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Implement nbe in typed racket

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Yiyun Liu 2025-05-10 12:36:00 -04:00
parent 7bf8bdde48
commit 212cbdbceb
2 changed files with 91 additions and 104 deletions
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62
nbe-test.rkt
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@ -1,6 +1,6 @@
#lang racket
#lang typed/racket
(require rackunit "nbe.rkt")
(require typed/rackunit "nbe.rkt")
(define-syntax tm-app
(syntax-rules ()
@ -11,64 +11,74 @@
(define-syntax-rule (tm-var a) `(var ,a))
(define-syntax-rule (tm-abs a) `(λ ,a))
(: tm-id Term)
(define tm-id '(λ (var 0)))
(: tm-fst Term)
(define tm-fst '(λ (λ (var 1))))
(: tm-snd Term)
(define tm-snd '(λ (λ (var 0))))
(: tm-pair Term)
(define tm-pair `(λ (λ (λ ,(tm-app '(var 0) '(var 2) '(var 1))))))
(define tm-fix
(let ([g (tm-abs (tm-app (tm-var 1) (tm-app (tm-var 0) (tm-var 0))))])
(tm-abs (tm-app g g))))
;; (define tm-fix
;; (let ([g (tm-abs (tm-app (tm-var 1) (tm-app (tm-var 0) (tm-var 0))))])
;; (tm-abs (tm-app g g))))
(: tm-zero Term)
(define tm-zero tm-snd)
(: tm-suc (-> Term Term))
(define (tm-suc a) (tm-abs (tm-abs (tm-app (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
(: tm-add (-> Term Term Term))
(define (tm-add a b)
(tm-abs (tm-abs
(tm-app b (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
(: tm-compose (-> Term Term Term))
(define (tm-compose a b)
(tm-abs (tm-app a (tm-app b (tm-var 0)))))
(: tm-mult (-> Term Term Term))
(define (tm-mult a b) (tm-compose a b))
(: tm-nat (-> V Term))
(define (tm-nat n)
(if (positive? n)
(tm-suc (tm-nat (- n 1)))
tm-zero))
(define (tm-pnat n)
(if (positive? n)
`(succ ,(tm-pnat (- n 1)))
'zero))
;; (define (tm-pnat n)
;; (if (positive? n)
;; `(succ ,(tm-pnat (- n 1)))
;; 'zero))
(define (tm-ifz a b c)
`(if-zero ,a ,b ,c))
;; (define (tm-ifz a b c)
;; `(if-zero ,a ,b ,c))
(define (tm-psuc a)
`(succ ,a))
;; (define (tm-psuc a)
;; `(succ ,a))
(define (tm-double m)
(tm-app tm-fix
(tm-abs (tm-abs (tm-ifz (tm-var 0) 'zero 'zero))) m ))
;; (define (tm-double m)
;; (tm-app tm-fix
;; (tm-abs (tm-abs (tm-ifz (tm-var 0) 'zero 'zero))) m ))
(define (tm-padd m n)
(tm-app tm-fix
(tm-abs (tm-abs (tm-abs (tm-ifz (tm-var 1) (tm-var 0) (tm-psuc (tm-app (tm-var 3) (tm-var 0) (tm-var 1))))))) m n))
;; (define (tm-padd m n)
;; (tm-app tm-fix
;; (tm-abs (tm-abs (tm-abs (tm-ifz (tm-var 1) (tm-var 0) (tm-psuc (tm-app (tm-var 3) (tm-var 0) (tm-var 1))))))) m n))
(check-equal? (normalize `(app ,tm-id ,tm-id)) tm-id)
(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-snd)) tm-fst)
(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-fst)) tm-id)
(check-equal? (normalize (tm-app tm-snd (tm-app tm-pair tm-id tm-fst) tm-fst)) tm-fst)
(check-equal? (normalize (tm-add (tm-nat 499) (tm-nat 777))) (normalize (tm-add (tm-nat 777) (tm-nat 499))))
(check-equal? (normalize (tm-mult (tm-nat 3) (tm-nat 2))) (normalize (tm-nat 6)))
(check-equal? (normalize (tm-mult (tm-nat 11) (tm-nat 116))) (normalize (tm-nat 1276)))
(check η-eq? (normalize (tm-add (tm-nat 499) (tm-nat 777))) (normalize (tm-add (tm-nat 777) (tm-nat 499))))
(check βη-eq? (tm-mult (tm-nat 6) (tm-nat 7)) (tm-nat 42))
(check βη-eq? '(if-zero (succ (succ zero)) zero (succ (succ (var 0)))) (tm-pnat 3))
(check βη-eq? (tm-padd (tm-pnat 8) (tm-pnat 11)) (tm-pnat 19))
(check βη-eq? (tm-padd (tm-pnat 2) (tm-psuc (tm-var 0))) '(succ (succ (succ (var 0)))))
;; (check-equal? (normalize (tm-mult (tm-nat 3) (tm-nat 2))) (normalize (tm-nat 6)))
;; (check-equal? (normalize (tm-mult (tm-nat 11) (tm-nat 116))) (normalize (tm-nat 1276)))
;; (check η-eq? (normalize (tm-add (tm-nat 499) (tm-nat 777))) (normalize (tm-add (tm-nat 777) (tm-nat 499))))
;; (check βη-eq? (tm-mult (tm-nat 6) (tm-nat 7)) (tm-nat 42))
;; (check βη-eq? '(if-zero (succ (succ zero)) zero (succ (succ (var 0)))) (tm-pnat 3))
;; (check βη-eq? (tm-padd (tm-pnat 8) (tm-pnat 11)) (tm-pnat 19))
;; (check βη-eq? (tm-padd (tm-pnat 2) (tm-psuc (tm-var 0))) '(succ (succ (succ (var 0)))))