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#lang racket
(require rackunit)
(require racket/trace)
(require syntax/location)
(require (for-syntax syntax/location))
(provide (all-defined-out) trace)
(define-syntax-rule (dbg body)
(let ([res body])
(eprintf "[~a:~a] ~v = ~a~%"
(syntax-source-file-name #'body)
(syntax-line #'body)
'body
res)
res))
(define-syntax-rule (err msg)
(error 'error
(format "[~a:~a] ~a"
(syntax-source-file-name #'msg)
(syntax-line #'msg)
msg)))
(define-syntax-rule (note msg)
(eprintf "note: ~a~%" msg))
(define-syntax-rule (print msg)
(eprintf "~a~%" msg))
(define-syntax (todo stx)
(with-syntax ([src (syntax-source-file-name stx)] [line (syntax-line stx)])
#'(error 'todo (format "[~a:~a] unimplemented" src line))))
(define (any? proc lst)
(foldl (λ (x acc) (if (proc x) #t acc)) #f lst))
(define (all? proc lst)
(foldl (λ (x acc) (if (proc x) acc #f)) #t lst))
(define (inc i) (+ i 1))
(define (dec i) (- i 1))
(define (char-inc c) (integer->char (inc (char->integer c))))
(define (char->string c) (list->string (list c)))
(define (symbol->list s) (string->list (symbol->string s)))
(define (list->symbol l) (string->symbol (list->string l)))
(define (symbol-append a b) (string->symbol (string-append (symbol->string a) (symbol->string b))))
(define (keys->set dict) (list->set (dict-keys dict)))
(define (values->set dict) (list->set (dict-values dict)))
;; Provides a "pretty" gensym: 'a -> 'b, 'z -> 'aa, 'az -> 'ba etc.
;; quite inefficient.
(define (fresh used)
(cond
[(list? used) (fresh-helper '|| (list->set used))]
[(symbol? used) (fresh-helper '|| (set used))]
[(set? used) (fresh-helper '|| used)]))
(define (fresh-helper prev used)
(let ([new (fresh-next prev)])
(if (set-member? used new) (fresh-helper new used) new)))
(define (fresh-next prev)
(if (equal? prev '||) 'a
(let ([prev (reverse (symbol->list prev))])
(if (zero? (length prev)) '||
(match (first prev)
[#\z (symbol-append (fresh-next (list->symbol (reverse (rest prev)))) 'a)]
[c (list->symbol (reverse (cons (char-inc c) (rest prev))))])))))
(check-equal? (fresh-next 'a) 'b)
(check-equal? (fresh-next 'zaa) 'zab)
(check-equal? (fresh-next 'azz) 'baa)
;; Normalizes an expression into binding variables descending
;; (α-convert Expr Table[Old New] Set[New])
(define (α-convert expr [used #hash()])
(match expr
[x #:when (dict-has-key? used x) (dict-ref used x)]
[`(λ (,x : ,t) ,e)
(let ([new (fresh (dict-values used))])
`(λ (,new : ,(α-convert t used)) ,(α-convert e (dict-set used x new))))]
[`(λ ,x ,e)
(let ([new (fresh (dict-values used))])
`(λ ,new ,(α-convert e (dict-set used x new))))]
[`(μ ,x ,t)
(let ([new (fresh (dict-values used))])
`(μ ,new ,(α-convert t (dict-set used x new))))]
[`(,e ...) `(,@(map (λ (x) (α-convert x used)) e))]
[v v]))
(check-equal? '(λ a (λ b (λ c (a (b c)))))
(α-convert '(λ a (λ b (λ c (a (b c)))))))
(check-equal? '(λ a (λ b (λ c (a (b c)))))
(α-convert '(λ c (λ a (λ b (c (a b)))))))
;; Provides a pretty-print utility for terms in the simply-typed lambda calculus
(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
; convenient aliases
['⟨⟩ '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))]
; desugar remaining constructions
[`(,e ...) `(,@(map desugar e))]
[e e]))
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