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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr)
(interpret-core (strip expr) #hash()))
(define (interpret-core 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-core e1 Γ)
[`(λ ,x ,e ,env) (interpret-core e (dict-set env x (interpret-core e2 Γ)))]
[e `(,e ,(interpret-core e2 Γ))])]
[e e]))
;; (check Expr Type Table[Sym, Type]): 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)))]
[_ #f])]
[_ (equal? (infer with Γ) with)]))
;; (infer Expr Table[Sym, Type]): 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))]))
(provide interpret check infer)
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