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
(** Copyright 2025-2026, Mikhail Gavrilenko,Danila Rudnev-Stepanyan, Daniel Vlasenko *)
(** SPDX-License-Identifier: LGPL-3.0-or-later *)
open Middleend.Infer
open Common.Parser
open Common.Pprinter
open Common.Ast.TypeExpr
let (let*) = Result.bind
let infer_exp_str ?(rst = true) ?(env = []) str =
let exp = parse_exp_str str in
if rst then reset_gensym ();
match infer_exp env exp with
| Ok (_, ty) ->
pprint_type Format.std_formatter ty
| Error err -> pprint_err Format.std_formatter err
let infer_pat_str ?(rst = true) ?(env = []) str =
let pat = parse_pat_str str in
if rst then reset_gensym ();
match infer_pat env pat with
| Ok (_, ty) ->
pprint_type Format.std_formatter ty
| Error err -> pprint_err Format.std_formatter err
let infer_prog_str ?(env = env_with_things) str =
let prog = parse_str str in
reset_gensym ();
match infer_program env prog with
| Ok (new_env, names) ->
pprint_env new_env names
| Error err -> pprint_err Format.std_formatter err
let show_etyp env exp =
match infer_exp env exp with
| Ok (_, ty) ->
Base.print_endline (Common.Ast.TypeExpr.show ty)
| Error err -> pprint_err Format.std_formatter err
let type_bool = Type_construct ("bool", [])
let type_unit = Type_construct ("unit", [])
let type_char = Type_construct ("char", [])
let type_int = Type_construct ("int", [])
let type_string = Type_construct ("string", [])
let env = env_with_things
(************************** Expressions **************************)
let%expect_test "char" =
infer_exp_str {| 'a' |};
[%expect{| char |}]
let%expect_test "int" =
infer_exp_str {| 1 |};
[%expect{| int |}]
let%expect_test "str" =
infer_exp_str {| "Kakadu" |};
[%expect{| string |}]
let%expect_test "id in env" =
infer_exp_str {| m |} ~env:[("m", Type_var {contents = Unbound ("a", 0)})];
[%expect{| 'a |}]
let%expect_test "id not in env" =
infer_exp_str {| m |};
[%expect{| Unbound variable m |}];;
let%expect_test "tuple 2" =
infer_exp_str {| (1, 2) |};
[%expect{| int * int |}]
let%expect_test "tuple 3" =
infer_exp_str {| (1, 2, 3) |};
[%expect{| int * int * int |}]
let%expect_test "tuple 4" =
infer_exp_str {| (1, 2, 3, 4) |};
[%expect{| int * int * int * int |}]
let%expect_test "tuples in tuple" =
infer_exp_str {| ((1, 2), (3, 4)) |};
[%expect{| (int * int) * (int * int) |}]
let%expect_test "construct none" =
infer_exp_str {| None |} ~env;
[%expect {| 'a option |}]
let%expect_test "construct some" =
infer_exp_str {| Some 1 |} ~env;
[%expect {| int option |}]
let%expect_test "if (string) " =
infer_exp_str {| if "trololo" then 1 |};
[%expect {| Cannot unify different constructors: string and bool |}]
let%expect_test "if (bool) then (not unit)" =
let env = ["cond", type_bool] in
infer_exp_str {| if cond then 1 |} ~env;
[%expect{| Cannot unify different constructors: int and unit |}]
let%expect_test "if (bool) then (unit)" =
let env = ["cond", type_bool; "bodyvar", type_unit] in
infer_exp_str {| if cond then bodyvar |} ~env;
[%expect{| unit |}]
let%expect_test "if (bool) then 'a else 'a" =
let env = ["cond", type_bool; "x", Type_var {contents = Unbound ("a", 0)}; "y", Type_var {contents = Unbound ("a", 0)}] in
infer_exp_str {| if cond then x else y |} ~env;
[%expect{| 'a |}]
let%expect_test "if (bool) then 'a else 'b" =
let env = ["cond", type_bool; "x", Type_var {contents = Unbound ("a", 0)}; "y", Type_var {contents = Unbound ("b", 0)}] in
infer_exp_str {| if cond then x else y |} ~env;
[%expect{| 'b |}]
let%expect_test "apply int -> int to int" =
let env = ["f", Type_arrow (type_int, type_int); "x", type_int] in
infer_exp_str {| f x |} ~env;
[%expect{| int |}]
let%expect_test "apply int -> int to string" =
let env = ["f", Type_arrow (type_int, type_int); "x", type_string] in
infer_exp_str {| f x |} ~env;
[%expect{| Cannot unify different constructors: int and string |}]
let%expect_test "apply 'a -> 'a to 'b" =
let env = ["f", Type_arrow (Type_var {contents = Unbound ("s", 0)}, Type_var {contents = Unbound ("s", 0)}); "x", Type_var {contents = Unbound ("t", 0)}] in
infer_exp_str {| f x |} ~env ~rst: false;
[%expect{| 'b |}]
(* not sure if this is right *)
let%expect_test "apply 'a to 'a (different vars)" =
let env = ["f", Type_var {contents = Unbound ("t", 0)}; "x", Type_var {contents = Unbound ("t", 0)}] in
infer_exp_str {| f x |} ~env ~rst: false;
[%expect {| 'c |}]
let%expect_test "apply 'a to 'a (same var)" =
let env = ["x", Type_var {contents = Unbound ("t", 0)}] in
infer_exp_str {| x x |} ~env ~rst: false;
[%expect{| Occurs check |}]
let%expect_test "apply 'a to 'b" =
let env = ["f", Type_var {contents = Unbound ("s", 0)}; "x", Type_var {contents = Unbound ("t", 0)}] in
infer_exp_str {| f x |} ~env ~rst: false;
[%expect{| 'e |}]
(************************** Patterns **************************)
let%expect_test "id in env" =
let env = ["m", (Type_var {contents = Unbound ("c", 0)})] in
infer_pat_str {| m |} ~env;
[%expect {| 'a |}];;
let%expect_test "id not in env" =
infer_pat_str {| m |};
[%expect {| 'a |}];;
let%expect_test "any" =
infer_pat_str {| _ |};
[%expect {| 'a |}];;
let%expect_test "char" =
infer_pat_str {| 'a' |};
[%expect {| char |}];;
let%expect_test "int" =
infer_pat_str {| 1 |};
[%expect {| int |}];;
let%expect_test "str" =
infer_pat_str {| "kakadu" |};
[%expect {| string |}];;
let%expect_test "tuple 2" =
infer_pat_str {| (1, 2) |};
[%expect {| int * int |}];;
let%expect_test "tuple 3" =
infer_pat_str {| (1, 2, 3) |};
[%expect {| int * int * int |}];;
let%expect_test "tuple 4" =
infer_pat_str {| (1, 2, 3, 4) |};
[%expect {| int * int * int * int |}];;
let%expect_test "tuples in tuple" =
infer_pat_str {| ((1, 2), (3, 4)) |};
[%expect {| (int * int) * (int * int) |}];;
let%expect_test "construct none" =
infer_pat_str {| None |} ~env;
[%expect {| 'a option |}]
let%expect_test "construct some" =
infer_pat_str {| Some 1 |} ~env;
[%expect{| int option |}]
(************************** Funs **************************)
let%expect_test "fun 'a -> 'a (new var)" =
infer_exp_str {| fun x -> x |};
[%expect {| 'a -> 'a |}]
let%expect_test "fun 'a -> 'a (shadow)" =
let env = ["x", Type_var {contents = Unbound ("s", 0)}] in
infer_exp_str {| fun x -> x |} ~env;
[%expect {| 'a -> 'a |}]
let%expect_test "fun 'a -> 'b (not in env)" =
infer_exp_str {| fun x -> y |};
[%expect{| Unbound variable y |}]
let%expect_test "fun 'a -> 'b (in env)" =
let env = ["y", Type_var {contents = Unbound ("s", 0)}] in
infer_exp_str {| fun x -> y |} ~env;
[%expect{| 'a -> 's |}]
let%expect_test _=
infer_exp_str {| fun x -> fun y -> x y |};
[%expect{| ('b -> 'c) -> 'b -> 'c |}]
let%expect_test _ =
infer_exp_str {| fun x y -> x y |};
[%expect{| ('b -> 'c) -> 'b -> 'c |}]
let%expect_test _ =
infer_exp_str {| (fun f a b -> f a, f b) (fun x -> x) 1 "mystr" |};
[%expect{| Cannot unify different constructors: int and string |}]
(************************** Match, function **************************)
let%expect_test "correct match" =
let env = [ "a", Type_construct("option", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match a with | Some x -> 1 | None -> 2 |} ~env;
[%expect {|
int |}]
let%expect_test "use match pattern in body" =
let env = [ "a", Type_construct("option", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match a with | Some x -> x | None -> 2 |} ~env;
[%expect {|
int |}]
let%expect_test "match different constructors" =
let env = [ "a", Type_construct("option", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match a with | Some x -> 1 | [] -> 2 |} ~env;
[%expect{| Cannot unify different constructors: list and option |}]
let%expect_test "match option with list constructors" =
let env = [ "a", Type_construct("option", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match a with | x :: tl -> 1 | [] -> 2 |} ~env;
[%expect{| Cannot unify different constructors: list and option |}]
let%expect_test "match different types of expr 1" =
let env = [ "a", Type_construct("option", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match a with | Some x -> 'a' | None -> 1234 |} ~env;
[%expect{| Cannot unify different constructors: char and int |}]
let%expect_test "match different types of expr 2" =
let env = [ "b", Type_construct("list", [Type_var {contents = Unbound ("a", 0)}])] @ env in
infer_exp_str {| match b with | x :: y :: tl -> 'a' | x :: tl -> 'b' | _ -> 1234 |} ~env;
[%expect{| Cannot unify different constructors: char and int |}]
let%expect_test "correct function" =
infer_exp_str {| function | Some x -> 1 | None -> 2 |} ~env;
[%expect {|
'd option -> int |}]
let%expect_test "use function pattern in body" =
infer_exp_str {| function | Some x -> x | None -> 2 |} ~env;
[%expect {|
int option -> int |}]
let%expect_test "function different constructors" =
infer_exp_str {| function | Some x -> 1 | [] -> 2 |} ~env;
[%expect{| Cannot unify different constructors: list and option |}]
let%expect_test "function different types of expr 1" =
infer_exp_str {| function | Some x -> 'a' | None -> 1234 |} ~env;
[%expect{| Cannot unify different constructors: char and int |}]
let%expect_test "function different types of expr 2" =
infer_exp_str {| function | x :: y :: tl -> 'a' | x :: tl -> 'b' | _ -> 1234 |} ~env;
[%expect{| Cannot unify different constructors: char and int |}]
(************************** Let in **************************)
let%expect_test _ =
infer_exp_str {| let 1 = 1 in 2 |};
[%expect{| int |}]
let%expect_test _ =
infer_exp_str {| let a = 1 in 2 |};
[%expect{| int |}]
let%expect_test _ =
infer_exp_str {| let a = 1 in a |};
[%expect{| int |}]
let%expect_test _ =
infer_exp_str {| let a = 1 in "str" |};
[%expect{| string |}]
let%expect_test "let poly" =
infer_exp_str {| let a = fun x -> x in a |};
[%expect {| 'c -> 'c |}]
let%expect_test "let poly 2" =
infer_exp_str {| let a = fun x -> x in (a 1, a "str") |};
[%expect{| int * string |}]
let%expect_test "poly in env" =
let env = ["=", Type_arrow (Quant_type_var "a", Type_arrow(Quant_type_var "a", type_bool))] in
infer_exp_str {| let a = 1 in 1 = 1, "str" = "str" |} ~env;
[%expect{| bool * bool |}]
let%expect_test _ =
infer_exp_str {| let a, b = 1, 2 in a |} ;
[%expect{| int |}]
let%expect_test _ =
infer_exp_str {| let a, b, c = 1, 2 in a |} ;
[%expect{| Cannot unify tuples of different sizes |}]
let%expect_test _ =
infer_exp_str {| let a, b = 1, 2, 3 in a |};
[%expect{| Cannot unify tuples of different sizes |}]
let%expect_test "let and" =
infer_exp_str {| let a = 1 and b = "punk" in b |};
[%expect {| string |}]
let%expect_test "factorial" =
infer_exp_str {| let rec fac n = if n = 1 then 1 else n * fac (n-1) in fac 4 |} ~env;
[%expect {| int |}]
let%expect_test "fibonacci" =
infer_exp_str {| let rec fib n = if n <= 1 then 1 else (fib (n-1)) + (fib (n-2)) in fib 4 |} ~env;
[%expect {| int |}]
let%expect_test "mutual recursion" =
let env = env @ ["not", Type_arrow (type_bool, type_bool); "true", type_bool] in
infer_exp_str ~env {|
let rec is_odd n =
if n = 0 then true else is_even (n-1)
and is_even n = not (is_odd n)
in is_odd 5
|};
[%expect {| bool |}]
let%expect_test "shadow with itself" =
infer_prog_str
{|
let test3 a b c =
let a = print_int a in 0
|};
[%expect{| val test3 : int -> 'a -> 'b -> int |}];;
let%expect_test "shadow" =
infer_prog_str {|
let x = 5
let x = "string"
|};
[%expect {|
val x : string |}]
let%expect_test "shadow with itself 2" =
infer_prog_str {|
let x = 5
let x = x
|};
[%expect {|
val x : int |}]
let%expect_test "weird let rec" =
infer_prog_str {| let rec x = x |};
[%expect{| This kind of expression is not allowed as right-hand side of `let rec' |}]
let%expect_test "too polymorphic1" =
infer_prog_str {| let map f p = let (a,b) = p in (f a, f b) |};
[%expect {| val map : ('a -> 'b) -> 'a * 'a -> 'b * 'b |}]