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 Ref = NReference
16 module E = NCicEnvironment
18 exception AssertFailure of string Lazy.t;;
20 module type Strategy = sig
23 type config = int * env_term list * C.term * stack_term list
25 reduce: (delta:int -> config -> config * bool) ->
26 unwind: (config -> C.term) ->
28 val from_stack : delta:int -> stack_term -> config
29 val from_stack_list_for_unwind :
30 unwind: (config -> C.term) -> stack_term list -> C.term list
31 val from_env : delta:int -> env_term -> config
32 val from_env_for_unwind :
33 unwind: (config -> C.term) -> env_term -> C.term
35 reduce: (delta:int -> config -> config * bool) ->
36 unwind: (config -> C.term) ->
37 stack_term -> env_term
39 reduce: (delta:int -> config -> config * bool) ->
40 unwind: (config -> C.term) ->
41 int -> env_term list -> C.term -> env_term
42 val compute_to_stack :
43 reduce: (delta:int -> config -> config * bool) ->
44 unwind: (config -> C.term) ->
49 module CallByValueByNameForUnwind' : Strategy = struct
50 type config = int * env_term list * C.term * stack_term list
52 config Lazy.t * (int -> config) * C.term Lazy.t
54 config Lazy.t (* cbneed ~delta:0 *)
55 * (int -> config) (* cbvalue ~delta *)
56 * C.term Lazy.t (* cbname ~delta:max_int *)
57 let to_env ~reduce ~unwind c =
58 lazy (fst (reduce ~delta:0 c)),
59 (fun delta -> fst (reduce ~delta c)),
61 let from_stack ~delta (c0,c,_) = if delta = 0 then Lazy.force c0 else c delta
62 let from_stack_list_for_unwind ~unwind:_ l =
63 List.map (fun (_,_,c) -> Lazy.force c) l
64 let from_env ~delta (c0,c,_) = if delta = 0 then Lazy.force c0 else c delta
65 let from_env_for_unwind ~unwind:_ (_,_,c) = Lazy.force c
66 let stack_to_env ~reduce:_ ~unwind:_ config = config
67 let compute_to_env ~reduce ~unwind k e t =
68 lazy (fst (reduce ~delta:0 (k,e,t,[]))),
69 (fun delta -> fst (reduce ~delta (k,e,t,[]))),
70 lazy (unwind (k,e,t,[]))
71 let compute_to_stack ~reduce ~unwind config =
72 lazy (fst (reduce ~delta:0 config)),
73 (fun delta -> fst (reduce ~delta config)),
78 module Reduction(RS : Strategy) = struct
79 type env = RS.env_term list
80 type stack = RS.stack_term list
81 type config = int * env * C.term * stack
83 let rec unwind (k,e,t,s) =
87 NCicSubstitution.psubst ~avoid_beta_redexes:true
88 (RS.from_env_for_unwind ~unwind) e t
91 else C.Appl(t::(RS.from_stack_list_for_unwind ~unwind s))
94 let list_nth l n = try List.nth l n with Failure _ -> assert false;;
95 let rec replace i s t =
98 | n,he::tl -> he::(replace (n - 1) tl t)
102 let rec reduce ~delta ?(subst = []) context : config -> config * bool =
103 let rec aux = function
104 | k, e, C.Rel n, s when n <= k ->
105 let k',e',t',s' = RS.from_env ~delta (list_nth e (n-1)) in
107 | k, _, C.Rel n, s as config (* when n > k *) ->
108 let x= try Some (List.nth context (n - 1 - k)) with Failure _ -> None in
110 | Some(_,C.Def(x,_)) -> aux (0,[],NCicSubstitution.lift (n - k) x,s)
112 | (k, e, C.Meta (n,l), s) as config ->
114 let _,_, term,_ = NCicUtils.lookup_subst n subst in
115 aux (k, e, NCicSubstitution.subst_meta l term,s)
116 with NCicUtils.Subst_not_found _ -> config, true)
117 | (_, _, C.Implicit _, _) -> assert false
118 | (_, _, C.Sort _, _)
119 | (_, _, C.Prod _, _)
120 | (_, _, C.Lambda _, []) as config -> config, true
121 | (k, e, C.Lambda (_,_,t), p::s) ->
122 aux (k+1, (RS.stack_to_env ~reduce:(reduce ~subst context) ~unwind p)::e, t,s)
123 | (k, e, C.LetIn (_,_,m,t), s) ->
124 let m' = RS.compute_to_env ~reduce:(reduce ~subst context) ~unwind k e m in
125 aux (k+1, m'::e, t, s)
126 | (_, _, C.Appl ([]|[_]), _) -> assert false
127 | (k, e, C.Appl (he::tl), s) ->
129 List.map (fun t->RS.compute_to_stack
130 ~reduce:(reduce ~subst context) ~unwind (k,e,t,[])) tl
132 aux (k, e, he, tl' @ s)
134 (Ref.Ref (_,Ref.Def height) as refer), s) as config ->
135 if delta >= height then
138 let _,_,body,_,_,_ = NCicEnvironment.get_checked_def refer in
140 | (_, _, C.Const (Ref.Ref (_,
141 (Ref.Decl|Ref.Ind _|Ref.Con _|Ref.CoFix _))), _) as config ->
143 | (_, _, (C.Const (Ref.Ref
144 (_,Ref.Fix (fixno,recindex,height)) as refer) as head),s) as config ->
145 (* if delta >= height then config else *)
147 try Some (RS.from_stack ~delta (List.nth s recindex))
148 with Failure _ -> None
150 | None -> config, true
152 let fixes,_,_ = NCicEnvironment.get_checked_fixes_or_cofixes refer in
153 match reduce ~delta:0 ~subst context recparam with
154 | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _
155 when delta >= height ->
157 replace recindex s (RS.compute_to_stack ~reduce:(reduce ~subst
160 (0, [], head, new_s), false
161 | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _ ->
163 replace recindex s (RS.compute_to_stack ~reduce:(reduce ~subst
166 let _,_,_,_,body = List.nth fixes fixno in
167 aux (0, [], body, new_s)
169 | (k, e, C.Match (_,_,term,pl),s) as config ->
170 let decofix = function
171 | (_,_,C.Const(Ref.Ref(_,Ref.CoFix c)as refer),s)->
173 NCicEnvironment.get_checked_fixes_or_cofixes refer in
174 let _,_,_,_,body = List.nth cofixes c in
175 let c,_ = reduce ~delta:0 ~subst context (0,[],body,s) in
179 let match_head = k,e,term,[] in
180 let reduced,_ = reduce ~delta:0 ~subst context match_head in
181 (match decofix reduced with
182 | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,_))),[]) ->
183 aux (k, e, List.nth pl (j-1), s)
184 | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,lno))), s')->
185 let _,params = HExtlib.split_nth lno s' in
186 aux (k, e, List.nth pl (j-1), params@s)
192 let whd ?(delta=0) ~subst context t =
193 unwind (fst (reduce ~delta ~subst context (0, [], t, [])))
200 module RS = CallByValueByNameForUnwind';;
201 module R = Reduction(RS);;
205 let (===) x y = Pervasives.compare x y = 0 ;;
207 let get_relevance = ref (fun ~metasenv:_ ~subst:_ _ _ -> assert false);;
209 let set_get_relevance f = get_relevance := f;;
211 let alpha_eq ~test_lambda_source aux test_eq_only metasenv subst context t1 t2 =
216 | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
217 NCicEnvironment.universe_leq a b
218 | (C.Sort (C.Type a), C.Sort (C.Type b)) ->
219 NCicEnvironment.universe_eq a b
220 | (C.Sort C.Prop,C.Sort (C.Type _)) -> (not test_eq_only)
221 | (C.Sort C.Prop, C.Sort C.Prop) -> true
223 | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
224 aux true context s1 s2 &&
225 aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
226 | (C.Lambda (name1,s1,t1), C.Lambda(_,_,t2)) ->
227 if test_lambda_source then
228 aux test_eq_only context t1 t2
230 (* thanks to inversion of well typedness, the source
231 * of these lambdas must be already convertible *)
232 aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
233 | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
234 aux test_eq_only context ty1 ty2 &&
235 aux test_eq_only context s1 s2 &&
236 aux test_eq_only ((name1, C.Def (s1,ty1))::context) t1 t2
238 | (C.Meta (n1,(s1, C.Irl _)), C.Meta (n2,(s2, C.Irl _)))
239 when n1 = n2 && s1 = s2 -> true
240 | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 &&
241 let l1 = NCicUtils.expand_local_context l1 in
242 let l2 = NCicUtils.expand_local_context l2 in
244 (fun t1 t2 -> aux test_eq_only context
245 (NCicSubstitution.lift s1 t1)
246 (NCicSubstitution.lift s2 t2))
248 with Invalid_argument "List.for_all2" ->
249 prerr_endline ("Meta " ^ string_of_int n1 ^
250 " occurrs with local contexts of different lenght\n"^
251 NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
252 NCicPp.ppterm ~metasenv ~subst ~context t2);
253 assert false) -> true
255 | C.Meta (n1,l1), _ ->
257 let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
258 let term = NCicSubstitution.subst_meta l1 term in
259 aux test_eq_only context term t2
260 with NCicUtils.Subst_not_found _ -> false)
261 | _, C.Meta (n2,l2) ->
263 let _,_,term,_ = NCicUtils.lookup_subst n2 subst in
264 let term = NCicSubstitution.subst_meta l2 term in
265 aux test_eq_only context t1 term
266 with NCicUtils.Subst_not_found _ -> false)
268 | (C.Appl ((C.Const r1) as hd1::tl1), C.Appl (C.Const r2::tl2))
269 when (Ref.eq r1 r2 &&
270 List.length (E.get_relevance r1) >= List.length tl1) ->
271 let relevance = E.get_relevance r1 in
272 let relevance = match r1 with
273 | Ref.Ref (_,Ref.Con (_,_,lno)) ->
274 let _,relevance = HExtlib.split_nth lno relevance in
275 HExtlib.mk_list false lno @ relevance
279 HExtlib.list_forall_default3_var
280 (fun t1 t2 b -> not b || aux true context t1 t2 )
281 tl1 tl2 true relevance
282 with Invalid_argument _ -> false
283 | HExtlib.FailureAt fail ->
285 !get_relevance ~metasenv ~subst context hd1 tl1 in
286 let _,relevance = HExtlib.split_nth fail relevance in
287 let b,relevance = (match relevance with
291 let _,tl1 = HExtlib.split_nth (fail+1) tl1 in
292 let _,tl2 = HExtlib.split_nth (fail+1) tl2 in
294 HExtlib.list_forall_default3
295 (fun t1 t2 b -> not b || aux true context t1 t2)
296 tl1 tl2 true relevance
297 with Invalid_argument _ -> false
300 | (C.Appl (hd1::tl1), C.Appl (hd2::tl2)) ->
301 aux test_eq_only context hd1 hd2 &&
302 let relevance = !get_relevance ~metasenv ~subst context hd1 tl1 in
304 HExtlib.list_forall_default3
305 (fun t1 t2 b -> not b || aux true context t1 t2)
306 tl1 tl2 true relevance
307 with Invalid_argument _ -> false)
309 | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
310 C.Match (ref2,outtype2,term2,pl2)) ->
311 let _,_,itl,_,_ = E.get_checked_indtys ref1 in
312 let _,_,ty,_ = List.nth itl tyno in
313 let rec remove_prods ~subst context ty =
314 let ty = whd ~subst context ty in
317 | C.Prod (name,so,ta) -> remove_prods ~subst ((name,(C.Decl so))::context) ta
321 match remove_prods ~subst [] ty with
322 | C.Sort C.Prop -> true
326 aux test_eq_only context outtype1 outtype2 &&
327 (is_prop || aux test_eq_only context term1 term2) &&
328 (try List.for_all2 (aux test_eq_only context) pl1 pl2
329 with Invalid_argument _ -> false)
330 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
334 (* t1, t2 must be well-typed *)
335 let are_convertible ~metasenv ~subst =
336 let rec aux test_eq_only context t1 t2 =
337 let alpha_eq test_eq_only =
338 alpha_eq ~test_lambda_source:false aux test_eq_only metasenv subst context
340 if alpha_eq test_eq_only t1 t2 then
343 let height_of = function
344 | C.Const (Ref.Ref (_,Ref.Def h))
345 | C.Const (Ref.Ref (_,Ref.Fix (_,_,h)))
346 | C.Appl(C.Const(Ref.Ref(_,Ref.Def h))::_)
347 | C.Appl(C.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
350 let put_in_whd m1 m2 =
351 R.reduce ~delta:max_int ~subst context m1,
352 R.reduce ~delta:max_int ~subst context m2
355 ((_,_,t1,_ as m1), norm1 as x1) ((_,_,t2,_ as m2), norm2 as x2)
357 assert(not (norm1 && norm2));
359 x1, R.reduce ~delta:(height_of t2 -1) ~subst context m2
361 R.reduce ~delta:(height_of t1 -1) ~subst context m1, x2
363 let h1 = height_of t1 in
364 let h2 = height_of t2 in
365 let delta = if h1 = h2 then max 0 (h1 -1) else min h1 h2 in
366 R.reduce ~delta ~subst context m1,
367 R.reduce ~delta ~subst context m2
369 let rec convert_machines test_eq_only
370 ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2), norm2 as m2)
372 (alpha_eq test_eq_only
373 (R.unwind (k1,e1,t1,[])) (R.unwind (k2,e2,t2,[])) &&
376 C.Const r -> NCicEnvironment.get_relevance r
379 HExtlib.list_forall_default3
382 let t1 = RS.from_stack ~delta:max_int t1 in
383 let t2 = RS.from_stack ~delta:max_int t2 in
384 convert_machines true (put_in_whd t1 t2)) s1 s2 true relevance
385 with Invalid_argument _ -> false) ||
386 (not (norm1 && norm2) && convert_machines test_eq_only (small_delta_step m1 m2))
388 convert_machines test_eq_only (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
393 let alpha_eq metasenv subst =
394 let rec aux test_lambda_source context t1 t2 =
395 alpha_eq ~test_lambda_source aux true metasenv subst context t1 t2
400 let rec head_beta_reduce ~delta ~upto ~subst t l =
401 match upto, t, l with
402 | 0, C.Appl l1, _ -> C.Appl (l1 @ l)
404 | 0, t, _ -> C.Appl (t::l)
405 | _, C.Meta (n,ctx), _ ->
407 let _,_, term,_ = NCicUtils.lookup_subst n subst in
408 head_beta_reduce ~delta ~upto ~subst
409 (NCicSubstitution.subst_meta ctx term) l
410 with NCicUtils.Subst_not_found _ -> if l = [] then t else C.Appl (t::l))
411 | _, C.Appl (hd::tl), _ -> head_beta_reduce ~delta ~upto ~subst hd (tl @ l)
412 | _, C.Lambda(_,_,bo), arg::tl ->
413 let bo = NCicSubstitution.subst arg bo in
414 head_beta_reduce ~delta ~upto:(upto - 1) ~subst bo tl
415 | _, C.Const (Ref.Ref (_, Ref.Def height) as re), _
416 when delta <= height ->
417 let _, _, bo, _, _, _ = NCicEnvironment.get_checked_def re in
418 head_beta_reduce ~upto ~delta ~subst bo l
420 | _, t, _ -> C.Appl (t::l)
423 let head_beta_reduce ?(delta=max_int) ?(upto= -1) ?(subst=[]) t =
424 head_beta_reduce ~delta ~upto ~subst t []
427 type stack_item = RS.stack_term
428 type environment_item = RS.env_term
430 type machine = int * environment_item list * NCic.term * stack_item list
432 let reduce_machine = R.reduce
433 let from_stack = RS.from_stack
434 let unwind = R.unwind
437 NCicUtils.set_head_beta_reduce (fun ~upto t -> head_beta_reduce ~upto t);
438 NCicPp.set_head_beta_reduce (fun ~upto t -> head_beta_reduce ~upto t);
441 (* if n < 0, then splits all prods from an arity, returning a sort *)
442 let rec split_prods ~subst context n te =
443 match (n, R.whd ~subst context te) with
444 | (0, _) -> context,te
445 | (n, C.Sort _) when n <= 0 -> context,te
446 | (n, C.Prod (name,so,ta)) ->
447 split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta
448 | (_, _) -> raise (AssertFailure (lazy "split_prods"))
451 (* vim:set foldmethod=marker: *)