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