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
|
(* TEST
* expect
*)
type (_, _) eq = Refl : ('a, 'a) eq;;
[%%expect {|
type (_, _) eq = Refl : ('a, 'a) eq
|}]
module type S = sig
type t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
end;;
let cast_type_under_equality (type t) (module M : S' with type t = t) :
(module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t end
module type S' = sig type _ t_aux type t val eq : (t, unit t_aux) eq end
val cast_type_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
val x : t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
val x : t
end;;
let cast_value_under_equality (type t) (module M : S' with type t = t) :
(module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t val x : t end
module type S' =
sig type _ t_aux type t val eq : (t, unit t_aux) eq val x : t end
val cast_value_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
type u = t
val x : u
end;;
module type S' = sig
type _ t_aux
type t
type u = unit t_aux
val eq : (t, unit t_aux) eq
val x : u
end;;
let cast_value_under_manifest_equality (type t) (module M : S' with type t = t)
: (module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t type u = t val x : u end
module type S' =
sig
type _ t_aux
type t
type u = unit t_aux
val eq : (t, unit t_aux) eq
val x : u
end
val cast_value_under_manifest_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
type u = A of t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = A of unit t_aux
end;;
let cast_constructor_under_equality (type t) (module M : S' with type t = t) :
(module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t type u = A of t end
module type S' =
sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = A of unit t_aux
end
val cast_constructor_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
type u = ..
type u += A of t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = ..
type u += A of unit t_aux
end;;
let cast_extension_constructor_under_equality (type t)
(module M : S' with type t = t) : (module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t type u = .. type u += A of t end
module type S' =
sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = ..
type u += A of unit t_aux
end
val cast_extension_constructor_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
type u = { x : t }
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = { x : unit t_aux }
end;;
let cast_record_under_equality (type t) (module M : S' with type t = t) :
(module S with type t = t) =
let Refl = M.eq in
(module M);;
[%%expect {|
module type S = sig type t type u = { x : t; } end
module type S' =
sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
type u = { x : unit t_aux; }
end
val cast_record_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
end;;
let cast_indirect_under_equality (type t)
(module M : S' with type t = t) : (module S with type t = t)
=
let module N : S' with type 'a t_aux = 'a M.t_aux = M in
let Refl = M.eq in
let Refl = N.eq in
if true then (module M) else (module N)
[%%expect {|
module type S = sig type t end
module type S' = sig type _ t_aux type t val eq : (t, unit t_aux) eq end
val cast_indirect_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
end;;
module type F = functor (M : S) -> S with type t = M.t;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
end;;
let cast_functor_argument_under_equality (type t)
(module M : S' with type t = t) (module F : F) : (module S with type t = t)
=
let Refl = M.eq in
(module F (M))
[%%expect {|
module type S = sig type t end
module type F = functor (M : S) -> sig type t = M.t end
module type S' = sig type _ t_aux type t val eq : (t, unit t_aux) eq end
val cast_functor_argument_under_equality :
(module S' with type t = 't) -> (module F) -> (module S with type t = 't) =
<fun>
|}]
module type S = sig
type t
end;;
module type F = functor (M : S) -> sig
module type S = sig
type t = M.t
end
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
end;;
let cast_functor_argument_signature_under_equality (type t)
(module M : S' with type t = t) (module F : F) : (module S with type t = t)
=
let Refl = M.eq in
(module M : F(M).S)
[%%expect {|
module type S = sig type t end
module type F =
functor (M : S) -> sig module type S = sig type t = M.t end end
module type S' = sig type _ t_aux type t val eq : (t, unit t_aux) eq end
val cast_functor_argument_signature_under_equality :
(module S' with type t = 't) -> (module F) -> (module S with type t = 't) =
<fun>
|}]
let cast_double_functor_argument_signature_under_equality (type t)
(module M : S' with type t = t) (module F : F) : (module S with type t = t)
=
let Refl = M.eq in
let module N : F(M).S = M in
let module O : F(N).S = N in
(module (O : F(M).S) : F(M).S)
[%%expect {|
val cast_double_functor_argument_signature_under_equality :
(module S' with type t = 't) -> (module F) -> (module S with type t = 't) =
<fun>
|}]
module type S = sig
type t
module type S_inner = sig
type nonrec t = t
end
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
module type S_inner = sig
type nonrec t = t
end
end;;
let cast_module_type_under_equality (type t) (module M : S' with type t = t) :
(module S with type t = t) =
let Refl = M.eq in
(module M)
[%%expect {|
module type S =
sig type t module type S_inner = sig type nonrec t = t end end
module type S' =
sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
module type S_inner = sig type nonrec t = t end
end
val cast_module_type_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
module type S = sig
type t
end;;
module type S' = sig
type _ t_aux
type t
val eq : (t, unit t_aux) eq
end;;
let cast_via_module_type_under_equality (type t) (module M : S' with type t = t)
: (module S with type t = t) =
let Refl = M.eq in
let module N = struct
module M : S' with type t = t = M
end in
(module N.M)
[%%expect {|
module type S = sig type t end
module type S' = sig type _ t_aux type t val eq : (t, unit t_aux) eq end
val cast_via_module_type_under_equality :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
let cast_via_module_type_under_equality2 (type t) (module M : S' with type t = t)
: (module S with type t = t) =
let Refl = M.eq in
let module N = struct
module M : S' with type t = M.t = M
end in
(module N.M)
[%%expect {|
val cast_via_module_type_under_equality2 :
(module S' with type t = 't) -> (module S with type t = 't) = <fun>
|}]
(* Test from issue #10768 *)
type _ t
module type S = sig type t end
type pack = Pack : 'a t * (module S with type t = 'a) -> pack
let dispatch : pack list ref = ref []
exception Not_registered
type (_,_) equal =
| Refl : 'a -> ('a,'a) equal
type equality =
{
equal: 'a 'b. ('a t * 'b t) -> ('a t,'b t) equal option
}
let equal : equality ref = ref {equal = fun _ -> None}
let get (type a) : a t -> (module S with type t = a) = fun index ->
let dispatch = !dispatch in
let rec unpack list =
match list with
| [] -> raise Not_registered
| Pack (index', (module P))::list' ->
match !equal.equal (index, index') with
| Some (Refl _) -> (module P : ( S with type t = a))
| None -> unpack list'
in
unpack dispatch
[%%expect {|
type _ t
module type S = sig type t end
type pack = Pack : 'a t * (module S with type t = 'a) -> pack
val dispatch : pack list ref = {contents = []}
exception Not_registered
type (_, _) equal = Refl : 'a -> ('a, 'a) equal
type equality = { equal : 'a 'b. 'a t * 'b t -> ('a t, 'b t) equal option; }
val equal : equality ref = {contents = {equal = <fun>}}
val get : 'a t -> (module S with type t = 'a) = <fun>
|}]
(* Ambivalance via module expression *)
(* Both should fail *)
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq) (g : a) =
let module M = struct let g = g end in
let Refl = w1 in let Refl = w2 in M.g 3;;
[%%expect {|
val f : ('a, 'b -> 'b) eq -> ('a, int -> int) eq -> 'a -> 'b = <fun>
|}, Principal{|
Line 3, characters 36-41:
3 | let Refl = w1 in let Refl = w2 in M.g 3;;
^^^^^
Error: This expression has type b = int
but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq) (g : a) =
let module M = struct let g = g end in
let Refl = w2 in let Refl = w1 in M.g 3;;
[%%expect{|
val f : ('a, 'b -> 'b) eq -> ('a, int -> int) eq -> 'a -> int = <fun>
|}, Principal{|
Line 3, characters 37-42:
3 | let Refl = w2 in let Refl = w1 in M.g 3;;
^^^^^
Error: This expression has type int but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
(* Ambivalance via packed module *)
(* Both should fail *)
module type S = sig
type a
val g : a
end;;
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq)
(module M : S with type a = a) =
let Refl = w1 in let Refl = w2 in M.g 3
[%%expect {|
module type S = sig type a val g : a end
val f :
('a, 'b -> 'b) eq ->
('a, int -> int) eq -> (module S with type a = 'a) -> 'b = <fun>
|}, Principal{|
module type S = sig type a val g : a end
Line 7, characters 36-41:
7 | let Refl = w1 in let Refl = w2 in M.g 3
^^^^^
Error: This expression has type b = int
but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq)
(module M : S with type a = a) =
let Refl = w2 in let Refl = w1 in M.g 3
[%%expect{|
val f :
('a, 'b -> 'b) eq ->
('a, int -> int) eq -> (module S with type a = 'a) -> int = <fun>
|}, Principal{|
Line 3, characters 36-41:
3 | let Refl = w2 in let Refl = w1 in M.g 3
^^^^^
Error: This expression has type int but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
(* Ambivalance in module expression *)
(* Both should fail *)
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq) (g : a) =
let Refl = w1 in let Refl = w2 in
let module M = struct let res = g 3 end in
M.res;;
[%%expect {|
val f : ('a, 'b -> 'b) eq -> ('a, int -> int) eq -> 'a -> 'b = <fun>
|}, Principal{|
Line 4, characters 2-7:
4 | M.res;;
^^^^^
Error: This expression has type b = int
but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
let f (type a b) (w1 : (a, b -> b) eq) (w2 : (a, int -> int) eq) (g : a) =
let Refl = w2 in let Refl = w1 in
let module M = struct let res = g 3 end in
M.res;;
[%%expect{|
val f : ('a, 'b -> 'b) eq -> ('a, int -> int) eq -> 'a -> int = <fun>
|}, Principal{|
Line 4, characters 3-8:
4 | M.res;;
^^^^^
Error: This expression has type int but an expression was expected of type 'a
This instance of int is ambiguous:
it would escape the scope of its equation
|}]
|
