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
|
#lang racket
(require "lib.rkt")
(require "base.rkt")
(provide (all-defined-out))
;; The Simply-Typed Lambda Calculus with references
; todo: rewrite to use call-by-reference or call-by-value or call-by-name explicitly
;; Checks an expression for syntactic well-formedness.
(define (stlc-ref/expr? expr)
(match expr
[x #:when (symbol? x) #t]
[n #:when (natural? n) #t]
[(or `(new ,e) `(! ,e)) (stlc-ref/expr? e)]
[(or `(set ,e1 ,e2) `(,e1 ,e2)) (and (stlc-ref/expr? e1) (stlc-ref/expr? e2))]
[`(λ (,x : ,t) ,e) (and (symbol? x) (stlc-ref/type? t) (stlc-ref/expr? e))]
[_ #f]))
;; Checks a type for syntactic well-formedness.
(define (stlc-ref/type? type)
(match type
[t #:when (symbol? t) #t]
[`(Ref ,t) (stlc-ref/type? t)]
[`(,t1 → ,t2) (and (stlc-ref/type? t1) (stlc-ref/type? t2))]
[_ #f]))
;; Checks a value for syntactic well-formedness.
(define (stlc-ref/value? value)
(match value
[x #:when (symbol? x) #t]
[n #:when (natural? n) #t]
[`(,v1 ,v2) (and (stlc-ref/value? v1) (stlc-ref/value? v2))]
[`(λ ,x ,e ,env) (and (symbol? x) (stlc-ref/expr? e) (dict? env))]
[_ #f]))
;; Interprets an expression down to a value, in a given context.
(define (interpret expr)
(interpret/core (desugar expr) #hash() (make-hash)))
(define/contract (interpret/core expr Γ Σ)
(-> stlc-ref/expr? dict? dict? stlc-ref/value?)
(match expr
[r #:when (dict-has-key? Σ r) r]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[f #:when (symbol? f) f]
[`(new ,e)
(let ([r (gensym)])
(dict-set! Σ r e) r)]
[`(! ,e)
(let ([r (interpret/core e Γ Σ)])
(if (dict-has-key? Σ r)
(interpret/core (dict-ref Σ r) Γ Σ)
(err (format "attempting to deref unknown reference ~a" r))))]
[`(set ,e1 ,e2)
(let ([r (interpret/core e1 Γ Σ)])
(if (dict-has-key? Σ r) (dict-set! Σ r (interpret/core e2 Γ Σ))
(err (format "attempting to update unknown reference ~a" r))))
'sole]
[`(λ (,x : ,t) ,e) `(λ ,x ,e ,Γ)]
[`(,e1 ,e2)
(match (interpret/core e1 Γ Σ)
[`(λ ,x ,e1 ,env)
(interpret/core e1 (dict-set env x (interpret/core e2 Γ Σ)) Σ)]
[e1 (err (format "attempting to interpret arg ~a applied to unknown expression ~a" e2 e1))])]))
;; Checks an expression against some type, in a given context.
(define (check expr with)
(check/core (desugar expr) with #hash()))
(define/contract (check/core expr with Γ)
(-> stlc-ref/expr? stlc-ref/type? dict? boolean?)
(match expr
[`(new ,e)
(match with
[`(Ref ,t) (check/core e t Γ)]
[_ #f])]
[`(! ,e) (check/core e `(Ref ,with) Γ)]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t1 t) (check/core e t2 (dict-set Γ x t1)))]
[_ #f])]
[_ (equal? (infer/core expr Γ) with)]))
;; Infers a type from some expression, in a given context.
(define (infer expr)
(infer/core (desugar expr) #hash()))
(define/contract (infer/core expr Γ)
(-> stlc-ref/expr? dict? stlc-ref/type?)
(match expr
['sole 'Unit]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[n #:when (natural? n) n]
[f #:when (symbol? f)
(err (format "attempting to infer type of free variable ~a" f))]
[`(new ,e) `(Ref ,(infer/core e Γ))]
[`(! ,e)
(match (infer/core e Γ)
[`(Ref ,t) t]
[t (err "attempting to deref term not of Ref type!")])]
[`(set ,e1 ,e2)
(match (infer/core e1 Γ)
[`(Ref ,t)
(if (check/core e2 t Γ) 'Unit
(err (format "attempting to update ~a: ~a with term ~a: ~a of differing type"
e1 t e2 (infer/core e2 Γ))))]
[t (err (format "attempting to update non-reference ~a: ~a" e1 t))])]
[`(λ (,x : ,t) ,e)
`(,t → ,(infer/core e (dict-set Γ x t)))]
[`(,e1 ,e2)
(match (infer/core e1 Γ)
[`(,t1 → ,t2)
(if (check/core e2 t1 Γ) t2
(err (format "inferred argument type ~a does not match arg ~a" t1 e2)))]
[t (err (format "expected → type on application body, got ~a" t))])]))
|
