8ba4ed17d9
elim was not checking that the arguments to be used for the parameters of the inductive matched the actual parameters expected, resulting in incorrect and non-deterministic unification, and thus incorrect reduction when the parameters were unified incorrectly.
50 lines
1.3 KiB
Racket
50 lines
1.3 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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(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* nat Type n () (lambda (x : nat) nat)
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[z z]
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[(s (x : nat)) IH: ((ih-n : 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 Type n1 () (lambda (x : nat) nat)
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[z n2]
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[(s (x : nat)) IH: ((ih-n1 : nat))
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(s ih-n1)]))
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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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;; Credit to this function goes to Max
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(define nat-equal?
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(elim nat Type (lambda (x : nat) (-> nat bool))
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(elim nat Type (lambda (x : nat) bool)
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btrue
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(lambda* (x : nat) (ih-n2 : bool) bfalse))
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(lambda* (x : nat) (ih : (-> nat bool))
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(elim nat Type (lambda (x : nat) bool)
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bfalse
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(lambda* (x : nat) (ih-bla : 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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