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#lang racket
(require "lib.rkt")
(require "base.rkt")
(require (only-in "stlc.rkt" stlc/type?))
;; The Simply-Typed Lambda Calculus, with general recursion
;; Checks an expression for syntactic well-formedness.
(define/contract (stlc-fix/expr? expr)
(-> any/c boolean?)
(match expr
[x #:when (symbol? x) #t]
[`(fix ,e) (stlc-fix/expr? e)]
[`(λ (,x : ,t) ,e) (and (symbol? x) (stlc/type? t) (stlc-fix/expr? e))]
[`(,e1 ,e2) (and (stlc-fix/expr? e1) (stlc-fix/expr? e2))]
[_ #f]))
;; Checks a value for syntactic well-formedness.
(define (stlc-fix/value? value)
(match value
[x #:when (symbol? x) #t]
[`(,v1 ,v2) (and (stlc-fix/value? v1) (stlc-fix/value? v2))]
[`(λ ,x ,e ,env) (and (symbol? x) (stlc-fix/expr? e) (dict? env))]
[_ #f]))
;; Interprets an expression down to a value, in a given context.
(define (interpret expr)
(interpret/core (desugar expr) #hash()))
(define/contract (interpret/core expr Γ)
(-> stlc-fix/expr? dict? stlc-fix/value?)
(match expr
['sole 'sole]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[x #:when (symbol? x) 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 env x `(fix (λ ,x ,e ,Γ))))]
[e (err (format "applying fix to unknown expression ~a" e))])]
[`(λ (,id : ,t) ,body) `(λ ,id ,body ,Γ)]
[`(,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))])]))
;; Checks an expression against some type, in a given context.
(define (check expr with)
(check/core (desugar expr) with #hash()))
(define/contract (check/core expr with Γ) ; FIXME
(-> stlc-fix/expr? stlc/type? dict? boolean?)
(let ([with (if (dict-has-key? Γ with) (dict-ref Γ with) with)])
(match expr
[`(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])]
[_ (equal? (infer/core expr Γ) with)])))
;; Infers a type from some expression, in a given context.
(define (infer expr)
(infer/core (desugar expr) #hash()))
(define/contract (infer/core expr Γ)
(-> stlc-fix/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))]
[`(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))])]))
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