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#lang racket
(require "lib.rkt")
(provide (all-defined-out))
;; Base utility functions for working with the simply-typed lambda calculus
;; Provides a pretty-print utility for terms in the simply-typed lambda calculus
;; (fmt Expr): String
(define (fmt expr)
(match expr
['sole "⟨⟩"]
[`(λ ,x ,e) (format "λ~a.[~a]" x (fmt e))]
[`((λ ,x ,e1) ,e2) (format "~a = ~a; ~a" x (fmt e2) (fmt e1))]
[`(λ (,x : ,t) ,e) (format "~a: ~a; ~a" x (fmt t) (fmt e))]
[`((λ (,x : ,t) ,e1) ,e2)
(format "~a: ~a; ~a = ~a; ~a" x (fmt t) x (fmt e2) (fmt e1))]
[`(λ ,x ,e ,env) (format "λ~a.[~a]" x (fmt e))]
[`(μ ,x ,t) (format "μ~a.~a" x (fmt t))]
[`(let (,x : ,t) ,e ,in)
(format "~a: ~a; ~a = ~a; ~a" x (fmt t) x (fmt e) (fmt in))]
[`(let ,x ,e ,in) (format "~a = ~a; ~a" x (fmt e) (fmt in))]
[`(set ,x ,e ,in) (format "~a := ~a; ~a" x (fmt e) (fmt in))]
[`(,a → ,b) (format "(~a → ~a)" (fmt a) (fmt b))]
[`(,a → ,k ,b) (format "(~a →~a ~a)" (fmt a) k (fmt b))]
[`(Ref ,a) (format "Ref ~a" (fmt a))]
[`(new ,a) (format "new ~a" (fmt a))]
[`(! ,a) (format "!~a" (fmt a))]
[`(,a ,b) (format "(~a ~a)" (fmt a) (fmt b))]
[(hash-table (keys values) ...)
(format "{~a}"
(foldl
(λ (k v acc)
(format "~a: ~a;" (fmt k) (fmt v)))
"" keys values))]
[_ (format "~a" expr)]))
;; Aliases from higher-level constructs to their core forms.
;; This lets us elide many typing annotations.
(define (desugar expr)
(match expr
['⟨⟩ 'sole]
[`(ref ,e) (desugar `(new ,e))]
[`(deref ,e) (desugar `(! ,e))]
[`(,e ⇑ ,k) (desugar `(,e :: ,k))]
; set-with-continuation
[`(set ,e1 ,e2 ,in)
(desugar `(let (_ : Unit) (set ,e1 ,e2) ,in))]
; many forms of let. this lets us elide many typing annotations
[`(let (,id : (,a → ,k ,b)) (λ (,x : ,a) ,e) ,in)
(desugar `((λ (,id : (,a → ,k ,b)) ,in) (λ (,x : ,a) ,e)))]
[`(let (,id : (,a → ,k ,b)) (λ ,x ,e) ,in)
(desugar `((λ (,id : (,a → ,k ,b)) ,in) (λ (,x : ,a) ,e)))]
[`(let (,id : (,a → ,b)) (λ (,x : ,a) ,e) ,in)
(desugar `((λ (,id : (,a → ,b)) ,in) (λ (,x : ,a) ,e)))]
[`(let (,id : (,a → ,b)) (λ ,x ,e) ,in)
(desugar `((λ (,id : (,a → ,b)) ,in) (λ (,x : ,a) ,e)))]
[`(let ,x (,e : ,t) ,in)
(desugar `((λ (,x : ,t) ,in) (,e : ,t)))]
[`(let ,x ,e ,in)
(desugar `((λ ,x ,in) ,e))]
[`(let ,x ,e)
(desugar `(let ,x ,e sole))]
; letrec as let + fix
[`(letrec (,x : ,t) ,e ,in)
(desugar `(let (,x : ,t) (fix (λ (,x : ,t) ,e)) ,in))]
[`(,e ...) `(,@(map desugar e))]
[e e]))
; [`(list ,exprs ...)
; (foldr (λ (expr res) `(cons ,expr ,res)) 'nil)]
; [`(type ,x ,type ,in) ; fails b/c types are not inferrable
; (desugar `(let (,x : Type) ,type ,in))]
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