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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)
(interpret-core (strip (desugar expr)) #hash()))
(define (interpret-core 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-core e Γ)
[`(λ ,x ,e ,env)
; FIXME: unsure what should be Γ and what should be env
(interpret-core 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-core body Γ)
[`(λ ,id ,body ,env)
(interpret-core body (dict-set env id (interpret-core 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)
(check-core (desugar expr) with #hash()))
(define (check-core expr with Γ)
(let ([with (if (dict-has-key? Γ with) (dict-ref Γ with) with)])
(match expr
['sole (equal? 'Unit with)]
[n #:when (natural? n) (equal? 'Nat with)]
[x #:when (dict-has-key? Γ x)
(equal? (dict-ref Γ x) with)]
[`(fix ,e)
(check-core (infer-core e) `(,with → ,with) Γ)]
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t1 t) (check-core e t2 (dict-set Γ x t1)))]
[_ #f])]
[`(,e1 ,e2)
(match (infer-core e1 Γ)
[`(,t1 → ,t2)
(and (equal? t2 with) (equal? t1 (infer-core e2 Γ)))]
[_ #f])]
[_ #f])))
;; (infer Expr Table[Sym, Type]): Type
(define (infer expr)
(infer-core (desugar expr) #hash()))
(define (infer-core 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-core 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-core e (dict-set Γ x t)))]
[`(,e1 ,e2)
(match (infer-core e1 Γ)
[`(,t1 → ,t2)
(if (check-core 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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