49 lines
1.4 KiB
Racket
49 lines
1.4 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 )
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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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;; TODO: Can't use -> syntax here due to issues with names
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(s : (forall (x : 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* nat n (lambda (x : nat) nat)
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[z z]
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[(s (x : nat)) IH: ((ih-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 (n1 : nat) (n2 : nat))
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(case* nat n1 (lambda (x : nat) nat)
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[z n2]
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[(s (x : nat)) IH: ((ih-x : nat))
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(s ih-x)]))
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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 (nat-equal? (n1 : nat) (n2 : nat))
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(case* nat n1 (lambda (x : nat) bool)
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[z (case* nat n2 (lambda (x : nat) bool)
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[z btrue]
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[(s (x : nat)) IH: ((ih-x : bool)) bfalse])]
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;; TODO: Can't finish correct definition due to issues with names
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[(s (x : nat)) IH: ((ih-x : bool))
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(case* nat n2 (lambda (x : nat) bool)
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[z bfalse]
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[(s (x : nat)) IH: ((ih-x : bool))
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ih-x])]))
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(module+ test
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(check-equal? (nat-equal? z z) btrue)
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(check-equal? (nat-equal? z (s z)) bfalse)
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(check-equal? (nat-equal? (s z) (s z)) btrue))
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