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_______________________________________________________________ *)
14 exception RefineFailure of (Stdpp.location * string) Lazy.t;;
15 exception Uncertain of (Stdpp.location * string) Lazy.t;;
16 exception AssertFailure of string Lazy.t;;
19 module Ref = NReference
22 let inside c = indent := !indent ^ String.make 1 c;;
23 let outside () = indent := String.sub !indent 0 (String.length !indent -1);;
28 prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
35 let wrap_exc msg = function
36 | NCicUnification.Uncertain _ -> Uncertain msg
37 | NCicUnification.UnificationFailure _ -> RefineFailure msg
38 | NCicTypeChecker.TypeCheckerFailure _ -> RefineFailure msg
42 let exp_implicit metasenv context expty =
43 let foo x = match expty with Some t -> `WithType t | None -> x in
45 | `Closed -> NCicMetaSubst.mk_meta metasenv [] (foo `Term)
46 | `Type -> NCicMetaSubst.mk_meta metasenv context (foo `Type)
47 | `Term -> NCicMetaSubst.mk_meta metasenv context (foo `Term)
52 let check_allowed_sort_elimination localise r orig =
55 | C.Appl l -> C.Appl (l @ [arg])
56 | t -> C.Appl [t;arg] in
57 (* ctx, ind_type @ lefts, sort_of_ind_ty@lefts, outsort *)
58 let rec aux metasenv subst context ind arity1 arity2 =
59 (*D*)inside 'S'; try let rc =
60 let arity1 = NCicReduction.whd ~subst context arity1 in
61 pp (lazy(NCicPp.ppterm ~subst ~metasenv ~context arity1 ^ " elimsto " ^
62 NCicPp.ppterm ~subst ~metasenv ~context arity2 ^ "\nMENV:\n"^
63 NCicPp.ppmetasenv ~subst metasenv));
65 | C.Prod (name,so1,de1) (* , t ==?== C.Prod _ *) ->
66 let metasenv, meta, _ =
67 NCicMetaSubst.mk_meta metasenv ((name,C.Decl so1)::context) `Type
70 try NCicUnification.unify metasenv subst context
71 arity2 (C.Prod (name, so1, meta))
72 with exc -> raise (wrap_exc (lazy (localise orig, Printf.sprintf
73 "expected %s, found %s" (* XXX localizzare meglio *)
74 (NCicPp.ppterm ~subst ~metasenv ~context (C.Prod (name, so1, meta)))
75 (NCicPp.ppterm ~subst ~metasenv ~context arity2))) exc)
77 aux metasenv subst ((name, C.Decl so1)::context)
78 (mkapp (NCicSubstitution.lift 1 ind) (C.Rel 1)) de1 meta
79 | C.Sort _ (* , t ==?== C.Prod _ *) ->
80 let metasenv, meta, _ = NCicMetaSubst.mk_meta metasenv [] `Type in
82 try NCicUnification.unify metasenv subst context
83 arity2 (C.Prod ("_", ind, meta))
84 with exc -> raise (wrap_exc (lazy (localise orig, Printf.sprintf
85 "expected %s, found %s" (* XXX localizzare meglio *)
86 (NCicPp.ppterm ~subst ~metasenv ~context (C.Prod ("_", ind, meta)))
87 (NCicPp.ppterm ~subst ~metasenv ~context arity2))) exc)
89 (try NCicTypeChecker.check_allowed_sort_elimination
90 ~metasenv ~subst r context ind arity1 arity2;
92 with exc -> raise (wrap_exc (lazy (localise orig,
93 "Sort elimination not allowed ")) exc))
95 (*D*)in outside(); rc with exc -> outside (); raise exc
101 ?(localise=fun _ -> Stdpp.dummy_loc)
102 ~look_for_coercion metasenv subst context term expty
104 let force_ty metasenv subst context orig t infty expty =
105 (*D*)inside 'F'; try let rc =
110 | C.Lambda _ -> metasenv, subst, t, expty
113 (NCicPp.ppterm ~metasenv ~subst ~context infty) ^ " === " ^
114 (NCicPp.ppterm ~metasenv ~subst ~context expty)));
116 let metasenv, subst =
117 NCicUnification.unify metasenv subst context infty expty
119 metasenv, subst, t, expty
121 try_coercions ~look_for_coercion ~localise
122 metasenv subst context t orig infty expty true exc)
123 | None -> metasenv, subst, t, infty
124 (*D*)in outside(); rc with exc -> outside (); raise exc
126 let rec typeof_aux metasenv subst context expty =
128 (*D*)inside 'R'; try let rc =
129 pp (lazy (NCicPp.ppterm ~metasenv ~subst ~context t));
130 pp (lazy (NCicPp.ppmetasenv ~subst metasenv));
131 let metasenv, subst, t, infty =
136 match List.nth context (n - 1) with
137 | (_,C.Decl ty) -> NCicSubstitution.lift n ty
138 | (_,C.Def (_,ty)) -> NCicSubstitution.lift n ty
140 raise (RefineFailure (lazy (localise t,"unbound variable"))))
142 metasenv, subst, t, infty
143 | C.Sort (C.Type [false,u]) -> metasenv,subst,t,(C.Sort (C.Type [true, u]))
144 | C.Sort (C.Type _) ->
145 raise (AssertFailure (lazy ("Cannot type an inferred type: "^
146 NCicPp.ppterm ~subst ~metasenv ~context t)))
147 | C.Sort _ -> metasenv,subst,t,(C.Sort (C.Type NCicEnvironment.type0))
148 | C.Implicit infos ->
149 let metasenv,t,ty = exp_implicit metasenv context expty infos in
150 metasenv, subst, t, ty
151 | C.Meta (n,l) as t ->
154 let _,_,_,ty = NCicUtils.lookup_subst n subst in ty
155 with NCicUtils.Subst_not_found _ -> try
156 let _,_,ty = NCicUtils.lookup_meta n metasenv in
157 match ty with C.Implicit _ -> assert false | _ -> ty
158 with NCicUtils.Meta_not_found _ ->
159 raise (AssertFailure (lazy (Printf.sprintf
160 "%s not found" (NCicPp.ppterm ~subst ~metasenv ~context t))))
162 metasenv, subst, t, NCicSubstitution.subst_meta l ty
164 metasenv, subst, t, NCicTypeChecker.typeof ~subst ~metasenv context t
165 | C.Prod (name,(s as orig_s),(t as orig_t)) ->
166 let metasenv, subst, s, s1 = typeof_aux metasenv subst context None s in
167 let metasenv, subst, s, s1 =
168 force_to_sort ~look_for_coercion
169 metasenv subst context s orig_s localise s1 in
170 let context1 = (name,(C.Decl s))::context in
171 let metasenv, subst, t, s2 = typeof_aux metasenv subst context1 None t in
172 let metasenv, subst, t, s2 =
173 force_to_sort ~look_for_coercion
174 metasenv subst context1 t orig_t localise s2 in
175 let metasenv, subst, s, t, ty =
176 sort_of_prod localise metasenv subst
177 context orig_s orig_t (name,s) t (s1,s2)
179 metasenv, subst, NCic.Prod(name,s,t), ty
180 | C.Lambda (n,(s as orig_s),t) ->
181 let exp_s, exp_ty_t =
185 match NCicReduction.whd ~subst context expty with
186 | C.Prod (_,s,t) -> Some s, Some t
187 | _ -> None, None (** XXX FUNCLASS |-> QUALCOSA *)
189 let metasenv, subst, s, ty_s =
190 typeof_aux metasenv subst context None s in
191 let metasenv, subst, s, _ =
192 force_to_sort ~look_for_coercion
193 metasenv subst context s orig_s localise ty_s in
194 let (metasenv,subst), exp_ty_t =
197 (try NCicUnification.unify metasenv subst context s exp_s,exp_ty_t
198 with exc -> raise (wrap_exc (lazy (localise orig_s, Printf.sprintf
199 "Source type %s was expected to be %s" (NCicPp.ppterm ~metasenv
200 ~subst ~context s) (NCicPp.ppterm ~metasenv ~subst ~context
202 | None -> (metasenv, subst), None
204 let context = (n,C.Decl s) :: context in
205 let metasenv, subst, t, ty_t =
206 typeof_aux metasenv subst context exp_ty_t t
208 metasenv, subst, C.Lambda(n,s,t), C.Prod (n,s,ty_t)
209 | C.LetIn (n,(ty as orig_ty),t,bo) ->
210 let metasenv, subst, ty, ty_ty =
211 typeof_aux metasenv subst context None ty in
212 let metasenv, subst, ty, _ =
213 force_to_sort ~look_for_coercion
214 metasenv subst context ty orig_ty localise ty_ty in
215 let metasenv, subst, t, _ =
216 typeof_aux metasenv subst context (Some ty) t in
217 let context1 = (n, C.Def (t,ty)) :: context in
218 let metasenv, subst, bo, bo_ty =
219 typeof_aux metasenv subst context1 None bo
221 let bo_ty = NCicSubstitution.subst ~avoid_beta_redexes:true t bo_ty in
222 metasenv, subst, C.LetIn (n, ty, t, bo), bo_ty
223 | C.Appl ((he as orig_he)::(_::_ as args)) ->
224 let metasenv, subst, he, ty_he =
225 typeof_aux metasenv subst context None he in
226 eat_prods ~localise ~look_for_coercion
227 metasenv subst context orig_he he ty_he args
228 | C.Appl _ -> raise (AssertFailure (lazy "Appl of length < 2"))
229 | C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as r,
230 outtype,(term as orig_term),pl) as orig ->
231 let _, leftno, itl, _, _ = NCicEnvironment.get_checked_indtys r in
232 let _, _, arity, cl = List.nth itl tyno in
233 let constructorsno = List.length cl in
234 let _, metasenv, args =
235 NCicMetaSubst.saturate metasenv subst context arity 0 in
236 let ind = if args = [] then C.Const r else C.Appl (C.Const r::args) in
237 let metasenv, subst, term, _ =
238 typeof_aux metasenv subst context (Some ind) term in
239 let metasenv, subst, outtype, outsort =
240 typeof_aux metasenv subst context None outtype in
241 let parameters, arguments = HExtlib.split_nth leftno args in
242 (* let's control if the sort elimination is allowed: [(I q1 ... qr)|B] *)
244 if parameters = [] then C.Const r
245 else C.Appl ((C.Const r)::parameters) in
246 let metasenv, subst, ind, ind_ty =
247 typeof_aux metasenv subst context None ind in
248 let metasenv, subst =
249 check_allowed_sort_elimination localise r orig_term metasenv subst
250 context ind ind_ty outsort
252 (* let's check if the type of branches are right *)
253 if List.length pl <> constructorsno then
254 raise (RefineFailure (lazy (localise orig,
255 "Wrong number of cases in a match")));
256 let _, metasenv, subst, pl_rev =
258 (fun (j, metasenv, subst, branches) p ->
260 let cons = Ref.mk_constructor j r in
261 if parameters = [] then C.Const cons
262 else C.Appl (C.Const cons::parameters)
264 let metasenv, subst, cons, ty_cons =
265 typeof_aux metasenv subst context None cons in
267 NCicTypeChecker.type_of_branch
268 ~subst context leftno outtype cons ty_cons in
269 pp (lazy ("TYPEOFBRANCH: " ^
270 NCicPp.ppterm ~metasenv ~subst ~context p ^ " ::: " ^
271 NCicPp.ppterm ~metasenv ~subst ~context ty_branch ));
272 let metasenv, subst, p, _ =
273 typeof_aux metasenv subst context (Some ty_branch) p in
274 j+1, metasenv, subst, p :: branches)
275 (1, metasenv, subst, []) pl
278 C.Match (r, outtype, term, List.rev pl_rev),
279 NCicReduction.head_beta_reduce (C.Appl (outtype::arguments@[term]))
280 | C.Match _ as orig ->
281 prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context orig);
284 pp (lazy (NCicPp.ppterm ~metasenv ~subst ~context t ^ " :: "^
285 NCicPp.ppterm ~metasenv ~subst ~context infty ));
286 force_ty metasenv subst context orig t infty expty
287 (*D*)in outside(); rc with exc -> outside (); raise exc
289 typeof_aux metasenv subst context expty term
292 ~localise ~look_for_coercion
293 metasenv subst context t orig_t infty expty perform_unification exc
295 (* we try with a coercion *)
296 let rec first exc = function
298 raise (wrap_exc (lazy (localise orig_t, Printf.sprintf
299 "The term %s has type %s but is here used with type %s"
300 (NCicPp.ppterm ~metasenv ~subst ~context t)
301 (NCicPp.ppterm ~metasenv ~subst ~context infty)
302 (NCicPp.ppterm ~metasenv ~subst ~context expty))) exc)
303 | (metasenv, newterm, newtype, meta)::tl ->
305 pp (lazy ( "UNIFICATION in CTX:\n"^
306 NCicPp.ppcontext ~metasenv ~subst context
308 NCicPp.ppmetasenv metasenv ~subst
310 NCicPp.ppterm ~metasenv ~subst ~context meta ^ " === " ^
311 NCicPp.ppterm ~metasenv ~subst ~context t ^ "\n"));
312 let metasenv, subst =
313 NCicUnification.unify metasenv subst context meta t
315 pp (lazy ( "UNIFICATION in CTX:\n"^
316 NCicPp.ppcontext ~metasenv ~subst context
318 NCicPp.ppmetasenv metasenv ~subst
320 NCicPp.ppterm ~metasenv ~subst ~context newtype ^ " === " ^
321 NCicPp.ppterm ~metasenv ~subst ~context expty ^ "\n"));
322 let metasenv, subst =
323 if perform_unification then
324 NCicUnification.unify metasenv subst context newtype expty
327 metasenv, subst, newterm, newtype
329 | NCicUnification.UnificationFailure _ -> first exc tl
330 | NCicUnification.Uncertain _ as exc -> first exc tl
333 (look_for_coercion metasenv subst context infty expty)
336 ~look_for_coercion metasenv subst context t orig_t localise ty
338 match NCicReduction.whd ~subst context ty with
339 | C.Meta (_,(0,(C.Irl 0 | C.Ctx []))) as ty ->
340 metasenv, subst, t, ty
341 | C.Meta (i,(_,(C.Irl 0 | C.Ctx []))) ->
342 metasenv, subst, t, C.Meta(i,(0,C.Irl 0))
343 | C.Meta (i,(_,lc)) ->
344 let len = match lc with C.Irl len->len | C.Ctx l->List.length l in
345 let metasenv, subst, newmeta =
347 NCicMetaSubst.restrict metasenv subst i (HExtlib.list_seq 1 (len+1))
348 else metasenv, subst, i
350 metasenv, subst, t, C.Meta (newmeta,(0,C.Irl 0))
351 | C.Sort _ as ty -> metasenv, subst, t, ty
353 try_coercions ~localise ~look_for_coercion metasenv subst context
354 t orig_t ty (NCic.Sort (NCic.Type NCicEnvironment.type0)) false
355 (Uncertain (lazy (localise orig_t,
356 "The type of " ^ NCicPp.ppterm ~metasenv ~subst ~context t
357 ^ " is not a sort: " ^ NCicPp.ppterm ~metasenv ~subst ~context ty)))
360 localise metasenv subst context orig_s orig_t (name,s) t (t1, t2)
362 (* force to sort is done in the Prod case in typeof *)
364 | C.Sort _, C.Sort C.Prop -> metasenv, subst, s, t, t2
365 | C.Sort (C.Type u1), C.Sort (C.Type u2) ->
366 metasenv, subst, s, t, C.Sort (C.Type (NCicEnvironment.max u1 u2))
367 | C.Sort C.Prop,C.Sort (C.Type _) -> metasenv, subst, s, t, t2
369 | C.Meta _, C.Meta (_,(_,_))
370 | C.Sort _, C.Meta (_,(_,_)) -> metasenv, subst, s, t, t2
371 | x, (C.Sort _ | C.Meta _) | _, x ->
372 let y, context, orig =
373 if x == t1 then s, context, orig_s
374 else t, ((name,C.Decl s)::context), orig_t
376 raise (RefineFailure (lazy (localise orig,Printf.sprintf
377 "%s is expected to be a type, but its type is %s that is not a sort"
378 (NCicPp.ppterm ~subst ~metasenv ~context y)
379 (NCicPp.ppterm ~subst ~metasenv ~context x))))
382 ~localise ~look_for_coercion metasenv subst context orig_he he ty_he args
384 (*D*)inside 'E'; try let rc =
385 let rec aux metasenv subst args_so_far he ty_he = function
386 | []->metasenv, subst, NCicUntrusted.mk_appl he (List.rev args_so_far), ty_he
388 match NCicReduction.whd ~subst context ty_he with
390 let metasenv, subst, arg, _ =
391 typeof ~look_for_coercion ~localise
392 metasenv subst context arg (Some s) in
393 let t = NCicSubstitution.subst ~avoid_beta_redexes:true arg t in
394 aux metasenv subst (arg :: args_so_far) he t tl
396 | C.Appl (C.Meta _ :: _) as t ->
397 let metasenv, subst, arg, ty_arg =
398 typeof ~look_for_coercion ~localise
399 metasenv subst context arg None in
400 let metasenv, meta, _ =
401 NCicMetaSubst.mk_meta metasenv
402 (("_",C.Decl ty_arg) :: context) `Type
404 let flex_prod = C.Prod ("_", ty_arg, meta) in
405 (* next line grants that ty_args is a type *)
406 let metasenv,subst, flex_prod, _ =
407 typeof ~look_for_coercion ~localise metasenv subst
408 context flex_prod None in
409 pp (lazy ( "UNIFICATION in CTX:\n"^
410 NCicPp.ppcontext ~metasenv ~subst context
412 NCicPp.ppterm ~metasenv ~subst ~context t ^ " === " ^
413 NCicPp.ppterm ~metasenv ~subst ~context flex_prod ^ "\n"));
414 let metasenv, subst =
415 try NCicUnification.unify metasenv subst context t flex_prod
416 with exc -> raise (wrap_exc (lazy (localise orig_he, Printf.sprintf
417 ("The term %s has an inferred type %s, but is applied to the" ^^
418 " argument %s of type %s")
419 (NCicPp.ppterm ~metasenv ~subst ~context he)
420 (NCicPp.ppterm ~metasenv ~subst ~context t)
421 (NCicPp.ppterm ~metasenv ~subst ~context arg)
422 (NCicPp.ppterm ~metasenv ~subst ~context ty_arg))) exc)
423 (* XXX coerce to funclass *)
425 let meta = NCicSubstitution.subst ~avoid_beta_redexes:true arg meta in
426 aux metasenv subst (arg :: args_so_far) he meta tl
427 | C.Match (_,_,C.Meta _,_)
428 | C.Match (_,_,C.Appl (C.Meta _ :: _),_)
429 | C.Appl (C.Const (NReference.Ref (_, NReference.Fix _)) :: _) ->
430 raise (Uncertain (lazy (localise orig_he, Printf.sprintf
431 ("The term %s is here applied to %d arguments but expects " ^^
432 "only %d arguments") (NCicPp.ppterm ~metasenv ~subst ~context he)
433 (List.length args) (List.length args_so_far))))
435 let metasenv, subst, newhead, newheadty =
436 try_coercions ~localise ~look_for_coercion metasenv subst context
437 (NCicUntrusted.mk_appl he (List.rev args_so_far)) orig_he ty
438 (NCic.Prod ("_",NCic.Implicit `Term,NCic.Implicit `Term))
440 (RefineFailure (lazy (localise orig_he, Printf.sprintf
441 ("The term %s is here applied to %d arguments but expects " ^^
442 "only %d arguments") (NCicPp.ppterm ~metasenv ~subst ~context he)
443 (List.length args) (List.length args_so_far))))
445 aux metasenv subst [] newhead newheadty (arg :: tl)
447 aux metasenv subst [] he ty_he args
448 (*D*)in outside(); rc with exc -> outside (); raise exc
450 (* vim:set foldmethod=marker: *)