only one variable, but it still has type like
850 \lambda X,Y:..., so we need to pass a dummy arg for Y
851 (I hope this makes some sense...)
856 (function Cic.Meta (i, _) -> i = v | _ -> assert false)
858 Hashtbl.replace table k first)
861 let rec fix_proof = function
863 | BasicProof term -> BasicProof (repl term)
864 | ProofBlock (subst, eq_URI, namety, bo, (pos, eq), p) ->
869 | Cic.Meta (i, l) -> (
871 let j = Hashtbl.find table i in
872 if List.mem_assoc i subst then
875 let _, context, ty = CicUtil.lookup_meta i menv in
876 (i, (context, Cic.Meta (j, l), ty))::s
877 with Not_found | CicUtil.Meta_not_found _ ->
883 ProofBlock (subst' @ subst, eq_URI, namety, bo(* t' *), (pos, eq), p)
886 let neweq = (w, fix_proof p, (ty, left, right, o), menv', newargs) in
891 let term_is_equality term =
892 let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in
894 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
899 exception TermIsNotAnEquality;;
901 let equality_of_term proof term =
902 let eq_uri = LibraryObjects.eq_URI () in
903 let iseq uri = UriManager.eq uri eq_uri in
905 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
906 let o = !Utils.compare_terms t1 t2 in
907 let w = compute_equality_weight ty t1 t2 in
908 let e = (w, BasicProof proof, (ty, t1, t2, o), [], []) in
911 raise TermIsNotAnEquality
915 type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph;;
918 let is_identity ((metasenv, context, ugraph) as env) = function
919 | ((_, _, (ty, left, right, _), menv, _) as equality) ->
920 (prerr_endline ("left = "^(CicPp.ppterm left));
921 prerr_endline ("right = "^(CicPp.ppterm right));
923 (* (meta_convertibility left right) || *)
924 (fst (CicReduction.are_convertible
925 ~metasenv:(metasenv @ menv) context left right ugraph))))
929 let term_of_equality equality =
930 let _, _, (ty, left, right, _), menv, args = equality in
931 let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
932 let argsno = List.length args in
934 CicSubstitution.lift argsno
935 (Cic.Appl [Cic.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right])
942 let name = Cic.Name ("X" ^ (string_of_int n)) in
943 let _, _, ty = CicUtil.lookup_meta i menv in
945 ProofEngineReduction.replace
946 ~equality:eq ~what:[i]
947 ~with_what:[Cic.Rel (argsno - (n - 1))] ~where:t
949 (n-1, Cic.Prod (name, ty, t))