53 lines
1.8 KiB
Racket
53 lines
1.8 KiB
Racket
#lang racket
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(require rackunit "nbe.rkt")
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(define-syntax tm-app
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(syntax-rules ()
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[(tm-app a) a]
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[(tm-app a b c ...)
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(tm-app `(app ,a ,b) c ...)]))
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(define-syntax-rule (tm-var a) `(var ,a))
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(define-syntax-rule (tm-abs a) `(λ ,a))
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(define tm-id '(λ (var 0)))
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(define tm-fst '(λ (λ (var 1))))
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(define tm-snd '(λ (λ (var 0))))
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(define tm-pair `(λ (λ (λ ,(tm-app '(var 0) '(var 2) '(var 1))))))
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(define tm-y
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(let ([g (tm-abs (tm-app (tm-var 1) (tm-app (tm-var 0) (tm-var 0))))])
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(tm-abs (tm-app g g))))
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(define tm-zero tm-snd)
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(define (tm-suc a) (tm-abs (tm-abs (tm-app (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
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(define (tm-add a b)
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(tm-abs (tm-abs
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(tm-app b (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
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(define (tm-compose a b)
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(tm-abs (tm-app a (tm-app b (tm-var 0)))))
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(define (tm-mult a b) (tm-compose a b))
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(define (tm-nat n)
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(if (positive? n)
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(tm-suc (tm-nat (- n 1)))
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tm-zero))
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(check-equal? (normalize `(app ,tm-id ,tm-id)) tm-id)
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(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-snd)) tm-fst)
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(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-fst)) tm-id)
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(check-equal? (normalize (tm-app tm-snd (tm-app tm-pair tm-id tm-fst) tm-fst)) tm-fst)
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(check-equal? (normalize (tm-add (tm-nat 499) (tm-nat 777))) (normalize (tm-add (tm-nat 777) (tm-nat 499))))
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(check-equal? (normalize (tm-mult (tm-nat 3) (tm-nat 2))) (normalize (tm-nat 6)))
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(check-equal? (normalize (tm-mult (tm-nat 11) (tm-nat 116))) (normalize (tm-nat 1276)))
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(check η-eq? (normalize (tm-add (tm-nat 499) (tm-nat 777))) (normalize (tm-add (tm-nat 777) (tm-nat 499))))
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(check βη-eq? (tm-mult (tm-nat 888) (tm-nat 999)) (tm-nat 887112))
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(check β-eq? (tm-mult (tm-nat 888) (tm-nat 999)) (tm-nat 887112))
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