1 (* Copyright (C) 2000, 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.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
28 exception Impossible of int;;
29 exception NotWellTyped of string;;
30 exception WrongUriToConstant of string;;
31 exception WrongUriToVariable of string;;
32 exception WrongUriToMutualInductiveDefinitions of string;;
33 exception ListTooShort;;
34 exception RelToHiddenHypothesis;;
36 let xxx_type_of_aux' m c t =
38 Some (fst (CicTypeChecker.type_of_aux' m c t CicUniv.empty_ugraph))
40 | CicTypeChecker.TypeCheckerFailure _ -> None (* because eta_expansion *)
43 type types = {synthesized : Cic.term ; expected : Cic.term option};;
45 (* does_not_occur n te *)
46 (* returns [true] if [Rel n] does not occur in [te] *)
47 let rec does_not_occur n =
50 C.Rel m when m = n -> false
54 | C.Implicit _ -> true
56 does_not_occur n te && does_not_occur n ty
57 | C.Prod (name,so,dest) ->
58 does_not_occur n so &&
59 does_not_occur (n + 1) dest
60 | C.Lambda (name,so,dest) ->
61 does_not_occur n so &&
62 does_not_occur (n + 1) dest
63 | C.LetIn (name,so,dest) ->
64 does_not_occur n so &&
65 does_not_occur (n + 1) dest
67 List.fold_right (fun x i -> i && does_not_occur n x) l true
68 | C.Var (_,exp_named_subst)
69 | C.Const (_,exp_named_subst)
70 | C.MutInd (_,_,exp_named_subst)
71 | C.MutConstruct (_,_,_,exp_named_subst) ->
72 List.fold_right (fun (_,x) i -> i && does_not_occur n x)
74 | C.MutCase (_,_,out,te,pl) ->
75 does_not_occur n out && does_not_occur n te &&
76 List.fold_right (fun x i -> i && does_not_occur n x) pl true
78 let len = List.length fl in
79 let n_plus_len = n + len in
82 i && does_not_occur n ty &&
83 does_not_occur n_plus_len bo
86 let len = List.length fl in
87 let n_plus_len = n + len in
90 i && does_not_occur n ty &&
91 does_not_occur n_plus_len bo
96 let module S = CicSubstitution in
100 | C.Var (uri,exp_named_subst) ->
101 let exp_named_subst' =
102 List.map (function (i,t) -> i, beta_reduce t) exp_named_subst
104 C.Var (uri,exp_named_subst')
108 (function None -> None | Some t -> Some (beta_reduce t)) l
111 | C.Implicit _ -> assert false
113 C.Cast (beta_reduce te, beta_reduce ty)
115 C.Prod (n, beta_reduce s, beta_reduce t)
116 | C.Lambda (n,s,t) ->
117 C.Lambda (n, beta_reduce s, beta_reduce t)
119 C.LetIn (n, beta_reduce s, beta_reduce t)
120 | C.Appl ((C.Lambda (name,s,t))::he::tl) ->
121 let he' = S.subst he t in
126 C.Appl l -> beta_reduce (C.Appl (l@tl))
127 | _ -> beta_reduce (C.Appl (he'::tl)))
129 C.Appl (List.map beta_reduce l)
130 | C.Const (uri,exp_named_subst) ->
131 let exp_named_subst' =
132 List.map (function (i,t) -> i, beta_reduce t) exp_named_subst
134 C.Const (uri,exp_named_subst')
135 | C.MutInd (uri,i,exp_named_subst) ->
136 let exp_named_subst' =
137 List.map (function (i,t) -> i, beta_reduce t) exp_named_subst
139 C.MutInd (uri,i,exp_named_subst')
140 | C.MutConstruct (uri,i,j,exp_named_subst) ->
141 let exp_named_subst' =
142 List.map (function (i,t) -> i, beta_reduce t) exp_named_subst
144 C.MutConstruct (uri,i,j,exp_named_subst')
145 | C.MutCase (sp,i,outt,t,pl) ->
146 C.MutCase (sp,i,beta_reduce outt,beta_reduce t,
147 List.map beta_reduce pl)
151 (function (name,i,ty,bo) ->
152 name,i,beta_reduce ty,beta_reduce bo
159 (function (name,ty,bo) ->
160 name,beta_reduce ty,beta_reduce bo
166 (* syntactic_equality up to the *)
167 (* distinction between fake dependent products *)
168 (* and non-dependent products, alfa-conversion *)
169 (*CSC: must alfa-conversion be considered or not? *)
170 let syntactic_equality t t' =
171 let module C = Cic in
172 let rec syntactic_equality t t' =
176 C.Var (uri,exp_named_subst), C.Var (uri',exp_named_subst') ->
177 UriManager.eq uri uri' &&
178 syntactic_equality_exp_named_subst exp_named_subst exp_named_subst'
179 | C.Cast (te,ty), C.Cast (te',ty') ->
180 syntactic_equality te te' &&
181 syntactic_equality ty ty'
182 | C.Prod (_,s,t), C.Prod (_,s',t') ->
183 syntactic_equality s s' &&
184 syntactic_equality t t'
185 | C.Lambda (_,s,t), C.Lambda (_,s',t') ->
186 syntactic_equality s s' &&
187 syntactic_equality t t'
188 | C.LetIn (_,s,t), C.LetIn(_,s',t') ->
189 syntactic_equality s s' &&
190 syntactic_equality t t'
191 | C.Appl l, C.Appl l' ->
192 List.fold_left2 (fun b t1 t2 -> b && syntactic_equality t1 t2) true l l'
193 | C.Const (uri,exp_named_subst), C.Const (uri',exp_named_subst') ->
194 UriManager.eq uri uri' &&
195 syntactic_equality_exp_named_subst exp_named_subst exp_named_subst'
196 | C.MutInd (uri,i,exp_named_subst), C.MutInd (uri',i',exp_named_subst') ->
197 UriManager.eq uri uri' && i = i' &&
198 syntactic_equality_exp_named_subst exp_named_subst exp_named_subst'
199 | C.MutConstruct (uri,i,j,exp_named_subst),
200 C.MutConstruct (uri',i',j',exp_named_subst') ->
201 UriManager.eq uri uri' && i = i' && j = j' &&
202 syntactic_equality_exp_named_subst exp_named_subst exp_named_subst'
203 | C.MutCase (sp,i,outt,t,pl), C.MutCase (sp',i',outt',t',pl') ->
204 UriManager.eq sp sp' && i = i' &&
205 syntactic_equality outt outt' &&
206 syntactic_equality t t' &&
208 (fun b t1 t2 -> b && syntactic_equality t1 t2) true pl pl'
209 | C.Fix (i,fl), C.Fix (i',fl') ->
212 (fun b (_,i,ty,bo) (_,i',ty',bo') ->
214 syntactic_equality ty ty' &&
215 syntactic_equality bo bo') true fl fl'
216 | C.CoFix (i,fl), C.CoFix (i',fl') ->
219 (fun b (_,ty,bo) (_,ty',bo') ->
221 syntactic_equality ty ty' &&
222 syntactic_equality bo bo') true fl fl'
223 | _, _ -> false (* we already know that t != t' *)
224 and syntactic_equality_exp_named_subst exp_named_subst1 exp_named_subst2 =
226 (fun b (_,t1) (_,t2) -> b && syntactic_equality t1 t2) true
227 exp_named_subst1 exp_named_subst2
230 syntactic_equality t t'
238 | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2)
239 | (_,_) -> raise ListTooShort
242 let type_of_constant uri =
243 let module C = Cic in
244 let module R = CicReduction in
245 let module U = UriManager in
247 match CicEnvironment.is_type_checked CicUniv.empty_ugraph uri with
248 CicEnvironment.CheckedObj (cobj,_) -> cobj
249 | CicEnvironment.UncheckedObj uobj ->
250 raise (NotWellTyped "Reference to an unchecked constant")
253 C.Constant (_,_,ty,_,_) -> ty
254 | C.CurrentProof (_,_,_,ty,_,_) -> ty
255 | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
258 let type_of_variable uri =
259 let module C = Cic in
260 let module R = CicReduction in
261 let module U = UriManager in
262 match CicEnvironment.is_type_checked CicUniv.empty_ugraph uri with
263 CicEnvironment.CheckedObj ((C.Variable (_,_,ty,_,_)),_) -> ty
264 | CicEnvironment.UncheckedObj (C.Variable _) ->
265 raise (NotWellTyped "Reference to an unchecked variable")
266 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
269 let type_of_mutual_inductive_defs uri i =
270 let module C = Cic in
271 let module R = CicReduction in
272 let module U = UriManager in
274 match CicEnvironment.is_type_checked CicUniv.empty_ugraph uri with
275 CicEnvironment.CheckedObj (cobj,_) -> cobj
276 | CicEnvironment.UncheckedObj uobj ->
277 raise (NotWellTyped "Reference to an unchecked inductive type")
280 C.InductiveDefinition (dl,_,_,_) ->
281 let (_,_,arity,_) = List.nth dl i in
283 | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
286 let type_of_mutual_inductive_constr uri i j =
287 let module C = Cic in
288 let module R = CicReduction in
289 let module U = UriManager in
291 match CicEnvironment.is_type_checked CicUniv.empty_ugraph uri with
292 CicEnvironment.CheckedObj (cobj,_) -> cobj
293 | CicEnvironment.UncheckedObj uobj ->
294 raise (NotWellTyped "Reference to an unchecked constructor")
297 C.InductiveDefinition (dl,_,_,_) ->
298 let (_,_,_,cl) = List.nth dl i in
299 let (_,ty) = List.nth cl (j-1) in
301 | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
304 let pack_coercion = ref (fun _ _ _ -> assert false);;
306 let profiler_for_find = HExtlib.profile "CicHash ADD" ;;
308 let cic_CicHash_add a b c =
309 profiler_for_find.HExtlib.profile (Cic.CicHash.add a b) c
312 let profiler_for_find1 = HExtlib.profile "CicHash MEM" ;;
314 let cic_CicHash_mem a b =
315 profiler_for_find1.HExtlib.profile (Cic.CicHash.mem a) b
318 (* type_of_aux' is just another name (with a different scope) for type_of_aux *)
319 let rec type_of_aux' subterms_to_types metasenv context t expectedty =
320 (* Coscoy's double type-inference algorithm *)
321 (* It computes the inner-types of every subterm of [t], *)
322 (* even when they are not needed to compute the types *)
323 (* of other terms. *)
324 let rec type_of_aux context t expectedty =
325 let module C = Cic in
326 let module R = CicReduction in
327 let module S = CicSubstitution in
328 let module U = UriManager in
330 match expectedty with
332 | Some t -> Some (!pack_coercion metasenv context t) in
337 match List.nth context (n - 1) with
338 Some (_,C.Decl t) -> S.lift n t
339 | Some (_,C.Def (_,Some ty)) -> S.lift n ty
340 | Some (_,C.Def (bo,None)) ->
341 type_of_aux context (S.lift n bo) expectedty
342 | None -> raise RelToHiddenHypothesis
344 _ -> raise (NotWellTyped "Not a close term")
346 | C.Var (uri,exp_named_subst) ->
347 visit_exp_named_subst context uri exp_named_subst ;
348 CicSubstitution.subst_vars exp_named_subst (type_of_variable uri)
350 (* Let's visit all the subterms that will not be visited later *)
351 let (_,canonical_context,_) = CicUtil.lookup_meta n metasenv in
352 let lifted_canonical_context =
356 | (Some (n,C.Decl t))::tl ->
357 (Some (n,C.Decl (S.subst_meta l (S.lift i t))))::(aux (i+1) tl)
358 | (Some (n,C.Def (t,None)))::tl ->
359 (Some (n,C.Def ((S.subst_meta l (S.lift i t)),None)))::
361 | None::tl -> None::(aux (i+1) tl)
362 | (Some (_,C.Def (_,Some _)))::_ -> assert false
364 aux 1 canonical_context
371 | Some t,Some (_,C.Def (ct,_)) ->
373 match xxx_type_of_aux' metasenv context ct with
375 | Some t -> Some (R.whd context t)
377 (* Maybe I am a bit too paranoid, because *)
378 (* if the term is well-typed than t and ct *)
379 (* are convertible. Nevertheless, I compute *)
380 (* the expected type. *)
381 ignore (type_of_aux context t expected_type)
382 | Some t,Some (_,C.Decl ct) ->
383 ignore (type_of_aux context t (Some ct))
384 | _,_ -> assert false (* the term is not well typed!!! *)
385 ) l lifted_canonical_context
387 let (_,canonical_context,ty) = CicUtil.lookup_meta n metasenv in
388 (* Checks suppressed *)
389 CicSubstitution.subst_meta l ty
390 | C.Sort (C.Type t) -> (* TASSI: CONSTRAINT *)
391 C.Sort (C.Type (CicUniv.fresh()))
392 | C.Sort _ -> C.Sort (C.Type (CicUniv.fresh())) (* TASSI: CONSTRAINT *)
393 | C.Implicit _ -> raise (Impossible 21)
395 (* Let's visit all the subterms that will not be visited later *)
396 let _ = type_of_aux context te (Some (beta_reduce ty)) in
397 let _ = type_of_aux context ty None in
398 (* Checks suppressed *)
400 | C.Prod (name,s,t) ->
401 let sort1 = type_of_aux context s None
402 and sort2 = type_of_aux ((Some (name,(C.Decl s)))::context) t None in
403 sort_of_prod context (name,s) (sort1,sort2)
404 | C.Lambda (n,s,t) ->
405 (* Let's visit all the subterms that will not be visited later *)
406 let _ = type_of_aux context s None in
407 let expected_target_type =
408 match expectedty with
410 | Some expectedty' ->
412 match R.whd context expectedty' with
413 C.Prod (_,_,expected_target_type) ->
414 beta_reduce expected_target_type
420 type_of_aux ((Some (n,(C.Decl s)))::context) t expected_target_type
422 (* Checks suppressed *)
425 (*CSC: What are the right expected types for the source and *)
426 (*CSC: target of a LetIn? None used. *)
427 (* Let's visit all the subterms that will not be visited later *)
428 let ty = type_of_aux context s None in
430 (* Checks suppressed *)
431 type_of_aux ((Some (n,(C.Def (s,Some ty))))::context) t None
432 in (* CicSubstitution.subst s t_typ *)
433 if does_not_occur 1 t_typ then
434 (* since [Rel 1] does not occur in typ, substituting any term *)
435 (* in place of [Rel 1] is equivalent to delifting once *)
436 CicSubstitution.subst (C.Implicit None) t_typ
439 | C.Appl (he::tl) when List.length tl > 0 ->
441 let expected_hetype =
442 (* Inefficient, the head is computed twice. But I know *)
443 (* of no other solution. *)
445 (R.whd context (xxx_type_of_aux' metasenv context he)))
447 let hetype = type_of_aux context he (Some expected_hetype) in
448 let tlbody_and_type =
452 | C.Prod (n,s,t),he::tl ->
453 (he, type_of_aux context he (Some (beta_reduce s)))::
454 (aux (R.whd context (S.subst he t), tl))
457 aux (expected_hetype, tl) *)
458 let hetype = R.whd context (type_of_aux context he None) in
459 let tlbody_and_type =
463 | C.Prod (n,s,t),he::tl ->
464 (he, type_of_aux context he (Some (beta_reduce s)))::
465 (aux (R.whd context (S.subst he t), tl))
470 eat_prods context hetype tlbody_and_type
471 | C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
472 | C.Const (uri,exp_named_subst) ->
473 visit_exp_named_subst context uri exp_named_subst ;
474 CicSubstitution.subst_vars exp_named_subst (type_of_constant uri)
475 | C.MutInd (uri,i,exp_named_subst) ->
476 visit_exp_named_subst context uri exp_named_subst ;
477 CicSubstitution.subst_vars exp_named_subst
478 (type_of_mutual_inductive_defs uri i)
479 | C.MutConstruct (uri,i,j,exp_named_subst) ->
480 visit_exp_named_subst context uri exp_named_subst ;
481 CicSubstitution.subst_vars exp_named_subst
482 (type_of_mutual_inductive_constr uri i j)
483 | C.MutCase (uri,i,outtype,term,pl) ->
484 let outsort = type_of_aux context outtype None in
485 let (need_dummy, k) =
486 let rec guess_args context t =
487 match CicReduction.whd context t with
488 C.Sort _ -> (true, 0)
489 | C.Prod (name, s, t) ->
490 let (b, n) = guess_args ((Some (name,(C.Decl s)))::context) t in
492 (* last prod before sort *)
493 match CicReduction.whd context s with
494 C.MutInd (uri',i',_) when U.eq uri' uri && i' = i ->
496 | C.Appl ((C.MutInd (uri',i',_)) :: _)
497 when U.eq uri' uri && i' = i -> (false, 1)
501 | _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
503 let (b, k) = guess_args context outsort in
504 if not b then (b, k - 1) else (b, k)
506 let (parameters, arguments,exp_named_subst) =
508 match xxx_type_of_aux' metasenv context term with
510 | Some t -> Some (beta_reduce t)
513 R.whd context (type_of_aux context term type_of_term)
515 (*CSC manca il caso dei CAST *)
516 C.MutInd (uri',i',exp_named_subst) ->
517 (* Checks suppressed *)
518 [],[],exp_named_subst
519 | C.Appl (C.MutInd (uri',i',exp_named_subst) :: tl) ->
521 split tl (List.length tl - k)
522 in params,args,exp_named_subst
524 raise (NotWellTyped "MutCase: the term is not an inductive one")
526 (* Checks suppressed *)
527 (* Let's visit all the subterms that will not be visited later *)
531 CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
532 with Not_found -> assert false
535 C.InductiveDefinition (tl,_,parsno,_) ->
536 let (_,_,_,cl) = List.nth tl i in (cl,parsno)
538 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
544 if parameters = [] then
545 (C.MutConstruct (uri,i,j,exp_named_subst))
547 (C.Appl (C.MutConstruct (uri,i,j,exp_named_subst)::parameters))
550 match xxx_type_of_aux' metasenv context cons with
555 (type_of_branch context parsno need_dummy outtype
558 ignore (type_of_aux context p expectedtype);
560 ) 1 (List.combine pl cl)
562 if not need_dummy then
563 C.Appl ((outtype::arguments)@[term])
564 else if arguments = [] then
567 C.Appl (outtype::arguments)
569 (* Let's visit all the subterms that will not be visited later *)
574 let _ = type_of_aux context ty None in
575 (Some (C.Name n,(C.Decl ty)))
584 beta_reduce (CicSubstitution.lift (List.length fl) ty)
586 ignore (type_of_aux context' bo (Some expectedty))
589 (* Checks suppressed *)
590 let (_,_,ty,_) = List.nth fl i in
593 (* Let's visit all the subterms that will not be visited later *)
598 let _ = type_of_aux context ty None in
599 (Some (C.Name n,(C.Decl ty)))
608 beta_reduce (CicSubstitution.lift (List.length fl) ty)
610 ignore (type_of_aux context' bo (Some expectedty))
613 (* Checks suppressed *)
614 let (_,ty,_) = List.nth fl i in
617 let synthesized' = beta_reduce synthesized in
618 let synthesized' = !pack_coercion metasenv context synthesized' in
620 match expectedty with
622 (* No expected type *)
623 {synthesized = synthesized' ; expected = None}, synthesized
624 | Some ty when syntactic_equality synthesized' ty ->
625 (* The expected type is synthactically equal to *)
626 (* the synthesized type. Let's forget it. *)
627 {synthesized = synthesized' ; expected = None}, synthesized
628 | Some expectedty' ->
629 {synthesized = synthesized' ; expected = Some expectedty'},
632 (* assert (not (cic_CicHash_mem subterms_to_types t));*)
633 cic_CicHash_add subterms_to_types t types ;
636 and visit_exp_named_subst context uri exp_named_subst =
640 CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
641 with Not_found -> assert false
643 let params = CicUtil.params_of_obj obj in
648 CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri
649 with Not_found -> assert false
652 Cic.Variable (_,None,ty,_,_) -> uri,ty
653 | _ -> assert false (* the theorem is well-typed *)
656 let rec check uris_and_types subst =
657 match uris_and_types,subst with
659 | (uri,ty)::tytl,(uri',t)::substtl when uri = uri' ->
660 ignore (type_of_aux context t (Some ty)) ;
663 (function uri,t' -> uri,(CicSubstitution.subst_vars [uri',t] t')) tytl
666 | _,_ -> assert false (* the theorem is well-typed *)
668 check uris_and_types exp_named_subst
670 and sort_of_prod context (name,s) (t1, t2) =
671 let module C = Cic in
672 let t1' = CicReduction.whd context t1 in
673 let t2' = CicReduction.whd ((Some (name,C.Decl s))::context) t2 in
674 match (t1', t2') with
675 (C.Sort _, C.Sort s2)
676 when (s2 = C.Prop or s2 = C.Set or s2 = C.CProp) ->
677 (* different from Coq manual!!! *)
679 | (C.Sort (C.Type t1), C.Sort (C.Type t2)) ->
680 C.Sort (C.Type (CicUniv.fresh()))
681 | (C.Sort _,C.Sort (C.Type t1)) ->
682 (* TASSI: CONSRTAINTS: the same in cictypechecker,cicrefine *)
683 C.Sort (C.Type t1) (* c'e' bisogno di un fresh? *)
684 | (C.Meta _, C.Sort _) -> t2'
685 | (C.Meta _, (C.Meta (_,_) as t))
686 | (C.Sort _, (C.Meta (_,_) as t)) when CicUtil.is_closed t ->
691 ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))
693 and eat_prods context hetype =
694 (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
698 | (hete, hety)::tl ->
699 (match (CicReduction.whd context hetype) with
701 (* Checks suppressed *)
702 eat_prods context (CicSubstitution.subst hete t) tl
703 | _ -> raise (NotWellTyped "Appl: wrong Prod-type")
706 and type_of_branch context argsno need_dummy outtype term constype =
707 let module C = Cic in
708 let module R = CicReduction in
709 match R.whd context constype with
714 C.Appl [outtype ; term]
715 | C.Appl (C.MutInd (_,_,_)::tl) ->
716 let (_,arguments) = split tl argsno
718 if need_dummy && arguments = [] then
721 C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
722 | C.Prod (name,so,de) ->
724 match CicSubstitution.lift 1 term with
725 C.Appl l -> C.Appl (l@[C.Rel 1])
726 | t -> C.Appl [t ; C.Rel 1]
728 C.Prod (C.Anonymous,so,type_of_branch
729 ((Some (name,(C.Decl so)))::context) argsno need_dummy
730 (CicSubstitution.lift 1 outtype) term' de)
731 | _ -> raise (Impossible 20)
734 type_of_aux context t expectedty
737 let double_type_of metasenv context t expectedty =
738 let subterms_to_types = Cic.CicHash.create 503 in
739 ignore (type_of_aux' subterms_to_types metasenv context t expectedty) ;