48 lines
1.2 KiB
Racket
48 lines
1.2 KiB
Racket
#lang s-exp "../redex-curnel.rkt"
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(require "sugar.rkt" "bool.rkt")
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;; TODO: override (all-defined-out) to enable exporting all these
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;; properly.
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(provide nat z s add1 sub1 plus nat-equal?)
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(module+ test
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(require rackunit))
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(data nat : Type
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(z : nat)
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(s : (-> nat nat)))
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(define (add1 (n : nat)) (s n))
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(module+ test
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(check-equal? (add1 (s z)) (s (s z))))
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(define (sub1 (n : nat))
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(case n
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[z z]
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[s (lambda (x : nat) x)]))
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(module+ test
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(check-equal? (sub1 (s z)) z))
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(define plus
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(fix (plus : (forall* (n1 : nat) (n2 : nat) nat))
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(lambda (n1 : nat)
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(lambda (n2 : nat)
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(case n1
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[z n2]
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[s (λ (x : nat) (plus x (s n2)))])))))
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(module+ test
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(check-equal? (plus z z) z)
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(check-equal? (plus (s (s z)) (s (s z))) (s (s (s (s z))))))
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(define-rec (nat-equal? (n1 : nat) (n2 : nat) : bool)
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(case* n1
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[z (case* n2
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[z btrue]
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[(s (n3 : nat)) bfalse])]
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[(s (n3 : nat))
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(case* n2
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[z btrue]
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[(s (n4 : nat)) (nat-equal? n3 n4)])]))
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(module+ test
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(check-equal? btrue (nat-equal? z z))
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(check-equal? bfalse (nat-equal? z (s z)))
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(check-equal? btrue (nat-equal? (s z) (s z))))
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