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
|
#lang racket ; note: do NOT use racket/base
(require "lib.rkt")
;; the simply-typed lambda calculus, with let sugar
(define (value? val) (or (number? val) (string? val)))
; note: default arguments MUST all be at the end
; no function overloading ;_;
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr [ctx #hash()]) (interpret- (strip expr) ctx))
(define (interpret- expr ctx)
(match expr
[val #:when (value? val) val]
[val #:when (symbol? val)
(with-handlers
([exn:fail? (λ (exn) val)])
(interpret- (dict-ref ctx val) ctx))]
[`(λ ,id ,body) `(λ ,id ,body ,ctx)]
[`(λ ,id ,body ,env) `(λ ,id ,body ,env)]
[`(,body ,arg)
(match (interpret- body ctx)
[`(λ ,id ,body) (interpret- body (dict-set ctx id (interpret- arg ctx)))]
[`(λ ,id ,body ,env) (interpret- body (dict-set env id (interpret- arg ctx)))]
[expr `(,(interpret- expr ctx) ,(interpret- arg ctx))])]
; desugaring and error handling
[`(let ,id ,expr ,body) (interpret- `((λ ,id ,body) ,expr) ctx)]
[expr (err (format "interpreting an unknown expression ~a" expr))]))
;; removes typing annotations. this is helpful for interpretation.
(define (strip expr)
(match expr
[`(,a ,b) `(,(strip a) ,(strip b))]
[`(λ ,id ,body) `(λ ,id ,(strip body))]
[`(let ,id ,expr ,body) `(let ,id ,(strip expr) ,(strip body))]
[`(λ ,id (: ,type) ,body) (strip `(λ ,id ,body))]
[`(let ,id (: ,type) ,expr ,body) (strip `(let ,id ,expr ,body))]
[expr expr]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [ctx #hash()])
(match expr
[val #:when (or (value? val) (symbol? val))
(equiv with (infer val ctx))]
[`(λ ,id ,body)
(match with
[`(→ ,a ,b) (check body b (dict-set ctx id a))]
[_ (err (format "expected → type to check λ with but received ~a" with))])]
[`((λ ,id ,body) ,arg)
(note "unable to check arg type from λ lacking annotation")
(check body with ctx)] ; hmm
[`(λ ,id (: ,type) ,body)
(and (check `(λ ,id ,body) type ctx) (equiv with type))]
[`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
(and (check arg a ctx) (equiv with b)
(check `(λ ,id ,body) `(→ ,a ,b) (dict-set ctx id a)))]
; desugaring and error handling
[`(let ,id ,expr ,body)
(check `((λ ,id ,body) ,expr) with ctx)]
[`(let ,id (: ,type) ,expr ,body)
(check `((λ ,id (: ,type) ,body) ,expr) with ctx)]
[`(λ ,id (: ,type) ,body)
(err (format "expected → type on λ but received ~a" type))]
[`((λ ,id (: ,type) ,body) ,arg)
(err (format "expected → type on λ but received ~a" type))]
[expr (err (format "inferring an unknown expression ~a" expr))]))
;; (equiv Type Type): Bool
(define (equiv a b)
(match* (a b)
[[`(→ ,a ,c) `(→ ,b ,d)] (and (equiv a b) (equiv c d))]
[[a b] (equal? a b)]))
;; (infer Expr Table[Sym, Type]) → Type
(define (infer expr [ctx #hash()])
(match expr
[val #:when (string? val) 'Str]
[val #:when (and (number? val) (>= val 0)) 'Nat]
[val #:when (symbol? val) (dict-get ctx val)]
[`((λ ,id ,body) ,arg)
(infer body (dict-set ctx id (infer arg ctx)))]
[`(λ ,id (: (→ ,a ,b)) ,body)
(note "unable to infer arg type from λ lacking annotation")
(if (check body b (dict-set ctx id a))
`(→ ,a ,b)
(err (format "inferred return type of ~a does not match annotated type ~a"
`(λ ,id ,body) b)))]
[`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
(if (check `((λ ,id ,body) ,arg) `(→ ,a ,b) ctx)
b
(err (format "inferred type of ~a does not match annotated type ~a"
`((λ ,id ,body) ,arg) `(: (→ ,a ,b)))))]
[`(let ,id ,expr ,body) ; desugaring
(infer `((λ ,id ,expr) ,body) ctx)]
[`(let ,id (: ,type) ,expr ,body)
(infer `((λ ,id (: ,type) ,expr) ,body) ctx)]
[`(λ ,id ,body) ; error handling
(err "unable to infer type from λ lacking annotation")] ; hmm
[`(λ ,id (: ,type) ,body)
(err (format "expected → type on λ but received ~a" type))]
[`((λ ,id (: ,type) ,body) ,arg)
(err (format "expected → type on λ but received ~a" type))]
[expr (err (format "inferring an unknown expression ~a" expr))]))
(define (dict-get dict key)
(dict-ref dict key (λ () (err (format "identifier ~a not found" key)))))
(require rackunit)
(check-equal? (interpret '(λ x x)) '(λ x x #hash()))
(check-equal? (interpret '((λ a a) (x y))) '(x y))
(check-equal? (interpret '((λ a (x y)) (λ z z))) '(x y))
(check-equal? (interpret '((λ a (a y)) x)) '(x y))
; todo: inference tests
|
