summaryrefslogtreecommitdiff
path: root/infer2.scm
blob: 03a8d320dbc90dd819dfb18f331897f8dff778f1 (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
512
513
514
515
516
(use-modules (ice-9 format)
             (ice-9 match)
             (srfi srfi-1)
             (srfi srfi-9)
             (srfi srfi-9 gnu))

(define (print-list lst)
  (for-each (lambda (x) (format #t "~a\n" x)) lst))

(define (difference a b)
  (match a
    (() b)
    ((x . rest)
     (if (memq x b)
         (difference rest (delq x b))
         (cons x (difference rest b))))))

(define-syntax-rule (define-matcher (name rules ...) body ...)
  (define name
    (match-lambda*
      ((rules ...) body ...)
      (_ 'unmatched))))

(define-syntax-rule (compose-matchers matcher ...)
  (lambda args
    (let loop ((matchers (list matcher ...)))
      (match matchers
        (() (error "unmatched" args))
        ((m . rest)
         (let ((result (apply m args)))
           (if (eq? result 'unmatched)
               (loop rest)
               result)))))))


;;;
;;; Types and environments
;;;

(define-record-type <primitive-type>
  (make-primitive-type name)
  primitive-type?
  (name primitive-type-name))

(define (display-primitive-type type port)
  (format port "#<primitive ~a>" (primitive-type-name type)))
(set-record-type-printer! <primitive-type> display-primitive-type)

(define int-type (make-primitive-type 'int))
(define float-type (make-primitive-type 'float))
(define bool-type (make-primitive-type 'bool))

(define-record-type <type-variable>
  (make-type-variable name)
  type-variable?
  (name type-variable-name))

(define (display-type-variable type port)
  (format port "#<tvar ~a>" (type-variable-name type)))
(set-record-type-printer! <type-variable> display-type-variable)

(define unique-counter (make-parameter 0))

(define (unique-number)
  (let ((n (unique-counter)))
    (unique-counter (+ n 1))
    n))

(define* (unique-identifier #:optional (prefix 'T))
  (string->symbol
   (format #f "~a~a" prefix (unique-number))))

(define (fresh-type-variable)
  (make-type-variable (unique-identifier)))

(define-record-type <procedure-type>
  (make-procedure-type parameter-types return-types)
  procedure-type?
  (parameter-types procedure-type-parameter-types)
  (return-types procedure-type-return-types))

(define (display-procedure-type type port)
  (format port "#<proc-type ~a → ~a>"
          (procedure-type-parameter-types type)
          (procedure-type-return-types type)))
(set-record-type-printer! <procedure-type> display-procedure-type)

(define-record-type <for-all-type>
  (make-for-all-type variables type)
  for-all-type?
  (variables for-all-type-variables)
  (type for-all-type-type))

(define (type? obj)
  (or (primitive-type? obj)
      (type-variable? obj)
      (procedure-type? obj)))

(define (top-level-env)
  '())

(define (lookup var env)
  (let ((type (assq-ref env var)))
    (cond
     ((type-variable? type) type)
     ((for-all-type? type) (instantiate type))
     (else (error "unbound variable" var)))))

(define (occurs-in? a b)
  (cond
   ((and (type-variable? a) (type-variable? b))
    (eq? a b))
   ((and (type-variable? a) (procedure-type? b))
    (or (occurs-in? a (procedure-type-parameter-types b))
        (occurs-in? a (procedure-type-return-types b))))
   ((and (type? a) (list? b))
    (any (lambda (b*) (occurs-in? a b*)) b))
   (else #f)))

(define (apply-substitution-to-type type from to)
  (cond
   ((primitive-type? type) type)
   ((type-variable? type)
    (if (eq? type from) to type))
   ((procedure-type? type)
    (make-procedure-type
     (map (lambda (param-type)
            (apply-substitution-to-type param-type from to))
          (procedure-type-parameter-types type))
     (map (lambda (return-type)
            (apply-substitution-to-type return-type from to))
          (procedure-type-return-types type))))))

(define (apply-substitutions-to-type type subs)
  (let loop ((type type)
             (subs subs))
    (match subs
      (() type)
      (((from . to) . rest)
       (loop (apply-substitution-to-type type from to)
             rest)))))

(define (apply-substitution-to-env from to env)
  (map (match-lambda
         ((a . b)
          (cons (if (eq? a from) to a)
                (if (eq? b from) to b))))
       env))

(define (substitute from to env)
  (let* ((to* (apply-substitutions-to-type to env)))
    (and (not (occurs-in? from to*))
         (let ((env* (apply-substitution-to-env from to* env)))
           (pk 'add-to-env from to*)
           (alist-cons from to* env*)))))

(define (free-variables-in-type type)
  (cond
   ((primitive-type? type) '())
   ((type-variable? type) type)
   ((procedure-type? type)
    (delete-duplicates
     (append (map free-variables-in-type
                  (procedure-type-parameter-types type))
             (map free-variables-in-type
                  (procedure-type-return-types type)))))))

(define (free-variables-in-for-all for-all)
  (difference (for-all-type-variables for-all)
              (free-variables-in-type (for-all-type-type for-all))))

(define (free-variables-in-env env)
  (delete-duplicates
   (let loop ((env env))
     (match env
       (() '())
       (((_ . type) . rest)
        (cond
         ((type-variable? type)
          (cons (free-variables-in-type type)
                (loop rest)))
         ((for-all-type? type)
          (cons (free-variables-in-for-all type)
                (loop rest)))
         (else
          (loop rest))))))))

(define (instantiate for-all)
  (define subs
    (map (lambda (var)
           (cons var (fresh-type-variable)))
         (for-all-type-variables for-all)))
  (pk 'instantiate for-all)
  (apply-substitutions-to-type (for-all-type-type for-all) subs))

(define (generalize type env)
  (define quantifiers
    (difference (free-variables-in-type type)
                (free-variables-in-env env)))
  (pk 'quantifiers quantifiers)
  (if (null? quantifiers)
      type
      (make-for-all-type quantifiers type)))

(define (constraints->env constraints)
  (map (lambda (c)
         (cons (constraint-lhs c) (constraint-rhs c)))
       constraints))


;;;
;;; Typed expression annotation
;;;

(define (make-texp types exp)
  `(t ,types ,exp))

(define (texp? obj)
  (match obj
    (('t _ _) #t)
    (_ #f)))

(define (texp-types texp)
  (match texp
    (('t types _) types)))

(define (texp-exp texp)
  (match texp
    (('t _ exp) exp)))

(define (single-type texp)
  (match (texp-types texp)
    ((type) type)
    (_ (error "expected only 1 type" texp))))

(define-matcher (annotate:bool (? boolean? b) env)
  (make-texp (list bool-type) b))

(define-matcher (annotate:int (and (? number?) (? exact-integer? n)) env)
  (make-texp (list int-type) n))

(define-matcher (annotate:float (and (? number?) (? inexact? n)) env)
  (make-texp (list float-type) n))

(define-matcher (annotate:var (? symbol? var) env)
  (make-texp (list (lookup var env)) var))

(define-matcher (annotate:if ('if predicate consequent alternate) env)
  (make-texp (list (fresh-type-variable))
             `(if ,(annotate-exp predicate env)
                  ,(annotate-exp consequent env)
                  ,(annotate-exp alternate env))))

(define-matcher (annotate:values ('values vals ...) env)
  (define vals* (map (lambda (val) (annotate-exp val env)) vals))
  (define val-types (map single-type vals*))
  (make-texp val-types `(values ,@vals*)))

(define-matcher (annotate:let ('let (((? symbol? vars) vals) ...) body) env)
  (define vals* (map (lambda (val) (annotate-exp val env)) vals))
  (define val-types (map (lambda (val)
                           (generalize (single-type val) env))
                         vals*))
  (define vals** (map (lambda (val type)
                        (make-texp (list type) (texp-exp val)))
                      vals* val-types))
  (define env* (append (map cons vars val-types) env))
  (define body* (annotate-exp body env*))
  (make-texp (texp-types body*)
             `(let ,(map list vars vals**) ,body*)))

(define-matcher (annotate:begin ('begin exps ... last) env)
  (define last* (annotate-exp last env))
  (make-texp (texp-types last*)
             `(begin ,@(map (lambda (exp) (annotate-exp exp env)) exps)
                     ,last*)))

(define-matcher (annotate:lambda ('lambda ((? symbol? args) ...) body) env)
  (define parameter-types (map (lambda (_name) (fresh-type-variable)) args))
  (define env* (append (map cons args parameter-types) env))
  (define body* (annotate-exp body env*))
  (define return-types (texp-types body*))
  (make-texp (list (make-procedure-type parameter-types return-types))
             `(lambda ,args ,body*)))

(define-matcher (annotate:call (operator args ...) env)
  (define operator* (annotate-exp operator env))
  (define args* (map (lambda (arg)
                       (annotate-exp arg env))
                     args))
  (make-texp (map (lambda (_type) (fresh-type-variable))
                  (texp-types operator*))
             (cons operator*
                   args*)))


(define annotate-exp
  (compose-matchers annotate:bool
                    annotate:int
                    annotate:float
                    annotate:var
                    annotate:if
                    annotate:values
                    annotate:let
                    annotate:begin
                    annotate:lambda
                    annotate:call))

(define (annotate-exp* exp)
  (annotate-exp exp (top-level-env)))


;;;
;;; Constraints
;;;

(define-record-type <constraint>
  (constrain lhs rhs)
  constraint?
  (lhs constraint-lhs)
  (rhs constraint-rhs))

(define (display-constraint constraint port)
  (format port "#<constraint ~a = ~a>"
          (constraint-lhs constraint)
          (constraint-rhs constraint)))
(set-record-type-printer! <constraint> display-constraint)

(define-matcher (constrain:other ((? type? _) ...) _) '())

(define-matcher (constrain:if ((? type? types) ...)
                              ('if (? texp? predicate)
                                   (? texp? consequent)
                                   (? texp? alternate)))
  (append (list (constrain (list bool-type) (texp-types predicate))
                (constrain types (texp-types consequent))
                (constrain types (texp-types alternate)))
          (program-constraints predicate)
          (program-constraints consequent)
          (program-constraints alternate)))

(define-matcher (constrain:values ((? type? types) ...)
                                  ('values (? texp? vals) ...))
  (append-map program-constraints vals))

(define-matcher (constrain:let ((? type? types) ...)
                               ('let (((? symbol? vars) (? texp? vals)) ...)
                                 (? texp? body)))
  (append (program-constraints body)
          (append-map program-constraints vals)))

(define-matcher (constrain:begin ((? type? types) ...)
                                 ('begin (? texp? texps) ... (? texp? last)))
  (append (program-constraints last)
                (append-map program-constraints texps)))

(define-matcher (constrain:for-all-lambda ((? for-all-type? type))
                                  ('lambda ((? symbol? args) ...)
                                    (? texp? body)))
  (cons (pk 'constrain-for-all-lambda
            (constrain (procedure-type-return-types
                        (for-all-type-type type))
                       (texp-types body)))
        (program-constraints body)))

(define-matcher (constrain:lambda ((? procedure-type? type))
                                  ('lambda ((? symbol? args) ...)
                                    (? texp? body)))
  (cons (pk 'constrain-lambda
            (constrain (procedure-type-return-types type)
                       (texp-types body)))
        (program-constraints body)))

(define-matcher (constrain:call ((? type? types) ...)
                                ((? texp? operator) (? texp? operands) ...))
  (cons (pk 'constrain-call (constrain (texp-types operator)
                    (list (make-procedure-type (map single-type operands)
                                               types))))
        (append (program-constraints operator)
                (append-map program-constraints operands))))

(define %program-constraints
  (compose-matchers constrain:if
                    constrain:values
                    constrain:let
                    constrain:begin
                    constrain:for-all-lambda
                    constrain:lambda
                    constrain:call
                    constrain:other))

(define (program-constraints texp)
  (%program-constraints (texp-types texp) (texp-exp texp)))


;;;
;;; Unification
;;;

(define %unify-prompt-tag (make-prompt-tag 'unify))

(define (unify-fail)
  (pk 'unify-fail)
  (abort-to-prompt %unify-prompt-tag))

(define (maybe-substitute var other dict)
  (cond
   ;; Tautology: matching 2 vars that are the same.
   ((and (type-variable? other) (eq? var other))
    (pk 'tautology var other)
    dict)
   ;; Variable has been bound to some other value, recursively follow
   ;; it and unify.
   ((assq-ref dict var) =>
    (lambda (type)
      (pk 'forward var other)
      (unify type other dict)))
   ;; Substitute variable for value.
   (else
    (pk 'substitute var other)
    (or (substitute var other dict)
        (unify-fail)))))

(define (constant? obj)
  (and (not (type-variable? obj))
       (not (procedure-type? obj))
       (not (list? obj))))

(define-matcher (unify:constants a b dict)
  (pk 'unify:constants a b)
  (if (eqv? a b)
      dict
      (unify-fail)))

(define-matcher (unify:lists (a rest-a ...) (b rest-b ...) dict)
  (pk 'unify:lists (cons a rest-a) (cons b rest-b))
  (let ((dict* (unify a b dict)))
    (unify rest-a rest-b dict*)))

(define-matcher (unify:variable-left (? type-variable? a) b dict)
  (pk 'unify:variable-left a b)
  (maybe-substitute a b dict))

(define-matcher (unify:variable-right a (? type-variable? b) dict)
  (pk 'unify:variable-right a b)
  (maybe-substitute b a dict))

(define-matcher (unify:procedures (? procedure-type? a) (? procedure-type? b) dict)
  (pk 'unify:procedures a b)
  (define dict* (unify (procedure-type-parameter-types a)
                       (procedure-type-parameter-types b)
                       dict))
  (pk 'dict* dict*)
  (unify (procedure-type-return-types a)
         (procedure-type-return-types b)
         dict*))

(define unify
  (compose-matchers unify:variable-left
                    unify:variable-right
                    unify:procedures
                    unify:lists
                    unify:constants))

(define (unify-constraints constraints)
  (call-with-prompt %unify-prompt-tag
    (lambda ()
      (unify (map constraint-lhs constraints)
             (map constraint-rhs constraints)
             '()))
    (lambda (_k) #f)))


;;;
;;; Type Resolution
;;;

(define-matcher (resolve:primitive x dict)
  (pk 'resolve-primitive)
  x)

(define-matcher (resolve:primitive-type (? primitive-type? type) dict)
  (pk 'resolve-primitive-type type)
  type)

(define-matcher (resolve:type-variable (? type-variable? var) dict)
  (pk 'resolve-var var)
  (let ((type (assq-ref dict var)))
    (if type
        (resolve-types type dict)
        var)))

(define-matcher (resolve:procedure-type (? procedure-type? type) dict)
  (pk 'resolve-proc type)
  (make-procedure-type (resolve-types (procedure-type-parameter-types type) dict)
                       (resolve-types (procedure-type-return-types type) dict)))

(define-matcher (resolve:list (exps ...) dict)
  (pk 'resolve-list exps)
  (map (lambda (texp) (resolve-types texp dict)) exps))

(define resolve-types
  (compose-matchers resolve:primitive-type
                    resolve:type-variable
                    resolve:procedure-type
                    resolve:list
                    resolve:primitive))

(define (infer-types exp)
  (parameterize ((unique-counter 0))
    (pk 'begin-inference)
    (let* ((texp (pk 'texp (annotate-exp* exp)))
           (constraints (pk 'constraints (program-constraints texp)))
           (substitutions (pk 'substitutions (unify-constraints constraints))))
      (and substitutions
           (resolve-types texp substitutions)))))