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
|
#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr [Γ #hash()])
(interpret- (strip expr) Γ))
(define (interpret- expr Γ)
(match expr
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(λ ,x ,e) `(λ ,x ,e ,Γ)]
[`(,e1 ,e2)
(match (interpret- e1 Γ)
[`(λ ,x ,e ,env) (interpret- e (dict-set env x (interpret- e2 Γ)))]
[e `(,e ,(interpret- e2 Γ))])]
[e e]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [Γ #hash()])
(match* (expr with)
[(x _) #:when (dict-has-key? Γ x)
(equal? (dict-ref Γ x) with)]
[(`(λ (,x : ,t) ,e) `(,t1 → ,t2))
(and (equal? t t1) (check e t2 (dict-set Γ x t1)))]
[(`(,e1 ,e2) t)
(match (infer e1 Γ)
[`(,t1 → ,t2) (and (equal? t2 t) (equal? t1 (infer e2 Γ)))]
[t #f])]
[(e t) #f]))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr [Γ #hash()])
(match expr
[`(λ (,x : ,t) ,e)
`(,t → ,(infer e (dict-set Γ x t)))]
[`(,e1 ,e2)
(match (infer e1 Γ)
[`(,t1 → ,t2)
(if (check 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)
|
