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 module type Strategy = sig
21 type config = int * env_term list * C.term * stack_term list
23 reduce: (config -> config * bool) -> unwind: (config -> C.term) ->
25 val from_stack : stack_term -> config
26 val from_stack_list_for_unwind :
27 unwind: (config -> C.term) -> stack_term list -> C.term list
28 val from_env : env_term -> config
29 val from_env_for_unwind :
30 unwind: (config -> C.term) -> env_term -> C.term
32 reduce: (config -> config * bool) -> unwind: (config -> C.term) ->
33 stack_term -> env_term
35 reduce: (config -> config * bool) -> unwind: (config -> C.term) ->
36 int -> env_term list -> C.term -> env_term
37 val compute_to_stack :
38 reduce: (config -> config * bool) -> unwind: (config -> C.term) ->
43 module CallByValueByNameForUnwind' = struct
44 type config = int * env_term list * C.term * stack_term list
45 and stack_term = config lazy_t * C.term lazy_t (* cbv, cbn *)
46 and env_term = config lazy_t * C.term lazy_t (* cbv, cbn *)
47 let to_env ~reduce ~unwind c = lazy (fst (reduce c)),lazy (unwind c)
48 let from_stack (c,_) = Lazy.force c
49 let from_stack_list_for_unwind ~unwind:_ l =
50 List.map (function (_,c) -> Lazy.force c) l
51 let from_env (c,_) = Lazy.force c
52 let from_env_for_unwind ~unwind:_ (_,c) = Lazy.force c
53 let stack_to_env ~reduce:_ ~unwind:_ config = config
54 let compute_to_env ~reduce ~unwind k e t =
55 lazy (fst (reduce (k,e,t,[]))), lazy (unwind (k,e,t,[]))
56 let compute_to_stack ~reduce ~unwind config =
57 lazy (fst (reduce config)), lazy (unwind config)
61 module Reduction(RS : Strategy) = struct
62 type env = RS.env_term list
63 type stack = RS.stack_term list
64 type config = int * env * C.term * stack
66 let rec unwind (k,e,t,s) =
70 NCicSubstitution.psubst ~avoid_beta_redexes:true
71 (RS.from_env_for_unwind ~unwind) e t
74 else C.Appl(t::(RS.from_stack_list_for_unwind ~unwind s))
77 let list_nth l n = try List.nth l n with Failure _ -> assert false;;
78 let rec replace i s t =
81 | n,he::tl -> he::(replace (n - 1) tl t)
85 let rec reduce ~delta ?(subst = []) context : config -> config * bool =
86 let rec aux = function
87 | k, e, C.Rel n, s when n <= k ->
88 let k',e',t',s' = RS.from_env (list_nth e (n-1)) in
90 | k, _, C.Rel n, s as config (* when n > k *) ->
91 let x= try Some (List.nth context (n - 1 - k)) with Failure _ -> None in
93 | Some(_,C.Def(x,_)) -> aux (0,[],NCicSubstitution.lift (n - k) x,s)
95 | (k, e, C.Meta (n,l), s) as config ->
97 let _,_, term,_ = NCicUtils.lookup_subst n subst in
98 aux (k, e, NCicSubstitution.subst_meta l term,s)
99 with NCicUtils.Subst_not_found _ -> config, true)
100 | (_, _, C.Implicit _, _) -> assert false
101 | (_, _, C.Sort _, _)
102 | (_, _, C.Prod _, _)
103 | (_, _, C.Lambda _, []) as config -> config, true
104 | (k, e, C.Lambda (_,_,t), p::s) ->
105 aux (k+1, (RS.stack_to_env ~reduce:aux ~unwind p)::e, t,s)
106 | (k, e, C.LetIn (_,_,m,t), s) ->
107 let m' = RS.compute_to_env ~reduce:aux ~unwind k e m in
108 aux (k+1, m'::e, t, s)
109 | (_, _, C.Appl ([]|[_]), _) -> assert false
110 | (k, e, C.Appl (he::tl), s) ->
112 List.map (fun t->RS.compute_to_stack ~reduce:aux ~unwind (k,e,t,[])) tl
114 aux (k, e, he, tl' @ s)
116 (Ref.Ref (_,Ref.Def height) as refer), s) as config ->
117 if delta >= height then config, false else
118 let _,_,body,_,_,_ = NCicEnvironment.get_checked_def refer in
120 | (_, _, C.Const (Ref.Ref (_,
121 (Ref.Decl|Ref.Ind _|Ref.Con _|Ref.CoFix _))), _) as config ->
123 | (_, _, (C.Const (Ref.Ref
124 (_,Ref.Fix (fixno,recindex,height)) as refer) as head),s) as config ->
125 (* if delta >= height then config else *)
127 try Some (RS.from_stack (List.nth s recindex))
128 with Failure _ -> None
130 | None -> config, true
132 let fixes,_,_ = NCicEnvironment.get_checked_fixes_or_cofixes refer in
133 match reduce ~delta:0 ~subst context recparam with
134 | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _
135 when delta >= height ->
137 replace recindex s (RS.compute_to_stack ~reduce:aux ~unwind c)
139 (0, [], head, new_s), false
140 | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _ ->
142 replace recindex s (RS.compute_to_stack ~reduce:aux ~unwind c)
144 let _,_,_,_,body = List.nth fixes fixno in
145 aux (0, [], body, new_s)
147 | (k, e, C.Match (_,_,term,pl),s) as config ->
148 let decofix = function
149 | (_,_,C.Const(Ref.Ref(_,Ref.CoFix c)as refer),s)->
151 NCicEnvironment.get_checked_fixes_or_cofixes refer in
152 let _,_,_,_,body = List.nth cofixes c in
153 let c,_ = reduce ~delta:0 ~subst context (0,[],body,s) in
157 (match decofix (fst (reduce ~delta:0 ~subst context (k,e,term,[]))) with
158 | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,_))),[]) ->
159 aux (k, e, List.nth pl (j-1), s)
160 | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,lno))), s')->
161 let _,params = HExtlib.split_nth lno s' in
162 aux (k, e, List.nth pl (j-1), params@s)
168 let whd ?(delta=0) ~subst context t =
169 unwind (fst (reduce ~delta ~subst context (0, [], t, [])))
176 module RS = CallByValueByNameForUnwind';;
177 module R = Reduction(RS);;
181 let (===) x y = Pervasives.compare x y = 0 ;;
183 let get_relevance = ref (fun ~metasenv:_ ~subst:_ _ _ -> assert false);;
185 let set_get_relevance f = get_relevance := f;;
187 (* t1, t2 must be well-typed *)
188 let are_convertible ~metasenv ~subst =
189 let rec aux test_eq_only context t1 t2 =
190 let alpha_eq test_eq_only t1 t2 =
195 | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
196 NCicEnvironment.universe_leq a b
197 | (C.Sort (C.Type a), C.Sort (C.Type b)) ->
198 NCicEnvironment.universe_eq a b
199 | (C.Sort C.Prop,C.Sort (C.Type _)) -> (not test_eq_only)
200 | (C.Sort C.Prop, C.Sort C.Prop) -> true
202 | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
203 aux true context s1 s2 &&
204 aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
205 | (C.Lambda (name1,s1,t1), C.Lambda(_,_,t2)) ->
206 (* thanks to inversion of well typedness, the source
207 * of these lambdas must be already convertible *)
208 aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
209 | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
210 aux test_eq_only context ty1 ty2 &&
211 aux test_eq_only context s1 s2 &&
212 aux test_eq_only ((name1, C.Def (s1,ty1))::context) t1 t2
214 | (C.Meta (n1,(s1, C.Irl _)), C.Meta (n2,(s2, C.Irl _)))
215 when n1 = n2 && s1 = s2 -> true
216 | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 &&
217 let l1 = NCicUtils.expand_local_context l1 in
218 let l2 = NCicUtils.expand_local_context l2 in
220 (fun t1 t2 -> aux test_eq_only context
221 (NCicSubstitution.lift s1 t1)
222 (NCicSubstitution.lift s2 t2))
224 with Invalid_argument "List.for_all2" ->
225 prerr_endline ("Meta " ^ string_of_int n1 ^
226 " occurrs with local contexts of different lenght\n"^
227 NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
228 NCicPp.ppterm ~metasenv ~subst ~context t2);
229 assert false) -> true
231 | C.Meta (n1,l1), _ ->
233 let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
234 let term = NCicSubstitution.subst_meta l1 term in
235 aux test_eq_only context term t2
236 with NCicUtils.Subst_not_found _ -> false)
237 | _, C.Meta (n2,l2) ->
239 let _,_,term,_ = NCicUtils.lookup_subst n2 subst in
240 let term = NCicSubstitution.subst_meta l2 term in
241 aux test_eq_only context t1 term
242 with NCicUtils.Subst_not_found _ -> false)
244 | (C.Appl ((C.Const r1) as hd1::tl1), C.Appl (C.Const r2::tl2))
245 when (Ref.eq r1 r2 &&
246 List.length (E.get_relevance r1) >= List.length tl1) ->
247 let relevance = E.get_relevance r1 in
248 let relevance = match r1 with
249 | Ref.Ref (_,Ref.Con (_,_,lno)) ->
250 let _,relevance = HExtlib.split_nth lno relevance in
251 HExtlib.mk_list false lno @ relevance
255 HExtlib.list_forall_default3_var
256 (fun t1 t2 b -> not b || aux test_eq_only context t1 t2 )
257 tl1 tl2 true relevance
258 with Invalid_argument _ -> false
259 | HExtlib.FailureAt fail ->
261 !get_relevance ~metasenv ~subst context hd1 tl1 in
262 let _,relevance = HExtlib.split_nth fail relevance in
263 let b,relevance = (match relevance with
267 let _,tl1 = HExtlib.split_nth (fail+1) tl1 in
268 let _,tl2 = HExtlib.split_nth (fail+1) tl2 in
270 HExtlib.list_forall_default3
271 (fun t1 t2 b -> not b || aux test_eq_only context t1 t2)
272 tl1 tl2 true relevance
273 with Invalid_argument _ -> false
276 | (C.Appl (hd1::tl1), C.Appl (hd2::tl2)) ->
277 aux test_eq_only context hd1 hd2 &&
278 let relevance = !get_relevance ~metasenv ~subst context hd1 tl1 in
280 HExtlib.list_forall_default3
281 (fun t1 t2 b -> not b || aux test_eq_only context t1 t2)
282 tl1 tl2 true relevance
283 with Invalid_argument _ -> false)
285 | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
286 C.Match (ref2,outtype2,term2,pl2)) ->
287 let _,_,itl,_,_ = E.get_checked_indtys ref1 in
288 let _,_,ty,_ = List.nth itl tyno in
289 let rec remove_prods ~subst context ty =
290 let ty = whd ~subst context ty in
293 | C.Prod (name,so,ta) -> remove_prods ~subst ((name,(C.Decl so))::context) ta
297 match remove_prods ~subst [] ty with
298 | C.Sort C.Prop -> true
302 aux test_eq_only context outtype1 outtype2 &&
303 (is_prop || aux test_eq_only context term1 term2) &&
304 (try List.for_all2 (aux test_eq_only context) pl1 pl2
305 with Invalid_argument _ -> false)
306 | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
309 if alpha_eq test_eq_only t1 t2 then
312 let height_of = function
313 | C.Const (Ref.Ref (_,Ref.Def h))
314 | C.Const (Ref.Ref (_,Ref.Fix (_,_,h)))
315 | C.Appl(C.Const(Ref.Ref(_,Ref.Def h))::_)
316 | C.Appl(C.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
319 let put_in_whd m1 m2 =
320 R.reduce ~delta:max_int ~subst context m1,
321 R.reduce ~delta:max_int ~subst context m2
324 ((_,_,t1,_ as m1), norm1 as x1) ((_,_,t2,_ as m2), norm2 as x2)
326 assert(not (norm1 && norm2));
328 x1, R.reduce ~delta:(height_of t2 -1) ~subst context m2
330 R.reduce ~delta:(height_of t1 -1) ~subst context m1, x2
332 let h1 = height_of t1 in
333 let h2 = height_of t2 in
334 let delta = if h1 = h2 then max 0 (h1 -1) else min h1 h2 in
335 R.reduce ~delta ~subst context m1,
336 R.reduce ~delta ~subst context m2
338 let rec convert_machines
339 ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2), norm2 as m2)
341 (alpha_eq test_eq_only
342 (R.unwind (k1,e1,t1,[])) (R.unwind (k2,e2,t2,[])) &&
345 C.Const r -> NCicEnvironment.get_relevance r
348 HExtlib.list_forall_default3
351 let t1 = RS.from_stack t1 in
352 let t2 = RS.from_stack t2 in
353 convert_machines (put_in_whd t1 t2)) s1 s2 true relevance
354 with Invalid_argument _ -> false) ||
355 (not (norm1 && norm2) && convert_machines (small_delta_step m1 m2))
357 convert_machines (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
362 let rec head_beta_reduce ?(delta=max_int) ?(upto=(-1)) t l =
363 match upto, t, l with
364 | 0, C.Appl l1, _ -> C.Appl (l1 @ l)
366 | 0, t, _ -> C.Appl (t::l)
367 | _, C.Appl (hd::tl), _ -> head_beta_reduce ~delta ~upto hd (tl @ l)
368 | _, C.Lambda(_,_,bo), arg::tl ->
369 let bo = NCicSubstitution.subst arg bo in
370 head_beta_reduce ~delta ~upto:(upto - 1) bo tl
371 | _, C.Const (Ref.Ref (_, Ref.Def height) as re), _
372 when delta <= height ->
373 let _, _, bo, _, _, _ = NCicEnvironment.get_checked_def re in
374 head_beta_reduce ~upto ~delta bo l
376 | _, t, _ -> C.Appl (t::l)
379 let head_beta_reduce ?delta ?upto t = head_beta_reduce ?delta ?upto t [];;
381 type stack_item = RS.stack_term
382 type environment_item = RS.env_term
384 type machine = int * environment_item list * NCic.term * stack_item list
386 let reduce_machine = R.reduce
387 let from_stack = RS.from_stack
388 let unwind = R.unwind
390 (* vim:set foldmethod=marker: *)