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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus, with let sugar
(define (value? val) (or (number? val) (string? val) (symbol? val)))
; note: no function overloading ;_;
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr) (interpret- (strip expr) '()))
(define (interpret- expr ctx)
(match expr
[`(λ ,id ,body) `(λ ,id ,body ,ctx)]
[`(λ ,id ,body ,env) `(λ ,id ,body ,env)]
[`((λ ,id ,body) ,arg)
(interpret- body (dict-set ctx id (interpret- arg ctx)))]
[`((λ ,id ,body ,env) ,arg)
(interpret- body (dict-set env id (interpret- arg ctx)))]
[`(,id ,arg) #:when (dict-has-key? ctx id)
(interpret- `(,(interpret- (dict-ref ctx id) ctx) ,arg) ctx)]
[`(,body ,arg) ; todo: how to recognize an irreducible term? this is kinda cheating, i think
(let ([reduced (interpret- body ctx)])
(if (equal? body reduced)
`(,reduced ,(interpret- arg ctx))
(interpret- `(,reduced ,arg) ctx)))]
[id #:when (dict-has-key? ctx id)
(interpret- (dict-ref ctx id) ctx)]
[val #:when (value? val) val]
[`(let ,id ,expr ,body) (interpret- `((λ ,id ,body) ,expr) ctx)]
[expr (err (format "interpreting an unknown expression ~a" expr))]))
;; (check Expr Type Table[Sym, Type]): Bool
(define (check expr with [ctx #hash()])
(match expr
[val #:when (or (value? val) (symbol? val))
(equiv with (infer val ctx))]
[`(λ ,id ,body)
(match with
[`(→ ,a ,b) (check body b (dict-set ctx id a))]
[_ (err (format "expected → type to check λ with but received ~a" with))])]
[`((λ ,id ,body) ,arg)
(note "unable to check arg type from λ lacking annotation")
(check body with ctx)] ; hmm
[`(λ ,id (: ,type) ,body)
(and (check `(λ ,id ,body) type ctx) (equiv with type))]
[`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
(and (check arg a ctx) (equiv with b)
(check `(λ ,id ,body) `(→ ,a ,b) (dict-set ctx id a)))]
; desugaring and error handling
[`(let ,id ,expr ,body)
(check `((λ ,id ,body) ,expr) with ctx)]
[`(let ,id (: ,type) ,expr ,body)
(check `((λ ,id (: ,type) ,body) ,expr) with ctx)]
[`(λ ,id (: ,type) ,body)
(err (format "expected → type on λ but received ~a" type))]
[`((λ ,id (: ,type) ,body) ,arg)
(err (format "expected → type on λ but received ~a" type))]
[expr (err (format "inferring an unknown expression ~a" expr))]))
;; (equiv Type Type): Bool
(define (equiv a b)
(match* (a b)
[[`(→ ,a ,c) `(→ ,b ,d)] (and (equiv a b) (equiv c d))]
[[a b] (equal? a b)]))
;; (infer Expr Table[Sym, Type]) → Type
(define (infer expr [ctx #hash()])
(match expr
[val #:when (string? val) 'Str]
[val #:when (and (number? val) (>= val 0)) 'Nat]
[val #:when (symbol? val) (dict-get ctx val)]
[`((λ ,id ,body) ,arg)
(infer body (dict-set ctx id (infer arg ctx)))]
[`(λ ,id (: (→ ,a ,b)) ,body)
(note "unable to infer arg type from λ lacking annotation")
(if (check body b (dict-set ctx id a))
`(→ ,a ,b)
(err (format "inferred return type of ~a does not match annotated type ~a"
`(λ ,id ,body) b)))]
[`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
(if (check `((λ ,id ,body) ,arg) `(→ ,a ,b) ctx)
b
(err (format "inferred type of ~a does not match annotated type ~a"
`((λ ,id ,body) ,arg) `(: (→ ,a ,b)))))]
[`(let ,id ,expr ,body) ; desugaring
(infer `((λ ,id ,expr) ,body) ctx)]
[`(let ,id (: ,type) ,expr ,body)
(infer `((λ ,id (: ,type) ,expr) ,body) ctx)]
[`(λ ,id ,body) ; error handling
(err "unable to infer type from λ lacking annotation")] ; hmm
[`(λ ,id (: ,type) ,body)
(err (format "expected → type on λ but received ~a" type))]
[`((λ ,id (: ,type) ,body) ,arg)
(err (format "expected → type on λ but received ~a" type))]
[expr (err (format "inferring an unknown expression ~a" expr))]))
(define (dict-get dict key)
(dict-ref dict key (λ () (err (format "identifier ~a not found" key)))))
(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))
; todo: inference tests
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