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_______________________________________________________________ *)
12 (* $Id: nCicReduction.ml 8250 2008-03-25 17:56:20Z tassi $ *)
14 (* web interface stuff *)
17 ref (function (`Start_type_checking _|`Type_checking_completed _) -> ())
20 let set_logger f = logger := f;;
22 exception TypeCheckerFailure of string Lazy.t
23 exception AssertFailure of string Lazy.t
25 let shift_k e (c,rf,x,safes) =
26 e::c,List.map (fun (k,v) -> k+1,v) rf,x+1,List.map ((+)1) safes
29 (* $Id: cicTypeChecker.ml 8213 2008-03-13 18:48:26Z sacerdot $ *)
34 (* the boolean h means already protected *)
35 (* args is the list of arguments the type of the constructor that may be *)
36 (* found in head position must be applied to. *)
37 and guarded_by_constructors ~subst context n nn h te args coInductiveTypeURI =
39 (*CSC: There is a lot of code replication between the cases X and *)
40 (*CSC: (C.Appl X tl). Maybe it will be better to define a function *)
41 (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *)
42 match CicReduction.whd ~subst context te with
43 C.Rel m when m > n && m <= nn -> h
51 (* the term has just been type-checked *)
52 raise (AssertFailure (lazy "17"))
53 | C.Lambda (name,so,de) ->
54 does_not_occur ~subst context n nn so &&
55 guarded_by_constructors ~subst ((Some (name,(C.Decl so)))::context)
56 (n + 1) (nn + 1) h de args coInductiveTypeURI
57 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
59 List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) tl true
60 | C.Appl ((C.MutConstruct (uri,i,j,exp_named_subst))::tl) ->
64 CicEnvironment.get_cooked_obj ~trust:false CicUniv.empty_ugraph uri
65 with Not_found -> assert false
68 C.InductiveDefinition (itl,_,_,_) ->
69 let (_,_,_,cl) = List.nth itl i in
70 let (_,cons) = List.nth cl (j - 1) in
71 CicSubstitution.subst_vars exp_named_subst cons
73 raise (TypeCheckerFailure
74 (lazy ("Unknown mutual inductive definition:" ^ UriManager.string_of_uri uri)))
76 let rec analyse_branch context ty te =
77 match CicReduction.whd ~subst context ty with
78 C.Meta _ -> raise (AssertFailure (lazy "34"))
82 does_not_occur ~subst context n nn te
85 raise (AssertFailure (lazy "24"))(* due to type-checking *)
86 | C.Prod (name,so,de) ->
87 analyse_branch ((Some (name,(C.Decl so)))::context) de te
90 raise (AssertFailure (lazy "25"))(* due to type-checking *)
91 | C.Appl ((C.MutInd (uri,_,_))::_) when uri == coInductiveTypeURI ->
92 guarded_by_constructors ~subst context n nn true te []
94 | C.Appl ((C.MutInd (uri,_,_))::_) ->
95 guarded_by_constructors ~subst context n nn true te tl
98 does_not_occur ~subst context n nn te
99 | C.Const _ -> raise (AssertFailure (lazy "26"))
100 | C.MutInd (uri,_,_) when uri == coInductiveTypeURI ->
101 guarded_by_constructors ~subst context n nn true te []
104 does_not_occur ~subst context n nn te
105 | C.MutConstruct _ -> raise (AssertFailure (lazy "27"))
106 (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
107 (*CSC: in head position. *)
111 raise (AssertFailure (lazy "28"))(* due to type-checking *)
113 let rec analyse_instantiated_type context ty l =
114 match CicReduction.whd ~subst context ty with
120 | C.Cast _ -> raise (AssertFailure (lazy "29"))(* due to type-checking *)
121 | C.Prod (name,so,de) ->
126 analyse_branch context so he &&
127 analyse_instantiated_type
128 ((Some (name,(C.Decl so)))::context) de tl
132 raise (AssertFailure (lazy "30"))(* due to type-checking *)
135 (fun i x -> i && does_not_occur ~subst context n nn x) true l
136 | C.Const _ -> raise (AssertFailure (lazy "31"))
139 (fun i x -> i && does_not_occur ~subst context n nn x) true l
140 | C.MutConstruct _ -> raise (AssertFailure (lazy "32"))
141 (*CSC: we do not consider backbones with a MutCase, Fix, Cofix *)
142 (*CSC: in head position. *)
146 raise (AssertFailure (lazy "33"))(* due to type-checking *)
148 let rec instantiate_type args consty =
152 let consty' = CicReduction.whd ~subst context consty in
158 let instantiated_de = CicSubstitution.subst he de in
159 (*CSC: siamo sicuri che non sia troppo forte? *)
160 does_not_occur ~subst context n nn tlhe &
161 instantiate_type tl instantiated_de tltl
163 (*CSC:We do not consider backbones with a MutCase, a *)
164 (*CSC:FixPoint, a CoFixPoint and so on in head position.*)
165 raise (AssertFailure (lazy "23"))
167 | [] -> analyse_instantiated_type context consty' l
168 (* These are all the other cases *)
170 instantiate_type args consty tl
171 | C.Appl ((C.CoFix (_,fl))::tl) ->
172 List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
173 let len = List.length fl in
174 let n_plus_len = n + len
175 and nn_plus_len = nn + len
176 (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
179 (fun (types,len) (n,ty,_) ->
180 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
186 i && does_not_occur ~subst context n nn ty &&
187 guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
188 h bo args coInductiveTypeURI
190 | C.Appl ((C.MutCase (_,_,out,te,pl))::tl) ->
191 List.fold_left (fun i x -> i && does_not_occur ~subst context n nn x) true tl &&
192 does_not_occur ~subst context n nn out &&
193 does_not_occur ~subst context n nn te &&
197 guarded_by_constructors ~subst context n nn h x args
201 List.fold_right (fun x i -> i && does_not_occur ~subst context n nn x) l true
202 | C.Var (_,exp_named_subst)
203 | C.Const (_,exp_named_subst) ->
205 (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
206 | C.MutInd _ -> assert false
207 | C.MutConstruct (_,_,_,exp_named_subst) ->
209 (fun (_,x) i -> i && does_not_occur ~subst context n nn x) exp_named_subst true
210 | C.MutCase (_,_,out,te,pl) ->
211 does_not_occur ~subst context n nn out &&
212 does_not_occur ~subst context n nn te &&
216 guarded_by_constructors ~subst context n nn h x args
220 let len = List.length fl in
221 let n_plus_len = n + len
222 and nn_plus_len = nn + len
223 (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
226 (fun (types,len) (n,_,ty,_) ->
227 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
232 (fun (_,_,ty,bo) i ->
233 i && does_not_occur ~subst context n nn ty &&
234 does_not_occur ~subst (tys@context) n_plus_len nn_plus_len bo
237 let len = List.length fl in
238 let n_plus_len = n + len
239 and nn_plus_len = nn + len
240 (*CSC: Is a Decl of the ty ok or should I use Def of a Fix? *)
243 (fun (types,len) (n,ty,_) ->
244 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
250 i && does_not_occur ~subst context n nn ty &&
251 guarded_by_constructors ~subst (tys@context) n_plus_len nn_plus_len
253 args coInductiveTypeURI
257 type_of_aux ~logger context t ugraph
261 (** wrappers which instantiate fresh loggers *)
263 (* check_allowed_sort_elimination uri i s1 s2
264 This function is used outside the kernel to determine in advance whether
265 a MutCase will be allowed or not.
266 [uri,i] is the type of the term to match
267 [s1] is the sort of the term to eliminate (i.e. the head of the arity
268 of the inductive type [uri,i])
269 [s2] is the sort of the goal (i.e. the head of the type of the outtype
271 let check_allowed_sort_elimination uri i s1 s2 =
272 fst (check_allowed_sort_elimination ~subst:[] ~metasenv:[]
273 ~logger:(new CicLogger.logger) [] uri i true
274 (Cic.Implicit None) (* never used *) (Cic.Sort s1) (Cic.Sort s2)
275 CicUniv.empty_ugraph)
278 Deannotate.type_of_aux' := fun context t -> fst (type_of_aux' [] context t CicUniv.oblivion_ugraph);;
283 module R = NCicReduction
284 module Ref = NReference
285 module S = NCicSubstitution
287 module E = NCicEnvironment
289 let rec split_prods ~subst context n te =
290 match (n, R.whd ~subst context te) with
291 | (0, _) -> context,te
292 | (n, C.Prod (name,so,ta)) when n > 0 ->
293 split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
294 | (_, _) -> raise (AssertFailure (lazy "split_prods"))
297 let debruijn ?(cb=fun _ _ -> ()) uri number_of_types =
301 | C.Meta (i,(s,C.Ctx l)) ->
302 let l1 = NCicUtils.sharing_map (aux (k-s)) l in
303 if l1 == l then t else C.Meta (i,(s,C.Ctx l1))
305 | C.Const (Ref.Ref (_,uri1,(Ref.Fix (no,_) | Ref.CoFix no)))
306 | C.Const (Ref.Ref (_,uri1,Ref.Ind no)) when NUri.eq uri uri1 ->
307 C.Rel (k + number_of_types - no)
308 | t -> NCicUtils.map (fun _ k -> k+1) k aux t
315 let sort_of_prod ~metasenv ~subst context (name,s) (t1, t2) =
316 let t1 = R.whd ~subst context t1 in
317 let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in
319 | C.Sort s1, C.Sort C.Prop -> t2
320 | C.Sort (C.Type u1), C.Sort (C.Type u2) -> C.Sort (C.Type (max u1 u2))
321 | C.Sort _,C.Sort (C.Type _) -> t2
322 | C.Sort (C.Type _) , C.Sort C.CProp -> t1
323 | C.Sort _, C.Sort C.CProp -> t2
326 | C.Sort _, C.Meta _ when U.is_closed t2 -> t2
328 raise (TypeCheckerFailure (lazy (Printf.sprintf
329 "Prod: expected two sorts, found = %s, %s"
330 (NCicPp.ppterm ~subst ~metasenv ~context t1)
331 (NCicPp.ppterm ~subst ~metasenv ~context t2))))
334 let eat_prods ~subst ~metasenv context he ty_he args_with_ty =
335 let rec aux ty_he = function
337 | (arg, ty_arg)::tl ->
338 match R.whd ~subst context ty_he with
341 prerr_endline (NCicPp.ppterm ~subst ~metasenv ~context s ^ " - Vs - "
342 ^ NCicPp.ppterm ~subst ~metasenv
344 prerr_endline (NCicPp.ppterm ~subst ~metasenv ~context (S.subst ~avoid_beta_redexes:true arg t));
346 if R.are_convertible ~subst ~metasenv context ty_arg s then
347 aux (S.subst ~avoid_beta_redexes:true arg t) tl
351 (lazy (Printf.sprintf
352 ("Appl: wrong application of %s: the parameter %s has type"^^
353 "\n%s\nbut it should have type \n%s\nContext:\n%s\n")
354 (NCicPp.ppterm ~subst ~metasenv ~context he)
355 (NCicPp.ppterm ~subst ~metasenv ~context arg)
356 (NCicPp.ppterm ~subst ~metasenv ~context ty_arg)
357 (NCicPp.ppterm ~subst ~metasenv ~context s)
358 (NCicPp.ppcontext ~subst ~metasenv context))))
362 (lazy (Printf.sprintf
363 "Appl: %s is not a function, it cannot be applied"
364 (NCicPp.ppterm ~subst ~metasenv ~context
365 (let res = List.length tl in
366 let eaten = List.length args_with_ty - res in
369 (fst (HExtlib.split_nth eaten args_with_ty)))))))))
371 aux ty_he args_with_ty
374 let fix_lefts_in_constrs ~subst uri paramsno tyl i =
375 let len = List.length tyl in
376 let _,_,arity,cl = List.nth tyl i in
377 let tys = List.map (fun (_,n,ty,_) -> n,C.Decl ty) tyl in
381 let debruijnedty = debruijn uri len ty in
382 id, snd (split_prods ~subst tys paramsno ty),
383 snd (split_prods ~subst tys paramsno debruijnedty))
386 let lefts = fst (split_prods ~subst [] paramsno arity) in
390 exception DoesOccur;;
392 let does_not_occur ~subst context n nn t =
393 let rec aux (context,n,nn as k) _ = function
394 | C.Rel m when m > n && m <= nn -> raise DoesOccur
396 (try (match List.nth context (m-1) with
397 | _,C.Def (bo,_) -> aux k () (S.lift m bo)
399 with Failure _ -> assert false)
400 | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) ()
401 | C.Meta (mno,(s,l)) ->
403 let _,_,term,_ = U.lookup_subst mno subst in
404 aux (context,n+s,nn+s) () (S.subst_meta (0,l) term)
405 with CicUtil.Subst_not_found _ -> match l with
406 | C.Irl len -> if not (n >= s+len || s > nn) then raise DoesOccur
407 | C.Ctx lc -> List.iter (aux (context,n+s,nn+s) ()) lc)
408 | t -> U.fold (fun e (ctx,n,nn) -> (e::ctx,n+1,nn+1)) k aux () t
410 try aux (context,n,nn) () t; true
411 with DoesOccur -> false
414 (*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
415 (*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
416 (*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *)
417 (*CSC strictly_positive *)
418 (*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *)
419 let rec weakly_positive ~subst context n nn uri te =
420 (*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*)
421 let dummy = C.Sort (C.Type ~-1) in
422 (*CSC: mettere in cicSubstitution *)
423 let rec subst_inductive_type_with_dummy _ = function
424 | C.Const (Ref.Ref (_,uri',Ref.Ind 0)) when NUri.eq uri' uri -> dummy
425 | C.Appl ((C.Const (Ref.Ref (_,uri',Ref.Ind 0)))::tl)
426 when NUri.eq uri' uri -> dummy
427 | t -> U.map (fun _ x->x) () subst_inductive_type_with_dummy t
429 match R.whd context te with
430 | C.Const (Ref.Ref (_,uri',Ref.Ind _))
431 | C.Appl ((C.Const (Ref.Ref (_,uri',Ref.Ind _)))::_)
432 when NUri.eq uri' uri -> true
433 | C.Prod (name,source,dest) when
434 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
435 (* dummy abstraction, so we behave as in the anonimous case *)
436 strictly_positive ~subst context n nn
437 (subst_inductive_type_with_dummy () source) &&
438 weakly_positive ~subst ((name,C.Decl source)::context)
439 (n + 1) (nn + 1) uri dest
440 | C.Prod (name,source,dest) ->
441 does_not_occur ~subst context n nn
442 (subst_inductive_type_with_dummy () source)&&
443 weakly_positive ~subst ((name,C.Decl source)::context)
444 (n + 1) (nn + 1) uri dest
446 raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))
448 (* instantiate_parameters ps (x1:T1)...(xn:Tn)C *)
449 (* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
450 and instantiate_parameters params c =
453 | C.Prod (_,_,ta), he::tl -> instantiate_parameters tl (S.subst he ta)
454 | t,l -> raise (AssertFailure (lazy "1"))
456 and strictly_positive ~subst context n nn te =
457 match R.whd context te with
458 | t when does_not_occur ~subst context n nn t -> true
460 | C.Prod (name,so,ta) ->
461 does_not_occur ~subst context n nn so &&
462 strictly_positive ~subst ((name,C.Decl so)::context) (n+1) (nn+1) ta
463 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
464 List.for_all (does_not_occur ~subst context n nn) tl
465 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind i) as r)::tl) ->
466 let _,paramsno,tyl,_,i = E.get_checked_indtys r in
467 let _,name,ity,cl = List.nth tyl i in
468 let ok = List.length tyl = 1 in
469 let params, arguments = HExtlib.split_nth paramsno tl in
470 let lifted_params = List.map (S.lift 1) params in
472 List.map (fun (_,_,te) -> instantiate_parameters lifted_params te) cl
475 List.for_all (does_not_occur ~subst context n nn) arguments &&
477 (weakly_positive ~subst ((name,C.Decl ity)::context) (n+1) (nn+1) uri) cl
480 (* the inductive type indexes are s.t. n < x <= nn *)
481 and are_all_occurrences_positive ~subst context uri indparamsno i n nn te =
482 match R.whd context te with
483 | C.Appl ((C.Rel m)::tl) as reduct when m = i ->
489 match R.whd context x with
490 | C.Rel m when m = n - (indparamsno - k) -> k - 1
491 | y -> raise (TypeCheckerFailure (lazy
492 ("Argument "^string_of_int (indparamsno - k + 1) ^ " (of " ^
493 string_of_int indparamsno ^ " fixed) is not homogeneous in "^
494 "appl:\n"^ NCicPp.ppterm ~context ~subst ~metasenv:[] reduct))))
498 List.for_all (does_not_occur ~subst context n nn) tl
500 raise (TypeCheckerFailure
501 (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
502 NUri.string_of_uri uri)))
503 | C.Rel m when m = i ->
504 if indparamsno = 0 then
507 raise (TypeCheckerFailure
508 (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^
509 NUri.string_of_uri uri)))
510 | C.Prod (name,source,dest) when
511 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
512 strictly_positive ~subst context n nn source &&
513 are_all_occurrences_positive ~subst
514 ((name,C.Decl source)::context) uri indparamsno
515 (i+1) (n + 1) (nn + 1) dest
516 | C.Prod (name,source,dest) ->
517 if not (does_not_occur ~subst context n nn source) then
518 raise (TypeCheckerFailure (lazy ("Non-positive occurrence in "^
519 NCicPp.ppterm ~context ~metasenv:[] ~subst te)));
520 are_all_occurrences_positive ~subst ((name,C.Decl source)::context)
521 uri indparamsno (i+1) (n + 1) (nn + 1) dest
524 (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^
525 (NUri.string_of_uri uri))))
528 exception NotGuarded of string Lazy.t;;
530 let rec typeof ~subst ~metasenv context term =
531 let rec typeof_aux context =
532 fun t -> (*prerr_endline (NCicPp.ppterm ~context t); *)
536 match List.nth context (n - 1) with
537 | (_,C.Decl ty) -> S.lift n ty
538 | (_,C.Def (_,ty)) -> S.lift n ty
539 with Failure _ -> raise (TypeCheckerFailure (lazy "unbound variable")))
540 | C.Sort (C.Type i) -> C.Sort (C.Type (i+1))
541 | C.Sort s -> C.Sort (C.Type 0)
542 | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found"))
543 | C.Meta (n,l) as t ->
544 let canonical_ctx,ty =
546 let _,c,_,ty = U.lookup_subst n subst in c,ty
547 with U.Subst_not_found _ -> try
548 let _,_,c,ty = U.lookup_meta n metasenv in c,ty
549 with U.Meta_not_found _ ->
550 raise (AssertFailure (lazy (Printf.sprintf
551 "%s not found" (NCicPp.ppterm ~subst ~metasenv ~context t))))
553 check_metasenv_consistency t ~subst ~metasenv context canonical_ctx l;
555 | C.Const ref -> type_of_constant ref
556 | C.Prod (name,s,t) ->
557 let sort1 = typeof_aux context s in
558 let sort2 = typeof_aux ((name,(C.Decl s))::context) t in
559 sort_of_prod ~metasenv ~subst context (name,s) (sort1,sort2)
560 | C.Lambda (n,s,t) ->
561 let sort = typeof_aux context s in
562 (match R.whd ~subst context sort with
563 | C.Meta _ | C.Sort _ -> ()
566 (TypeCheckerFailure (lazy (Printf.sprintf
567 ("Not well-typed lambda-abstraction: " ^^
568 "the source %s should be a type; instead it is a term " ^^
569 "of type %s") (NCicPp.ppterm ~subst ~metasenv ~context s)
570 (NCicPp.ppterm ~subst ~metasenv ~context sort)))));
571 let ty = typeof_aux ((n,(C.Decl s))::context) t in
573 | C.LetIn (n,ty,t,bo) ->
574 let ty_t = typeof_aux context t in
575 let _ = typeof_aux context ty in
576 if not (R.are_convertible ~subst ~metasenv context ty ty_t) then
579 (lazy (Printf.sprintf
580 "The type of %s is %s but it is expected to be %s"
581 (NCicPp.ppterm ~subst ~metasenv ~context t)
582 (NCicPp.ppterm ~subst ~metasenv ~context ty_t)
583 (NCicPp.ppterm ~subst ~metasenv ~context ty))))
585 let ty_bo = typeof_aux ((n,C.Def (t,ty))::context) bo in
586 S.subst ~avoid_beta_redexes:true t ty_bo
587 | C.Appl (he::(_::_ as args)) ->
588 let ty_he = typeof_aux context he in
589 let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in
591 prerr_endline ("HEAD: " ^ NCicPp.ppterm ~subst ~metasenv ~context ty_he);
592 prerr_endline ("TARGS: " ^ String.concat " | " (List.map (NCicPp.ppterm
593 ~subst ~metasenv ~context) (List.map snd args_with_ty)));
594 prerr_endline ("ARGS: " ^ String.concat " | " (List.map (NCicPp.ppterm
595 ~subst ~metasenv ~context) (List.map fst args_with_ty)));
597 eat_prods ~subst ~metasenv context he ty_he args_with_ty
598 | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
599 | C.Match (Ref.Ref (_,_,Ref.Ind tyno) as r,outtype,term,pl) ->
600 let outsort = typeof_aux context outtype in
601 let inductive,leftno,itl,_,_ = E.get_checked_indtys r in
603 let _,_,_,cl = List.nth itl tyno in List.length cl
605 let parameters, arguments =
606 let ty = R.whd ~subst context (typeof_aux context term) in
609 C.Const (Ref.Ref (_,_,Ref.Ind _) as r') -> r',[]
610 | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _) as r') :: tl) -> r',tl
613 (TypeCheckerFailure (lazy (Printf.sprintf
614 "Case analysis: analysed term %s is not an inductive one"
615 (NCicPp.ppterm ~subst ~metasenv ~context term)))) in
616 if not (Ref.eq r r') then
618 (TypeCheckerFailure (lazy (Printf.sprintf
619 ("Case analysys: analysed term type is %s, but is expected " ^^
620 "to be (an application of) %s")
621 (NCicPp.ppterm ~subst ~metasenv ~context ty)
622 (NCicPp.ppterm ~subst ~metasenv ~context (C.Const r')))))
624 try HExtlib.split_nth leftno tl
627 raise (TypeCheckerFailure (lazy (Printf.sprintf
628 "%s is partially applied"
629 (NCicPp.ppterm ~subst ~metasenv ~context ty)))) in
630 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
631 let sort_of_ind_type =
632 if parameters = [] then C.Const r
633 else C.Appl ((C.Const r)::parameters) in
634 let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in
635 check_allowed_sort_elimination ~subst ~metasenv r context
636 sort_of_ind_type type_of_sort_of_ind_ty outsort;
637 (* let's check if the type of branches are right *)
638 if List.length pl <> constructorsno then
639 raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match")));
640 let j,branches_ok,p_ty, exp_p_ty =
642 (fun (j,b,old_p_ty,old_exp_p_ty) p ->
645 let cons = Ref.mk_constructor j r in
646 if parameters = [] then C.Const cons
647 else C.Appl (C.Const cons::parameters)
649 let ty_p = typeof_aux context p in
650 let ty_cons = typeof_aux context cons in
652 type_of_branch ~subst context leftno outtype cons ty_cons 0
654 j+1, R.are_convertible ~subst ~metasenv context ty_p ty_branch,
657 j,false,old_p_ty,old_exp_p_ty
658 ) (1,true,C.Sort C.Prop,C.Sort C.Prop) pl
660 if not branches_ok then
663 (lazy (Printf.sprintf ("Branch for constructor %s :=\n%s\n"^^
664 "has type %s\nnot convertible with %s")
665 (NCicPp.ppterm ~subst ~metasenv ~context
666 (C.Const (Ref.mk_constructor (j-1) r)))
667 (NCicPp.ppterm ~metasenv ~subst ~context (List.nth pl (j-2)))
668 (NCicPp.ppterm ~metasenv ~subst ~context p_ty)
669 (NCicPp.ppterm ~metasenv ~subst ~context exp_p_ty))));
670 let res = outtype::arguments@[term] in
671 R.head_beta_reduce (C.Appl res)
672 | C.Match _ -> assert false
674 and type_of_branch ~subst context leftno outty cons tycons liftno =
675 match R.whd ~subst context tycons with
676 | C.Const (Ref.Ref (_,_,Ref.Ind _)) -> C.Appl [S.lift liftno outty ; cons]
677 | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _))::tl) ->
678 let _,arguments = HExtlib.split_nth leftno tl in
679 C.Appl (S.lift liftno outty::arguments@[cons])
680 | C.Prod (name,so,de) ->
682 match S.lift 1 cons with
683 | C.Appl l -> C.Appl (l@[C.Rel 1])
684 | t -> C.Appl [t ; C.Rel 1]
687 type_of_branch ~subst ((name,(C.Decl so))::context)
688 leftno outty cons de (liftno+1))
689 | _ -> raise (AssertFailure (lazy "type_of_branch"))
691 (* check_metasenv_consistency checks that the "canonical" context of a
692 metavariable is consitent - up to relocation via the relocation list l -
693 with the actual context *)
694 and check_metasenv_consistency
695 ~subst ~metasenv term context canonical_context l
698 | shift, NCic.Irl n ->
699 let context = snd (HExtlib.split_nth shift context) in
700 let rec compare = function
704 raise (AssertFailure (lazy (Printf.sprintf
705 "Local and canonical context %s have different lengths"
706 (NCicPp.ppterm ~subst ~context ~metasenv term))))
708 raise (TypeCheckerFailure (lazy (Printf.sprintf
709 "Unbound variable -%d in %s" m
710 (NCicPp.ppterm ~subst ~metasenv ~context term))))
713 (_,C.Decl t1), (_,C.Decl t2)
714 | (_,C.Def (t1,_)), (_,C.Def (t2,_))
715 | (_,C.Def (_,t1)), (_,C.Decl t2) ->
716 if not (R.are_convertible ~subst ~metasenv tl t1 t2) then
719 (lazy (Printf.sprintf
720 ("Not well typed metavariable local context for %s: " ^^
721 "%s expected, which is not convertible with %s")
722 (NCicPp.ppterm ~subst ~metasenv ~context term)
723 (NCicPp.ppterm ~subst ~metasenv ~context t2)
724 (NCicPp.ppterm ~subst ~metasenv ~context t1))))
727 (TypeCheckerFailure (lazy (Printf.sprintf
728 ("Not well typed metavariable local context for %s: " ^^
729 "a definition expected, but a declaration found")
730 (NCicPp.ppterm ~subst ~metasenv ~context term)))));
731 compare (m - 1,tl,ctl)
733 compare (n,context,canonical_context)
735 (* we avoid useless lifting by shortening the context*)
736 let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in
737 let lifted_canonical_context =
738 let rec lift_metas i = function
740 | (n,C.Decl t)::tl ->
741 (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl)
742 | (n,C.Def (t,ty))::tl ->
743 (n,C.Def ((S.subst_meta l (S.lift i t)),
744 S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl)
746 lift_metas 1 canonical_context in
747 let l = U.expand_local_context lc_kind in
752 | t, (_,C.Def (ct,_)) ->
753 (*CSC: the following optimization is to avoid a possibly expensive
754 reduction that can be easily avoided and that is quite
755 frequent. However, this is better handled using levels to
761 match List.nth context (n - 1) with
762 | (_,C.Def (te,_)) -> S.lift n te
767 if not (R.are_convertible ~subst ~metasenv context optimized_t ct)
771 (lazy (Printf.sprintf
772 ("Not well typed metavariable local context: " ^^
773 "expected a term convertible with %s, found %s")
774 (NCicPp.ppterm ~subst ~metasenv ~context ct)
775 (NCicPp.ppterm ~subst ~metasenv ~context t))))
776 | t, (_,C.Decl ct) ->
777 let type_t = typeof_aux context t in
778 if not (R.are_convertible ~subst ~metasenv context type_t ct) then
779 raise (TypeCheckerFailure
780 (lazy (Printf.sprintf
781 ("Not well typed metavariable local context: "^^
782 "expected a term of type %s, found %s of type %s")
783 (NCicPp.ppterm ~subst ~metasenv ~context ct)
784 (NCicPp.ppterm ~subst ~metasenv ~context t)
785 (NCicPp.ppterm ~subst ~metasenv ~context type_t))))
786 ) l lifted_canonical_context
788 Invalid_argument _ ->
789 raise (AssertFailure (lazy (Printf.sprintf
790 "Local and canonical context %s have different lengths"
791 (NCicPp.ppterm ~subst ~metasenv ~context term))))
793 and is_non_informative context paramsno c =
794 let rec aux context c =
795 match R.whd context c with
796 | C.Prod (n,so,de) ->
797 let s = typeof_aux context so in
798 s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de
800 let context',dx = split_prods ~subst:[] context paramsno c in
803 and check_allowed_sort_elimination ~subst ~metasenv r =
806 | C.Appl l -> C.Appl (l @ [arg])
807 | t -> C.Appl [t;arg] in
808 let rec aux context ind arity1 arity2 =
809 let arity1 = R.whd ~subst context arity1 in
810 let arity2 = R.whd ~subst context arity2 in
811 match arity1,arity2 with
812 | C.Prod (name,so1,de1), C.Prod (_,so2,de2) ->
813 if not (R.are_convertible ~subst ~metasenv context so1 so2) then
814 raise (TypeCheckerFailure (lazy (Printf.sprintf
815 "In outtype: expected %s, found %s"
816 (NCicPp.ppterm ~subst ~metasenv ~context so1)
817 (NCicPp.ppterm ~subst ~metasenv ~context so2)
819 aux ((name, C.Decl so1)::context)
820 (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2
821 | C.Sort _, C.Prod (name,so,ta) ->
822 if not (R.are_convertible ~subst ~metasenv context so ind) then
823 raise (TypeCheckerFailure (lazy (Printf.sprintf
824 "In outtype: expected %s, found %s"
825 (NCicPp.ppterm ~subst ~metasenv ~context ind)
826 (NCicPp.ppterm ~subst ~metasenv ~context so)
828 (match arity1,ta with
829 | (C.Sort (C.CProp | C.Type _), C.Sort _)
830 | (C.Sort C.Prop, C.Sort C.Prop) -> ()
831 | (C.Sort C.Prop, C.Sort (C.CProp | C.Type _)) ->
832 (* TODO: we should pass all these parameters since we
833 * have them already *)
834 let inductive,leftno,itl,_,i = E.get_checked_indtys r in
835 let itl_len = List.length itl in
836 let _,name,ty,cl = List.nth itl i in
837 let cl_len = List.length cl in
838 (* is it a singleton or empty non recursive and non informative
842 (itl_len = 1 && cl_len = 1 &&
843 is_non_informative [name,C.Decl ty] leftno
844 (let _,_,x = List.nth cl 0 in x)))
846 raise (TypeCheckerFailure (lazy
847 ("Sort elimination not allowed")));
854 typeof_aux context term
856 and check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl =
857 (* let's check if the arity of the inductive types are well formed *)
858 List.iter (fun (_,_,x,_) -> ignore (typeof ~subst ~metasenv [] x)) tyl;
859 (* let's check if the types of the inductive constructors are well formed. *)
860 let len = List.length tyl in
861 let tys = List.rev (List.map (fun (_,n,ty,_) -> (n,(C.Decl ty))) tyl) in
867 let debruijnedte = debruijn uri len te in
868 ignore (typeof ~subst ~metasenv tys debruijnedte);
869 (* let's check also the positivity conditions *)
872 (are_all_occurrences_positive ~subst tys uri leftno i 0 len
877 (lazy ("Non positive occurence in "^NUri.string_of_uri uri))))
882 and eat_lambdas ~subst ~metasenv context n te =
883 match (n, R.whd ~subst context te) with
884 | (0, _) -> (te, context)
885 | (n, C.Lambda (name,so,ta)) when n > 0 ->
886 eat_lambdas ~subst ~metasenv ((name,(C.Decl so))::context) (n - 1) ta
888 raise (AssertFailure (lazy (Printf.sprintf "9 (%d, %s)" n
889 (NCicPp.ppterm ~subst ~metasenv ~context te))))
891 and guarded_by_destructors ~subst ~metasenv context recfuns t =
892 let recursor f k t = NCicUtils.fold shift_k k (fun k () -> f k) () t in
893 let rec aux (context, recfuns, x, safes as k) t =
894 match R.whd ~subst context t with (* TODO: use ~delta:false as mush as poss*)
895 | C.Rel m as t when List.mem_assoc m recfuns ->
896 raise (NotGuarded (lazy
897 (NCicPp.ppterm ~subst ~metasenv ~context t ^ " passed around")))
899 (match List.nth context (m-1) with
901 | _,C.Def (bo,_) -> aux (context, recfuns, x, safes) (S.lift m bo))
903 | C.Appl ((C.Rel m)::tl) as t when List.mem_assoc m recfuns ->
904 let rec_no = List.assoc m recfuns in
905 if not (List.length tl > rec_no) then
906 raise (NotGuarded (lazy
907 (NCicPp.ppterm ~context ~subst ~metasenv t ^
908 " is a partial application of a fix")))
910 let rec_arg = List.nth tl rec_no in
911 if not (is_really_smaller ~subst ~metasenv k rec_arg) then
912 raise (NotGuarded (lazy
913 (NCicPp.ppterm ~context ~subst ~metasenv rec_arg ^ " not smaller")));
916 | C.Appl (C.Const ((Ref.Ref (_,_,Ref.Fix (i,j))) as r)::args) ->
917 List.iter (aux k) args;
918 let fixes,_,_ = E.get_checked_fixes r in
919 let _,_,_,_,bo = List.nth fixes i in
920 let bo_wout_lam, context = eat_lambdas ~subst ~metasenv context j in
921 (* debruijna body..... *) assert false
923 | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) as t ->
924 (match R.whd ~subst context term with
925 | C.Rel m | C.Appl (C.Rel m :: _ ) as t when List.mem m safes || m = x ->
926 let isinductive, paramsno, tl, _, i = E.get_checked_indtys ref in
927 if not isinductive then recursor aux k t
929 let c_ctx,len,cl = fix_lefts_in_constrs ~subst uri paramsno tl i in
930 let args = match t with C.Appl (_::tl) -> tl | _ -> [] in
932 List.iter (aux k) args;
934 (fun p (_,_,bruijnedc) ->
935 let rl = recursive_args ~subst ~metasenv c_ctx 0 len bruijnedc in
936 let p, k = get_new_safes ~subst k p rl in
939 | _ -> recursor aux k t)
940 | t -> recursor aux k t
942 try aux (context, recfuns, 1, []) t
943 with NotGuarded s -> raise (TypeCheckerFailure s)
947 let len = List.length fl in
948 let n_plus_len = n + len
949 and nn_plus_len = nn + len
950 and x_plus_len = x + len
953 (fun (types,len) (n,_,ty,_) ->
954 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
957 and safes' = List.map (fun x -> x + len) safes in
959 (fun (_,_,ty,bo) i ->
960 i && guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
961 guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
965 let len = List.length fl in
966 let n_plus_len = n + len
967 and nn_plus_len = nn + len
968 and x_plus_len = x + len
971 (fun (types,len) (n,ty,_) ->
972 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
975 and safes' = List.map (fun x -> x + len) safes in
979 guarded_by_destructors ~subst context n nn kl x_plus_len safes' ty &&
980 guarded_by_destructors ~subst (tys@context) n_plus_len nn_plus_len kl
985 and guarded_by_constructors ~subst ~metasenv _ _ _ _ _ _ _ = true
987 and recursive_args ~subst ~metasenv context n nn te =
988 match R.whd context te with
989 | C.Rel _ | C.Appl _ -> []
990 | C.Prod (name,so,de) ->
991 (not (does_not_occur ~subst context n nn so)) ::
992 (recursive_args ~subst ~metasenv
993 ((name,(C.Decl so))::context) (n+1) (nn + 1) de)
995 raise (AssertFailure (lazy ("recursive_args:" ^ NCicPp.ppterm ~subst
996 ~metasenv ~context:[] t)))
998 and get_new_safes ~subst (context, recfuns, x, safes as k) p rl =
999 match R.whd ~subst context p, rl with
1000 | C.Lambda (name,so,ta), b::tl ->
1001 let safes = (if b then [0] else []) @ safes in
1002 get_new_safes ~subst
1003 (shift_k (name,(C.Decl so)) (context, recfuns, x, safes)) ta tl
1004 | C.Meta _ as e, _ | e, [] -> e, k
1005 | _ -> raise (AssertFailure (lazy "Ill formed pattern"))
1007 and split_prods ~subst context n te =
1008 match n, R.whd ~subst context te with
1009 | 0, _ -> context,te
1010 | n, C.Prod (name,so,ta) when n > 0 ->
1011 split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
1012 | _ -> raise (AssertFailure (lazy "split_prods"))
1014 and is_really_smaller ~subst ~metasenv (context, recfuns, x, safes as k) te =
1015 match R.whd ~subst context te with
1016 | C.Rel m when List.mem m safes -> true
1017 | C.Lambda (name, s, t) ->
1018 is_really_smaller ~subst ~metasenv (shift_k (name, C.Decl s) k) t
1020 is_really_smaller ~subst ~metasenv k he
1023 | C.Const (Ref.Ref (_,_,Ref.Con _)) -> false
1024 | C.Const (Ref.Ref (_,_,Ref.Fix _)) -> assert false
1025 (*| C.Fix (_, fl) ->
1026 let len = List.length fl in
1027 let n_plus_len = n + len
1028 and nn_plus_len = nn + len
1029 and x_plus_len = x + len
1032 (fun (types,len) (n,_,ty,_) ->
1033 (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types,
1036 and safes' = List.map (fun x -> x + len) safes in
1038 (fun (_,_,ty,bo) i ->
1040 is_really_smaller ~subst (tys@context) n_plus_len nn_plus_len kl
1041 x_plus_len safes' bo
1044 | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) ->
1046 | C.Rel m | C.Appl (C.Rel m :: _ ) when List.mem m safes || m = x ->
1047 let isinductive, paramsno, tl, _, i = E.get_checked_indtys ref in
1048 if not isinductive then
1049 List.for_all (is_really_smaller ~subst ~metasenv k) pl
1051 let c_ctx,len,cl = fix_lefts_in_constrs ~subst uri paramsno tl i in
1053 (fun p (_,_,debruijnedte) ->
1054 let rl'=recursive_args ~subst ~metasenv c_ctx 0 len debruijnedte in
1055 let e, k = get_new_safes ~subst k p rl' in
1056 is_really_smaller ~subst ~metasenv k e)
1058 | _ -> List.for_all (is_really_smaller ~subst ~metasenv k) pl)
1061 and returns_a_coinductive ~subst context ty =
1062 match R.whd ~subst context ty with
1063 | C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)
1064 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)::_) ->
1065 let isinductive, _, _, _, _ = E.get_checked_indtys ref in
1066 if isinductive then None else (Some uri)
1067 | C.Prod (n,so,de) ->
1068 returns_a_coinductive ~subst ((n,C.Decl so)::context) de
1071 and type_of_constant ((Ref.Ref (_,uri,_)) as ref) =
1073 match E.get_obj uri with
1074 | true, cobj -> cobj
1076 !logger (`Start_type_checking uri);
1077 check_obj_well_typed uobj;
1079 !logger (`Type_checking_completed uri);
1082 match cobj, ref with
1083 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Ind i) ->
1084 let _,_,arity,_ = List.nth tl i in arity
1085 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Con (i,j)) ->
1086 let _,_,_,cl = List.nth tl i in
1087 let _,_,arity = List.nth cl (j-1) in
1089 | (_,_,_,_,C.Fixpoint (_,fl,_)), Ref.Ref (_,_,(Ref.Fix (i,_)|Ref.CoFix i)) ->
1090 let _,_,_,arity,_ = List.nth fl i in
1092 | (_,_,_,_,C.Constant (_,_,_,ty,_)), Ref.Ref (_,_,(Ref.Def |Ref.Decl)) -> ty
1093 | _ -> raise (AssertFailure (lazy "type_of_constant: environment/reference"))
1095 and check_obj_well_typed (uri,height,metasenv,subst,kind) =
1096 (* CSC: here we should typecheck the metasenv and the subst *)
1097 assert (metasenv = [] && subst = []);
1099 | C.Constant (_,_,Some te,ty,_) ->
1100 let _ = typeof ~subst ~metasenv [] ty in
1101 let ty_te = typeof ~subst ~metasenv [] te in
1102 if not (R.are_convertible ~subst ~metasenv [] ty_te ty) then
1103 raise (TypeCheckerFailure (lazy (Printf.sprintf (
1104 "the type of the body is not convertible with the declared one.\n"^^
1105 "inferred type:\n%s\nexpected type:\n%s")
1106 (NCicPp.ppterm ~subst ~metasenv ~context:[] ty_te)
1107 (NCicPp.ppterm ~subst ~metasenv ~context:[] ty))))
1108 | C.Constant (_,_,None,ty,_) -> ignore (typeof ~subst ~metasenv [] ty)
1109 | C.Inductive (is_ind, leftno, tyl, _) ->
1110 check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl
1111 | C.Fixpoint (inductive,fl,_) ->
1114 (fun (types,kl,len) (_,name,k,ty,_) ->
1115 let _ = typeof ~subst ~metasenv [] ty in
1116 ((name,(C.Decl (S.lift len ty)))::types, k::kl,len+1)
1119 List.iter (fun (_,name,x,ty,bo) ->
1120 let bo = debruijn uri len bo in
1121 let ty_bo = typeof ~subst ~metasenv types bo in
1122 if not (R.are_convertible ~subst ~metasenv types ty_bo (S.lift len ty))
1123 then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
1125 if inductive then begin
1126 let m, context = eat_lambdas ~subst ~metasenv types (x + 1) bo in
1127 (* guarded by destructors conditions D{f,k,x,M} *)
1128 let rec enum_from k =
1129 function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl
1131 guarded_by_destructors
1132 ~subst ~metasenv context (enum_from (x+2) kl) m
1134 match returns_a_coinductive ~subst [] ty with
1136 raise (TypeCheckerFailure
1137 (lazy "CoFix: does not return a coinductive type"))
1139 (* guarded by constructors conditions C{f,M} *)
1140 if not (guarded_by_constructors ~subst ~metasenv
1141 types 0 len false bo [] uri)
1143 raise (TypeCheckerFailure
1144 (lazy "CoFix: not guarded by constructors"))
1147 let typecheck_obj = check_obj_well_typed;;