my code：
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ;Church计数 (define zero (lambda (f) (lambda (x) x))) (define (add-1 n) (lambda (f) (lambda (x) (f ((n f) x))))) (define (show-num n)((n (lambda (x) ( 1 x))) 0)) (define (add a b) (lambda (f) (lambda (x) ((a f) ((b f) x))))) (define one (lambda (f) (lambda (x) (f x)))) (define two (lambda (f) (lambda (x) (f (f x))))) (show-num zero) (show-num one) (show-num two) (newline) (show-num (add-1 zero)) (show-num (add-1 (add-1 zero))) (show-num (add-1 (add-1 (add-1 zero)))) (show-num (add-1 (add-1 (add-1 (add-1 zero))))) (newline) (display "my addn") (show-num (add zero zero)) (show-num (add (add-1 zero) (add-1 zero))) (show-num (add (add-1 zero) (add-1 (add-1 zero)))) (define (multi a b) (lambda (f) (lambda (x) ((a (b f) ) x)))) (define (expon a b) (lambda (f) (lambda (x) (((a b) f) x)))) (show-num (multi two two)) (show-num (multi (add one two) two)) (show-num (expon two two)) (show-num (expon (expon two two) two)) |
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Church计数，通过(lambda (f))把f作为参数，这样f就不会被求值，而f的执行次数就代表了数字。
lambda中的形参其值是未知的，所以不会被求值。
形参好比糖果的包装纸，要把一段代码包起来，把它放到一个匿名函数里就行了
比如有一个函数
(lambda (a b) ( a b))
要把它包装起来，可以写成
(lambda (x) (lambda (a b) ( a b)) )
要剥开糖纸，传个参数就行了。
Church计数就是这个思想。
show-num用来把Church计数方式的数字转换成普通数字。
