2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
12 (* $Id: nCicReduction.ml 8250 2008-03-25 17:56:20Z tassi $ *)
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 | Evil of int (* rno *)
27 | UnfFix of bool list (* fixed arguments *)
31 let is_dangerous i l =
32 List.exists (function (j,Evil _) when j=i -> true | _ -> false) l
36 List.exists (function (j,UnfFix _) when j=i -> true | _ -> false) l
40 List.exists (function (j,Safe) when j=i -> true | _ -> false) l
44 try match List.assoc i l with Evil rno -> rno | _ -> assert false
45 with Not_found -> assert false
48 let get_fixed_args i l =
49 try match List.assoc i l with UnfFix fa -> fa | _ -> assert false
50 with Not_found -> assert false
53 let shift_k e (c,rf,x) = e::c,List.map (fun (k,v) -> k+1,v) rf,x+1;;
55 let string_of_recfuns ~subst ~metasenv ~context l =
56 let pp = PP.ppterm ~subst ~metasenv ~context in
57 let safe, rest = List.partition (function (_,Safe) -> true | _ -> false) l in
58 let dang,unf = List.partition (function (_,UnfFix _)-> false | _->true)rest in
59 "\n\tsafes: "^String.concat "," (List.map (fun (i,_)->pp (C.Rel i)) safe) ^
60 "\n\tfix : "^String.concat ","
62 (function (i,UnfFix l)-> pp(C.Rel i)^"/"^String.concat "," (List.map
64 | _ ->assert false) unf) ^
65 "\n\trec : "^String.concat ","
67 (function (i,Evil rno)->pp(C.Rel i)^"/"^string_of_int rno
68 | _ -> assert false) dang)
71 let fixed_args bos j n nn =
72 let rec aux k acc = function
73 | C.Appl (C.Rel i::args) when i-k > n && i-k <= nn ->
74 let rec combine l1 l2 =
77 | he1::tl1, he2::tl2 -> (he1,he2)::combine tl1 tl2
78 | he::tl, [] -> (false,C.Rel ~-1)::combine tl [] (* dummy term *)
79 | [],_::_ -> assert false
81 let lefts, _ = HExtlib.split_nth (min j (List.length args)) args in
82 List.map (fun ((b,x),i) -> b && x = C.Rel (k-i))
83 (HExtlib.list_mapi (fun x i -> x,i) (combine acc lefts))
84 | t -> U.fold (fun _ k -> k+1) k aux acc t
86 List.fold_left (aux 0)
87 (let rec f = function 0 -> [] | n -> true :: f (n-1) in f j) bos
90 let rec list_iter_default2 f l1 def l2 =
93 | a::ta, b::tb -> f a b; list_iter_default2 f ta def tb
94 | a::ta, [] -> f a def; list_iter_default2 f ta def []
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 ?(cb=fun _ _ -> ()) uri number_of_types context =
109 | C.Meta (i,(s,C.Ctx l)) ->
110 let l1 = U.sharing_map (aux (k-s)) l in
111 if l1 == l then t else C.Meta (i,(s,C.Ctx l1))
113 | C.Const (Ref.Ref (_,uri1,(Ref.Fix (no,_) | Ref.CoFix no)))
114 | C.Const (Ref.Ref (_,uri1,Ref.Ind no)) when NUri.eq uri uri1 ->
115 C.Rel (k + number_of_types - no)
116 | t -> U.map (fun _ k -> k+1) k aux t
120 aux (List.length context)
123 let sort_of_prod ~metasenv ~subst context (name,s) (t1, t2) =
124 let t1 = R.whd ~subst context t1 in
125 let t2 = R.whd ~subst ((name,C.Decl s)::context) t2 in
127 | C.Sort s1, C.Sort C.Prop -> t2
128 | C.Sort (C.Type u1), C.Sort (C.Type u2) -> C.Sort (C.Type (max u1 u2))
129 | C.Sort _,C.Sort (C.Type _) -> t2
130 | C.Sort (C.Type _) , C.Sort C.CProp -> t1
131 | C.Sort _, C.Sort C.CProp -> t2
134 | C.Sort _, C.Meta _ when U.is_closed t2 -> t2
136 raise (TypeCheckerFailure (lazy (Printf.sprintf
137 "Prod: expected two sorts, found = %s, %s"
138 (PP.ppterm ~subst ~metasenv ~context t1)
139 (PP.ppterm ~subst ~metasenv ~context t2))))
142 let eat_prods ~subst ~metasenv context he ty_he args_with_ty =
143 let rec aux ty_he = function
145 | (arg, ty_arg)::tl ->
146 match R.whd ~subst context ty_he with
149 prerr_endline (PP.ppterm ~subst ~metasenv ~context s ^ " - Vs - "
150 ^ PP.ppterm ~subst ~metasenv ~context ty_arg);
151 prerr_endline (PP.ppterm ~subst ~metasenv ~context
152 (S.subst ~avoid_beta_redexes:true arg t));
154 if R.are_convertible ~subst ~metasenv context ty_arg s then
155 aux (S.subst ~avoid_beta_redexes:true arg t) tl
159 (lazy (Printf.sprintf
160 ("Appl: wrong application of %s: the parameter %s has type"^^
161 "\n%s\nbut it should have type \n%s\nContext:\n%s\n")
162 (PP.ppterm ~subst ~metasenv ~context he)
163 (PP.ppterm ~subst ~metasenv ~context arg)
164 (PP.ppterm ~subst ~metasenv ~context ty_arg)
165 (PP.ppterm ~subst ~metasenv ~context s)
166 (PP.ppcontext ~subst ~metasenv context))))
170 (lazy (Printf.sprintf
171 "Appl: %s is not a function, it cannot be applied"
172 (PP.ppterm ~subst ~metasenv ~context
173 (let res = List.length tl in
174 let eaten = List.length args_with_ty - res in
177 (fst (HExtlib.split_nth eaten args_with_ty)))))))))
179 aux ty_he args_with_ty
182 (* instantiate_parameters ps (x1:T1)...(xn:Tn)C *)
183 (* returns ((x_|ps|:T_|ps|)...(xn:Tn)C){ps_1 / x1 ; ... ; ps_|ps| / x_|ps|} *)
184 let rec instantiate_parameters params c =
187 | C.Prod (_,_,ta), he::tl -> instantiate_parameters tl (S.subst he ta)
188 | t,l -> raise (AssertFailure (lazy "1"))
191 let specialize_inductive_type_constrs ~subst context ty_term =
192 match R.whd ~subst context ty_term with
193 | C.Const (Ref.Ref (_,uri,Ref.Ind i) as ref)
194 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind i) as ref) :: _ ) as ty ->
195 let args = match ty with C.Appl (_::tl) -> tl | _ -> [] in
196 let is_ind, leftno, itl, attrs, i = E.get_checked_indtys ref in
197 let left_args,_ = HExtlib.split_nth leftno args in
198 let _,_,_,cl = List.nth itl i in
200 (fun (rel,name,ty) -> rel, name, instantiate_parameters left_args ty) cl
204 let specialize_and_abstract_constrs ~subst r_uri r_len context ty_term =
205 let cl = specialize_inductive_type_constrs ~subst context ty_term in
206 let len = List.length context in
208 match E.get_checked_obj r_uri with
209 | _,_,_,_, NCic.Inductive (_,_,tys,_) ->
210 context @ List.map (fun (_,name,arity,_) -> name,C.Decl arity) tys
214 List.map (fun (_,id,ty) -> id, debruijn r_uri r_len context ty) cl,
218 exception DoesOccur;;
220 let does_not_occur ~subst context n nn t =
221 let rec aux (context,n,nn as k) _ = function
222 | C.Rel m when m > n && m <= nn -> raise DoesOccur
224 (try (match List.nth context (m-1) with
225 | _,C.Def (bo,_) -> aux k () (S.lift m bo)
227 with Failure _ -> assert false)
228 | C.Meta (_,(_,(C.Irl 0 | C.Ctx []))) -> (* closed meta *) ()
229 | C.Meta (mno,(s,l)) ->
231 let _,_,term,_ = U.lookup_subst mno subst in
232 aux (context,n+s,nn+s) () (S.subst_meta (0,l) term)
233 with CicUtil.Subst_not_found _ -> match l with
234 | C.Irl len -> if not (n >= s+len || s > nn) then raise DoesOccur
235 | C.Ctx lc -> List.iter (aux (context,n+s,nn+s) ()) lc)
236 | t -> U.fold (fun e (ctx,n,nn) -> (e::ctx,n+1,nn+1)) k aux () t
238 try aux (context,n,nn) () t; true
239 with DoesOccur -> false
242 (*CSC l'indice x dei tipi induttivi e' t.c. n < x <= nn *)
243 (*CSC questa funzione e' simile alla are_all_occurrences_positive, ma fa *)
244 (*CSC dei controlli leggermente diversi. Viene invocata solamente dalla *)
245 (*CSC strictly_positive *)
246 (*CSC definizione (giusta???) tratta dalla mail di Hugo ;-) *)
247 let rec weakly_positive ~subst context n nn uri te =
248 (*CSC: Che schifo! Bisogna capire meglio e trovare una soluzione ragionevole!*)
249 let dummy = C.Sort (C.Type ~-1) in
250 (*CSC: mettere in cicSubstitution *)
251 let rec subst_inductive_type_with_dummy _ = function
252 | C.Const (Ref.Ref (_,uri',Ref.Ind 0)) when NUri.eq uri' uri -> dummy
253 | C.Appl ((C.Const (Ref.Ref (_,uri',Ref.Ind 0)))::tl)
254 when NUri.eq uri' uri -> dummy
255 | t -> U.map (fun _ x->x) () subst_inductive_type_with_dummy t
257 match R.whd context te with
258 | C.Const (Ref.Ref (_,uri',Ref.Ind _))
259 | C.Appl ((C.Const (Ref.Ref (_,uri',Ref.Ind _)))::_)
260 when NUri.eq uri' uri -> true
261 | C.Prod (name,source,dest) when
262 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
263 (* dummy abstraction, so we behave as in the anonimous case *)
264 strictly_positive ~subst context n nn
265 (subst_inductive_type_with_dummy () source) &&
266 weakly_positive ~subst ((name,C.Decl source)::context)
267 (n + 1) (nn + 1) uri dest
268 | C.Prod (name,source,dest) ->
269 does_not_occur ~subst context n nn
270 (subst_inductive_type_with_dummy () source)&&
271 weakly_positive ~subst ((name,C.Decl source)::context)
272 (n + 1) (nn + 1) uri dest
274 raise (TypeCheckerFailure (lazy "Malformed inductive constructor type"))
276 and strictly_positive ~subst context n nn te =
277 match R.whd context te with
278 | t when does_not_occur ~subst context n nn t -> true
280 | C.Prod (name,so,ta) ->
281 does_not_occur ~subst context n nn so &&
282 strictly_positive ~subst ((name,C.Decl so)::context) (n+1) (nn+1) ta
283 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
284 List.for_all (does_not_occur ~subst context n nn) tl
285 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind i) as r)::tl) ->
286 let _,paramsno,tyl,_,i = E.get_checked_indtys r in
287 let _,name,ity,cl = List.nth tyl i in
288 let ok = List.length tyl = 1 in
289 let params, arguments = HExtlib.split_nth paramsno tl in
290 let lifted_params = List.map (S.lift 1) params in
292 List.map (fun (_,_,te) -> instantiate_parameters lifted_params te) cl
295 List.for_all (does_not_occur ~subst context n nn) arguments &&
297 (weakly_positive ~subst ((name,C.Decl ity)::context) (n+1) (nn+1) uri) cl
300 (* the inductive type indexes are s.t. n < x <= nn *)
301 and are_all_occurrences_positive ~subst context uri indparamsno i n nn te =
302 match R.whd context te with
303 | C.Appl ((C.Rel m)::tl) as reduct when m = i ->
309 match R.whd context x with
310 | C.Rel m when m = n - (indparamsno - k) -> k - 1
311 | y -> raise (TypeCheckerFailure (lazy
312 ("Argument "^string_of_int (indparamsno - k + 1) ^ " (of " ^
313 string_of_int indparamsno ^ " fixed) is not homogeneous in "^
314 "appl:\n"^ PP.ppterm ~context ~subst ~metasenv:[] reduct))))
318 List.for_all (does_not_occur ~subst context n nn) tl
320 raise (TypeCheckerFailure
321 (lazy ("Non-positive occurence in mutual inductive definition(s) [2]"^
322 NUri.string_of_uri uri)))
323 | C.Rel m when m = i ->
324 if indparamsno = 0 then
327 raise (TypeCheckerFailure
328 (lazy ("Non-positive occurence in mutual inductive definition(s) [3]"^
329 NUri.string_of_uri uri)))
330 | C.Prod (name,source,dest) when
331 does_not_occur ~subst ((name,C.Decl source)::context) 0 1 dest ->
332 strictly_positive ~subst context n nn source &&
333 are_all_occurrences_positive ~subst
334 ((name,C.Decl source)::context) uri indparamsno
335 (i+1) (n + 1) (nn + 1) dest
336 | C.Prod (name,source,dest) ->
337 if not (does_not_occur ~subst context n nn source) then
338 raise (TypeCheckerFailure (lazy ("Non-positive occurrence in "^
339 PP.ppterm ~context ~metasenv:[] ~subst te)));
340 are_all_occurrences_positive ~subst ((name,C.Decl source)::context)
341 uri indparamsno (i+1) (n + 1) (nn + 1) dest
344 (TypeCheckerFailure (lazy ("Malformed inductive constructor type " ^
345 (NUri.string_of_uri uri))))
348 exception NotGuarded of string Lazy.t;;
350 let rec typeof ~subst ~metasenv context term =
351 let rec typeof_aux context =
352 fun t -> (*prerr_endline (PP.ppterm ~metasenv ~subst ~context t);*)
356 match List.nth context (n - 1) with
357 | (_,C.Decl ty) -> S.lift n ty
358 | (_,C.Def (_,ty)) -> S.lift n ty
359 with Failure _ -> raise (TypeCheckerFailure (lazy "unbound variable")))
360 | C.Sort (C.Type i) -> C.Sort (C.Type (i+1))
361 | C.Sort s -> C.Sort (C.Type 0)
362 | C.Implicit _ -> raise (AssertFailure (lazy "Implicit found"))
363 | C.Meta (n,l) as t ->
364 let canonical_ctx,ty =
366 let _,c,_,ty = U.lookup_subst n subst in c,ty
367 with U.Subst_not_found _ -> try
368 let _,_,c,ty = U.lookup_meta n metasenv in c,ty
369 with U.Meta_not_found _ ->
370 raise (AssertFailure (lazy (Printf.sprintf
371 "%s not found" (PP.ppterm ~subst ~metasenv ~context t))))
373 check_metasenv_consistency t ~subst ~metasenv context canonical_ctx l;
375 | C.Const ref -> type_of_constant ref
376 | C.Prod (name,s,t) ->
377 let sort1 = typeof_aux context s in
378 let sort2 = typeof_aux ((name,(C.Decl s))::context) t in
379 sort_of_prod ~metasenv ~subst context (name,s) (sort1,sort2)
380 | C.Lambda (n,s,t) ->
381 let sort = typeof_aux context s in
382 (match R.whd ~subst context sort with
383 | C.Meta _ | C.Sort _ -> ()
386 (TypeCheckerFailure (lazy (Printf.sprintf
387 ("Not well-typed lambda-abstraction: " ^^
388 "the source %s should be a type; instead it is a term " ^^
389 "of type %s") (PP.ppterm ~subst ~metasenv ~context s)
390 (PP.ppterm ~subst ~metasenv ~context sort)))));
391 let ty = typeof_aux ((n,(C.Decl s))::context) t in
393 | C.LetIn (n,ty,t,bo) ->
394 let ty_t = typeof_aux context t in
395 let _ = typeof_aux context ty in
396 if not (R.are_convertible ~subst ~metasenv context ty ty_t) then
399 (lazy (Printf.sprintf
400 "The type of %s is %s but it is expected to be %s"
401 (PP.ppterm ~subst ~metasenv ~context t)
402 (PP.ppterm ~subst ~metasenv ~context ty_t)
403 (PP.ppterm ~subst ~metasenv ~context ty))))
405 let ty_bo = typeof_aux ((n,C.Def (t,ty))::context) bo in
406 S.subst ~avoid_beta_redexes:true t ty_bo
407 | C.Appl (he::(_::_ as args)) ->
408 let ty_he = typeof_aux context he in
409 let args_with_ty = List.map (fun t -> t, typeof_aux context t) args in
411 prerr_endline ("HEAD: " ^ PP.ppterm ~subst ~metasenv ~context ty_he);
412 prerr_endline ("TARGS: " ^ String.concat " | " (List.map (PP.ppterm
413 ~subst ~metasenv ~context) (List.map snd args_with_ty)));
414 prerr_endline ("ARGS: " ^ String.concat " | " (List.map (PP.ppterm
415 ~subst ~metasenv ~context) (List.map fst args_with_ty)));
417 eat_prods ~subst ~metasenv context he ty_he args_with_ty
418 | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
419 | C.Match (Ref.Ref (_,_,Ref.Ind tyno) as r,outtype,term,pl) ->
420 let outsort = typeof_aux context outtype in
421 let inductive,leftno,itl,_,_ = E.get_checked_indtys r in
423 let _,_,_,cl = List.nth itl tyno in List.length cl
425 let parameters, arguments =
426 let ty = R.whd ~subst context (typeof_aux context term) in
429 C.Const (Ref.Ref (_,_,Ref.Ind _) as r') -> r',[]
430 | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _) as r') :: tl) -> r',tl
433 (TypeCheckerFailure (lazy (Printf.sprintf
434 "Case analysis: analysed term %s is not an inductive one"
435 (PP.ppterm ~subst ~metasenv ~context term)))) in
436 if not (Ref.eq r r') then
438 (TypeCheckerFailure (lazy (Printf.sprintf
439 ("Case analysys: analysed term type is %s, but is expected " ^^
440 "to be (an application of) %s")
441 (PP.ppterm ~subst ~metasenv ~context ty)
442 (PP.ppterm ~subst ~metasenv ~context (C.Const r')))))
444 try HExtlib.split_nth leftno tl
447 raise (TypeCheckerFailure (lazy (Printf.sprintf
448 "%s is partially applied"
449 (PP.ppterm ~subst ~metasenv ~context ty)))) in
450 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
451 let sort_of_ind_type =
452 if parameters = [] then C.Const r
453 else C.Appl ((C.Const r)::parameters) in
454 let type_of_sort_of_ind_ty = typeof_aux context sort_of_ind_type in
455 check_allowed_sort_elimination ~subst ~metasenv r context
456 sort_of_ind_type type_of_sort_of_ind_ty outsort;
457 (* let's check if the type of branches are right *)
458 if List.length pl <> constructorsno then
459 raise (TypeCheckerFailure (lazy ("Wrong number of cases in a match")));
460 let j,branches_ok,p_ty, exp_p_ty =
462 (fun (j,b,old_p_ty,old_exp_p_ty) p ->
465 let cons = Ref.mk_constructor j r in
466 if parameters = [] then C.Const cons
467 else C.Appl (C.Const cons::parameters)
469 let ty_p = typeof_aux context p in
470 let ty_cons = typeof_aux context cons in
472 type_of_branch ~subst context leftno outtype cons ty_cons 0
474 j+1, R.are_convertible ~subst ~metasenv context ty_p ty_branch,
477 j,false,old_p_ty,old_exp_p_ty
478 ) (1,true,C.Sort C.Prop,C.Sort C.Prop) pl
480 if not branches_ok then
483 (lazy (Printf.sprintf ("Branch for constructor %s :=\n%s\n"^^
484 "has type %s\nnot convertible with %s")
485 (PP.ppterm ~subst ~metasenv ~context
486 (C.Const (Ref.mk_constructor (j-1) r)))
487 (PP.ppterm ~metasenv ~subst ~context (List.nth pl (j-2)))
488 (PP.ppterm ~metasenv ~subst ~context p_ty)
489 (PP.ppterm ~metasenv ~subst ~context exp_p_ty))));
490 let res = outtype::arguments@[term] in
491 R.head_beta_reduce (C.Appl res)
492 | C.Match _ -> assert false
494 and type_of_branch ~subst context leftno outty cons tycons liftno =
495 match R.whd ~subst context tycons with
496 | C.Const (Ref.Ref (_,_,Ref.Ind _)) -> C.Appl [S.lift liftno outty ; cons]
497 | C.Appl (C.Const (Ref.Ref (_,_,Ref.Ind _))::tl) ->
498 let _,arguments = HExtlib.split_nth leftno tl in
499 C.Appl (S.lift liftno outty::arguments@[cons])
500 | C.Prod (name,so,de) ->
502 match S.lift 1 cons with
503 | C.Appl l -> C.Appl (l@[C.Rel 1])
504 | t -> C.Appl [t ; C.Rel 1]
507 type_of_branch ~subst ((name,(C.Decl so))::context)
508 leftno outty cons de (liftno+1))
509 | _ -> raise (AssertFailure (lazy "type_of_branch"))
511 (* check_metasenv_consistency checks that the "canonical" context of a
512 metavariable is consitent - up to relocation via the relocation list l -
513 with the actual context *)
514 and check_metasenv_consistency
515 ~subst ~metasenv term context canonical_context l
519 let context = snd (HExtlib.split_nth shift context) in
520 let rec compare = function
524 raise (AssertFailure (lazy (Printf.sprintf
525 "Local and canonical context %s have different lengths"
526 (PP.ppterm ~subst ~context ~metasenv term))))
528 raise (TypeCheckerFailure (lazy (Printf.sprintf
529 "Unbound variable -%d in %s" m
530 (PP.ppterm ~subst ~metasenv ~context term))))
533 (_,C.Decl t1), (_,C.Decl t2)
534 | (_,C.Def (t1,_)), (_,C.Def (t2,_))
535 | (_,C.Def (_,t1)), (_,C.Decl t2) ->
536 if not (R.are_convertible ~subst ~metasenv tl t1 t2) then
539 (lazy (Printf.sprintf
540 ("Not well typed metavariable local context for %s: " ^^
541 "%s expected, which is not convertible with %s")
542 (PP.ppterm ~subst ~metasenv ~context term)
543 (PP.ppterm ~subst ~metasenv ~context t2)
544 (PP.ppterm ~subst ~metasenv ~context t1))))
547 (TypeCheckerFailure (lazy (Printf.sprintf
548 ("Not well typed metavariable local context for %s: " ^^
549 "a definition expected, but a declaration found")
550 (PP.ppterm ~subst ~metasenv ~context term)))));
551 compare (m - 1,tl,ctl)
553 compare (n,context,canonical_context)
555 (* we avoid useless lifting by shortening the context*)
556 let l,context = (0,lc_kind), snd (HExtlib.split_nth shift context) in
557 let lifted_canonical_context =
558 let rec lift_metas i = function
560 | (n,C.Decl t)::tl ->
561 (n,C.Decl (S.subst_meta l (S.lift i t)))::(lift_metas (i+1) tl)
562 | (n,C.Def (t,ty))::tl ->
563 (n,C.Def ((S.subst_meta l (S.lift i t)),
564 S.subst_meta l (S.lift i ty)))::(lift_metas (i+1) tl)
566 lift_metas 1 canonical_context in
567 let l = U.expand_local_context lc_kind in
572 | t, (_,C.Def (ct,_)) ->
573 (*CSC: the following optimization is to avoid a possibly expensive
574 reduction that can be easily avoided and that is quite
575 frequent. However, this is better handled using levels to
581 match List.nth context (n - 1) with
582 | (_,C.Def (te,_)) -> S.lift n te
587 if not (R.are_convertible ~subst ~metasenv context optimized_t ct)
591 (lazy (Printf.sprintf
592 ("Not well typed metavariable local context: " ^^
593 "expected a term convertible with %s, found %s")
594 (PP.ppterm ~subst ~metasenv ~context ct)
595 (PP.ppterm ~subst ~metasenv ~context t))))
596 | t, (_,C.Decl ct) ->
597 let type_t = typeof_aux context t in
598 if not (R.are_convertible ~subst ~metasenv context type_t ct) then
599 raise (TypeCheckerFailure
600 (lazy (Printf.sprintf
601 ("Not well typed metavariable local context: "^^
602 "expected a term of type %s, found %s of type %s")
603 (PP.ppterm ~subst ~metasenv ~context ct)
604 (PP.ppterm ~subst ~metasenv ~context t)
605 (PP.ppterm ~subst ~metasenv ~context type_t))))
606 ) l lifted_canonical_context
608 Invalid_argument _ ->
609 raise (AssertFailure (lazy (Printf.sprintf
610 "Local and canonical context %s have different lengths"
611 (PP.ppterm ~subst ~metasenv ~context term))))
613 and is_non_informative context paramsno c =
614 let rec aux context c =
615 match R.whd context c with
616 | C.Prod (n,so,de) ->
617 let s = typeof_aux context so in
618 s = C.Sort C.Prop && aux ((n,(C.Decl so))::context) de
620 let context',dx = split_prods ~subst:[] context paramsno c in
623 and check_allowed_sort_elimination ~subst ~metasenv r =
626 | C.Appl l -> C.Appl (l @ [arg])
627 | t -> C.Appl [t;arg] in
628 let rec aux context ind arity1 arity2 =
629 let arity1 = R.whd ~subst context arity1 in
630 let arity2 = R.whd ~subst context arity2 in
631 match arity1,arity2 with
632 | C.Prod (name,so1,de1), C.Prod (_,so2,de2) ->
633 if not (R.are_convertible ~subst ~metasenv context so1 so2) then
634 raise (TypeCheckerFailure (lazy (Printf.sprintf
635 "In outtype: expected %s, found %s"
636 (PP.ppterm ~subst ~metasenv ~context so1)
637 (PP.ppterm ~subst ~metasenv ~context so2)
639 aux ((name, C.Decl so1)::context)
640 (mkapp (S.lift 1 ind) (C.Rel 1)) de1 de2
641 | C.Sort _, C.Prod (name,so,ta) ->
642 if not (R.are_convertible ~subst ~metasenv context so ind) then
643 raise (TypeCheckerFailure (lazy (Printf.sprintf
644 "In outtype: expected %s, found %s"
645 (PP.ppterm ~subst ~metasenv ~context ind)
646 (PP.ppterm ~subst ~metasenv ~context so)
648 (match arity1,ta with
649 | (C.Sort (C.CProp | C.Type _), C.Sort _)
650 | (C.Sort C.Prop, C.Sort C.Prop) -> ()
651 | (C.Sort C.Prop, C.Sort (C.CProp | C.Type _)) ->
652 (* TODO: we should pass all these parameters since we
653 * have them already *)
654 let inductive,leftno,itl,_,i = E.get_checked_indtys r in
655 let itl_len = List.length itl in
656 let _,name,ty,cl = List.nth itl i in
657 let cl_len = List.length cl in
658 (* is it a singleton or empty non recursive and non informative
662 (itl_len = 1 && cl_len = 1 &&
663 is_non_informative [name,C.Decl ty] leftno
664 (let _,_,x = List.nth cl 0 in x)))
666 raise (TypeCheckerFailure (lazy
667 ("Sort elimination not allowed")));
674 typeof_aux context term
676 and check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl =
677 (* let's check if the arity of the inductive types are well formed *)
678 List.iter (fun (_,_,x,_) -> ignore (typeof ~subst ~metasenv [] x)) tyl;
679 (* let's check if the types of the inductive constructors are well formed. *)
680 let len = List.length tyl in
681 let tys = List.rev (List.map (fun (_,n,ty,_) -> (n,(C.Decl ty))) tyl) in
687 let debruijnedte = debruijn uri len [] te in
688 ignore (typeof ~subst ~metasenv tys debruijnedte);
689 (* let's check also the positivity conditions *)
692 (are_all_occurrences_positive ~subst tys uri leftno i 0 len
697 (lazy ("Non positive occurence in "^NUri.string_of_uri uri))))
702 and eat_lambdas ~subst ~metasenv context n te =
703 match (n, R.whd ~subst context te) with
704 | (0, _) -> (te, context)
705 | (n, C.Lambda (name,so,ta)) when n > 0 ->
706 eat_lambdas ~subst ~metasenv ((name,(C.Decl so))::context) (n - 1) ta
708 raise (AssertFailure (lazy (Printf.sprintf "eat_lambdas (%d, %s)" n
709 (PP.ppterm ~subst ~metasenv ~context te))))
711 and eat_or_subst_lambdas ~subst ~metasenv n te to_be_subst args
712 (context, recfuns, x as k)
714 match n, R.whd ~subst context te, to_be_subst, args with
715 | (n, C.Lambda (name,so,ta),true::to_be_subst,arg::args) when n > 0 ->
716 eat_or_subst_lambdas ~subst ~metasenv (n - 1) (S.subst arg ta)
718 | (n, C.Lambda (name,so,ta),false::to_be_subst,arg::args) when n > 0 ->
719 eat_or_subst_lambdas ~subst ~metasenv (n - 1) ta to_be_subst args
720 (shift_k (name,(C.Decl so)) k)
721 | (_, te, _, _) -> te, k
723 and guarded_by_destructors r_uri r_len ~subst ~metasenv context recfuns t =
724 let recursor f k t = U.fold shift_k k (fun k () -> f k) () t in
725 let rec aux (context, recfuns, x as k) t =
727 prerr_endline ("GB:\n" ^
728 PP.ppcontext ~subst ~metasenv context^
729 PP.ppterm ~metasenv ~subst ~context t^
730 string_of_recfuns ~subst ~metasenv ~context recfuns);
734 | C.Rel m as t when is_dangerous m recfuns ->
735 raise (NotGuarded (lazy
736 (PP.ppterm ~subst ~metasenv ~context t ^
737 " is a partial application of a fix")))
738 | C.Appl ((C.Rel m)::tl) as t when is_dangerous m recfuns ->
739 let rec_no = get_recno m recfuns in
740 if not (List.length tl > rec_no) then
741 raise (NotGuarded (lazy
742 (PP.ppterm ~context ~subst ~metasenv t ^
743 " is a partial application of a fix")))
745 let rec_arg = List.nth tl rec_no in
746 if not (is_really_smaller r_uri r_len ~subst ~metasenv k rec_arg) then
747 raise (NotGuarded (lazy (Printf.sprintf ("Recursive call %s, %s is not"
748 ^^ " smaller.\ncontext:\n%s") (PP.ppterm ~context ~subst ~metasenv
749 t) (PP.ppterm ~context ~subst ~metasenv rec_arg)
750 (PP.ppcontext ~subst ~metasenv context))));
752 | C.Appl ((C.Rel m)::tl) when is_unfolded m recfuns ->
753 let fixed_args = get_fixed_args m recfuns in
754 list_iter_default2 (fun x b -> if not b then aux k x) tl false fixed_args
756 (match List.nth context (m-1) with
758 | _,C.Def (bo,_) -> aux k (S.lift m bo))
760 | C.Appl (C.Const ((Ref.Ref (_,uri,Ref.Fix (i,recno))) as r)::args) ->
761 if List.exists (fun t -> try aux k t;false with NotGuarded _ -> true) args
763 let fl,_,_ = E.get_checked_fixes_or_cofixes r in
765 List.split (List.map (fun (_,name,_,ty,bo) -> (name, C.Decl ty), bo) fl)
767 let fl_len = List.length fl in
768 let bos = List.map (debruijn uri fl_len context) bos in
769 let j = List.fold_left min max_int (List.map (fun (_,_,i,_,_)->i) fl) in
770 let ctx_len = List.length context in
771 (* we may look for fixed params not only up to j ... *)
772 let fa = fixed_args bos j ctx_len (ctx_len + fl_len) in
773 list_iter_default2 (fun x b -> if not b then aux k x) args false fa;
774 let context = context@ctx_tys in
775 let ctx_len = List.length context in
777 HExtlib.list_mapi (fun _ i -> ctx_len - i, UnfFix fa) ctx_tys
779 let new_k = context, extra_recfuns@recfuns, x in
784 eat_or_subst_lambdas ~subst ~metasenv j bo fa args new_k
788 List.length args > recno &&
789 (*case where the recursive argument is already really_smaller *)
790 is_really_smaller r_uri r_len ~subst ~metasenv k
791 (List.nth args recno)
793 let bo,(context, _, _ as new_k) = bo_and_k in
795 eat_lambdas ~subst ~metasenv context (recno + 1 - j) bo in
796 let new_context_part,_ =
797 HExtlib.split_nth (List.length context' - List.length context)
799 let k = List.fold_right shift_k new_context_part new_k in
800 let context, recfuns, x = k in
801 let k = context, (1,Safe)::recfuns, x in
807 List.iter (fun (bo,k) -> aux k bo) bos_and_ks
808 | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) as t ->
809 (match R.whd ~subst context term with
810 | C.Rel m | C.Appl (C.Rel m :: _ ) as t when is_safe m recfuns || m = x ->
811 (* TODO: add CoInd to references so that this call is useless *)
812 let isinductive, _, _, _, _ = E.get_checked_indtys ref in
813 if not isinductive then recursor aux k t
815 let ty = typeof ~subst ~metasenv context term in
816 let dc_ctx, dcl, start, stop =
817 specialize_and_abstract_constrs ~subst r_uri r_len context ty in
818 let args = match t with C.Appl (_::tl) -> tl | _ -> [] in
820 List.iter (aux k) args;
823 let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in
824 let p, k = get_new_safes ~subst k p rl in
827 | _ -> recursor aux k t)
828 | t -> recursor aux k t
830 NotGuarded _ as exc ->
831 let t' = R.whd ~delta:0 ~subst context t in
832 if t = t' then raise exc
835 try aux (context, recfuns, 1) t
836 with NotGuarded s -> raise (TypeCheckerFailure s)
838 and guarded_by_constructors ~subst ~metasenv context t indURI indlen nn =
839 let rec aux context n nn h te =
840 match R.whd ~subst context te with
841 | C.Rel m when m > n && m <= nn -> h
842 | C.Rel _ | C.Meta _ -> true
846 | C.Const (Ref.Ref (_,_,Ref.Ind _))
847 | C.LetIn _ -> raise (AssertFailure (lazy "17"))
848 | C.Lambda (name,so,de) ->
849 does_not_occur ~subst context n nn so &&
850 aux ((name,C.Decl so)::context) (n + 1) (nn + 1) h de
851 | C.Appl ((C.Rel m)::tl) when m > n && m <= nn ->
852 h && List.for_all (does_not_occur ~subst context n nn) tl
853 | C.Const (Ref.Ref (_,_,Ref.Con _)) -> true
854 | C.Appl (C.Const (Ref.Ref (_,uri, Ref.Con (_,j)) as ref) :: tl) as t ->
855 let _, paramsno, _, _, _ = E.get_checked_indtys ref in
856 let ty_t = typeof ~subst ~metasenv context t in
857 let dc_ctx, dcl, start, stop =
858 specialize_and_abstract_constrs ~subst indURI indlen context ty_t in
859 let _, dc = List.nth dcl (j-1) in
861 prerr_endline (PP.ppterm ~subst ~metasenv ~context:dc_ctx dc);
862 prerr_endline (PP.ppcontext ~subst ~metasenv dc_ctx);
864 let rec_params = recursive_args ~subst ~metasenv dc_ctx start stop dc in
865 let rec analyse_instantiated_type rec_spec args =
866 match rec_spec, args with
867 | h::rec_spec, he::args ->
868 aux context n nn h he && analyse_instantiated_type rec_spec args
870 | _ -> raise (AssertFailure (lazy
871 ("Too many args for constructor: " ^ String.concat " "
872 (List.map (fun x-> PP.ppterm ~subst ~metasenv ~context x) args))))
874 let left, args = HExtlib.split_nth paramsno tl in
875 List.for_all (does_not_occur ~subst context n nn) left &&
876 analyse_instantiated_type rec_params args
877 | C.Appl ((C.Match (_,out,te,pl))::_)
878 | C.Match (_,out,te,pl) as t ->
879 let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
880 List.for_all (does_not_occur ~subst context n nn) tl &&
881 does_not_occur ~subst context n nn out &&
882 does_not_occur ~subst context n nn te &&
883 List.for_all (aux context n nn h) pl
884 | C.Const (Ref.Ref (_,u,(Ref.Fix _| Ref.CoFix _)) as ref)
885 | C.Appl(C.Const (Ref.Ref(_,u,(Ref.Fix _| Ref.CoFix _)) as ref) :: _) as t ->
886 let tl = match t with C.Appl (_::tl) -> tl | _ -> [] in
887 let fl,_,_ = E.get_checked_fixes_or_cofixes ref in
888 let len = List.length fl in
889 let tys = List.map (fun (_,n,_,ty,_) -> n, C.Decl ty) fl in
890 List.for_all (does_not_occur ~subst context n nn) tl &&
893 aux (context@tys) n nn h (debruijn u len context bo))
896 | C.Appl _ as t -> does_not_occur ~subst context n nn t
898 aux context 0 nn false t
900 and recursive_args ~subst ~metasenv context n nn te =
901 match R.whd context te with
902 | C.Rel _ | C.Appl _ | C.Const _ -> []
903 | C.Prod (name,so,de) ->
904 (not (does_not_occur ~subst context n nn so)) ::
905 (recursive_args ~subst ~metasenv
906 ((name,(C.Decl so))::context) (n+1) (nn + 1) de)
908 raise (AssertFailure (lazy ("recursive_args:" ^ PP.ppterm ~subst
909 ~metasenv ~context:[] t)))
911 and get_new_safes ~subst (context, recfuns, x as k) p rl =
912 match R.whd ~subst context p, rl with
913 | C.Lambda (name,so,ta), b::tl ->
914 let recfuns = (if b then [0,Safe] else []) @ recfuns in
916 (shift_k (name,(C.Decl so)) (context, recfuns, x)) ta tl
917 | C.Meta _ as e, _ | e, [] -> e, k
918 | _ -> raise (AssertFailure (lazy "Ill formed pattern"))
920 and is_really_smaller
921 r_uri r_len ~subst ~metasenv (context, recfuns, x as k) te
923 match R.whd ~subst context te with
924 | C.Rel m when is_safe m recfuns -> true
925 | C.Lambda (name, s, t) ->
926 is_really_smaller r_uri r_len ~subst ~metasenv (shift_k (name,C.Decl s) k) t
928 is_really_smaller r_uri r_len ~subst ~metasenv k he
930 | C.Const (Ref.Ref (_,_,Ref.Con _)) -> false
932 | C.Const (Ref.Ref (_,_,Ref.Fix _)) -> assert false
934 | C.Match (Ref.Ref (_,uri,_) as ref,outtype,term,pl) ->
936 | C.Rel m | C.Appl (C.Rel m :: _ ) when is_safe m recfuns || m = x ->
937 (* TODO: add CoInd to references so that this call is useless *)
938 let isinductive, _, _, _, _ = E.get_checked_indtys ref in
939 if not isinductive then
940 List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl
942 let ty = typeof ~subst ~metasenv context term in
943 let dc_ctx, dcl, start, stop =
944 specialize_and_abstract_constrs ~subst r_uri r_len context ty in
947 let rl = recursive_args ~subst ~metasenv dc_ctx start stop dc in
948 let e, k = get_new_safes ~subst k p rl in
949 is_really_smaller r_uri r_len ~subst ~metasenv k e)
951 | _ -> List.for_all (is_really_smaller r_uri r_len ~subst ~metasenv k) pl)
954 and returns_a_coinductive ~subst context ty =
955 match R.whd ~subst context ty with
956 | C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)
957 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)::_) ->
958 let isinductive, _, itl, _, _ = E.get_checked_indtys ref in
959 if isinductive then None else (Some (uri,List.length itl))
960 | C.Prod (n,so,de) ->
961 returns_a_coinductive ~subst ((n,C.Decl so)::context) de
964 and type_of_constant ((Ref.Ref (_,uri,_)) as ref) =
965 match E.get_checked_obj uri, ref with
966 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Ind i) ->
967 let _,_,arity,_ = List.nth tl i in arity
968 | (_,_,_,_,C.Inductive (_,_,tl,_)), Ref.Ref (_,_,Ref.Con (i,j)) ->
969 let _,_,_,cl = List.nth tl i in
970 let _,_,arity = List.nth cl (j-1) in
972 | (_,_,_,_,C.Fixpoint (_,fl,_)), Ref.Ref (_,_,(Ref.Fix (i,_)|Ref.CoFix i)) ->
973 let _,_,_,arity,_ = List.nth fl i in
975 | (_,_,_,_,C.Constant (_,_,_,ty,_)), Ref.Ref (_,_,(Ref.Def |Ref.Decl)) -> ty
976 | _ -> raise (AssertFailure (lazy "type_of_constant: environment/reference"))
979 let typecheck_obj (uri,height,metasenv,subst,kind) =
980 (* CSC: here we should typecheck the metasenv and the subst *)
981 assert (metasenv = [] && subst = []);
983 | C.Constant (_,_,Some te,ty,_) ->
984 let _ = typeof ~subst ~metasenv [] ty in
985 let ty_te = typeof ~subst ~metasenv [] te in
986 if not (R.are_convertible ~subst ~metasenv [] ty_te ty) then
987 raise (TypeCheckerFailure (lazy (Printf.sprintf (
988 "the type of the body is not convertible with the declared one.\n"^^
989 "inferred type:\n%s\nexpected type:\n%s")
990 (PP.ppterm ~subst ~metasenv ~context:[] ty_te)
991 (PP.ppterm ~subst ~metasenv ~context:[] ty))))
992 | C.Constant (_,_,None,ty,_) -> ignore (typeof ~subst ~metasenv [] ty)
993 | C.Inductive (is_ind, leftno, tyl, _) ->
994 check_mutual_inductive_defs uri ~metasenv ~subst is_ind leftno tyl
995 | C.Fixpoint (inductive,fl,_) ->
998 (fun (types,kl) (_,name,k,ty,_) ->
999 let _ = typeof ~subst ~metasenv [] ty in
1000 ((name,C.Decl ty)::types, k::kl)
1003 let len = List.length types in
1005 List.split (List.map2
1006 (fun (_,_,_,_,bo) rno ->
1007 let dbo = debruijn uri len [] bo in
1011 List.iter2 (fun (_,name,x,ty,_) bo ->
1012 let ty_bo = typeof ~subst ~metasenv types bo in
1013 if not (R.are_convertible ~subst ~metasenv types ty_bo ty)
1014 then raise (TypeCheckerFailure (lazy ("(Co)Fix: ill-typed bodies")))
1016 if inductive then begin
1017 let m, context = eat_lambdas ~subst ~metasenv types (x + 1) bo in
1020 match List.hd context with _,C.Decl t -> t | _ -> assert false
1022 match R.whd ~subst (List.tl context) he with
1023 | C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref)
1024 | C.Appl (C.Const (Ref.Ref (_,uri,Ref.Ind _) as ref) :: _) ->
1025 let _,_,itl,_,_ = E.get_checked_indtys ref in
1026 uri, List.length itl
1029 (* guarded by destructors conditions D{f,k,x,M} *)
1030 let rec enum_from k =
1031 function [] -> [] | v::tl -> (k,v)::enum_from (k+1) tl
1033 guarded_by_destructors r_uri r_len
1034 ~subst ~metasenv context (enum_from (x+2) kl) m
1036 match returns_a_coinductive ~subst [] ty with
1038 raise (TypeCheckerFailure
1039 (lazy "CoFix: does not return a coinductive type"))
1040 | Some (r_uri, r_len) ->
1041 (* guarded by constructors conditions C{f,M} *)
1043 (guarded_by_constructors ~subst ~metasenv types bo r_uri r_len len)
1045 raise (TypeCheckerFailure
1046 (lazy "CoFix: not guarded by constructors"))
1050 (* web interface stuff *)
1053 ref (function (`Start_type_checking _|`Type_checking_completed _|`Type_checking_interrupted _|`Type_checking_failed _) -> ())
1056 let set_logger f = logger := f;;
1058 let typecheck_obj obj =
1059 let u,_,_,_,_ = obj in
1061 !logger (`Start_type_checking u);
1063 !logger (`Type_checking_completed u)
1066 !logger (`Type_checking_interrupted u);
1069 !logger (`Type_checking_failed u);
1073 E.set_typecheck_obj typecheck_obj;;