summaryrefslogtreecommitdiff
path: root/contrib/subtac/subtac_coercion.ml
blob: b046f0b3da545a61bcbeb8eff062aea9f66c6940 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
(* -*- compile-command: "make -C ../.. bin/coqtop.byte" -*- *)
(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)
(* $Id: subtac_coercion.ml 11282 2008-07-28 11:51:53Z msozeau $ *)

open Util
open Names
open Term
open Reductionops
open Environ
open Typeops
open Pretype_errors
open Classops
open Recordops
open Evarutil
open Evarconv
open Retyping
open Evd

open Global
open Subtac_utils
open Coqlib
open Printer
open Subtac_errors
open Eterm
open Pp

let pair_of_array a = (a.(0), a.(1))
let make_name s = Name (id_of_string s)

module Coercion = struct

  exception NoSubtacCoercion

  let rec disc_subset x = 
    match kind_of_term x with
      | App (c, l) ->
	  (match kind_of_term c with
	       Ind i ->
		 let len = Array.length l in
		 let sig_ = Lazy.force sig_ in
		   if len = 2 && i = Term.destInd sig_.typ
		   then
		     let (a, b) = pair_of_array l in
		       Some (a, b)
		   else None
	     | _ -> None)
      | _ -> None
	  
  and disc_exist env x =
    match kind_of_term x with
      | App (c, l) ->
	  (match kind_of_term c with
	       Construct c ->	       
		 if c = Term.destConstruct (Lazy.force sig_).intro
		 then Some (l.(0), l.(1), l.(2), l.(3))
		 else None
	     | _ -> None)
      | _ -> None


  let disc_proj_exist env x =
    match kind_of_term x with
      | App (c, l) ->
	  (if Term.eq_constr c (Lazy.force sig_).proj1 
	     && Array.length l = 3 
	   then disc_exist env l.(2)
	   else None)
      | _ -> None


  let sort_rel s1 s2 = 
    match s1, s2 with
	Prop Pos, Prop Pos -> Prop Pos
      | Prop Pos, Prop Null -> Prop Null
      | Prop Null, Prop Null -> Prop Null
      | Prop Null, Prop Pos -> Prop Pos
      | Type _, Prop Pos -> Prop Pos
      | Type _, Prop Null -> Prop Null
      | _, Type _ -> s2

  let hnf env isevars c = whd_betadeltaiota env (evars_of !isevars) c

  let lift_args n sign =
    let rec liftrec k = function
      | t::sign -> liftn n k t :: (liftrec (k-1) sign)
      | [] -> []
    in
      liftrec (List.length sign) sign

  let rec mu env isevars t =   
    let isevars = ref isevars in
    let rec aux v = 
      let v = hnf env isevars v in
      match disc_subset v with
	  Some (u, p) -> 
	    let f, ct = aux u in
	      (Some (fun x ->		   
		       app_opt f (mkApp ((Lazy.force sig_).proj1, 
					 [| u; p; x |]))),
	       ct)
	| None -> (None, v)
    in aux t

  and coerce loc env isevars (x : Term.constr) (y : Term.constr) 
      : (Term.constr -> Term.constr) option 
      =
    let x = nf_evar (evars_of !isevars) x and y = nf_evar (evars_of !isevars) y in
    let rec coerce_unify env x y =
      let x = hnf env isevars x and y = hnf env isevars y in
	try 
	  isevars := the_conv_x_leq env x y !isevars;
	  None
	with Reduction.NotConvertible -> coerce' env x y
    and coerce' env x y : (Term.constr -> Term.constr) option =
      let subco () = subset_coerce env isevars x y in
      let dest_prod c =
	match Reductionops.decomp_n_prod env (evars_of !isevars) 1 c with
	| [(na,b,t)], c -> (na,t), c
	| _ -> raise NoSubtacCoercion
      in
      let rec coerce_application typ typ' c c' l l' =
	let len = Array.length l in
	let rec aux tele typ typ' i co = 
	  if i < len then
	    let hdx = l.(i) and hdy = l'.(i) in
	      try isevars := the_conv_x_leq env hdx hdy !isevars;
		let (n, eqT), restT = dest_prod typ in
		let (n', eqT'), restT' = dest_prod typ' in
		aux (hdx :: tele) (subst1 hdx restT) (subst1 hdy restT') (succ i) co
	      with Reduction.NotConvertible ->
		let (n, eqT), restT = dest_prod typ in
		let (n', eqT'), restT' = dest_prod typ' in
		let _ = 
		  try isevars := the_conv_x_leq env eqT eqT' !isevars
		  with Reduction.NotConvertible -> raise NoSubtacCoercion
		in
		(* Disallow equalities on arities *)
		if Reduction.is_arity env eqT then raise NoSubtacCoercion;
		let restargs = lift_args 1 
		  (List.rev (Array.to_list (Array.sub l (succ i) (len - (succ i)))))
		in 
		let args = List.rev (restargs @ mkRel 1 :: lift_args 1 tele) in
		let pred = mkLambda (n, eqT, applistc (lift 1 c) args) in
		let eq = mkApp (Lazy.force eq_ind, [| eqT; hdx; hdy |]) in
		let evar = make_existential loc env isevars eq in
		let eq_app x = mkApp (Lazy.force eq_rect,
				      [| eqT; hdx; pred; x; hdy; evar|]) in
		  aux (hdy :: tele) (subst1 hdx restT) (subst1 hdy restT') (succ i)  (fun x -> eq_app (co x))
	  else Some co
	in 
	  if isEvar c || isEvar c' then
	    (* Second-order unification needed. *)
	    raise NoSubtacCoercion;
	  aux [] typ typ' 0 (fun x -> x)
      in
	match (kind_of_term x, kind_of_term y) with
	  | Sort s, Sort s' -> 
	      (match s, s' with
		   Prop x, Prop y when x = y -> None
		 | Prop _, Type _ -> None
		 | Type x, Type y when x = y -> None (* false *)
		 | _ -> subco ())
	  | Prod (name, a, b), Prod (name', a', b') ->
	      let name' = Name (Nameops.next_ident_away (id_of_string "x") (Termops.ids_of_context env)) in
	      let env' = push_rel (name', None, a') env in
	      let c1 = coerce_unify env' (lift 1 a') (lift 1 a) in
		(* env, x : a' |- c1 : lift 1 a' > lift 1 a *)
	      let coec1 = app_opt c1 (mkRel 1) in
		(* env, x : a' |- c1[x] : lift 1 a *)
	      let c2 = coerce_unify env' (subst1 coec1 (liftn 1 2 b)) b' in
		(* env, x : a' |- c2 : b[c1[x]/x]] > b' *)
		(match c1, c2 with
		     None, None -> failwith "subtac.coerce': Should have detected equivalence earlier"
		   | _, _ ->
		       Some
			 (fun f -> 
			   mkLambda (name', a',
				    app_opt c2
				      (mkApp (Term.lift 1 f, [| coec1 |])))))
		  
	  | App (c, l), App (c', l') ->
	      (match kind_of_term c, kind_of_term c' with
		   Ind i, Ind i' -> (* Inductive types *)
		     let len = Array.length l in
		     let existS = Lazy.force existS in
		     let prod = Lazy.force prod in
		       (* Sigma types *)
		       if len = Array.length l' && len = 2 && i = i'
			 && (i = Term.destInd existS.typ || i = Term.destInd prod.typ)
		       then 
			 if i = Term.destInd existS.typ 
			 then
			   begin 
			     let (a, pb), (a', pb') = 
			       pair_of_array l, pair_of_array l' 
			     in
			     let c1 = coerce_unify env a a' in
			     let rec remove_head a c = 
			       match kind_of_term c with 
				 | Lambda (n, t, t') -> c, t'
				     (*| Prod (n, t, t') -> t'*)
				 | Evar (k, args) ->
				     let (evs, t) = Evarutil.define_evar_as_lambda !isevars (k,args) in
				       isevars := evs;
				       let (n, dom, rng) = destLambda t in
				       let (domk, args) = destEvar dom in
					 isevars := evar_define domk a !isevars;
					 t, rng
				 | _ -> raise NoSubtacCoercion
			     in
			     let (pb, b), (pb', b') = remove_head a pb, remove_head a' pb' in
			     let env' = push_rel (make_name "x", None, a) env in
			     let c2 = coerce_unify env' b b' in
			       match c1, c2 with
				   None, None -> 
				     None
				 | _, _ ->
				     Some 
				       (fun x ->
					  let x, y = 
					    app_opt c1 (mkApp (existS.proj1,
							       [| a; pb; x |])),
					    app_opt c2 (mkApp (existS.proj2, 
							       [| a; pb; x |]))
					  in
					    mkApp (existS.intro, [| a'; pb'; x ; y |]))
			   end
			 else 
			   begin 
			     let (a, b), (a', b') = 
			       pair_of_array l, pair_of_array l' 
			     in
			     let c1 = coerce_unify env a a' in
			     let c2 = coerce_unify env b b' in
			       match c1, c2 with
				   None, None -> None
				 | _, _ ->
				     Some 
				       (fun x ->
					  let x, y = 
					    app_opt c1 (mkApp (prod.proj1,
							       [| a; b; x |])),
					    app_opt c2 (mkApp (prod.proj2, 
							       [| a; b; x |]))
					  in
					    mkApp (prod.intro, [| a'; b'; x ; y |]))
			   end
		       else
			 if i = i' && len = Array.length l' then
			   let evm = evars_of !isevars in
			     (try subco () 
			       with NoSubtacCoercion ->
				 let typ = Typing.type_of env evm c in
				 let typ' = Typing.type_of env evm c' in
				   (* 			     if not (is_arity env evm typ) then *)
				   coerce_application typ typ' c c' l l')
			       (* 			     else subco () *)
			 else
			   subco ()
		 | x, y when x = y ->
		     if Array.length l = Array.length l' then
		       let evm = evars_of !isevars in
		       let lam_type = Typing.type_of env evm c in
		       let lam_type' = Typing.type_of env evm c' in
(* 			 if not (is_arity env evm lam_type) then ( *)
			 coerce_application lam_type lam_type' c c' l l'
(* 			 ) else subco () *)
		     else subco ()
		 | _ -> subco ())
	  | _, _ ->  subco ()

    and subset_coerce env isevars x y =
      match disc_subset x with
	  Some (u, p) -> 
	    let c = coerce_unify env u y in
	    let f x = 
	      app_opt c (mkApp ((Lazy.force sig_).proj1, 
				[| u; p; x |]))
	    in Some f
	| None ->
	    match disc_subset y with
		Some (u, p) ->
		  let c = coerce_unify env x u in
		    Some 
		      (fun x ->
			 let cx = app_opt c x in
			 let evar = make_existential loc env isevars (mkApp (p, [| cx |]))
			 in
			   (mkApp 
			      ((Lazy.force sig_).intro, 
			       [| u; p; cx; evar |])))
	      | None -> 
		  raise NoSubtacCoercion
		    (*isevars := Evd.add_conv_pb (Reduction.CONV, x, y) !isevars;
		  None*)
    in coerce_unify env x y

  let coerce_itf loc env isevars v t c1 =
    let evars = ref isevars in
    let coercion = coerce loc env evars t c1 in
      !evars, Option.map (app_opt coercion) v
	
  (* Taken from pretyping/coercion.ml *)

  (* Typing operations dealing with coercions *)

  let class_of1 env sigma t = class_of env sigma (nf_evar sigma t)

  (* Here, funj is a coercion therefore already typed in global context *)
  let apply_coercion_args env argl funj =
    let rec apply_rec acc typ = function
      | [] -> { uj_val = applist (j_val funj,argl);
		uj_type = typ }
      | h::restl ->
	  (* On devrait pouvoir s'arranger pour qu'on n'ait pas à faire hnf_constr *)
  	  match kind_of_term (whd_betadeltaiota env Evd.empty typ) with
	    | Prod (_,c1,c2) -> 
		(* Typage garanti par l'appel à app_coercion*)
		apply_rec (h::acc) (subst1 h c2) restl
	    | _ -> anomaly "apply_coercion_args"
    in 
      apply_rec [] funj.uj_type argl

  (* appliquer le chemin de coercions de patterns p *)
  exception NoCoercion

  let apply_pattern_coercion loc pat p =
    List.fold_left
      (fun pat (co,n) ->
	 let f i = if i<n then Rawterm.PatVar (loc, Anonymous) else pat in
	   Rawterm.PatCstr (loc, co, list_tabulate f (n+1), Anonymous))
      pat p

  (* raise Not_found if no coercion found *)
  let inh_pattern_coerce_to loc pat ind1 ind2 =
    let i1 = inductive_class_of ind1 in
    let i2 = inductive_class_of ind2 in
    let p = lookup_pattern_path_between (i1,i2) in
      apply_pattern_coercion loc pat p

  (* appliquer le chemin de coercions p à hj *)

  let apply_coercion env p hj typ_cl =
    try 
      fst (List.fold_left
             (fun (ja,typ_cl) i -> 
		let fv,isid = coercion_value i in
		let argl = (class_args_of typ_cl)@[ja.uj_val] in
		let jres = apply_coercion_args env argl fv in
		  (if isid then 
		     { uj_val = ja.uj_val; uj_type = jres.uj_type }
		   else 
		     jres),
		jres.uj_type)
             (hj,typ_cl) p)
    with _ -> anomaly "apply_coercion"

  let inh_app_fun env isevars j = 
    let t = whd_betadeltaiota env (evars_of isevars) j.uj_type in
      match kind_of_term t with
	| Prod (_,_,_) -> (isevars,j)
	| Evar ev when not (is_defined_evar isevars ev) ->
	    let (isevars',t) = define_evar_as_product isevars ev in
	      (isevars',{ uj_val = j.uj_val; uj_type = t })
	| _ ->
       	    (try
 	       let t,i1 = class_of1 env (evars_of isevars) j.uj_type in
      	       let p = lookup_path_to_fun_from i1 in
		 (isevars,apply_coercion env p j t)
	     with Not_found ->
	       try 
		 let coercef, t = mu env isevars t in
		   (isevars, { uj_val = app_opt coercef j.uj_val; uj_type = t })
	       with NoSubtacCoercion | NoCoercion ->
		 (isevars,j))

  let inh_tosort_force loc env isevars j =
    try
      let t,i1 = class_of1 env (evars_of isevars) j.uj_type in
      let p = lookup_path_to_sort_from i1 in
      let j1 = apply_coercion env p j t in 
	(isevars,type_judgment env (j_nf_evar (evars_of isevars) j1))
    with Not_found ->
      error_not_a_type_loc loc env (evars_of isevars) j

  let inh_coerce_to_sort loc env isevars j =
    let typ = whd_betadeltaiota env (evars_of isevars) j.uj_type in
      match kind_of_term typ with
	| Sort s -> (isevars,{ utj_val = j.uj_val; utj_type = s })
	| Evar ev when not (is_defined_evar isevars ev) ->
	    let (isevars',s) = define_evar_as_sort isevars ev in
	      (isevars',{ utj_val = j.uj_val; utj_type = s })
	| _ ->
	    inh_tosort_force loc env isevars j

  let inh_coerce_to_base loc env isevars j =
    let typ = whd_betadeltaiota env (evars_of isevars) j.uj_type in
    let ct, typ' = mu env isevars typ in
      isevars, { uj_val = app_opt ct j.uj_val; 
		 uj_type = typ' }

  let inh_coerce_to_prod loc env isevars t =
    let typ = whd_betadeltaiota env (evars_of isevars) (snd t) in
    let _, typ' = mu env isevars typ in
      isevars, (fst t, typ')
	
  let inh_coerce_to_fail env evd rigidonly v t c1 =
    if rigidonly & not (Heads.is_rigid env c1 && Heads.is_rigid env t)
    then
      raise NoCoercion
    else
    let v', t' =
      try 
	let t1,i1 = class_of1 env (evars_of evd) c1 in
	let t2,i2 = class_of1 env (evars_of evd) t in
	let p = lookup_path_between (i2,i1) in
	  match v with
	      Some v -> 
		let j = apply_coercion env p {uj_val = v; uj_type = t} t2 in
		  Some j.uj_val, j.uj_type
	    | None -> None, t
      with Not_found -> raise NoCoercion 
    in
      try (the_conv_x_leq env t' c1 evd, v')
      with Reduction.NotConvertible -> raise NoCoercion


  let rec inh_conv_coerce_to_fail loc env evd rigidonly v t c1 =
    try (the_conv_x_leq env t c1 evd, v)
    with Reduction.NotConvertible ->
    try inh_coerce_to_fail env evd rigidonly v t c1
    with NoCoercion ->
    match
      kind_of_term (whd_betadeltaiota env (evars_of evd) t),
      kind_of_term (whd_betadeltaiota env (evars_of evd) c1)
    with
    | Prod (name,t1,t2), Prod (_,u1,u2) -> 
        (* Conversion did not work, we may succeed with a coercion. *)
        (* We eta-expand (hence possibly modifying the original term!) *)
	(* and look for a coercion c:u1->t1 s.t. fun x:u1 => v' (c x)) *)
	(* has type forall (x:u1), u2 (with v' recursively obtained) *)
	let name = match name with 
	  | Anonymous -> Name (id_of_string "x")
	  | _ -> name in
	let env1 = push_rel (name,None,u1) env in
	let (evd', v1) =
	  inh_conv_coerce_to_fail loc env1 evd rigidonly
            (Some (mkRel 1)) (lift 1 u1) (lift 1 t1) in
        let v1 = Option.get v1 in
	let v2 = Option.map (fun v -> beta_applist (lift 1 v,[v1])) v in
        let t2 = Termops.subst_term v1 t2 in
	let (evd'',v2') = inh_conv_coerce_to_fail loc env1 evd' rigidonly v2 t2 u2 in
	(evd'', Option.map (fun v2' -> mkLambda (name, u1, v2')) v2')
    | _ -> raise NoCoercion

  (* Look for cj' obtained from cj by inserting coercions, s.t. cj'.typ = t *)
  let inh_conv_coerce_to_gen rigidonly loc env evd cj ((n, t) as _tycon) =
    let evd = nf_evar_defs evd in
    match n with
	None ->
	  let (evd', val') = 
	    try 
	      inh_conv_coerce_to_fail loc env evd rigidonly
		(Some (nf_isevar evd cj.uj_val))
		(nf_isevar evd cj.uj_type) (nf_isevar evd t)
	    with NoCoercion ->
	      let sigma = evars_of evd in
		try
		  coerce_itf loc env evd (Some cj.uj_val) cj.uj_type t
		with NoSubtacCoercion ->
		  error_actual_type_loc loc env sigma cj t
	  in
	  let val' = match val' with Some v -> v | None -> assert(false) in
	    (evd',{ uj_val = val'; uj_type = t })
      | Some (init, cur) ->
	  (evd, cj)

  let inh_conv_coerce_to = inh_conv_coerce_to_gen false
  let inh_conv_coerce_rigid_to = inh_conv_coerce_to_gen true

  let inh_conv_coerces_to loc env isevars t ((abs, t') as _tycon) =
    let nabsinit, nabs =
      match abs with
	  None -> 0, 0
	| Some (init, cur) -> init, cur
    in
      try 
	let rels, rng = Reductionops.decomp_n_prod env (evars_of isevars) nabs t in
	(* The final range free variables must have been replaced by evars, we accept only that evars
	   in rng are applied to free vars. *)
	if noccur_with_meta 1 (succ nabs) rng then (
	  let env', t, t' =
	    let env' = push_rel_context rels env in
	      env', rng, lift nabs t'
	  in
	    try
	      fst (try inh_conv_coerce_to_fail loc env' isevars false None t t'
		   with NoCoercion ->
		     coerce_itf loc env' isevars None t t')
	    with NoSubtacCoercion ->
	      let sigma = evars_of isevars in
		error_cannot_coerce env' sigma (t, t'))
	else isevars
      with _ -> isevars
end