1 (* Copyright (C) 2005, HELM Team.
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4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
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34 (Cic.term * (* type *)
35 Cic.term * (* left side *)
36 Cic.term * (* right side *)
37 Utils.comparison) * (* ordering *)
38 Cic.metasenv * (* environment for metas *)
39 Cic.term list (* arguments *)
43 | BasicProof of Cic.term
45 Cic.substitution * UriManager.uri *
46 (Cic.name * Cic.term) * Cic.term * (Utils.pos * equality) * proof
47 | ProofGoalBlock of proof * proof
48 | ProofSymBlock of Cic.term list * proof
49 | SubProof of Cic.term * int * proof
53 let string_of_equality ?env =
57 | w, _, (ty, left, right, o), _, _ ->
58 Printf.sprintf "Weight: %d, {%s}: %s =(%s) %s" w (CicPp.ppterm ty)
59 (CicPp.ppterm left) (string_of_comparison o) (CicPp.ppterm right)
61 | Some (_, context, _) -> (
62 let names = names_of_context context in
64 | w, _, (ty, left, right, o), _, _ ->
65 Printf.sprintf "Weight: %d, {%s}: %s =(%s) %s" w (CicPp.pp ty names)
66 (CicPp.pp left names) (string_of_comparison o)
67 (CicPp.pp right names)
72 let rec string_of_proof = function
73 | NoProof -> "NoProof"
74 | BasicProof t -> "BasicProof " ^ (CicPp.ppterm t)
75 | SubProof (t, i, p) ->
76 Printf.sprintf "SubProof(%s, %s, %s)"
77 (CicPp.ppterm t) (string_of_int i) (string_of_proof p)
78 | ProofSymBlock _ -> "ProofSymBlock"
79 | ProofBlock _ -> "ProofBlock"
80 | ProofGoalBlock (p1, p2) ->
81 Printf.sprintf "ProofGoalBlock(%s, %s)"
82 (string_of_proof p1) (string_of_proof p2)
86 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
87 let build_ens_for_sym_eq sym_eq_URI termlist =
88 let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph sym_eq_URI in
90 | Cic.Constant (_, _, _, uris, _) ->
91 assert (List.length uris <= List.length termlist);
92 let rec aux = function
94 | (uri::uris), (term::tl) ->
95 let ens, args = aux (uris, tl) in
96 (uri, term)::ens, args
97 | _, _ -> assert false
104 let build_proof_term proof =
105 let rec do_build_proof proof =
108 Printf.fprintf stderr "WARNING: no proof!\n";
110 | BasicProof term -> term
111 | ProofGoalBlock (proofbit, proof) ->
112 print_endline "found ProofGoalBlock, going up...";
113 do_build_goal_proof proofbit proof
114 | ProofSymBlock (termlist, proof) ->
115 let proof = do_build_proof proof in
116 let ens, args = build_ens_for_sym_eq (Utils.sym_eq_URI ()) termlist in
117 Cic.Appl ([Cic.Const (Utils.sym_eq_URI (), ens)] @ args @ [proof])
118 | ProofBlock (subst, eq_URI, (name, ty), bo, (pos, eq), eqproof) ->
119 let t' = Cic.Lambda (name, ty, bo) in
121 let _, proof', _, _, _ = eq in
122 do_build_proof proof'
124 let eqproof = do_build_proof eqproof in
125 let _, _, (ty, what, other, _), menv', args' = eq in
127 if pos = Utils.Left then what, other else other, what
129 CicMetaSubst.apply_subst subst
130 (Cic.Appl [Cic.Const (eq_URI, []); ty;
131 what; t'; eqproof; other; proof'])
132 | SubProof (term, meta_index, proof) ->
133 let proof = do_build_proof proof in
135 | Cic.Meta (j, _) -> i = j
138 ProofEngineReduction.replace
139 ~equality:eq ~what:[meta_index] ~with_what:[proof] ~where:term
141 and do_build_goal_proof proofbit proof =
143 | ProofGoalBlock (pb, p) ->
144 do_build_proof (ProofGoalBlock (replace_proof proofbit pb, p))
145 | _ -> do_build_proof (replace_proof proofbit proof)
147 and replace_proof newproof = function
148 | ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof) ->
149 let eqproof' = replace_proof newproof eqproof in
150 ProofBlock (subst, eq_URI, namety, bo, poseq, eqproof')
151 | ProofGoalBlock (pb, p) ->
152 let pb' = replace_proof newproof pb in
153 ProofGoalBlock (pb', p)
154 | BasicProof _ -> newproof
155 | SubProof (term, meta_index, p) ->
156 SubProof (term, meta_index, replace_proof newproof p)
163 let rec metas_of_term = function
164 | Cic.Meta (i, c) -> [i]
167 | Cic.MutInd (_, _, ens)
168 | Cic.MutConstruct (_, _, _, ens) ->
169 List.flatten (List.map (fun (u, t) -> metas_of_term t) ens)
172 | Cic.Lambda (_, s, t)
173 | Cic.LetIn (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
174 | Cic.Appl l -> List.flatten (List.map metas_of_term l)
175 | Cic.MutCase (uri, i, s, t, l) ->
176 (metas_of_term s) @ (metas_of_term t) @
177 (List.flatten (List.map metas_of_term l))
180 (List.map (fun (s, i, t1, t2) ->
181 (metas_of_term t1) @ (metas_of_term t2)) il)
182 | Cic.CoFix (i, il) ->
184 (List.map (fun (s, t1, t2) ->
185 (metas_of_term t1) @ (metas_of_term t2)) il)
190 exception NotMetaConvertible;;
192 let meta_convertibility_aux table t1 t2 =
193 let module C = Cic in
197 (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
199 let rec aux ((table_l, table_r) as table) t1 t2 =
201 | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
202 let m1_binding, table_l =
203 try List.assoc m1 table_l, table_l
204 with Not_found -> m2, (m1, m2)::table_l
205 and m2_binding, table_r =
206 try List.assoc m2 table_r, table_r
207 with Not_found -> m1, (m2, m1)::table_r
209 if (m1_binding <> m2) || (m2_binding <> m1) then
210 raise NotMetaConvertible
216 | None, Some _ | Some _, None -> raise NotMetaConvertible
218 | Some t1, Some t2 -> (aux res t1 t2))
219 (table_l, table_r) tl1 tl2
220 with Invalid_argument _ ->
221 raise NotMetaConvertible
223 | C.Var (u1, ens1), C.Var (u2, ens2)
224 | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
225 aux_ens table ens1 ens2
226 | C.Cast (s1, t1), C.Cast (s2, t2)
227 | C.Prod (_, s1, t1), C.Prod (_, s2, t2)
228 | C.Lambda (_, s1, t1), C.Lambda (_, s2, t2)
229 | C.LetIn (_, s1, t1), C.LetIn (_, s2, t2) ->
230 let table = aux table s1 s2 in
232 | C.Appl l1, C.Appl l2 -> (
233 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
234 with Invalid_argument _ -> raise NotMetaConvertible
236 | C.MutInd (u1, i1, ens1), C.MutInd (u2, i2, ens2)
237 when (UriManager.eq u1 u2) && i1 = i2 -> aux_ens table ens1 ens2
238 | C.MutConstruct (u1, i1, j1, ens1), C.MutConstruct (u2, i2, j2, ens2)
239 when (UriManager.eq u1 u2) && i1 = i2 && j1 = j2 ->
240 aux_ens table ens1 ens2
241 | C.MutCase (u1, i1, s1, t1, l1), C.MutCase (u2, i2, s2, t2, l2)
242 when (UriManager.eq u1 u2) && i1 = i2 ->
243 let table = aux table s1 s2 in
244 let table = aux table t1 t2 in (
245 try List.fold_left2 (fun res t1 t2 -> (aux res t1 t2)) table l1 l2
246 with Invalid_argument _ -> raise NotMetaConvertible
248 | C.Fix (i1, il1), C.Fix (i2, il2) when i1 = i2 -> (
251 (fun res (n1, i1, s1, t1) (n2, i2, s2, t2) ->
252 if i1 <> i2 then raise NotMetaConvertible
254 let res = (aux res s1 s2) in aux res t1 t2)
256 with Invalid_argument _ -> raise NotMetaConvertible
258 | C.CoFix (i1, il1), C.CoFix (i2, il2) when i1 = i2 -> (
261 (fun res (n1, s1, t1) (n2, s2, t2) ->
262 let res = aux res s1 s2 in aux res t1 t2)
264 with Invalid_argument _ -> raise NotMetaConvertible
266 | t1, t2 when t1 = t2 -> table
267 | _, _ -> raise NotMetaConvertible
269 and aux_ens table ens1 ens2 =
270 let cmp (u1, t1) (u2, t2) =
271 compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2)
273 let ens1 = List.sort cmp ens1
274 and ens2 = List.sort cmp ens2 in
277 (fun res (u1, t1) (u2, t2) ->
278 if not (UriManager.eq u1 u2) then raise NotMetaConvertible
281 with Invalid_argument _ -> raise NotMetaConvertible
287 let meta_convertibility_eq eq1 eq2 =
288 let _, _, (ty, left, right, _), _, _ = eq1
289 and _, _, (ty', left', right', _), _, _ = eq2 in
292 else if (left = left') && (right = right') then
294 else if (left = right') && (right = left') then
298 let table = meta_convertibility_aux ([], []) left left' in
299 let _ = meta_convertibility_aux table right right' in
301 with NotMetaConvertible ->
303 let table = meta_convertibility_aux ([], []) left right' in
304 let _ = meta_convertibility_aux table right left' in
306 with NotMetaConvertible ->
311 let meta_convertibility t1 t2 =
315 (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
321 let l, r = meta_convertibility_aux ([], []) t1 t2 in
323 with NotMetaConvertible ->
328 let rec check_irl start = function
330 | None::tl -> check_irl (start+1) tl
331 | (Some (Cic.Rel x))::tl ->
332 if x = start then check_irl (start+1) tl else false
337 let rec is_simple_term = function
338 | Cic.Appl ((Cic.Meta _)::_) -> false
339 | Cic.Appl l -> List.for_all is_simple_term l
340 | Cic.Meta (i, l) -> check_irl 1 l
342 | Cic.Const _ -> true
343 | Cic.MutInd (_, _, []) -> true
344 | Cic.MutConstruct (_, _, _, []) -> true
349 let lookup_subst meta subst =
351 | Cic.Meta (i, _) -> (
352 try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
353 with Not_found -> meta
359 let unification_simple metasenv context t1 t2 ugraph =
360 let module C = Cic in
361 let module M = CicMetaSubst in
362 let module U = CicUnification in
363 let lookup = lookup_subst in
364 let rec occurs_check subst what where =
366 | t when what = t -> true
367 | C.Appl l -> List.exists (occurs_check subst what) l
369 let t = lookup where subst in
370 if t <> where then occurs_check subst what t else false
373 let rec unif subst menv s t =
374 let s = match s with C.Meta _ -> lookup s subst | _ -> s
375 and t = match t with C.Meta _ -> lookup t subst | _ -> t
378 | s, t when s = t -> subst, menv
379 | C.Meta (i, _), C.Meta (j, _) when i > j ->
381 | C.Meta _, t when occurs_check subst s t ->
383 (U.UnificationFailure (lazy "Inference.unification.unif"))
384 | C.Meta (i, l), t -> (
386 let _, _, ty = CicUtil.lookup_meta i menv in
388 if not (List.mem_assoc i subst) then (i, (context, t, ty))::subst
391 let menv = menv in (* List.filter (fun (m, _, _) -> i <> m) menv in *)
393 with CicUtil.Meta_not_found m ->
394 let names = names_of_context context in
397 (Printf.sprintf "Meta_not_found %d!: %s %s\n%s\n\n%s" m
398 (CicPp.pp t1 names) (CicPp.pp t2 names)
399 (print_metasenv menv) (print_metasenv metasenv)));
402 | _, C.Meta _ -> unif subst menv t s
403 | C.Appl (hds::_), C.Appl (hdt::_) when hds <> hdt ->
404 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
405 | C.Appl (hds::tls), C.Appl (hdt::tlt) -> (
408 (fun (subst', menv) s t -> unif subst' menv s t)
409 (subst, menv) tls tlt
410 with Invalid_argument _ ->
411 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
414 raise (U.UnificationFailure (lazy "Inference.unification.unif"))
416 let subst, menv = unif [] metasenv t1 t2 in
420 try let _ = List.find (fun (i, _) -> m = i) subst in false
421 with Not_found -> true)
424 List.rev subst, menv, ugraph
428 let unification metasenv context t1 t2 ugraph =
429 let subst, menv, ug =
430 if not (is_simple_term t1) || not (is_simple_term t2) then (
433 (Printf.sprintf "NOT SIMPLE TERMS: %s %s"
434 (CicPp.ppterm t1) (CicPp.ppterm t2)));
435 CicUnification.fo_unif metasenv context t1 t2 ugraph
437 unification_simple metasenv context t1 t2 ugraph
439 let rec fix_term = function
440 | (Cic.Meta (i, l) as t) ->
441 let t' = lookup_subst t subst in
442 if t <> t' then fix_term t' else t
443 | Cic.Appl l -> Cic.Appl (List.map fix_term l)
446 let rec fix_subst = function
448 | (i, (c, t, ty))::tl -> (i, (c, fix_term t, fix_term ty))::(fix_subst tl)
450 fix_subst subst, menv, ug
454 let unification = CicUnification.fo_unif;;
456 exception MatchingFailure;;
460 let matching_simple metasenv context t1 t2 ugraph =
461 let module C = Cic in
462 let module M = CicMetaSubst in
463 let module U = CicUnification in
464 let lookup meta subst =
467 try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
468 with Not_found -> meta
472 let rec do_match subst menv s t =
474 | s, t when s = t -> subst, menv
475 | s, C.Meta (i, l) ->
476 let filter_menv i menv =
477 List.filter (fun (m, _, _) -> i <> m) menv
480 let value = lookup t subst in
482 | value when value = t ->
483 let _, _, ty = CicUtil.lookup_meta i menv in
484 (i, (context, s, ty))::subst, filter_menv i menv
485 | value when value <> s ->
486 raise MatchingFailure
487 | value -> do_match subst menv s value
490 | C.Appl ls, C.Appl lt -> (
493 (fun (subst, menv) s t -> do_match subst menv s t)
495 with Invalid_argument _ ->
496 raise MatchingFailure
499 raise MatchingFailure
501 let subst, menv = do_match [] metasenv t1 t2 in
507 let matching metasenv context t1 t2 ugraph =
509 let subst, metasenv, ugraph =
510 unification metasenv context t1 t2 ugraph
512 let t' = CicMetaSubst.apply_subst subst t1 in
513 if not (meta_convertibility t1 t') then
514 raise MatchingFailure
516 let metas = metas_of_term t1 in
517 let fix_subst = function
518 | (i, (c, Cic.Meta (j, lc), ty)) when List.mem i metas ->
519 (j, (c, Cic.Meta (i, lc), ty))
522 let subst = List.map fix_subst subst in
523 subst, metasenv, ugraph
525 | CicUnification.UnificationFailure _
526 | CicUnification.Uncertain _ ->
527 raise MatchingFailure
531 let find_equalities context proof =
532 let module C = Cic in
533 let module S = CicSubstitution in
534 let module T = CicTypeChecker in
535 let eq_uri = LibraryObjects.eq_URI () in
536 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
537 let ok_types ty menv =
538 List.for_all (fun (_, _, mt) -> mt = ty) menv
540 let rec aux index newmeta = function
542 | (Some (_, C.Decl (term)))::tl ->
543 let do_find context term =
545 | C.Prod (name, s, t) ->
546 let (head, newmetas, args, newmeta) =
547 ProofEngineHelpers.saturate_term newmeta []
548 context (S.lift index term) 0
551 if List.length args = 0 then
554 C.Appl ((C.Rel index)::args)
557 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
558 when (UriManager.eq uri eq_uri) && (ok_types ty newmetas) ->
561 (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
562 let o = !Utils.compare_terms t1 t2 in
563 let w = compute_equality_weight ty t1 t2 in
564 let proof = BasicProof p in
565 let e = (w, proof, (ty, t1, t2, o), newmetas, args) in
569 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
570 when UriManager.eq uri eq_uri ->
571 let t1 = S.lift index t1
572 and t2 = S.lift index t2 in
573 let o = !Utils.compare_terms t1 t2 in
574 let w = compute_equality_weight ty t1 t2 in
575 let e = (w, BasicProof (C.Rel index), (ty, t1, t2, o), [], []) in
579 match do_find context term with
581 let tl, newmeta' = (aux (index+1) newmeta tl) in
582 (index, p)::tl, max newmeta newmeta'
584 aux (index+1) newmeta tl
587 aux (index+1) newmeta tl
589 let il, maxm = aux 1 newmeta context in
590 let indexes, equalities = List.split il in
591 indexes, equalities, maxm
596 let equations_blacklist =
598 (fun s u -> UriManager.UriSet.add (UriManager.uri_of_string u) s)
599 UriManager.UriSet.empty [
600 "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)";
601 "cic:/Coq/Init/Logic/trans_eq.con";
602 "cic:/Coq/Init/Logic/f_equal.con";
603 "cic:/Coq/Init/Logic/f_equal2.con";
604 "cic:/Coq/Init/Logic/f_equal3.con";
605 "cic:/Coq/Init/Logic/f_equal4.con";
606 "cic:/Coq/Init/Logic/f_equal5.con";
607 "cic:/Coq/Init/Logic/sym_eq.con";
608 "cic:/Coq/Init/Logic/eq_ind.con";
609 "cic:/Coq/Init/Logic/eq_ind_r.con";
610 "cic:/Coq/Init/Logic/eq_rec.con";
611 "cic:/Coq/Init/Logic/eq_rec_r.con";
612 "cic:/Coq/Init/Logic/eq_rect.con";
613 "cic:/Coq/Init/Logic/eq_rect_r.con";
614 "cic:/Coq/Logic/Eqdep/UIP.con";
615 "cic:/Coq/Logic/Eqdep/UIP_refl.con";
616 "cic:/Coq/Logic/Eqdep_dec/eq2eqT.con";
617 "cic:/Coq/ZArith/Zcompare/rename.con";
618 (* ALB !!!! questo e` imbrogliare, ma x ora lo lasciamo cosi`...
619 perche' questo cacchio di teorema rompe le scatole :'( *)
620 "cic:/Rocq/SUBST/comparith/mult_n_2.con";
622 "cic:/matita/logic/equality/eq_f.con";
623 "cic:/matita/logic/equality/eq_f2.con";
624 "cic:/matita/logic/equality/eq_rec.con";
625 "cic:/matita/logic/equality/eq_rect.con";
629 let equations_blacklist = UriManager.UriSet.empty;;
632 let find_library_equalities dbd context status maxmeta =
633 let module C = Cic in
634 let module S = CicSubstitution in
635 let module T = CicTypeChecker in
638 (fun s u -> UriManager.UriSet.add u s)
640 [eq_XURI (); sym_eq_URI (); trans_eq_URI (); eq_ind_URI ();
646 let suri = UriManager.string_of_uri uri in
647 if UriManager.UriSet.mem uri blacklist then
650 let t = CicUtil.term_of_uri uri in
652 CicTypeChecker.type_of_aux' [] context t CicUniv.empty_ugraph
656 (let t1 = Unix.gettimeofday () in
657 let eqs = (MetadataQuery.equations_for_goal ~dbd status) in
658 let t2 = Unix.gettimeofday () in
661 (Printf.sprintf "Tempo di MetadataQuery.equations_for_goal: %.9f\n"
665 let eq_uri1 = eq_XURI ()
666 and eq_uri2 = LibraryObjects.eq_URI () in
668 (UriManager.eq uri eq_uri1) || (UriManager.eq uri eq_uri2)
670 let ok_types ty menv =
671 List.for_all (fun (_, _, mt) -> mt = ty) menv
673 let rec has_vars = function
674 | C.Meta _ | C.Rel _ | C.Const _ -> false
676 | C.Appl l -> List.exists has_vars l
677 | C.Prod (_, s, t) | C.Lambda (_, s, t)
678 | C.LetIn (_, s, t) | C.Cast (s, t) ->
679 (has_vars s) || (has_vars t)
682 let rec aux newmeta = function
684 | (uri, term, termty)::tl ->
687 (Printf.sprintf "Examining: %s (%s)"
688 (CicPp.ppterm term) (CicPp.ppterm termty)));
691 | C.Prod (name, s, t) when not (has_vars termty) ->
692 let head, newmetas, args, newmeta =
693 ProofEngineHelpers.saturate_term newmeta [] context termty 0
696 if List.length args = 0 then
702 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
703 when (iseq uri) && (ok_types ty newmetas) ->
706 (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
707 let o = !Utils.compare_terms t1 t2 in
708 let w = compute_equality_weight ty t1 t2 in
709 let proof = BasicProof p in
710 let e = (w, proof, (ty, t1, t2, o), newmetas, args) in
714 | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
715 when iseq uri && not (has_vars termty) ->
716 let o = !Utils.compare_terms t1 t2 in
717 let w = compute_equality_weight ty t1 t2 in
718 let e = (w, BasicProof term, (ty, t1, t2, o), [], []) in
724 let tl, newmeta' = aux newmeta tl in
725 (uri, e)::tl, max newmeta newmeta'
729 let found, maxm = aux maxmeta candidates in
732 (fun (s, l) (u, e) ->
733 if List.exists (meta_convertibility_eq e) (List.map snd l) then (
736 (Printf.sprintf "NO!! %s already there!"
737 (string_of_equality e)));
738 (UriManager.UriSet.add u s, l)
739 ) else (UriManager.UriSet.add u s, (u, e)::l))
740 (UriManager.UriSet.empty, []) found)
746 let find_library_theorems dbd env status equalities_uris =
747 let module C = Cic in
748 let module S = CicSubstitution in
749 let module T = CicTypeChecker in
752 UriManager.uri_of_string "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)" in
754 UriManager.UriSet.remove refl_equal
755 (UriManager.UriSet.union equalities_uris equations_blacklist)
758 (fun s u -> UriManager.UriSet.add u s)
759 s [eq_XURI () ;sym_eq_URI (); trans_eq_URI (); eq_ind_URI ();
762 let metasenv, context, ugraph = env in
766 if UriManager.UriSet.mem uri blacklist then l
768 let t = CicUtil.term_of_uri uri in
769 let ty, _ = CicTypeChecker.type_of_aux' metasenv context t ugraph in
771 [] (MetadataQuery.signature_of_goal ~dbd status)
774 let u = eq_XURI () in
775 let t = CicUtil.term_of_uri u in
776 let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
779 refl_equal::candidates
783 let find_context_hypotheses env equalities_indexes =
784 let metasenv, context, ugraph = env in
791 if List.mem n equalities_indexes then
796 CicTypeChecker.type_of_aux' metasenv context t ugraph in
797 (n+1, (t, ty, [])::l))
804 let fix_metas newmeta ((w, p, (ty, left, right, o), menv, args) as equality) =
805 let table = Hashtbl.create (List.length args) in
806 let newargs, newmeta =
808 (fun t (newargs, index) ->
811 if Hashtbl.mem table i then
812 let idx = Hashtbl.find table i in
813 ((Cic.Meta (idx, l))::newargs, index+1)
815 let _ = Hashtbl.add table i index in
816 ((Cic.Meta (index, l))::newargs, index+1)
821 ProofEngineReduction.replace ~equality:(=) ~what:args ~with_what:newargs
826 (fun (i, context, term) menv ->
828 let index = Hashtbl.find table i in
829 (index, context, term)::menv
831 (i, context, term)::menv)
836 and right = repl right in
837 let metas = (metas_of_term left) @ (metas_of_term right) in
838 let menv' = List.filter (fun (i, _, _) -> List.mem i metas) menv' in
841 (function Cic.Meta (i, _) -> List.mem i metas | _ -> assert false) newargs
844 if List.length metas > 0 then
845 let first = List.hd metas in
846 (* this new equality might have less variables than its parents: here
847 we fill the gap with a dummy arg. Example:
848 with (f X Y) = X we can simplify
851 So the new equation has only one variable, but it still has type like
852 \lambda X,Y:..., so we need to pass a dummy arg for Y
853 (I hope this makes some sense...)
858 (function Cic.Meta (i, _) -> i = v | _ -> assert false)
860 Hashtbl.replace table k first)
863 let rec fix_proof = function
865 | BasicProof term -> BasicProof (repl term)
866 | ProofBlock (subst, eq_URI, namety, bo, (pos, eq), p) ->
871 | Cic.Meta (i, l) -> (
873 let j = Hashtbl.find table i in
874 if List.mem_assoc i subst then
877 let _, context, ty = CicUtil.lookup_meta i menv in
878 (i, (context, Cic.Meta (j, l), ty))::s
879 with Not_found | CicUtil.Meta_not_found _ ->
885 ProofBlock (subst' @ subst, eq_URI, namety, bo(* t' *), (pos, eq), p)
888 let neweq = (w, fix_proof p, (ty, left, right, o), menv', newargs) in
893 let term_is_equality term =
894 let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in
896 | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
901 exception TermIsNotAnEquality;;
903 let equality_of_term proof term =
904 let eq_uri = LibraryObjects.eq_URI () in
905 let iseq uri = UriManager.eq uri eq_uri in
907 | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
908 let o = !Utils.compare_terms t1 t2 in
909 let w = compute_equality_weight ty t1 t2 in
910 let e = (w, BasicProof proof, (ty, t1, t2, o), [], []) in
913 raise TermIsNotAnEquality
917 type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph;;
920 let is_identity ((metasenv, context, ugraph) as env) = function
921 | ((_, _, (ty, left, right, _), menv, _) as equality) ->
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))