42 lines
1.1 KiB
Racket
42 lines
1.1 KiB
Racket
|
#lang plait
|
||
|
|
(define-type Nat
|
||
|
|
[Z]
|
||
|
|
[S (pred : Nat)])
|
||
|
|
|
||
|
|
(define (plus nat1 nat2)
|
||
|
|
(type-case Nat nat1
|
||
|
|
[(Z) nat2]
|
||
|
|
[(S pred) (S (plus pred nat2))]))
|
||
|
|
|
||
|
|
(define (compare nat1 nat2)
|
||
|
|
(type-case Nat nat1
|
||
|
|
[(Z)
|
||
|
|
(type-case Nat nat2
|
||
|
|
[(Z) 'equal]
|
||
|
|
[(S pred) 'less])]
|
||
|
|
[(S pred1)
|
||
|
|
(type-case Nat nat2
|
||
|
|
[(Z) 'greater]
|
||
|
|
[(S pred2) (compare pred1 pred2)])]))
|
||
|
|
|
||
|
|
(define (times nat1 nat2)
|
||
|
|
(type-case Nat nat1
|
||
|
|
[(Z) (Z)]
|
||
|
|
[(S pred)
|
||
|
|
(type-case Nat nat2
|
||
|
|
[(Z) (Z)]
|
||
|
|
[(S pred2) (plus nat2 (times pred nat2))])]))
|
||
|
|
|
||
|
|
(test (plus (Z) (S (Z))) (S (Z)))
|
||
|
|
(test (plus (S (Z)) (Z)) (S (Z)))
|
||
|
|
(test (compare (Z) (Z)) 'equal)
|
||
|
|
(test (compare (Z) (S (Z))) 'less)
|
||
|
|
(test (compare (S (Z)) (Z)) 'greater)
|
||
|
|
(test (compare (S (S (Z))) (S (Z))) 'greater)
|
||
|
|
(test (times (Z) (Z)) (Z))
|
||
|
|
(test (times (Z) (S (Z))) (Z))
|
||
|
|
(test (times (S (Z)) (Z)) (Z))
|
||
|
|
(test (times (S (S (Z))) (S (Z))) (S (S (Z)))) ; 2 x 1
|
||
|
|
(test (times (S (Z)) (S (S (Z)))) (S (S (Z)))) ; 1 x 2
|
||
|
|
(test (times (S (Z)) (S (Z))) (S (Z))) ; 1 x 1
|
||
|
|
(test (times (S (S (Z))) (S (S (Z)))) (S (S (S (S (Z)))))) ; 2 x 2
|