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#lang racket
(require "lib.rkt")
;; The Simply-Typed Lambda Calculus with iso-recursive types
; Γ ⊢ e: [x ↦ μx.t] t
; ------------------------
; Γ ⊢ fold [μx.t] e: μx.t
; Γ ⊢ e: μx.t
; -----------------------------------
; Γ ⊢ unfold [μx.t] e: [x ↦ μx.t] t
;; (interpret Expr Table[Sym, Expr]): Value
(define (interpret expr [Γ #hash()])
(interpret- (strip (desugar expr)) Γ))
(define (interpret- expr Γ)
(match expr
['sole 'sole]
[n #:when (natural? n) n]
[x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
[`(fold ,t ,e) `(fold ,t ,(interpret- e))]
[`(unfold ,t ,e) `(unfold ,t ,(interpret- e))]
[`(λ ,x ,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 (err (format "applying arg ~a to unknown expression ~a" e2 e))])]
[e (err (format "interpreting an 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)]
[(`(fold (μ ,x ,t) ,e) `(μ ,x ,t))
(check- e t (dict-set Γ x `(μ ,x ,t)))]
[(`(unfold (μ ,x ,t) ,e) with)
(and (check- e `(μ ,x ,t) Γ)
(equiv? with t #hash() #hash((x . `(μ ,x ,t)))))]
[(`(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]
[b #:when (boolean? b) 'Bool]
[x #:when (dict-has-key? Γ x)
(dict-ref Γ x)]
[`(fold (μ ,x ,t) ,e)
(if (check- e t (dict-set Γ x `(μ ,x ,t))) `(μ ,x ,t)
(err (format ("expected ~a to be of type ~a, got ~a"
e t (infer e (dict-set Γ x `(μ ,x ,t)))))))]
[`(unfold (μ ,x ,t) ,e)
(if (check- e `(μ ,x ,t)) (α-convert t #hash((x . `(μ ,x ,t))))
(err (format ("expected ~a to be of type ~a, got ~a"
e `(μ ,x ,t) (infer- e Γ)))))]
[`(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))]))
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