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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus, with let sugar and some base types
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr [Γ #hash()])
(interpret- (strip (desugar expr)) Γ))
(define (interpret- expr Γ)
(match expr
['sole 'sole]
[n #:when (natural? n) n]
[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 ,e1 ,env) (interpret- e1 (dict-set env x (interpret- e2 Γ)))]
[e1 `(,e1 ,(interpret- e2 Γ))])]
[e e]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [Γ #hash()])
(check- (desugar expr) with Γ))
(define (check- expr with Γ)
(match* (expr with)
[('sole 'Unit) #t]
[(n 'Nat) #:when (natural? n) #t]
[(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()])
(infer- (desugar expr) Γ))
(define (infer- expr Γ)
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
[`(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)
(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))
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