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/.
26 exception NotImplemented;;
27 exception Impossible of int;;
28 exception NotWellTyped of string;;
29 exception WrongUriToConstant of string;;
30 exception WrongUriToVariable of string;;
31 exception WrongUriToMutualInductiveDefinitions of string;;
32 exception ListTooShort;;
33 exception NotPositiveOccurrences of string;;
34 exception NotWellFormedTypeOfInductiveConstructor of string;;
35 exception WrongRequiredArgument of string;;
38 let module U = UriManager in
41 `Start_type_checking uri ->
43 (String.make !indent ' ') ^
44 "<div style=\"margin-left: " ^
45 string_of_float (float_of_int !indent *. 0.5) ^ "cm\">" ^
46 "Type-Checking of " ^ (U.string_of_uri uri) ^ " started</div>\n"
50 | `Type_checking_completed uri ->
53 (String.make !indent ' ') ^
54 "<div style=\"color: green ; margin-left: " ^
55 string_of_float (float_of_int !indent *. 0.5) ^ "cm\">" ^
56 "Type-Checking of " ^ (U.string_of_uri uri) ^ " completed.</div>\n"
63 let rec debug_aux t i =
65 let module U = UriManager in
66 CicPp.ppobj (C.Variable ("DEBUG", None, t)) ^ "\n" ^ i
69 raise (NotWellTyped ("\n" ^ List.fold_right debug_aux (t::env) ""))
70 (*print_endline ("\n" ^ List.fold_right debug_aux (t::env) "") ; flush stdout*)
76 | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2)
77 | (_,_) -> raise ListTooShort
80 exception CicEnvironmentError;;
82 let rec cooked_type_of_constant uri cookingsno =
84 let module R = CicReduction in
85 let module U = UriManager in
87 match CicEnvironment.is_type_checked uri cookingsno with
88 CicEnvironment.CheckedObj cobj -> cobj
89 | CicEnvironment.UncheckedObj uobj ->
90 log (`Start_type_checking uri) ;
91 (* let's typecheck the uncooked obj *)
93 C.Definition (_,te,ty,_) ->
95 if not (R.are_convertible (type_of te) ty) then
96 raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
98 (* only to check that ty is well-typed *)
99 let _ = type_of ty in ()
100 | C.CurrentProof (_,_,te,ty) ->
101 let _ = type_of ty in
102 if not (R.are_convertible (type_of te) ty) then
103 raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
104 | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
106 CicEnvironment.set_type_checking_info uri ;
107 log (`Type_checking_completed uri) ;
108 match CicEnvironment.is_type_checked uri cookingsno with
109 CicEnvironment.CheckedObj cobj -> cobj
110 | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
113 C.Definition (_,_,ty,_) -> ty
114 | C.Axiom (_,ty,_) -> ty
115 | C.CurrentProof (_,_,_,ty) -> ty
116 | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
118 and type_of_variable uri =
119 let module C = Cic in
120 let module R = CicReduction in
121 let module U = UriManager in
122 (* 0 because a variable is never cooked => no partial cooking at one level *)
123 match CicEnvironment.is_type_checked uri 0 with
124 CicEnvironment.CheckedObj (C.Variable (_,_,ty)) -> ty
125 | CicEnvironment.UncheckedObj (C.Variable (_,bo,ty)) ->
126 log (`Start_type_checking uri) ;
127 (* only to check that ty is well-typed *)
128 let _ = type_of ty in
132 if not (R.are_convertible (type_of bo) ty) then
133 raise (NotWellTyped ("Variable " ^ (U.string_of_uri uri)))
135 CicEnvironment.set_type_checking_info uri ;
136 log (`Type_checking_completed uri) ;
138 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
140 and does_not_occur n nn te =
141 let module C = Cic in
142 (*CSC: whd sembra essere superflua perche' un caso in cui l'occorrenza *)
143 (*CSC: venga mangiata durante la whd sembra presentare problemi di *)
145 match CicReduction.whd te with
146 C.Rel m when m > n && m <= nn -> false
152 | C.Cast (te,ty) -> does_not_occur n nn te && does_not_occur n nn ty
153 | C.Prod (_,so,dest) ->
154 does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
155 | C.Lambda (_,so,dest) ->
156 does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
157 | C.LetIn (_,so,dest) ->
158 does_not_occur n nn so && does_not_occur (n + 1) (nn + 1) dest
160 List.fold_right (fun x i -> i && does_not_occur n nn x) l true
164 | C.MutConstruct _ -> true
165 | C.MutCase (_,_,_,out,te,pl) ->
166 does_not_occur n nn out && does_not_occur n nn te &&
167 List.fold_right (fun x i -> i && does_not_occur n nn x) pl true
169 let len = List.length fl in
170 let n_plus_len = n + len in
171 let nn_plus_len = nn + len in
173 (fun (_,_,ty,bo) i ->
174 i && does_not_occur n_plus_len nn_plus_len ty &&
175 does_not_occur n_plus_len nn_plus_len bo
178 let len = List.length fl in
179 let n_plus_len = n + len in
180 let nn_plus_len = nn + len in
183 i && does_not_occur n_plus_len nn_plus_len ty &&
184 does_not_occur n_plus_len nn_plus_len bo
187 (*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
188 (*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
189 (*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *)
190 (*CSC strictly_positive *)
191 (*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *)
192 and weakly_positive n nn uri te =
193 let module C = Cic in
194 (*CSC mettere in cicSubstitution *)
195 let rec subst_inductive_type_with_dummy_rel =
197 C.MutInd (uri',_,0) when UriManager.eq uri' uri ->
198 C.Rel 0 (* dummy rel *)
199 | C.Appl ((C.MutInd (uri',_,0))::tl) when UriManager.eq uri' uri ->
200 C.Rel 0 (* dummy rel *)
201 | C.Cast (te,ty) -> subst_inductive_type_with_dummy_rel te
202 | C.Prod (name,so,ta) ->
203 C.Prod (name, subst_inductive_type_with_dummy_rel so,
204 subst_inductive_type_with_dummy_rel ta)
205 | C.Lambda (name,so,ta) ->
206 C.Lambda (name, subst_inductive_type_with_dummy_rel so,
207 subst_inductive_type_with_dummy_rel ta)
209 C.Appl (List.map subst_inductive_type_with_dummy_rel tl)
210 | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
211 C.MutCase (uri,cookingsno,i,
212 subst_inductive_type_with_dummy_rel outtype,
213 subst_inductive_type_with_dummy_rel term,
214 List.map subst_inductive_type_with_dummy_rel pl)
216 C.Fix (i,List.map (fun (name,i,ty,bo) -> (name,i,
217 subst_inductive_type_with_dummy_rel ty,
218 subst_inductive_type_with_dummy_rel bo)) fl)
220 C.CoFix (i,List.map (fun (name,ty,bo) -> (name,
221 subst_inductive_type_with_dummy_rel ty,
222 subst_inductive_type_with_dummy_rel bo)) fl)
225 match CicReduction.whd te with
226 C.Appl ((C.MutInd (uri',_,0))::tl) when UriManager.eq uri' uri -> true
227 | C.MutInd (uri',_,0) when UriManager.eq uri' uri -> true
228 | C.Prod (C.Anonimous,source,dest) ->
229 strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
230 weakly_positive (n + 1) (nn + 1) uri dest
231 | C.Prod (name,source,dest) when does_not_occur 0 n dest ->
232 (* dummy abstraction, so we behave as in the anonimous case *)
233 strictly_positive n nn (subst_inductive_type_with_dummy_rel source) &&
234 weakly_positive (n + 1) (nn + 1) uri dest
235 | C.Prod (_,source,dest) ->
236 does_not_occur n nn (subst_inductive_type_with_dummy_rel source) &&
237 weakly_positive (n + 1) (nn + 1) uri dest
238 | _ -> raise (NotWellFormedTypeOfInductiveConstructor ("Guess where the error is ;-)"))
240 (* instantiate_parameters ps (x1:T1)...(xn:Tn)C *)
241 (* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
242 and instantiate_parameters params c =
243 let module C = Cic in
244 match (c,params) with
246 | (C.Prod (_,_,ta), he::tl) ->
247 instantiate_parameters tl
248 (CicSubstitution.subst he ta)
249 | (C.Cast (te,_), _) -> instantiate_parameters params te
250 | (t,l) -> raise (Impossible 1)
252 and strictly_positive n nn te =
253 let module C = Cic in
254 let module U = UriManager in
255 match CicReduction.whd te with
258 (*CSC: bisogna controllare ty????*)
259 strictly_positive n nn te
260 | C.Prod (_,so,ta) ->
261 does_not_occur n nn so &&
262 strictly_positive (n+1) (nn+1) ta
263 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
264 List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
265 | C.Appl ((C.MutInd (uri,_,i))::tl) ->
266 let (ok,paramsno,cl) =
267 match CicEnvironment.get_obj uri with
268 C.InductiveDefinition (tl,_,paramsno) ->
269 let (_,_,_,cl) = List.nth tl i in
270 (List.length tl = 1, paramsno, cl)
271 | _ -> raise(WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
273 let (params,arguments) = split tl paramsno in
274 let lifted_params = List.map (CicSubstitution.lift 1) params in
276 List.map (fun (_,te,_) -> instantiate_parameters lifted_params te) cl
280 (fun x i -> i && does_not_occur n nn x)
282 (*CSC: MEGAPATCH3 (sara' quella giusta?)*)
286 weakly_positive (n+1) (nn+1) uri x
288 | t -> does_not_occur n nn t
290 (*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
291 and are_all_occurrences_positive uri indparamsno i n nn te =
292 let module C = Cic in
293 match CicReduction.whd te with
294 C.Appl ((C.Rel m)::tl) when m = i ->
295 (*CSC: riscrivere fermandosi a 0 *)
296 (* let's check if the inductive type is applied at least to *)
297 (* indparamsno parameters *)
303 match CicReduction.whd x with
304 C.Rel m when m = n - (indparamsno - k) -> k - 1
305 | _ -> raise (WrongRequiredArgument (UriManager.string_of_uri uri))
309 List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
311 raise (WrongRequiredArgument (UriManager.string_of_uri uri))
312 | C.Rel m when m = i ->
313 if indparamsno = 0 then
316 raise (WrongRequiredArgument (UriManager.string_of_uri uri))
317 | C.Prod (C.Anonimous,source,dest) ->
318 strictly_positive n nn source &&
319 are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
320 | C.Prod (name,source,dest) when does_not_occur 0 n dest ->
321 (* dummy abstraction, so we behave as in the anonimous case *)
322 strictly_positive n nn source &&
323 are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
324 | C.Prod (_,source,dest) ->
325 does_not_occur n nn source &&
326 are_all_occurrences_positive uri indparamsno (i+1) (n + 1) (nn + 1) dest
327 | _ -> raise (NotWellFormedTypeOfInductiveConstructor (UriManager.string_of_uri uri))
329 (*CSC: cambiare il nome, torna unit! *)
330 and cooked_mutual_inductive_defs uri =
331 let module U = UriManager in
333 Cic.InductiveDefinition (itl, _, indparamsno) ->
334 (* let's check if the arity of the inductive types are well *)
336 List.iter (fun (_,_,x,_) -> let _ = type_of x in ()) itl ;
338 (* let's check if the types of the inductive constructors *)
339 (* are well formed. *)
340 (* In order not to use type_of_aux we put the types of the *)
341 (* mutual inductive types at the head of the types of the *)
342 (* constructors using Prods *)
343 (*CSC: piccola??? inefficienza *)
344 let len = List.length itl in
352 (fun (name,_,ty,_) i -> Cic.Prod (Cic.Name name, ty, i))
355 let _ = type_of augmented_term in
356 (* let's check also the positivity conditions *)
357 if not (are_all_occurrences_positive uri indparamsno i 0 len te)
359 raise (NotPositiveOccurrences (U.string_of_uri uri))
362 Some _ -> raise (Impossible 2)
363 | None -> r := Some (recursive_args 0 len te)
370 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
372 and cooked_type_of_mutual_inductive_defs uri cookingsno i =
373 let module C = Cic in
374 let module R = CicReduction in
375 let module U = UriManager in
377 match CicEnvironment.is_type_checked uri cookingsno with
378 CicEnvironment.CheckedObj cobj -> cobj
379 | CicEnvironment.UncheckedObj uobj ->
380 log (`Start_type_checking uri) ;
381 cooked_mutual_inductive_defs uri uobj ;
382 CicEnvironment.set_type_checking_info uri ;
383 log (`Type_checking_completed uri) ;
384 (match CicEnvironment.is_type_checked uri cookingsno with
385 CicEnvironment.CheckedObj cobj -> cobj
386 | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
390 C.InductiveDefinition (dl,_,_) ->
391 let (_,_,arity,_) = List.nth dl i in
393 | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
395 and cooked_type_of_mutual_inductive_constr uri cookingsno i j =
396 let module C = Cic in
397 let module R = CicReduction in
398 let module U = UriManager in
400 match CicEnvironment.is_type_checked uri cookingsno with
401 CicEnvironment.CheckedObj cobj -> cobj
402 | CicEnvironment.UncheckedObj uobj ->
403 log (`Start_type_checking uri) ;
404 cooked_mutual_inductive_defs uri uobj ;
405 CicEnvironment.set_type_checking_info uri ;
406 log (`Type_checking_completed uri) ;
407 (match CicEnvironment.is_type_checked uri cookingsno with
408 CicEnvironment.CheckedObj cobj -> cobj
409 | CicEnvironment.UncheckedObj _ -> raise CicEnvironmentError
413 C.InductiveDefinition (dl,_,_) ->
414 let (_,_,_,cl) = List.nth dl i in
415 let (_,ty,_) = List.nth cl (j-1) in
417 | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
419 and recursive_args n nn te =
420 let module C = Cic in
421 match CicReduction.whd te with
427 | C.Cast _ (*CSC ??? *) -> raise (Impossible 3) (* due to type-checking *)
428 | C.Prod (_,so,de) ->
429 (not (does_not_occur n nn so))::(recursive_args (n+1) (nn + 1) de)
431 | C.LetIn _ -> raise (Impossible 4) (* due to type-checking *)
434 | C.Abst _ -> raise (Impossible 5)
439 | C.CoFix _ -> raise (Impossible 6) (* due to type-checking *)
441 and get_new_safes p c rl safes n nn x =
442 let module C = Cic in
443 let module U = UriManager in
444 let module R = CicReduction in
445 match (R.whd c, R.whd p, rl) with
446 (C.Prod (_,_,ta1), C.Lambda (_,_,ta2), b::tl) ->
447 (* we are sure that the two sources are convertible because we *)
448 (* have just checked this. So let's go along ... *)
450 List.map (fun x -> x + 1) safes
453 if b then 1::safes' else safes'
455 get_new_safes ta2 ta1 tl safes'' (n+1) (nn+1) (x+1)
456 | (C.Prod _, (C.MutConstruct _ as e), _)
457 | (C.Prod _, (C.Rel _ as e), _)
458 | (C.MutInd _, e, [])
459 | (C.Appl _, e, []) -> (e,safes,n,nn,x)
461 (* CSC: If the next exception is raised, it just means that *)
462 (* CSC: the proof-assistant allows to use very strange things *)
463 (* CSC: as a branch of a case whose type is a Prod. In *)
464 (* CSC: particular, this means that a new (C.Prod, x,_) case *)
465 (* CSC: must be considered in this match. (e.g. x = MutCase) *)
468 and split_prods n te =
469 let module C = Cic in
470 let module R = CicReduction in
471 match (n, R.whd te) with
473 | (n, C.Prod (_,so,ta)) when n > 0 ->
474 let (l1,l2) = split_prods (n - 1) ta in
476 | (_, _) -> raise (Impossible 8)
478 and eat_lambdas n te =
479 let module C = Cic in
480 let module R = CicReduction in
481 match (n, R.whd te) with
483 | (n, C.Lambda (_,_,ta)) when n > 0 ->
484 let (te, k) = eat_lambdas (n - 1) ta in
486 | (_, _) -> raise (Impossible 9)
488 (*CSC: Tutto quello che segue e' l'intuzione di luca ;-) *)
489 and check_is_really_smaller_arg n nn kl x safes te =
490 (*CSC: forse la whd si puo' fare solo quando serve veramente. *)
491 (*CSC: cfr guarded_by_destructors *)
492 let module C = Cic in
493 let module U = UriManager in
494 match CicReduction.whd te with
495 C.Rel m when List.mem m safes -> true
502 (* | C.Cast (te,ty) ->
503 check_is_really_smaller_arg n nn kl x safes te &&
504 check_is_really_smaller_arg n nn kl x safes ty*)
505 (* | C.Prod (_,so,ta) ->
506 check_is_really_smaller_arg n nn kl x safes so &&
507 check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
508 (List.map (fun x -> x + 1) safes) ta*)
509 | C.Prod _ -> raise (Impossible 10)
510 | C.Lambda (_,so,ta) ->
511 check_is_really_smaller_arg n nn kl x safes so &&
512 check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
513 (List.map (fun x -> x + 1) safes) ta
514 | C.LetIn (_,so,ta) ->
515 check_is_really_smaller_arg n nn kl x safes so &&
516 check_is_really_smaller_arg (n+1) (nn+1) kl (x+1)
517 (List.map (fun x -> x + 1) safes) ta
519 (*CSC: sulla coda ci vogliono dei controlli? secondo noi no, ma *)
520 (*CSC: solo perche' non abbiamo trovato controesempi *)
521 check_is_really_smaller_arg n nn kl x safes he
522 | C.Appl [] -> raise (Impossible 11)
525 | C.MutInd _ -> raise (Impossible 12)
526 | C.MutConstruct _ -> false
527 | C.MutCase (uri,_,i,outtype,term,pl) ->
529 C.Rel m when List.mem m safes || m = x ->
530 let (isinductive,paramsno,cl) =
531 match CicEnvironment.get_obj uri with
532 C.InductiveDefinition (tl,_,paramsno) ->
533 let (_,isinductive,_,cl) = List.nth tl i in
535 List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
537 (isinductive,paramsno,cl')
539 raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
541 if not isinductive then
543 (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
547 (fun (p,(_,c,rl)) i ->
551 let (_,rl'') = split rl' paramsno in
553 | None -> raise (Impossible 13)
555 let (e,safes',n',nn',x') =
556 get_new_safes p c rl' safes n nn x
559 check_is_really_smaller_arg n' nn' kl x' safes' e
560 ) (List.combine pl cl) true
561 | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
562 let (isinductive,paramsno,cl) =
563 match CicEnvironment.get_obj uri with
564 C.InductiveDefinition (tl,_,paramsno) ->
565 let (_,isinductive,_,cl) = List.nth tl i in
567 List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
569 (isinductive,paramsno,cl')
571 raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
573 if not isinductive then
575 (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
578 (*CSC: supponiamo come prima che nessun controllo sia necessario*)
579 (*CSC: sugli argomenti di una applicazione *)
581 (fun (p,(_,c,rl)) i ->
585 let (_,rl'') = split rl' paramsno in
587 | None -> raise (Impossible 14)
589 let (e, safes',n',nn',x') =
590 get_new_safes p c rl' safes n nn x
593 check_is_really_smaller_arg n' nn' kl x' safes' e
594 ) (List.combine pl cl) true
597 (fun p i -> i && check_is_really_smaller_arg n nn kl x safes p)
601 let len = List.length fl in
602 let n_plus_len = n + len
603 and nn_plus_len = nn + len
604 and x_plus_len = x + len
605 and safes' = List.map (fun x -> x + len) safes in
607 (fun (_,_,ty,bo) i ->
609 check_is_really_smaller_arg n_plus_len nn_plus_len kl x_plus_len
613 let len = List.length fl in
614 let n_plus_len = n + len
615 and nn_plus_len = nn + len
616 and x_plus_len = x + len
617 and safes' = List.map (fun x -> x + len) safes in
621 check_is_really_smaller_arg n_plus_len nn_plus_len kl x_plus_len
625 and guarded_by_destructors n nn kl x safes =
626 let module C = Cic in
627 let module U = UriManager in
629 C.Rel m when m > n && m <= nn -> false
636 guarded_by_destructors n nn kl x safes te &&
637 guarded_by_destructors n nn kl x safes ty
638 | C.Prod (_,so,ta) ->
639 guarded_by_destructors n nn kl x safes so &&
640 guarded_by_destructors (n+1) (nn+1) kl (x+1)
641 (List.map (fun x -> x + 1) safes) ta
642 | C.Lambda (_,so,ta) ->
643 guarded_by_destructors n nn kl x safes so &&
644 guarded_by_destructors (n+1) (nn+1) kl (x+1)
645 (List.map (fun x -> x + 1) safes) ta
646 | C.LetIn (_,so,ta) ->
647 guarded_by_destructors n nn kl x safes so &&
648 guarded_by_destructors (n+1) (nn+1) kl (x+1)
649 (List.map (fun x -> x + 1) safes) ta
650 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
651 let k = List.nth kl (m - n - 1) in
652 if not (List.length tl > k) then false
656 i && guarded_by_destructors n nn kl x safes param
658 check_is_really_smaller_arg n nn kl x safes (List.nth tl k)
660 List.fold_right (fun t i -> i && guarded_by_destructors n nn kl x safes t)
665 | C.MutConstruct _ -> true
666 | C.MutCase (uri,_,i,outtype,term,pl) ->
668 C.Rel m when List.mem m safes || m = x ->
669 let (isinductive,paramsno,cl) =
670 match CicEnvironment.get_obj uri with
671 C.InductiveDefinition (tl,_,paramsno) ->
672 let (_,isinductive,_,cl) = List.nth tl i in
674 List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
676 (isinductive,paramsno,cl')
678 raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
680 if not isinductive then
681 guarded_by_destructors n nn kl x safes outtype &&
682 guarded_by_destructors n nn kl x safes term &&
683 (*CSC: manca ??? il controllo sul tipo di term? *)
685 (fun p i -> i && guarded_by_destructors n nn kl x safes p)
688 guarded_by_destructors n nn kl x safes outtype &&
689 (*CSC: manca ??? il controllo sul tipo di term? *)
691 (fun (p,(_,c,rl)) i ->
695 let (_,rl'') = split rl' paramsno in
697 | None -> raise (Impossible 15)
699 let (e,safes',n',nn',x') =
700 get_new_safes p c rl' safes n nn x
703 guarded_by_destructors n' nn' kl x' safes' e
704 ) (List.combine pl cl) true
705 | C.Appl ((C.Rel m)::tl) when List.mem m safes || m = x ->
706 let (isinductive,paramsno,cl) =
707 match CicEnvironment.get_obj uri with
708 C.InductiveDefinition (tl,_,paramsno) ->
709 let (_,isinductive,_,cl) = List.nth tl i in
711 List.map (fun (id,ty,r) -> (id, snd (split_prods paramsno ty), r)) cl
713 (isinductive,paramsno,cl')
715 raise (WrongUriToMutualInductiveDefinitions(U.string_of_uri uri))
717 if not isinductive then
718 guarded_by_destructors n nn kl x safes outtype &&
719 guarded_by_destructors n nn kl x safes term &&
720 (*CSC: manca ??? il controllo sul tipo di term? *)
722 (fun p i -> i && guarded_by_destructors n nn kl x safes p)
725 guarded_by_destructors n nn kl x safes outtype &&
726 (*CSC: manca ??? il controllo sul tipo di term? *)
728 (fun t i -> i && guarded_by_destructors n nn kl x safes t)
731 (fun (p,(_,c,rl)) i ->
735 let (_,rl'') = split rl' paramsno in
737 | None -> raise (Impossible 16)
739 let (e, safes',n',nn',x') =
740 get_new_safes p c rl' safes n nn x
743 guarded_by_destructors n' nn' kl x' safes' e
744 ) (List.combine pl cl) true
746 guarded_by_destructors n nn kl x safes outtype &&
747 guarded_by_destructors n nn kl x safes term &&
748 (*CSC: manca ??? il controllo sul tipo di term? *)
750 (fun p i -> i && guarded_by_destructors n nn kl x safes p)
754 let len = List.length fl in
755 let n_plus_len = n + len
756 and nn_plus_len = nn + len
757 and x_plus_len = x + len
758 and safes' = List.map (fun x -> x + len) safes in
760 (fun (_,_,ty,bo) i ->
761 i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
763 guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
767 let len = List.length fl in
768 let n_plus_len = n + len
769 and nn_plus_len = nn + len
770 and x_plus_len = x + len
771 and safes' = List.map (fun x -> x + len) safes in
774 i && guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len
776 guarded_by_destructors n_plus_len nn_plus_len kl x_plus_len safes'
780 (*CSC h = 0 significa non ancora protetto *)
781 and guarded_by_constructors n nn h =
782 let module C = Cic in
784 C.Rel m when m > n && m <= nn -> h = 1
789 | C.Implicit -> true (*CSC: ma alcuni sono impossibili!!!! vedi Prod *)
791 guarded_by_constructors n nn h te &&
792 guarded_by_constructors n nn h ty
793 | C.Prod (_,so,de) ->
794 raise (Impossible 17) (* the term has just been type-checked *)
795 | C.Lambda (_,so,de) ->
796 does_not_occur n nn so &&
797 guarded_by_constructors (n + 1) (nn + 1) h de
798 | C.LetIn (_,so,de) ->
799 does_not_occur n nn so &&
800 guarded_by_constructors (n + 1) (nn + 1) h de
801 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
803 List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
804 | C.Appl ((C.MutConstruct (uri,cookingsno,i,j))::tl) ->
805 let (is_coinductive, rl) =
806 match CicEnvironment.get_cooked_obj uri cookingsno with
807 C.InductiveDefinition (itl,_,_) ->
808 let (_,is_inductive,_,cl) = List.nth itl i in
809 let (_,cons,rrec_args) = List.nth cl (j - 1) in
810 (match !rrec_args with
811 None -> raise (Impossible 18)
812 | Some rec_args -> (not is_inductive, rec_args)
815 raise (WrongUriToMutualInductiveDefinitions
816 (UriManager.string_of_uri uri))
823 guarded_by_constructors n nn 1 x
825 does_not_occur n nn x
826 ) (List.combine tl rl) true
828 List.fold_right (fun x i -> i && does_not_occur n nn x) l true
832 | C.MutConstruct _ -> true (*CSC: ma alcuni sono impossibili!!!! vedi Prod *)
833 | C.MutCase (_,_,_,out,te,pl) ->
834 let rec returns_a_coinductive =
836 (*CSC: per le regole di tipaggio, la chiamata ricorsiva verra' *)
837 (*CSC: effettata solo una volta, per mangiarsi l'astrazione *)
839 C.Lambda (_,_,de) -> returns_a_coinductive de
840 | C.MutInd (uri,_,i) ->
841 (*CSC: definire una funzioncina per questo codice sempre replicato *)
842 (match CicEnvironment.get_obj uri with
843 C.InductiveDefinition (itl,_,_) ->
844 let (_,is_inductive,_,_) = List.nth itl i in
847 raise (WrongUriToMutualInductiveDefinitions
848 (UriManager.string_of_uri uri))
850 (*CSC: bug nella prossima riga (manca la whd) *)
851 | C.Appl ((C.MutInd (uri,_,i))::_) ->
852 (match CicEnvironment.get_obj uri with
853 C.InductiveDefinition (itl,_,_) ->
854 let (_,is_inductive,_,_) = List.nth itl i in
857 raise (WrongUriToMutualInductiveDefinitions
858 (UriManager.string_of_uri uri))
862 does_not_occur n nn out &&
863 does_not_occur n nn te &&
864 if returns_a_coinductive out then
866 (fun x i -> i && guarded_by_constructors n nn h x) pl true
868 List.fold_right (fun x i -> i && does_not_occur n nn x) pl true
870 let len = List.length fl in
871 let n_plus_len = n + len
872 and nn_plus_len = nn + len in
874 (fun (_,_,ty,bo) i ->
875 i && does_not_occur n_plus_len nn_plus_len ty &&
876 does_not_occur n_plus_len nn_plus_len bo
879 let len = List.length fl in
880 let n_plus_len = n + len
881 and nn_plus_len = nn + len in
884 i && does_not_occur n_plus_len nn_plus_len ty &&
885 does_not_occur n_plus_len nn_plus_len bo
888 and check_allowed_sort_elimination uri i need_dummy ind arity1 arity2 =
889 let module C = Cic in
890 let module U = UriManager in
891 match (CicReduction.whd arity1, CicReduction.whd arity2) with
892 (C.Prod (_,so1,de1), C.Prod (_,so2,de2))
893 when CicReduction.are_convertible so1 so2 ->
894 check_allowed_sort_elimination uri i need_dummy
895 (C.Appl [CicSubstitution.lift 1 ind ; C.Rel 1]) de1 de2
896 | (C.Sort C.Prop, C.Sort C.Prop) when need_dummy -> true
897 | (C.Sort C.Prop, C.Sort C.Set) when need_dummy ->
898 (match CicEnvironment.get_obj uri with
899 C.InductiveDefinition (itl,_,_) ->
900 let (_,_,_,cl) = List.nth itl i in
901 (* is a singleton definition? *)
904 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
906 | (C.Sort C.Set, C.Sort C.Prop) when need_dummy -> true
907 | (C.Sort C.Set, C.Sort C.Set) when need_dummy -> true
908 | (C.Sort C.Set, C.Sort C.Type) when need_dummy ->
909 (match CicEnvironment.get_obj uri with
910 C.InductiveDefinition (itl,_,paramsno) ->
911 let (_,_,_,cl) = List.nth itl i in
912 List.fold_right (fun (_,x,_) i -> i && is_small paramsno x) cl true
914 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
916 | (C.Sort C.Type, C.Sort _) when need_dummy -> true
917 | (C.Sort C.Prop, C.Prod (_,so,ta)) when not need_dummy ->
918 let res = CicReduction.are_convertible so ind
921 (match CicReduction.whd ta with
922 C.Sort C.Prop -> true
924 (match CicEnvironment.get_obj uri with
925 C.InductiveDefinition (itl,_,_) ->
926 let (_,_,_,cl) = List.nth itl i in
927 (* is a singleton definition? *)
930 raise (WrongUriToMutualInductiveDefinitions
931 (U.string_of_uri uri))
935 | (C.Sort C.Set, C.Prod (_,so,ta)) when not need_dummy ->
936 let res = CicReduction.are_convertible so ind
939 (match CicReduction.whd ta with
941 | C.Sort C.Set -> true
943 (match CicEnvironment.get_obj uri with
944 C.InductiveDefinition (itl,_,paramsno) ->
945 let (_,_,_,cl) = List.nth itl i in
947 (fun (_,x,_) i -> i && is_small paramsno x) cl true
949 raise (WrongUriToMutualInductiveDefinitions
950 (U.string_of_uri uri))
952 | _ -> raise (Impossible 19)
954 | (C.Sort C.Type, C.Prod (_,so,_)) when not need_dummy ->
955 CicReduction.are_convertible so ind
958 and type_of_branch argsno need_dummy outtype term constype =
959 let module C = Cic in
960 let module R = CicReduction in
961 match R.whd constype with
966 C.Appl [outtype ; term]
967 | C.Appl (C.MutInd (_,_,_)::tl) ->
968 let (_,arguments) = split tl argsno
970 if need_dummy && arguments = [] then
973 C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
974 | C.Prod (name,so,de) ->
975 C.Prod (C.Name "pippo",so,type_of_branch argsno need_dummy
976 (CicSubstitution.lift 1 outtype)
977 (C.Appl [CicSubstitution.lift 1 term ; C.Rel 1]) de)
978 | _ -> raise (Impossible 20)
981 (* type_of_aux' is just another name (with a different scope) for type_of_aux *)
982 and type_of_aux' env t =
983 let rec type_of_aux env =
984 let module C = Cic in
985 let module R = CicReduction in
986 let module S = CicSubstitution in
987 let module U = UriManager in
994 _ -> raise (NotWellTyped "Not a close term")
999 let ty = type_of_variable uri in
1002 | C.Meta n -> raise NotImplemented
1003 | C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
1004 | C.Implicit -> raise (Impossible 21)
1006 let _ = type_of ty in
1007 if R.are_convertible (type_of_aux env te) ty then ty
1008 else raise (NotWellTyped "Cast")
1010 let sort1 = type_of_aux env s
1011 and sort2 = type_of_aux (s::env) t in
1012 sort_of_prod (sort1,sort2)
1013 | C.Lambda (n,s,t) ->
1014 let sort1 = type_of_aux env s
1015 and type2 = type_of_aux (s::env) t in
1016 let sort2 = type_of_aux (s::env) type2 in
1017 (* only to check if the product is well-typed *)
1018 let _ = sort_of_prod (sort1,sort2) in
1020 | C.LetIn (n,s,t) ->
1021 let t' = CicSubstitution.subst s t in
1023 | C.Appl (he::tl) when List.length tl > 0 ->
1024 let hetype = type_of_aux env he
1025 and tlbody_and_type = List.map (fun x -> (x, type_of_aux env x)) tl in
1026 eat_prods hetype tlbody_and_type
1027 | C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
1028 | C.Const (uri,cookingsno) ->
1030 let cty = cooked_type_of_constant uri cookingsno in
1033 | C.Abst _ -> raise (Impossible 22)
1034 | C.MutInd (uri,cookingsno,i) ->
1036 let cty = cooked_type_of_mutual_inductive_defs uri cookingsno i in
1039 | C.MutConstruct (uri,cookingsno,i,j) ->
1040 let cty = cooked_type_of_mutual_inductive_constr uri cookingsno i j
1043 | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
1044 let outsort = type_of_aux env outtype in
1045 let (need_dummy, k) =
1046 let rec guess_args t =
1047 match CicReduction.whd t with
1048 C.Sort _ -> (true, 0)
1049 | C.Prod (_, s, t) ->
1050 let (b, n) = guess_args t in
1052 (* last prod before sort *)
1053 match CicReduction.whd s with
1054 (*CSC vedi nota delirante su cookingsno in cicReduction.ml *)
1055 C.MutInd (uri',_,i') when U.eq uri' uri && i' = i -> (false, 1)
1056 | C.Appl ((C.MutInd (uri',_,i')) :: _)
1057 when U.eq uri' uri && i' = i -> (false, 1)
1061 | _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
1063 (*CSC whd non serve dopo type_of_aux ? *)
1064 let (b, k) = guess_args outsort in
1065 if not b then (b, k - 1) else (b, k)
1067 let (parameters, arguments) =
1068 match R.whd (type_of_aux env term) with
1069 (*CSC manca il caso dei CAST *)
1070 C.MutInd (uri',_,i') ->
1071 (*CSC vedi nota delirante sui cookingsno in cicReduction.ml*)
1072 if U.eq uri uri' && i = i' then ([],[])
1073 else raise (NotWellTyped ("MutCase: the term is of type " ^
1074 (U.string_of_uri uri') ^ "," ^ string_of_int i' ^
1075 " instead of type " ^ (U.string_of_uri uri') ^ "," ^
1077 | C.Appl (C.MutInd (uri',_,i') :: tl) ->
1078 if U.eq uri uri' && i = i' then split tl (List.length tl - k)
1079 else raise (NotWellTyped ("MutCase: the term is of type " ^
1080 (U.string_of_uri uri') ^ "," ^ string_of_int i' ^
1081 " instead of type " ^ (U.string_of_uri uri) ^ "," ^
1083 | _ -> raise (NotWellTyped "MutCase: the term is not an inductive one")
1085 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
1086 let sort_of_ind_type =
1087 if parameters = [] then
1088 C.MutInd (uri,cookingsno,i)
1090 C.Appl ((C.MutInd (uri,cookingsno,i))::parameters)
1092 if not (check_allowed_sort_elimination uri i need_dummy
1093 sort_of_ind_type (type_of_aux env sort_of_ind_type) outsort)
1095 raise (NotWellTyped "MutCase: not allowed sort elimination") ;
1097 (* let's check if the type of branches are right *)
1099 match CicEnvironment.get_cooked_obj uri cookingsno with
1100 C.InductiveDefinition (tl,_,parsno) ->
1101 let (_,_,_,cl) = List.nth tl i in (cl,parsno)
1103 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
1105 let (_,branches_ok) =
1107 (fun (j,b) (p,(_,c,_)) ->
1109 if parameters = [] then
1110 (C.MutConstruct (uri,cookingsno,i,j))
1112 (C.Appl (C.MutConstruct (uri,cookingsno,i,j)::parameters))
1115 R.are_convertible (type_of_aux env p)
1116 (type_of_branch parsno need_dummy outtype cons
1117 (type_of_aux env cons))
1119 ) (1,true) (List.combine pl cl)
1121 if not branches_ok then
1122 raise (NotWellTyped "MutCase: wrong type of a branch") ;
1124 if not need_dummy then
1125 C.Appl ((outtype::arguments)@[term])
1126 else if arguments = [] then
1129 C.Appl (outtype::arguments)
1131 let types_times_kl =
1133 (List.map (fun (_,k,ty,_) -> let _ = type_of_aux env ty in (ty,k)) fl)
1135 let (types,kl) = List.split types_times_kl in
1136 let len = List.length types in
1138 (fun (name,x,ty,bo) ->
1139 if (R.are_convertible (type_of_aux (types @ env) bo)
1140 (CicSubstitution.lift len ty))
1143 let (m, eaten) = eat_lambdas (x + 1) bo in
1144 (*let's control the guarded by destructors conditions D{f,k,x,M}*)
1145 if not (guarded_by_destructors eaten (len + eaten) kl 1 [] m) then
1146 raise (NotWellTyped "Fix: not guarded by destructors")
1149 raise (NotWellTyped "Fix: ill-typed bodies")
1152 (*CSC: controlli mancanti solo su D{f,k,x,M} *)
1153 let (_,_,ty,_) = List.nth fl i in
1157 List.rev (List.map (fun (_,ty,_) -> let _ = type_of_aux env ty in ty) fl)
1159 let len = List.length types in
1162 if (R.are_convertible (type_of_aux (types @ env) bo)
1163 (CicSubstitution.lift len ty))
1166 (* let's control the guarded by constructors conditions C{f,M} *)
1167 if not (guarded_by_constructors 0 len 0 bo) then
1168 raise (NotWellTyped "CoFix: not guarded by constructors")
1171 raise (NotWellTyped "CoFix: ill-typed bodies")
1174 let (_,ty,_) = List.nth fl i in
1177 and sort_of_prod (t1, t2) =
1178 let module C = Cic in
1179 let t1' = CicReduction.whd t1 in
1180 let t2' = CicReduction.whd t2 in
1181 match (t1', t2') with
1182 (C.Sort s1, C.Sort s2)
1183 when (s2 = C.Prop or s2 = C.Set) -> (* different from Coq manual!!! *)
1185 | (C.Sort s1, C.Sort s2) -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
1189 ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))
1191 and eat_prods hetype =
1192 (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
1196 | (hete, hety)::tl ->
1197 (match (CicReduction.whd hetype) with
1199 if CicReduction.are_convertible s hety then
1200 (CicReduction.fdebug := -1 ;
1201 eat_prods (CicSubstitution.subst hete t) tl
1205 CicReduction.fdebug := 0 ;
1206 ignore (CicReduction.are_convertible s hety) ;
1209 raise (NotWellTyped "Appl: wrong parameter-type")
1211 | _ -> raise (NotWellTyped "Appl: wrong Prod-type")
1216 (* is a small constructor? *)
1217 (*CSC: ottimizzare calcolando staticamente *)
1218 and is_small paramsno c =
1219 let rec is_small_aux env c =
1220 let module C = Cic in
1221 match CicReduction.whd c with
1223 let s = type_of_aux' env so in
1224 (s = C.Sort C.Prop || s = C.Sort C.Set) &&
1225 is_small_aux (so::env) de
1226 | _ -> true (*CSC: we trust the type-checker *)
1228 let (sx,dx) = split_prods paramsno c in
1229 is_small_aux (List.rev sx) dx
1236 let module C = Cic in
1237 let module R = CicReduction in
1238 let module U = UriManager in
1239 match CicEnvironment.is_type_checked uri 0 with
1240 CicEnvironment.CheckedObj _ -> ()
1241 | CicEnvironment.UncheckedObj uobj ->
1242 (* let's typecheck the uncooked object *)
1243 log (`Start_type_checking uri) ;
1245 C.Definition (_,te,ty,_) ->
1246 let _ = type_of ty in
1247 if not (R.are_convertible (type_of te ) ty) then
1248 raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
1249 | C.Axiom (_,ty,_) ->
1250 (* only to check that ty is well-typed *)
1251 let _ = type_of ty in ()
1252 | C.CurrentProof (_,_,te,ty) ->
1254 let _ = type_of ty in
1255 debug (type_of te) [] ;
1256 if not (R.are_convertible (type_of te) ty) then
1257 raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
1258 | C.Variable (_,bo,ty) ->
1259 (* only to check that ty is well-typed *)
1260 let _ = type_of ty in
1264 if not (R.are_convertible (type_of bo) ty) then
1265 raise (NotWellTyped ("Variable" ^ (U.string_of_uri uri)))
1267 | C.InductiveDefinition _ ->
1268 cooked_mutual_inductive_defs uri uobj
1270 CicEnvironment.set_type_checking_info uri ;
1271 log (`Type_checking_completed uri)