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#lang racket
(require "../lib.rkt")
(provide (all-defined-out))
;; The Simply-Typed Lambda Calculus
;; Checks an expression for syntactic well-formedness.
(define (stlc/expr? expr)
(match expr
[x #:when (symbol? x) #t]
[`(,e1 ,e2) (and (stlc/expr? e1) (stlc/expr? e2))]
[`(λ (,x : ,t) ,e) (and (symbol? x) (stlc/type? t) (stlc/expr? e))]
[_ #f]))
;; Checks a type for syntactic well-formedness.
(define (stlc/type? type)
(match type
[t #:when (symbol? t) #t]
[`(,t1 → ,t2) (and (stlc/type? t1) (stlc/type? t2))]
[_ #f]))
;; Checks a value for syntactic well-formedness.
(define (stlc/value? value)
(match value
[x #:when (symbol? x) #t]
[`(,v1 ,v2) (and (stlc/value? v1) (stlc/value? v2))]
[`(λ ,x ,e ,env) (and (symbol? x) (stlc/expr? e) (dict? env))]
[_ #f]))
;; Interprets an expression down to a value, in a given context.
(define/contract (interpret expr [Γ #hash()])
(->* (stlc/expr?) (dict?) stlc/value?)
(match expr
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[f #:when (symbol? f) f]
[`(λ (,x : ,t) ,e) `(λ ,x ,e ,Γ)]
[`(,e1 ,e2)
(match (interpret e1 Γ)
[`(λ ,x ,e ,env) (interpret e (dict-set env x (interpret e2 Γ)))]
[e `(,e ,(interpret e2 Γ))])]))
;; Checks an expression against some type, in a given context.
(define/contract (check expr with [Γ #hash()])
(->* (stlc/expr? stlc/type?) (dict?) boolean?)
(match expr
[`(λ (,x : ,t) ,e)
(match with
[`(,t1 → ,t2)
(and (equal? t t1) (check e t2 (dict-set Γ x t)))]
[_ #f])]
[_ (equal? with (infer with Γ))]))
;; Infers a type from some expression, in a given context.
(define/contract (infer expr [Γ #hash()])
(->* (stlc/expr?) (dict?) stlc/type?)
(match expr
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[f #:when (symbol? f)
(err (format "attempting to infer type of free variable ~a" f))]
[`(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))])]))
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