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_______________________________________________________________ *)
15 module R = NCicReduction
16 module Ref = NReference
17 module S = NCicSubstitution
19 module E = NCicEnvironment
22 exception TypeCheckerFailure of string Lazy.t
23 exception AssertFailure of string Lazy.t
26 | TypeCheckerFailure s as e -> prerr_endline (Lazy.force s); raise e
31 | Evil of int (* rno *)
32 | UnfFix of bool list (* fixed arguments *)
36 let is_dangerous i l =
37 List.exists (function (j,Evil _) when j=i -> true | _ -> false) l
41 List.exists (function (j,UnfFix _) when j=i -> true | _ -> false) l
45 List.exists (function (j,Safe) when j=i -> true | _ -> false) l
49 try match List.assoc i l with Evil rno -> rno | _ -> assert false
50 with Not_found -> assert false
53 let get_fixed_args i l =
54 try match List.assoc i l with UnfFix fa -> fa | _ -> assert false
55 with Not_found -> assert false
58 let shift_k e (c,rf,x) = e::c,List.map (fun (k,v) -> k+1,v) rf,x+1;;
61 let string_of_recfuns ~subst ~metasenv ~context l =
62 let pp = PP.ppterm ~subst ~metasenv ~context in
63 let safe, rest = List.partition (function (_,Safe) -> true | _ -> false) l in
64 let dang,unf = List.partition (function (_,UnfFix _)-> false | _->true)rest in
65 "\n\tsafes: "^String.concat "," (List.map (fun (i,_)->pp (C.Rel i)) safe) ^
66 "\n\tfix : "^String.concat ","
68 (function (i,UnfFix l)-> pp(C.Rel i)^"/"^String.concat "," (List.map
70 | _ ->assert false) unf) ^
71 "\n\trec : "^String.concat ","
73 (function (i,Evil rno)->pp(C.Rel i)^"/"^string_of_int rno
74 | _ -> assert false) dang)
78 let fixed_args bos j n nn =
79 let rec aux k acc = function
80 | C.Appl (C.Rel i::args) when i-k > n && i-k <= nn ->
81 let rec combine l1 l2 =
84 | he1::tl1, he2::tl2 -> (he1,he2)::combine tl1 tl2
85 | he::tl, [] -> (false,C.Rel ~-1)::combine tl [] (* dummy term *)
86 | [],_::_ -> assert false
88 let lefts, _ = HExtlib.split_nth (min j (List.length args)) args in
89 List.map (fun ((b,x),i) -> b && x = C.Rel (k-i))
90 (HExtlib.list_mapi (fun x i -> x,i) (combine acc lefts))
91 | t -> U.fold (fun _ k -> k+1) k aux acc t
93 List.fold_left (aux 0)
94 (let rec f = function 0 -> [] | n -> true :: f (n-1) in f j) bos
97 let rec split_prods ~subst context n te =
98 match (n, R.whd ~subst context te) with
99 | (0, _) -> context,te
100 | (n, C.Prod (name,so,ta)) when n > 0 ->
101 split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
102 | (_, _) -> raise (AssertFailure (lazy "split_prods"))
105 let debruijn uri number_of_types context =
108 | C.Meta (i,(s,C.Ctx l)) ->
109 let l1 = HExtlib.sharing_map (aux (k-s)) l in
110 if l1 == l then t else C.Meta (i,(s,C.Ctx l1))
112 | C.Const (Ref.Ref (uri1,(Ref.Fix (no,_,_) | Ref.CoFix no)))
113 | C.Const (Ref.Ref (uri1,Ref.Ind (_,no))) when NUri.eq uri uri1 ->
114 C.Rel (k + number_of_types - no)
115 | t -> U.map (fun _ k -> k+1) k aux t
117 aux (List.length context)
120 let sort_of_prod ~metasenv ~subst context (name,s) (t1, t2) =
121 let t1 = R.whd ~subst context t1 in
122 let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in
124 | C.Sort s1, C.Sort C.Prop -> t2
125 | C.Sort (C.Type u1), C.Sort (C.Type u2) -> C.Sort (C.Type (max u1 u2))
126 | C.Sort _,C.Sort (C.Type _) -> t2
127 | C.Sort (C.Type _) , C.Sort C.CProp -> t1
128 | C.Sort _, C.Sort C.CProp
129 | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))), C.Sort _
130 | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))), C.Meta (_,(_,(C.Irl 0 | C.Ctx [])))
131 | C.Sort _, C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> t2
133 raise (TypeCheckerFailure (lazy (Printf.sprintf
134 "Prod: expected two sorts, found = %s, %s"
135 (PP.ppterm ~subst ~metasenv ~context t1)
136 (PP.ppterm ~subst ~metasenv ~context t2))))
139 let eat_prods ~subst ~metasenv context he ty_he args_with_ty =
140 let rec aux ty_he = function
142 | (arg, ty_arg)::tl ->
143 match R.whd ~subst context ty_he with
146 prerr_endline (PP.ppterm ~subst ~metasenv ~context s ^ " - Vs - "
147 ^ PP.ppterm ~subst ~metasenv ~context ty_arg);
148 prerr_endline (PP.ppterm ~subst ~metasenv ~context
149 (S.subst ~avoid_beta_redexes:true arg t));
151 if R.are_convertible ~subst context ty_arg s then
152 aux (S.subst ~avoid_beta_redexes:true arg t) tl
156 (lazy (Printf.sprintf
157 ("Appl: wrong application of %s: the parameter %s has type"^^
158 "\n%s\nbut it should have type \n%s\nContext:\n%s\n")
159 (PP.ppterm ~subst ~metasenv ~context he)
160 (PP.ppterm ~subst ~metasenv ~context arg)
161 (PP.ppterm ~subst ~metasenv ~context ty_arg)
162 (PP.ppterm ~subst ~metasenv ~context s)
163 (PP.ppcontext ~subst ~metasenv context))))
167 (lazy (Printf.sprintf
168 "Appl: %s is not a function, it cannot be applied"
169 (PP.ppterm ~subst ~metasenv ~context
170 (let res = List.length tl in
171 let eaten = List.length args_with_ty - res in
174 (fst (HExtlib.split_nth eaten args_with_ty)))))))))
176 aux ty_he args_with_ty
179 (* instantiate_parameters ps (x1:T1)...(xn:Tn)C *)
180 (* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
181 let rec instantiate_parameters params c =
184 | C.Prod (_,_,ta), he::tl -> instantiate_parameters tl (S.subst he ta)
185 | t,l -> raise (AssertFailure (lazy "1"))
188 let specialize_inductive_type_constrs ~subst context ty_term =
189 match R.whd ~subst context ty_term with
190 | C.Const (Ref.Ref (uri,Ref.Ind (_,i)) as ref)
191 | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind (_,i)) as ref) :: _ ) as ty ->
192 let args = match ty with C.Appl (_::tl) -> tl | _ -> [] in
193 let is_ind, leftno, itl, attrs, i = E.get_checked_indtys ref in
194 let left_args,_ = HExtlib.split_nth leftno args in
195 let _,_,_,cl = List.nth itl i in
197 (fun (rel,name,ty) -> rel, name, instantiate_parameters left_args ty) cl
201 let specialize_and_abstract_constrs ~subst r_uri r_len context ty_term =
202 let cl = specialize_inductive_type_constrs ~subst context ty_term in
203 let len = List.length context in
205 match E.get_checked_obj r_uri with
206 | _,_,_,_, NCic.Inductive (_,_,tys,_) ->
207 context @ List.map (fun (_,name,arity,_) -> name,C.Decl arity) tys
211 List.map (fun (_,id,ty) -> id, debruijn r_uri r_len context ty) cl,
215 exception DoesOccur;;
217 let does_not_occur ~subst context n nn t =
218 let rec aux k _ = function
219 | C.Rel m when m > n+k && m <= nn+k -> raise DoesOccur
220 | C.Rel m when m <= k || m > nn+k -> ()
222 (try match List.nth context (m-1-k) with
223 | _,C.Def (bo,_) -> aux (n-m) () bo
225 with Failure _ -> assert false)
226 | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) ()
227 | C.Meta (mno,(s,l)) ->
229 (* possible optimization here: try does_not_occur on l and
230 perform substitution only if DoesOccur is raised *)
231 let _,_,term,_ = U.lookup_subst mno subst in
232 aux (k-s) () (S.subst_meta (0,l) term)
233 with U.Subst_not_found _ -> match l with
234 | C.Irl len -> if not (n+k >= s+len || s > nn+k) then raise DoesOccur
235 | C.Ctx lc -> List.iter (aux (k-s) ()) lc)
236 | t -> U.fold (fun _ k -> k + 1) k aux () t
239 with DoesOccur -> false
242 let rec eat_lambdas ~subst ~metasenv context n te =
243 match (n, R.whd ~subst context te) with
244 | (0, _) -> (te, context)
245 | (n, C.Lambda (name,so,ta)) when n > 0 ->
246 eat_lambdas ~subst ~metasenv ((name,(C.Decl so))::context) (n - 1) ta
248 raise (AssertFailure (lazy (Printf.sprintf "eat_lambdas (%d, %s)" n
249 (PP.ppterm ~subst ~metasenv ~context te))))
252 let rec eat_or_subst_lambdas ~subst ~metasenv n te to_be_subst args
253 (context, recfuns, x as k)
255 match n, R.whd ~subst context te, to_be_subst, args with
256 | (n, C.Lambda (name,so,ta),true::to_be_subst,arg::args) when n > 0 ->
257 eat_or_subst_lambdas ~subst ~metasenv (n - 1) (S.subst arg ta)
259 | (n, C.Lambda (name,so,ta),false::to_be_subst,arg::args) when n > 0 ->
260 eat_or_subst_lambdas ~subst ~metasenv (n - 1) ta to_be_subst args
261 (shift_k (name,(C.Decl so)) k)
262 | (_, te, _, _) -> te, k
266 (*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
267 (*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
268 (*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *)
269 (*CSC strictly_positive *)
270 (*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *)
271 let rec weakly_positive ~subst context n nn uri te =
272 (*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*)
273 let dummy = C.Sort C.Prop in
274 (*CSC: mettere in cicSubstitution *)
275 let rec subst_inductive_type_with_dummy _ = function
276 | C.Const (Ref.Ref (uri',Ref.Ind (true,0))) when NUri.eq uri' uri -> dummy
277 | C.Appl ((C.Const (Ref.Ref (uri',Ref.Ind (true,0))))::tl)
278 when NUri.eq uri' uri -> dummy
279 | t -> U.map (fun _ x->x) () subst_inductive_type_with_dummy t
281 match R.whd context te with
282 | C.Const (Ref.Ref (uri',Ref.Ind _))
283 | C.Appl ((C.Const (Ref.Ref (uri',Ref.Ind _)))::_)
284 when NUri.eq uri' uri -> true
285 | C.Prod (name,source,dest) when
286 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
287 (* dummy abstraction, so we behave as in the anonimous case *)
288 strictly_positive ~subst context n nn
289 (subst_inductive_type_with_dummy () source) &&
290 weakly_positive ~subst ((name,C.Decl source)::context)
291 (n + 1) (nn + 1) uri dest
292 | C.Prod (name,source,dest) ->
293 does_not_occur ~subst context n nn
294 (subst_inductive_type_with_dummy () source)&&
295 weakly_positive ~subst ((name,C.Decl source)::context)
296 (n + 1) (nn + 1) uri dest
298 raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))
300 and strictly_positive ~subst context n nn te =
301 match R.whd context te with
302 | t when does_not_occur ~subst context n nn t -> true
304 | C.Prod (name,so,ta) ->
305 does_not_occur ~subst context n nn so &&
306 strictly_positive ~subst ((name,C.Decl so)::context) (n+1) (nn+1) ta
307 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
308 List.for_all (does_not_occur ~subst context n nn) tl
309 | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind (_,i)) as r)::tl) ->
310 let _,paramsno,tyl,_,i = E.get_checked_indtys r in
311 let _,name,ity,cl = List.nth tyl i in
312 let ok = List.length tyl = 1 in
313 let params, arguments = HExtlib.split_nth paramsno tl in
314 let lifted_params = List.map (S.lift 1) params in
316 List.map (fun (_,_,te) -> instantiate_parameters lifted_params te) cl
319 List.for_all (does_not_occur ~subst context n nn) arguments &&
321 (weakly_positive ~subst ((name,C.Decl ity)::context) (n+1) (nn+1) uri) cl
324 (* the inductive type indexes are s.t. n < x <= nn *)
325 and are_all_occurrences_positive ~subst context uri indparamsno i n nn te =
326 match R.whd context te with
327 | C.Appl ((C.Rel m)::tl) as reduct when m = i ->
333 match R.whd context x with
334 | C.Rel m when m = n - (indparamsno - k) -> k - 1
335 | y -> raise (TypeCheckerFailure (lazy
336 ("Argument "^string_of_int (indparamsno - k + 1) ^ " (of " ^
337 string_of_int indparamsno ^ " fixed) is not homogeneous in "^
338 "appl:\n"^ PP.ppterm ~context ~subst ~metasenv:[] reduct))))
342 List.for_all (does_not_occur ~subst context n nn) tl
344 raise (TypeCheckerFailure
345 (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
346 NUri.string_of_uri uri)))
347 | C.Rel m when m = i ->
348 if indparamsno = 0 then
351 raise (TypeCheckerFailure
352 (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^
353 NUri.string_of_uri uri)))
354 | C.Prod (name,source,dest) when
355 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
356 strictly_positive ~subst context n nn source &&
357 are_all_occurrences_positive ~subst
358 ((name,C.Decl source)::context) uri indparamsno
359 (i+1) (n + 1) (nn + 1) dest
360 | C.Prod (name,source,dest) ->
361 if not (does_not_occur ~subst context n nn source) then
362 raise (TypeCheckerFailure (lazy ("Non-positive occurrence in "^
363 PP.ppterm ~context ~metasenv:[] ~subst te)));
364 are_all_occurrences_positive ~subst ((name,C.Decl source)::context)
365 uri indparamsno (i+1) (n + 1) (nn + 1) dest
368 (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^
369 (NUri.string_of_uri uri))))
372 exception NotGuarded of string Lazy.t;;
374 let rec typeof ~subst ~metasenv context term =
375 let rec typeof_aux context =
376 fun t -> (*prerr_endline (PP.ppterm ~metasenv ~subst ~context t);*)
380 match List.nth context (n - 1) with
381 | (_,C.Decl ty) -> S.lift n ty
382 | (_,C.Def (_,ty)) -> S.lift n ty
383 with Failure _ -> raise (TypeCheckerFailure (lazy "unbound variable")))
384 | C.Sort (C.Type [false,u]) -> C.Sort (C.Type [true, u])
385 | C.Sort (C.Type _) ->
386 raise (AssertFailure (lazy ("Cannot type an inferred type: "^
387 NCicPp.ppterm ~subst ~metasenv ~context t)))
388 | C.Sort _ -> C.Sort (C.Type NCicEnvironment.type0)
389 | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found"))
390 | C.Meta (n,l) as t ->
391 let canonical_ctx,ty =
393 let _,c,_,ty = U.lookup_subst n subst in c,ty
394 with U.Subst_not_found _ -> try
395 let _,c,ty = U.lookup_meta n metasenv in c,ty
396 with U.Meta_not_found _ ->
397 raise (AssertFailure (lazy (Printf.sprintf
398 "%s not found" (PP.ppterm ~subst ~metasenv ~context t))))
400 check_metasenv_consistency t ~subst ~metasenv context canonical_ctx l;
402 | C.Const ref -> type_of_constant ref
403 | C.Prod (name,s,t) ->
404 let sort1 = typeof_aux context s in
405 let sort2 = typeof_aux ((name,(C.Decl s))::context) t in
406 sort_of_prod ~metasenv ~subst context (name,s) (sort1,sort2)
407 | C.Lambda (n,s,t) ->
408 let sort = typeof_aux context s in
409 (match R.whd ~subst context sort with
410 | C.Meta _ | C.Sort _ -> ()
413 (TypeCheckerFailure (lazy (Printf.sprintf
414 ("Not well-typed lambda-abstraction: " ^^
415 "the source %s should be a type; instead it is a term " ^^
416 "of type %s") (PP.ppterm ~subst ~metasenv ~context s)
417 (PP.ppterm ~subst ~metasenv ~context sort)))));
418 let ty = typeof_aux ((n,(C.Decl s))::context) t in
420 | C.LetIn (n,ty,t,bo) ->
421 let ty_t = typeof_aux context t in
422 let _ = typeof_aux context ty in
423 if not (R.are_convertible ~subst context ty_t ty) then
426 (lazy (Printf.sprintf
427 "The type of %s is %s but it is expected to be %s"
428 (PP.ppterm ~subst ~metasenv ~context t)
429 (PP.ppterm ~subst ~metasenv ~context ty_t)
430 (PP.ppterm ~subst ~metasenv ~context ty))))
432 let ty_bo = typeof_aux ((n,C.Def (t,ty))::context) bo in
433 S.subst ~avoid_beta_redexes:true t ty_bo
434 | C.Appl (he::(_::_ as args)) ->
435 let ty_he = typeof_aux context he in
436 let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in
438 prerr_endline ("HEAD: " ^ PP.ppterm ~subst ~metasenv ~context ty_he);
439 prerr_endline ("TARGS: " ^ String.concat " | " (List.map (PP.ppterm
440 ~subst ~metasenv ~context) (List.map snd args_with_ty)));
441 prerr_endline ("ARGS: " ^ String.concat " | " (List.map (PP.ppterm
442 ~subst ~metasenv ~context) (List.map fst args_with_ty)));
444 eat_prods ~subst ~metasenv context he ty_he args_with_ty
445 | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
446 | C.Match (Ref.Ref (_,Ref.Ind (_,tyno)) as r,outtype,term,pl) ->
447 let outsort = typeof_aux context outtype in
448 let inductive,leftno,itl,_,_ = E.get_checked_indtys r in
450 let _,_,_,cl = List.nth itl tyno in List.length cl
452 let parameters, arguments =
453 let ty = R.whd ~subst context (typeof_aux context term) in
456 C.Const (Ref.Ref (_,Ref.Ind _) as r') -> r',[]
457 | C.Appl (C.Const (Ref.Ref (_,Ref.Ind _) as r') :: tl) -> r',tl
460 (TypeCheckerFailure (lazy (Printf.sprintf
461 "Case analysis: analysed term %s is not an inductive one"
462 (PP.ppterm ~subst ~metasenv ~context term)))) in
463 if not (Ref.eq r r') then
465 (TypeCheckerFailure (lazy (Printf.sprintf
466 ("Case analysys: analysed term type is %s, but is expected " ^^
467 "to be (an application of) %s")
468 (PP.ppterm ~subst ~metasenv ~context ty)
469 (PP.ppterm ~subst ~metasenv ~context (C.Const r')))))
471 try HExtlib.split_nth leftno tl
474 raise (TypeCheckerFailure (lazy (Printf.sprintf
475 "%s is partially applied"
476 (PP.ppterm ~subst ~metasenv ~context ty)))) in
477 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
478 let sort_of_ind_type =
479 if parameters = [] then C.Const r
480 else C.Appl ((C.Const r)::parameters) in
481 let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in
482 check_allowed_sort_elimination ~subst ~metasenv r context
483 sort_of_ind_type type_of_sort_of_ind_ty outsort;
484 (* let's check if the type of branches are right *)
485 if List.length pl <> constructorsno then
486 raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match")));
487 let j,branches_ok,p_ty, exp_p_ty =
489 (fun (j,b,old_p_ty,old_exp_p_ty) p ->
492 let cons = Ref.mk_constructor j r in
493 if parameters = [] then C.Const cons
494 else C.Appl (C.Const cons::parameters)
496 let ty_p = typeof_aux context p in
497 let ty_cons = typeof_aux context cons in
499 type_of_branch ~subst context leftno outtype cons ty_cons 0
501 j+1, R.are_convertible ~subst context ty_p ty_branch,
504 j,false,old_p_ty,old_exp_p_ty
505 ) (1,true,C.Sort C.Prop,C.Sort C.Prop) pl
507 if not branches_ok then
510 (lazy (Printf.sprintf ("Branch for constructor %s :=\n%s\n"^^
511 "has type %s\nnot convertible with %s")
512 (PP.ppterm ~subst ~metasenv ~context
513 (C.Const (Ref.mk_constructor (j-1) r)))
514 (PP.ppterm ~metasenv ~subst ~context (List.nth pl (j-2)))
515 (PP.ppterm ~metasenv ~subst ~context p_ty)
516 (PP.ppterm ~metasenv ~subst ~context exp_p_ty))));
517 let res = outtype::arguments@[term] in
518 R.head_beta_reduce (C.Appl res)
519 | C.Match _ -> assert false
521 and type_of_branch ~subst context leftno outty cons tycons liftno =
522 match R.whd ~subst context tycons with
523 | C.Const (Ref.Ref (_,Ref.Ind _)) -> C.Appl [S.lift liftno outty ; cons]
524 | C.Appl (C.Const (Ref.Ref (_,Ref.Ind _))::tl) ->
525 let _,arguments = HExtlib.split_nth leftno tl in
526 C.Appl (S.lift liftno outty::arguments@[cons])
527 | C.Prod (name,so,de) ->
529 match S.lift 1 cons with
530 | C.Appl l -> C.Appl (l@[C.Rel 1])
531 | t -> C.Appl [t ; C.Rel 1]
534 type_of_branch ~subst ((name,(C.Decl so))::context)
535 leftno outty cons de (liftno+1))
536 | _ -> raise (AssertFailure (lazy "type_of_branch"))
538 (* check_metasenv_consistency checks that the "canonical" context of a
539 metavariable is consitent - up to relocation via the relocation list l -
540 with the actual context *)
541 and check_metasenv_consistency
542 ~subst ~metasenv term context canonical_context l
546 let context = snd (HExtlib.split_nth shift context) in
547 let rec compare = function
551 raise (AssertFailure (lazy (Printf.sprintf
552 "Local and canonical context %s have different lengths"
553 (PP.ppterm ~subst ~context ~metasenv term))))
555 raise (TypeCheckerFailure (lazy (Printf.sprintf
556 "Unbound variable -%d in %s" m
557 (PP.ppterm ~subst ~metasenv ~context term))))
560 (_,C.Decl t1), (_,C.Decl t2)
561 | (_,C.Def (t1,_)), (_,C.Def (t2,_))
562 | (_,C.Def (_,t1)), (_,C.Decl t2) ->
563 if not (R.are_convertible ~subst tl t1 t2) then
566 (lazy (Printf.sprintf
567 ("Not well typed metavariable local context for %s: " ^^
568 "%s expected, which is not convertible with %s")
569 (PP.ppterm ~subst ~metasenv ~context term)
570 (PP.ppterm ~subst ~metasenv ~context t2)
571 (PP.ppterm ~subst ~metasenv ~context t1))))
574 (TypeCheckerFailure (lazy (Printf.sprintf
575 ("Not well typed metavariable local context for %s: " ^^
576 "a definition expected, but a declaration found")
577 (PP.ppterm ~subst ~metasenv ~context term)))));
578 compare (m - 1,tl,ctl)
580 compare (n,context,canonical_context)
582 (* we avoid useless lifting by shortening the context*)
583 let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in
584 let lifted_canonical_context =
585 let rec lift_metas i = function
587 | (n,C.Decl t)::tl ->
588 (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl)
589 | (n,C.Def (t,ty))::tl ->
590 (n,C.Def ((S.subst_meta l (S.lift i t)),
591 S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl)
593 lift_metas 1 canonical_context in
594 let l = U.expand_local_context lc_kind in
599 | t, (_,C.Def (ct,_)) ->
600 (*CSC: the following optimization is to avoid a possibly expensive
601 reduction that can be easily avoided and that is quite
602 frequent. However, this is better handled using levels to
608 match List.nth context (n - 1) with
609 | (_,C.Def (te,_)) -> S.lift n te
614 if not (R.are_convertible ~subst context optimized_t ct)
618 (lazy (Printf.sprintf
619 ("Not well typed metavariable local context: " ^^
620 "expected a term convertible with %s, found %s")
621 (PP.ppterm ~subst ~metasenv ~context ct)
622 (PP.ppterm ~subst ~metasenv ~context t))))
623 | t, (_,C.Decl ct) ->
624 let type_t = typeof_aux context t in
625 if not (R.are_convertible ~subst context type_t ct) then
626 raise (TypeCheckerFailure
627 (lazy (Printf.sprintf
628 ("Not well typed metavariable local context: "^^
629 "expected a term of type %s, found %s of type %s")
630 (PP.ppterm ~subst ~metasenv ~context ct)
631 (PP.ppterm ~subst ~metasenv ~context t)
632 (PP.ppterm ~subst ~metasenv ~context type_t))))
633 ) l lifted_canonical_context
635 Invalid_argument _ ->
636 raise (AssertFailure (lazy (Printf.sprintf
637 "Local and canonical context %s have different lengths"
638 (PP.ppterm ~subst ~metasenv ~context term))))
640 and is_non_informative context paramsno c =
641 let rec aux context c =
642 match R.whd context c with
643 | C.Prod (n,so,de) ->
644 let s = typeof_aux context so in
645 s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de
647 let context',dx = split_prods ~subst:[] context paramsno c in
650 and check_allowed_sort_elimination ~subst ~metasenv r =
653 | C.Appl l -> C.Appl (l @ [arg])
654 | t -> C.Appl [t;arg] in
655 let rec aux context ind arity1 arity2 =
656 let arity1 = R.whd ~subst context arity1 in
657 let arity2 = R.whd ~subst context arity2 in
658 match arity1,arity2 with
659 | C.Prod (name,so1,de1), C.Prod (_,so2,de2) ->
660 if not (R.are_convertible ~subst context so1 so2) then
661 raise (TypeCheckerFailure (lazy (Printf.sprintf
662 "In outtype: expected %s, found %s"
663 (PP.ppterm ~subst ~metasenv ~context so1)
664 (PP.ppterm ~subst ~metasenv ~context so2)
666 aux ((name, C.Decl so1)::context)
667 (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2
668 | C.Sort _, C.Prod (name,so,ta) ->
669 if not (R.are_convertible ~subst context so ind) then
670 raise (TypeCheckerFailure (lazy (Printf.sprintf
671 "In outtype: expected %s, found %s"
672 (PP.ppterm ~subst ~metasenv ~context ind)
673 (PP.ppterm ~subst ~metasenv ~context so)
675 (match arity1, R.whd ~subst ((name,C.Decl so)::context) ta with
676 | (C.Sort (C.CProp | C.Type _), C.Sort _)
677 | (C.Sort C.Prop, C.Sort C.Prop) -> ()
678 | (C.Sort C.Prop, C.Sort (C.CProp | C.Type _)) ->
679 (* TODO: we should pass all these parameters since we
680 * have them already *)
681 let inductive,leftno,itl,_,i = E.get_checked_indtys r in
682 let itl_len = List.length itl in
683 let _,name,ty,cl = List.nth itl i in
684 let cl_len = List.length cl in
685 (* is it a singleton or empty non recursive and non informative
689 (itl_len = 1 && cl_len = 1 &&
690 is_non_informative [name,C.Decl ty] leftno
691 (let _,_,x = List.nth cl 0 in x)))
693 raise (TypeCheckerFailure (lazy
694 ("Sort elimination not allowed")));
701 typeof_aux context term
703 and check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl =
704 (* let's check if the arity of the inductive types are well formed *)
705 List.iter (fun (_,_,x,_) -> ignore (typeof ~subst ~metasenv [] x)) tyl;
706 (* let's check if the types of the inductive constructors are well formed. *)
707 let len = List.length tyl in
708 let tys = List.rev (List.map (fun (_,n,ty,_) -> (n,(C.Decl ty))) tyl) in
714 let debruijnedte = debruijn uri len [] te in
715 ignore (typeof ~subst ~metasenv tys debruijnedte);
716 (* let's check also the positivity conditions *)
719 (are_all_occurrences_positive ~subst tys uri leftno i 0 len
724 (lazy ("Non positive occurence in "^NUri.string_of_uri uri))))
729 and guarded_by_destructors r_uri r_len ~subst ~metasenv context recfuns t =
730 let recursor f k t = U.fold shift_k k (fun k () -> f k) () t in
731 let rec aux (context, recfuns, x as k) t =
733 prerr_endline ("GB:\n" ^
734 PP.ppcontext ~subst ~metasenv context^
735 PP.ppterm ~metasenv ~subst ~context t^
736 string_of_recfuns ~subst ~metasenv ~context recfuns);
740 | C.Rel m as t when is_dangerous m recfuns ->
741 raise (NotGuarded (lazy
742 (PP.ppterm ~subst ~metasenv ~context t ^
743 " is a partial application of a fix")))
744 | C.Appl ((C.Rel m)::tl) as t when is_dangerous m recfuns ->
745 let rec_no = get_recno m recfuns in
746 if not (List.length tl > rec_no) then
747 raise (NotGuarded (lazy
748 (PP.ppterm ~context ~subst ~metasenv t ^
749 " is a partial application of a fix")))
751 let rec_arg = List.nth tl rec_no in
752 if not (is_really_smaller r_uri r_len ~subst ~metasenv k rec_arg) then
753 raise (NotGuarded (lazy (Printf.sprintf ("Recursive call %s, %s is not"
754 ^^ " smaller.\ncontext:\n%s") (PP.ppterm ~context ~subst ~metasenv
755 t) (PP.ppterm ~context ~subst ~metasenv rec_arg)
756 (PP.ppcontext ~subst ~metasenv context))));
758 | C.Appl ((C.Rel m)::tl) when is_unfolded m recfuns ->
759 let fixed_args = get_fixed_args m recfuns in
760 HExtlib.list_iter_default2
761 (fun x b -> if not b then aux k x) tl false fixed_args
763 (match List.nth context (m-1) with
765 | _,C.Def (bo,_) -> aux k (S.lift m bo))
767 | C.Appl (C.Const ((Ref.Ref (uri,Ref.Fix (i,recno,_))) as r)::args) ->
768 if List.exists (fun t -> try aux k t;false with NotGuarded _ -> true) args
770 let fl,_,_ = E.get_checked_fixes_or_cofixes r in
772 List.split (List.map (fun (_,name,_,ty,bo) -> (name, C.Decl ty), bo) fl)
774 let fl_len = List.length fl in
775 let bos = List.map (debruijn uri fl_len context) bos in
776 let j = List.fold_left min max_int (List.map (fun (_,_,i,_,_)->i) fl) in
777 let ctx_len = List.length context in
778 (* we may look for fixed params not only up to j ... *)
779 let fa = fixed_args bos j ctx_len (ctx_len + fl_len) in
780 HExtlib.list_iter_default2
781 (fun x b -> if not b then aux k x) args false fa;
782 let context = context@ctx_tys in
783 let ctx_len = List.length context in
785 HExtlib.list_mapi (fun _ i -> ctx_len - i, UnfFix fa) ctx_tys
787 let new_k = context, extra_recfuns@recfuns, x in
792 eat_or_subst_lambdas ~subst ~metasenv j bo fa args new_k
796 List.length args > recno &&
797 (*case where the recursive argument is already really_smaller *)
798 is_really_smaller r_uri r_len ~subst ~metasenv k
799 (List.nth args recno)
801 let bo,(context, _, _ as new_k) = bo_and_k in
803 eat_lambdas ~subst ~metasenv context (recno + 1 - j) bo in
804 let new_context_part,_ =
805 HExtlib.split_nth (List.length context' - List.length context)
807 let k = List.fold_right shift_k new_context_part new_k in
808 let context, recfuns, x = k in
809 let k = context, (1,Safe)::recfuns, x in
815 List.iter (fun (bo,k) -> aux k bo) bos_and_ks
816 | C.Match (Ref.Ref (uri,Ref.Ind (true,_)),outtype,term,pl) as t ->
817 (match R.whd ~subst context term with
818 | C.Rel m | C.Appl (C.Rel m :: _ ) as t when is_safe m recfuns || m = x ->
819 let ty = typeof ~subst ~metasenv context term in
820 let dc_ctx, dcl, start, stop =
821 specialize_and_abstract_constrs ~subst r_uri r_len context ty in
822 let args = match t with C.Appl (_::tl) -> tl | _ -> [] in
824 List.iter (aux k) args;
827 let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in
828 let p, k = get_new_safes ~subst k p rl in
831 | _ -> recursor aux k t)
832 | t -> recursor aux k t
834 NotGuarded _ as exc ->
835 let t' = R.whd ~delta:0 ~subst context t in
836 if t = t' then raise exc
839 try aux (context, recfuns, 1) t
840 with NotGuarded s -> raise (TypeCheckerFailure s)
842 and guarded_by_constructors ~subst ~metasenv context t indURI indlen nn =
843 let rec aux context n nn h te =
844 match R.whd ~subst context te with
845 | C.Rel m when m > n && m <= nn -> h
846 | C.Rel _ | C.Meta _ -> true
850 | C.Const (Ref.Ref (_,Ref.Ind _))
851 | C.LetIn _ -> raise (AssertFailure (lazy "17"))
852 | C.Lambda (name,so,de) ->
853 does_not_occur ~subst context n nn so &&
854 aux ((name,C.Decl so)::context) (n + 1) (nn + 1) h de
855 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
856 h && List.for_all (does_not_occur ~subst context n nn) tl
857 | C.Const (Ref.Ref (_,Ref.Con _)) -> true
858 | C.Appl (C.Const (Ref.Ref (uri, Ref.Con (_,j)) as ref) :: tl) as t ->
859 let _, paramsno, _, _, _ = E.get_checked_indtys ref in
860 let ty_t = typeof ~subst ~metasenv context t in
861 let dc_ctx, dcl, start, stop =
862 specialize_and_abstract_constrs ~subst indURI indlen context ty_t in
863 let _, dc = List.nth dcl (j-1) in
865 prerr_endline (PP.ppterm ~subst ~metasenv ~context:dc_ctx dc);
866 prerr_endline (PP.ppcontext ~subst ~metasenv dc_ctx);
868 let rec_params = recursive_args ~subst ~metasenv dc_ctx start stop dc in
869 let rec analyse_instantiated_type rec_spec args =
870 match rec_spec, args with
871 | h::rec_spec, he::args ->
872 aux context n nn h he && analyse_instantiated_type rec_spec args
874 | _ -> raise (AssertFailure (lazy
875 ("Too many args for constructor: " ^ String.concat " "
876 (List.map (fun x-> PP.ppterm ~subst ~metasenv ~context x) args))))
878 let left, args = HExtlib.split_nth paramsno tl in
879 List.for_all (does_not_occur ~subst context n nn) left &&
880 analyse_instantiated_type rec_params args
881 | C.Appl ((C.Match (_,out,te,pl))::_)
882 | C.Match (_,out,te,pl) as t ->
883 let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
884 List.for_all (does_not_occur ~subst context n nn) tl &&
885 does_not_occur ~subst context n nn out &&
886 does_not_occur ~subst context n nn te &&
887 List.for_all (aux context n nn h) pl
888 | C.Const (Ref.Ref (u,(Ref.Fix _| Ref.CoFix _)) as ref)
889 | C.Appl(C.Const (Ref.Ref(u,(Ref.Fix _| Ref.CoFix _)) as ref) :: _) as t ->
890 let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
891 let fl,_,_ = E.get_checked_fixes_or_cofixes ref in
892 let len = List.length fl in
893 let tys = List.map (fun (_,n,_,ty,_) -> n, C.Decl ty) fl in
894 List.for_all (does_not_occur ~subst context n nn) tl &&
897 aux (context@tys) n nn h (debruijn u len context bo))
900 | C.Appl _ as t -> does_not_occur ~subst context n nn t
902 aux context 0 nn false t
904 and recursive_args ~subst ~metasenv context n nn te =
905 match R.whd context te with
906 | C.Rel _ | C.Appl _ | C.Const _ -> []
907 | C.Prod (name,so,de) ->
908 (not (does_not_occur ~subst context n nn so)) ::
909 (recursive_args ~subst ~metasenv
910 ((name,(C.Decl so))::context) (n+1) (nn + 1) de)
912 raise (AssertFailure (lazy ("recursive_args:" ^ PP.ppterm ~subst
913 ~metasenv ~context:[] t)))
915 and get_new_safes ~subst (context, recfuns, x as k) p rl =
916 match R.whd ~subst context p, rl with
917 | C.Lambda (name,so,ta), b::tl ->
918 let recfuns = (if b then [0,Safe] else []) @ recfuns in
920 (shift_k (name,(C.Decl so)) (context, recfuns, x)) ta tl
921 | C.Meta _ as e, _ | e, [] -> e, k
922 | _ -> raise (AssertFailure (lazy "Ill formed pattern"))
924 and is_really_smaller
925 r_uri r_len ~subst ~metasenv (context, recfuns, x as k) te
927 match R.whd ~subst context te with
928 | C.Rel m when is_safe m recfuns -> true
929 | C.Lambda (name, s, t) ->
930 is_really_smaller r_uri r_len ~subst ~metasenv (shift_k (name,C.Decl s) k) t
932 is_really_smaller r_uri r_len ~subst ~metasenv k he
934 | C.Const (Ref.Ref (_,Ref.Con _)) -> false
936 | C.Const (Ref.Ref (_,Ref.Fix _)) -> assert false
938 | C.Match (Ref.Ref (uri,Ref.Ind (isinductive,_)),outtype,term,pl) ->
940 | C.Rel m | C.Appl (C.Rel m :: _ ) when is_safe m recfuns || m = x ->
941 if not isinductive then
942 List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl
944 let ty = typeof ~subst ~metasenv context term in
945 let dc_ctx, dcl, start, stop =
946 specialize_and_abstract_constrs ~subst r_uri r_len context ty in
949 let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in
950 let e, k = get_new_safes ~subst k p rl in
951 is_really_smaller r_uri r_len ~subst ~metasenv k e)
953 | _ -> List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl)
956 and returns_a_coinductive ~subst context ty =
957 match R.whd ~subst context ty with
958 | C.Const (Ref.Ref (uri,Ref.Ind (false,_)) as ref)
959 | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind (false,_)) as ref)::_) ->
960 let _, _, itl, _, _ = E.get_checked_indtys ref in
961 Some (uri,List.length itl)
962 | C.Prod (n,so,de) ->
963 returns_a_coinductive ~subst ((n,C.Decl so)::context) de
966 and type_of_constant ((Ref.Ref (uri,_)) as ref) =
967 match E.get_checked_obj uri, ref with
968 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,Ref.Ind (_,i)) ->
969 let _,_,arity,_ = List.nth tl i in arity
970 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,Ref.Con (i,j)) ->
971 let _,_,_,cl = List.nth tl i in
972 let _,_,arity = List.nth cl (j-1) in
974 | (_,_,_,_,C.Fixpoint (_,fl,_)), Ref.Ref (_,(Ref.Fix (i,_,_)|Ref.CoFix i)) ->
975 let _,_,_,arity,_ = List.nth fl i in
977 | (_,_,_,_,C.Constant (_,_,_,ty,_)), Ref.Ref (_,(Ref.Def _|Ref.Decl)) -> ty
978 | _ -> raise (AssertFailure (lazy "type_of_constant: environment/reference"))
981 let typecheck_context ~metasenv ~subst context =
987 _,C.Decl t -> ignore (typeof ~metasenv ~subst:[] context t)
988 | name,C.Def (te,ty) ->
989 ignore (typeof ~metasenv ~subst:[] context ty);
990 let ty' = typeof ~metasenv ~subst:[] context te in
991 if not (R.are_convertible ~subst context ty' ty) then
992 raise (AssertFailure (lazy (Printf.sprintf (
993 "the type of the definiens for %s in the context is not "^^
994 "convertible with the declared one.\n"^^
995 "inferred type:\n%s\nexpected type:\n%s")
997 (PP.ppterm ~subst ~metasenv ~context ty')
998 (PP.ppterm ~subst ~metasenv ~context ty))))
1004 let typecheck_metasenv metasenv =
1007 (fun metasenv (i,(_,context,ty) as conj) ->
1008 if List.mem_assoc i metasenv then
1009 raise (TypeCheckerFailure (lazy ("duplicate meta " ^ string_of_int i ^
1011 typecheck_context ~metasenv ~subst:[] context;
1012 ignore (typeof ~metasenv ~subst:[] context ty);
1017 let typecheck_subst ~metasenv subst =
1020 (fun subst (i,(_,context,ty,bo) as conj) ->
1021 if List.mem_assoc i subst then
1022 raise (AssertFailure (lazy ("duplicate meta " ^ string_of_int i ^
1023 " in substitution")));
1024 if List.mem_assoc i metasenv then
1025 raise (AssertFailure (lazy ("meta " ^ string_of_int i ^
1026 " is both in the metasenv and in the substitution")));
1027 typecheck_context ~metasenv ~subst context;
1028 ignore (typeof ~metasenv ~subst context ty);
1029 let ty' = typeof ~metasenv ~subst context bo in
1030 if not (R.are_convertible ~subst context ty' ty) then
1031 raise (AssertFailure (lazy (Printf.sprintf (
1032 "the type of the definiens for %d in the substitution is not "^^
1033 "convertible with the declared one.\n"^^
1034 "inferred type:\n%s\nexpected type:\n%s")
1036 (PP.ppterm ~subst ~metasenv ~context ty')
1037 (PP.ppterm ~subst ~metasenv ~context ty))));
1042 let typecheck_obj (uri,height,metasenv,subst,kind) =
1043 typecheck_metasenv metasenv;
1044 typecheck_subst ~metasenv subst;
1046 | C.Constant (_,_,Some te,ty,_) ->
1047 let _ = typeof ~subst ~metasenv [] ty in
1048 let ty_te = typeof ~subst ~metasenv [] te in
1049 if not (R.are_convertible ~subst [] ty_te ty) then
1050 raise (TypeCheckerFailure (lazy (Printf.sprintf (
1051 "the type of the body is not convertible with the declared one.\n"^^
1052 "inferred type:\n%s\nexpected type:\n%s")
1053 (PP.ppterm ~subst ~metasenv ~context:[] ty_te)
1054 (PP.ppterm ~subst ~metasenv ~context:[] ty))))
1055 | C.Constant (_,_,None,ty,_) -> ignore (typeof ~subst ~metasenv [] ty)
1056 | C.Inductive (is_ind, leftno, tyl, _) ->
1057 check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl
1058 | C.Fixpoint (inductive,fl,_) ->
1061 (fun (types,kl) (_,name,k,ty,_) ->
1062 let _ = typeof ~subst ~metasenv [] ty in
1063 ((name,C.Decl ty)::types, k::kl)
1066 let len = List.length types in
1068 List.split (List.map2
1069 (fun (_,_,_,_,bo) rno ->
1070 let dbo = debruijn uri len [] bo in
1074 List.iter2 (fun (_,name,x,ty,_) bo ->
1075 let ty_bo = typeof ~subst ~metasenv types bo in
1076 if not (R.are_convertible ~subst types ty_bo ty)
1077 then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
1079 if inductive then begin
1080 let m, context = eat_lambdas ~subst ~metasenv types (x + 1) bo in
1083 match List.hd context with _,C.Decl t -> t | _ -> assert false
1085 match R.whd ~subst (List.tl context) he with
1086 | C.Const (Ref.Ref (uri,Ref.Ind _) as ref)
1087 | C.Appl (C.Const (Ref.Ref (uri,Ref.Ind _) as ref) :: _) ->
1088 let _,_,itl,_,_ = E.get_checked_indtys ref in
1089 uri, List.length itl
1092 (* guarded by destructors conditions D{f,k,x,M} *)
1093 let rec enum_from k =
1094 function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl
1096 guarded_by_destructors r_uri r_len
1097 ~subst ~metasenv context (enum_from (x+2) kl) m
1099 match returns_a_coinductive ~subst [] ty with
1101 raise (TypeCheckerFailure
1102 (lazy "CoFix: does not return a coinductive type"))
1103 | Some (r_uri, r_len) ->
1104 (* guarded by constructors conditions C{f,M} *)
1106 (guarded_by_constructors ~subst ~metasenv types bo r_uri r_len len)
1108 raise (TypeCheckerFailure
1109 (lazy "CoFix: not guarded by constructors"))
1115 let trust = ref (fun _ -> false);;
1116 let set_trust f = trust := f
1117 let trust_obj obj = !trust obj
1120 (* web interface stuff *)
1123 ref (function (`Start_type_checking _|`Type_checking_completed _|`Type_checking_interrupted _|`Type_checking_failed _|`Trust_obj _) -> ())
1126 let set_logger f = logger := f;;
1128 let typecheck_obj obj =
1129 let u,_,_,_,_ = obj in
1131 !logger (`Start_type_checking u);
1133 !logger (`Type_checking_completed u)
1136 !logger (`Type_checking_interrupted u);
1139 !logger (`Type_checking_failed u);
1145 if trust_obj obj then
1146 let u,_,_,_,_ = obj in
1147 !logger (`Trust_obj u)