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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus with references
;; (interpret Expr Table[Sym, Expr] Table[Sym, Expr]): Value
(define (interpret expr [Γ #hash()] [Σ (make-hash)])
(interpret- (strip (desugar expr)) Γ Σ))
(define (interpret- expr Γ Σ)
; (print (format "interpret: ~a" (fmt expr)))
(match expr
['sole 'sole]
[n #:when (natural? n) n]
[r #:when (dict-has-key? Σ r) r]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(new ,e)
(let ([r (gensym)])
(dict-set! Σ r e) r)]
[`(! ,e)
(let ([r (interpret- e Γ Σ)])
(if (dict-has-key? Σ r)
(interpret- (dict-ref Σ r) Γ Σ)
(err (format "attempting to deref unknown reference ~a" r))))]
[`(set ,e1 ,e2)
(let ([r (interpret- e1 Γ Σ)])
(if (dict-has-key? Σ r) (dict-set! Σ r (interpret- e2 Γ Σ))
(err (format "attempting to update unknown reference ~a" r))))
'sole]
[`(λ ,x ,e) `(λ ,x ,e ,Γ)]
[`(λ ,x ,e ,env) `(λ ,x ,e ,env)] ; ???
[`(,e1 ,e2)
(match (interpret- e1 Γ Σ)
[`(λ ,x ,e1 ,env)
(interpret- e1 (dict-set env x (interpret- e2 Γ Σ)) Σ)]
[e1 (err (format "attempting to interpret arg ~a applied to unknown expression ~a" e2 e1))])]
[e (err (format "attempting to interpret 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)
; (print (format "check: ~a" (fmt expr)))
(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)]
[(`(new ,e) `(Ref ,t)) (check- e t Γ)]
[(`(! ,e) t) (check- e `(Ref ,t) Γ)]
[(`(set ,e1 ,e2) 'Unit)
(match (infer- e1 Γ)
[`(Ref ,t) (check- e2 t Γ)]
[t #f])]
[(`(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)
; (print (format "infer: ~a" (fmt expr)))
(match expr
['sole 'Unit]
[n #:when (natural? n) 'Nat]
[x #:when (dict-has-key? Γ x)
(dict-ref Γ x)]
[`(new ,e) `(Ref ,(infer- e Γ))]
[`(! ,e)
(match (infer- e Γ)
[`(Ref ,t) t]
[t (err "attempting to deref term not of Ref type!")])]
[`(set ,e1 ,e2)
(match (infer- e1 Γ)
[`(Ref ,t)
(if (check- e2 t Γ) 'Unit
(err (format "attempting to update ~a: ~a with term ~a: ~a of differing type"
e1 t e2 (infer- e2 Γ))))]
[t (err (format "attempting to update non-reference ~a: ~a" e1 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 "attempting to infer an unknown expression ~a" e))]))
(provide interpret check infer)
; simple diverging program in STLC-ref
; https://www.youtube.com/watch?v=XNgE8kBfSz8
#;
(interpret '
(let id (: (→ Nat Nat)) (λ x x)
(let r (: (Ref (→ Nat Nat))) (new id)
(let f (: (→ Nat Nat)) (λ x ((! r) x))
(set r f
(f 0))))))
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