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 te =
782 let module C = Cic in
783 (*CSC: There is a lot of code replication between the cases X and *)
784 (*CSC: (C.Appl X tl). Maybe it will be better to define a function *)
785 (*CSC: that maps X into (C.Appl X []) when X is not already a C.Appl *)
786 match CicReduction.whd te with
787 C.Rel m when m > n && m <= nn -> h = 1
796 raise (Impossible 17) (* the term has just been type-checked *)
797 | C.Lambda (_,so,de) ->
798 does_not_occur n nn so &&
799 guarded_by_constructors (n + 1) (nn + 1) h de
800 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
802 List.fold_right (fun x i -> i && does_not_occur n nn x) tl true
803 | C.Appl ((C.MutConstruct (uri,cookingsno,i,j))::tl) ->
804 (* Invariant: we are sure that the constructor is a constructor *)
805 (* of the output inductive type of the whole co-fixpoint. *)
807 match CicEnvironment.get_cooked_obj uri cookingsno with
808 C.InductiveDefinition (itl,_,_) ->
809 let (_,is_inductive,_,cl) = List.nth itl i in
810 let (_,cons,rrec_args) = List.nth cl (j - 1) in
811 (match !rrec_args with
812 None -> raise (Impossible 18)
813 | Some rec_args -> assert (not is_inductive) ; rec_args
816 raise (WrongUriToMutualInductiveDefinitions
817 (UriManager.string_of_uri uri))
825 guarded_by_constructors n nn 1 x
829 prerr_endline ("BECCATO: " ^ CicPp.ppterm x) ; flush stderr ; assert false
834 does_not_occur n nn x
835 ) (List.combine tl rl) true
836 | C.Appl ((C.CoFix (_,fl))::tl) ->
837 List.fold_left (fun i x -> i && does_not_occur n nn x) true tl &&
838 let len = List.length fl in
839 let n_plus_len = n + len
840 and nn_plus_len = nn + len in
843 i && does_not_occur n_plus_len nn_plus_len ty &&
844 guarded_by_constructors n_plus_len nn_plus_len h bo
846 | C.Appl ((C.MutCase (_,_,_,out,te,pl))::tl) ->
847 List.fold_left (fun i x -> i && does_not_occur n nn x) true tl &&
848 does_not_occur n nn out &&
849 does_not_occur n nn te &&
851 (fun x i -> i && guarded_by_constructors n nn h x) pl true
853 List.fold_right (fun x i -> i && does_not_occur n nn x) l true
856 | C.MutInd _ -> assert false
857 | C.MutConstruct _ -> true
858 | C.MutCase (_,_,_,out,te,pl) ->
859 does_not_occur n nn out &&
860 does_not_occur n nn te &&
862 (fun x i -> i && guarded_by_constructors n nn h x) pl true
864 let len = List.length fl in
865 let n_plus_len = n + len
866 and nn_plus_len = nn + len in
868 (fun (_,_,ty,bo) i ->
869 i && does_not_occur n_plus_len nn_plus_len ty &&
870 does_not_occur n_plus_len nn_plus_len bo
873 let len = List.length fl in
874 let n_plus_len = n + len
875 and nn_plus_len = nn + len in
878 i && does_not_occur n_plus_len nn_plus_len ty &&
879 guarded_by_constructors n_plus_len nn_plus_len h bo
882 and check_allowed_sort_elimination uri i need_dummy ind arity1 arity2 =
883 let module C = Cic in
884 let module U = UriManager in
885 match (CicReduction.whd arity1, CicReduction.whd arity2) with
886 (C.Prod (_,so1,de1), C.Prod (_,so2,de2))
887 when CicReduction.are_convertible so1 so2 ->
888 check_allowed_sort_elimination uri i need_dummy
889 (C.Appl [CicSubstitution.lift 1 ind ; C.Rel 1]) de1 de2
890 | (C.Sort C.Prop, C.Sort C.Prop) when need_dummy -> true
891 | (C.Sort C.Prop, C.Sort C.Set) when need_dummy ->
892 (match CicEnvironment.get_obj uri with
893 C.InductiveDefinition (itl,_,_) ->
894 let (_,_,_,cl) = List.nth itl i in
895 (* is a singleton definition? *)
898 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
900 | (C.Sort C.Set, C.Sort C.Prop) when need_dummy -> true
901 | (C.Sort C.Set, C.Sort C.Set) when need_dummy -> true
902 | (C.Sort C.Set, C.Sort C.Type) when need_dummy ->
903 (match CicEnvironment.get_obj uri with
904 C.InductiveDefinition (itl,_,paramsno) ->
905 let (_,_,_,cl) = List.nth itl i in
906 List.fold_right (fun (_,x,_) i -> i && is_small paramsno x) cl true
908 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
910 | (C.Sort C.Type, C.Sort _) when need_dummy -> true
911 | (C.Sort C.Prop, C.Prod (_,so,ta)) when not need_dummy ->
912 let res = CicReduction.are_convertible so ind
915 (match CicReduction.whd ta with
916 C.Sort C.Prop -> true
918 (match CicEnvironment.get_obj uri with
919 C.InductiveDefinition (itl,_,_) ->
920 let (_,_,_,cl) = List.nth itl i in
921 (* is a singleton definition? *)
924 raise (WrongUriToMutualInductiveDefinitions
925 (U.string_of_uri uri))
929 | (C.Sort C.Set, C.Prod (_,so,ta)) when not need_dummy ->
930 let res = CicReduction.are_convertible so ind
933 (match CicReduction.whd ta with
935 | C.Sort C.Set -> true
937 (match CicEnvironment.get_obj uri with
938 C.InductiveDefinition (itl,_,paramsno) ->
939 let (_,_,_,cl) = List.nth itl i in
941 (fun (_,x,_) i -> i && is_small paramsno x) cl true
943 raise (WrongUriToMutualInductiveDefinitions
944 (U.string_of_uri uri))
946 | _ -> raise (Impossible 19)
948 | (C.Sort C.Type, C.Prod (_,so,_)) when not need_dummy ->
949 CicReduction.are_convertible so ind
952 and type_of_branch argsno need_dummy outtype term constype =
953 let module C = Cic in
954 let module R = CicReduction in
955 match R.whd constype with
960 C.Appl [outtype ; term]
961 | C.Appl (C.MutInd (_,_,_)::tl) ->
962 let (_,arguments) = split tl argsno
964 if need_dummy && arguments = [] then
967 C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
968 | C.Prod (name,so,de) ->
969 C.Prod (C.Name "pippo",so,type_of_branch argsno need_dummy
970 (CicSubstitution.lift 1 outtype)
971 (C.Appl [CicSubstitution.lift 1 term ; C.Rel 1]) de)
972 | _ -> raise (Impossible 20)
975 (* type_of_aux' is just another name (with a different scope) for type_of_aux *)
976 and type_of_aux' env t =
977 let rec type_of_aux env =
978 let module C = Cic in
979 let module R = CicReduction in
980 let module S = CicSubstitution in
981 let module U = UriManager in
988 _ -> raise (NotWellTyped "Not a close term")
993 let ty = type_of_variable uri in
996 | C.Meta n -> raise NotImplemented
997 | C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
998 | C.Implicit -> raise (Impossible 21)
1000 let _ = type_of ty in
1001 if R.are_convertible (type_of_aux env te) ty then ty
1002 else raise (NotWellTyped "Cast")
1004 let sort1 = type_of_aux env s
1005 and sort2 = type_of_aux (s::env) t in
1006 sort_of_prod (sort1,sort2)
1007 | C.Lambda (n,s,t) ->
1008 let sort1 = type_of_aux env s
1009 and type2 = type_of_aux (s::env) t in
1010 let sort2 = type_of_aux (s::env) type2 in
1011 (* only to check if the product is well-typed *)
1012 let _ = sort_of_prod (sort1,sort2) in
1014 | C.LetIn (n,s,t) ->
1015 let t' = CicSubstitution.subst s t in
1017 | C.Appl (he::tl) when List.length tl > 0 ->
1018 let hetype = type_of_aux env he
1019 and tlbody_and_type = List.map (fun x -> (x, type_of_aux env x)) tl in
1020 eat_prods hetype tlbody_and_type
1021 | C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
1022 | C.Const (uri,cookingsno) ->
1024 let cty = cooked_type_of_constant uri cookingsno in
1027 | C.Abst _ -> raise (Impossible 22)
1028 | C.MutInd (uri,cookingsno,i) ->
1030 let cty = cooked_type_of_mutual_inductive_defs uri cookingsno i in
1033 | C.MutConstruct (uri,cookingsno,i,j) ->
1034 let cty = cooked_type_of_mutual_inductive_constr uri cookingsno i j
1037 | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
1038 let outsort = type_of_aux env outtype in
1039 let (need_dummy, k) =
1040 let rec guess_args t =
1041 match CicReduction.whd t with
1042 C.Sort _ -> (true, 0)
1043 | C.Prod (_, s, t) ->
1044 let (b, n) = guess_args t in
1046 (* last prod before sort *)
1047 match CicReduction.whd s with
1048 (*CSC vedi nota delirante su cookingsno in cicReduction.ml *)
1049 C.MutInd (uri',_,i') when U.eq uri' uri && i' = i -> (false, 1)
1050 | C.Appl ((C.MutInd (uri',_,i')) :: _)
1051 when U.eq uri' uri && i' = i -> (false, 1)
1055 | _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
1057 (*CSC whd non serve dopo type_of_aux ? *)
1058 let (b, k) = guess_args outsort in
1059 if not b then (b, k - 1) else (b, k)
1061 let (parameters, arguments) =
1062 match R.whd (type_of_aux env term) with
1063 (*CSC manca il caso dei CAST *)
1064 C.MutInd (uri',_,i') ->
1065 (*CSC vedi nota delirante sui cookingsno in cicReduction.ml*)
1066 if U.eq uri uri' && i = i' then ([],[])
1067 else raise (NotWellTyped ("MutCase: the term is of type " ^
1068 (U.string_of_uri uri') ^ "," ^ string_of_int i' ^
1069 " instead of type " ^ (U.string_of_uri uri') ^ "," ^
1071 | C.Appl (C.MutInd (uri',_,i') :: tl) ->
1072 if U.eq uri uri' && i = i' then split tl (List.length tl - k)
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 | _ -> raise (NotWellTyped "MutCase: the term is not an inductive one")
1079 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
1080 let sort_of_ind_type =
1081 if parameters = [] then
1082 C.MutInd (uri,cookingsno,i)
1084 C.Appl ((C.MutInd (uri,cookingsno,i))::parameters)
1086 if not (check_allowed_sort_elimination uri i need_dummy
1087 sort_of_ind_type (type_of_aux env sort_of_ind_type) outsort)
1089 raise (NotWellTyped "MutCase: not allowed sort elimination") ;
1091 (* let's check if the type of branches are right *)
1093 match CicEnvironment.get_cooked_obj uri cookingsno with
1094 C.InductiveDefinition (tl,_,parsno) ->
1095 let (_,_,_,cl) = List.nth tl i in (cl,parsno)
1097 raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
1099 let (_,branches_ok) =
1101 (fun (j,b) (p,(_,c,_)) ->
1103 if parameters = [] then
1104 (C.MutConstruct (uri,cookingsno,i,j))
1106 (C.Appl (C.MutConstruct (uri,cookingsno,i,j)::parameters))
1109 R.are_convertible (type_of_aux env p)
1110 (type_of_branch parsno need_dummy outtype cons
1111 (type_of_aux env cons))
1113 ) (1,true) (List.combine pl cl)
1115 if not branches_ok then
1116 raise (NotWellTyped "MutCase: wrong type of a branch") ;
1118 if not need_dummy then
1119 C.Appl ((outtype::arguments)@[term])
1120 else if arguments = [] then
1123 C.Appl (outtype::arguments)
1125 let types_times_kl =
1127 (List.map (fun (_,k,ty,_) -> let _ = type_of_aux env ty in (ty,k)) fl)
1129 let (types,kl) = List.split types_times_kl in
1130 let len = List.length types in
1132 (fun (name,x,ty,bo) ->
1133 if (R.are_convertible (type_of_aux (types @ env) bo)
1134 (CicSubstitution.lift len ty))
1137 let (m, eaten) = eat_lambdas (x + 1) bo in
1138 (*let's control the guarded by destructors conditions D{f,k,x,M}*)
1139 if not (guarded_by_destructors eaten (len + eaten) kl 1 [] m) then
1140 raise (NotWellTyped "Fix: not guarded by destructors")
1143 raise (NotWellTyped "Fix: ill-typed bodies")
1146 (*CSC: controlli mancanti solo su D{f,k,x,M} *)
1147 let (_,_,ty,_) = List.nth fl i in
1151 List.rev (List.map (fun (_,ty,_) -> let _ = type_of_aux env ty in ty) fl)
1153 let len = List.length types in
1156 if (R.are_convertible (type_of_aux (types @ env) bo)
1157 (CicSubstitution.lift len ty))
1160 (* let's control the guarded by constructors conditions C{f,M} *)
1161 if not (guarded_by_constructors 0 len 0 bo) then
1162 raise (NotWellTyped "CoFix: not guarded by constructors") ;
1163 if not (returns_a_coinductive ty) then
1164 raise (NotWellTyped "CoFix: does not return a coinductive type")
1167 raise (NotWellTyped "CoFix: ill-typed bodies")
1170 let (_,ty,_) = List.nth fl i in
1173 and sort_of_prod (t1, t2) =
1174 let module C = Cic in
1175 let t1' = CicReduction.whd t1 in
1176 let t2' = CicReduction.whd t2 in
1177 match (t1', t2') with
1178 (C.Sort s1, C.Sort s2)
1179 when (s2 = C.Prop or s2 = C.Set) -> (* different from Coq manual!!! *)
1181 | (C.Sort s1, C.Sort s2) -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
1185 ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))
1187 and eat_prods hetype =
1188 (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
1192 | (hete, hety)::tl ->
1193 (match (CicReduction.whd hetype) with
1195 if CicReduction.are_convertible s hety then
1196 (CicReduction.fdebug := -1 ;
1197 eat_prods (CicSubstitution.subst hete t) tl
1201 CicReduction.fdebug := 0 ;
1202 ignore (CicReduction.are_convertible s hety) ;
1205 raise (NotWellTyped "Appl: wrong parameter-type")
1207 | _ -> raise (NotWellTyped "Appl: wrong Prod-type")
1210 and returns_a_coinductive ty =
1211 let module C = Cic in
1212 match CicReduction.whd ty with
1213 C.MutInd (uri,_,i) ->
1214 (*CSC: definire una funzioncina per questo codice sempre replicato *)
1215 (match CicEnvironment.get_obj uri with
1216 C.InductiveDefinition (itl,_,_) ->
1217 let (_,is_inductive,_,_) = List.nth itl i in
1220 raise (WrongUriToMutualInductiveDefinitions
1221 (UriManager.string_of_uri uri))
1223 | C.Appl ((C.MutInd (uri,_,i))::_) ->
1224 (match CicEnvironment.get_obj uri with
1225 C.InductiveDefinition (itl,_,_) ->
1226 let (_,is_inductive,_,_) = List.nth itl i in
1229 raise (WrongUriToMutualInductiveDefinitions
1230 (UriManager.string_of_uri uri))
1232 | C.Prod (_,_,de) -> returns_a_coinductive de
1238 (* is a small constructor? *)
1239 (*CSC: ottimizzare calcolando staticamente *)
1240 and is_small paramsno c =
1241 let rec is_small_aux env c =
1242 let module C = Cic in
1243 match CicReduction.whd c with
1245 let s = type_of_aux' env so in
1246 (s = C.Sort C.Prop || s = C.Sort C.Set) &&
1247 is_small_aux (so::env) de
1248 | _ -> true (*CSC: we trust the type-checker *)
1250 let (sx,dx) = split_prods paramsno c in
1251 is_small_aux (List.rev sx) dx
1258 let module C = Cic in
1259 let module R = CicReduction in
1260 let module U = UriManager in
1261 match CicEnvironment.is_type_checked uri 0 with
1262 CicEnvironment.CheckedObj _ -> ()
1263 | CicEnvironment.UncheckedObj uobj ->
1264 (* let's typecheck the uncooked object *)
1265 log (`Start_type_checking uri) ;
1267 C.Definition (_,te,ty,_) ->
1268 let _ = type_of ty in
1269 if not (R.are_convertible (type_of te ) ty) then
1270 raise (NotWellTyped ("Constant " ^ (U.string_of_uri uri)))
1271 | C.Axiom (_,ty,_) ->
1272 (* only to check that ty is well-typed *)
1273 let _ = type_of ty in ()
1274 | C.CurrentProof (_,_,te,ty) ->
1276 let _ = type_of ty in
1277 debug (type_of te) [] ;
1278 if not (R.are_convertible (type_of te) ty) then
1279 raise (NotWellTyped ("CurrentProof" ^ (U.string_of_uri uri)))
1280 | C.Variable (_,bo,ty) ->
1281 (* only to check that ty is well-typed *)
1282 let _ = type_of ty in
1286 if not (R.are_convertible (type_of bo) ty) then
1287 raise (NotWellTyped ("Variable" ^ (U.string_of_uri uri)))
1289 | C.InductiveDefinition _ ->
1290 cooked_mutual_inductive_defs uri uobj
1292 CicEnvironment.set_type_checking_info uri ;
1293 log (`Type_checking_completed uri)