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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus, with general recursion
;; (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)]
[`(fix ,e)
(match (interpret- e Γ)
[`(λ ,x ,e ,env)
; FIXME: unsure what should be Γ and what should be env
(interpret- e (dict-set Γ x `(fix (λ ,x ,e ,Γ))))]
[e (err (format "applying fix to unknown expression ~a" e))])]
[`(λ ,id ,body) `(λ ,id ,body ,Γ)]
[`(λ ,id ,body ,env) `(λ ,id ,body ,env)]
[`(,body ,arg)
(match (interpret- body Γ)
[`(λ ,id ,body ,env)
(interpret- body (dict-set env id (interpret- arg Γ)))]
[e (err (format "applying arg ~a to unknown expression ~a" arg e))])]
[e (err (format "interpreting an unknown expression ~a" e))]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [Γ #hash()])
(check- (desugar expr) with Γ))
(define (check- expr with Γ)
(let ([with (if (dict-has-key? Γ with) (dict-ref Γ with) with)])
(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)]
[(`(fix ,e) with)
(check- (infer- e) `(,with → ,with) Γ)]
[(`(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]
[x #:when (dict-has-key? Γ x)
(dict-ref Γ x)]
[`(fix ,e)
(match (infer- e Γ)
[`(,t → ,t) t]
[t (err (format "fix expects a term of type t → t, got ~a" t))])]
[`(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 "inferring an unknown expression ~a" e))]))
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