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
|
#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus with references
;; (interpret Expr Table[Sym, Expr] Table[Sym, Expr]): Value
(define (interpret expr)
(interpret-core (strip (desugar expr)) #hash() (make-hash)))
(define (interpret-core expr Γ Σ)
(match expr
['sole 'sole]
[n #:when (natural? n) n]
[r #:when (dict-has-key? Σ r) r]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(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 ,e) `(λ ,x ,e ,Γ)]
[`(λ ,x ,e ,env) `(λ ,x ,e ,env)] ; ???
[`(,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))])]
[e (err (format "attempting to interpret unknown expression ~a" e))]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with)
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(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)]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
(infer-core (desugar expr) #hash()))
(define (infer-core expr Γ)
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(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))])]
[e (err (format "attempting to infer an unknown expression ~a" e))]))
(provide interpret check infer)
; simple diverging program in STLC-ref
; https://www.youtube.com/watch?v=XNgE8kBfSz8
#;
(interpret '
(let (id : (Nat → Nat)) (λ x x)
(let (r : (Ref (Nat → Nat))) (new id)
(let (f : (Nat → Nat)) (λ x ((! r) x))
(set r f
(f 0))))))
|
