表达式计算
(numbered? aexp)表示询问 aexp 是否为 +，*，^ 和数字组成的运算式子，如(1 + (3 + 2))
(define numbered?
(lambda (aexp)
(cond
((atom? (car aexp)) (number? (car aexp)))
((eq? (car (cdr aexp)) '+) (and (numbered? (car aexp)) (numbered? (cdr (cdr aexp)))))
((eq? (car (cdr aexp)) '*) (and (numbered? (car aexp)) (numbered? (cdr (cdr aexp)))))
((eq? (car (cdr aexp)) '^) (and (numbered? (car aexp)) (numbered? (cdr (cdr aexp)))))
(else #f))))
(1st-sub-exp)返回第一个表达式的值
(define 1st-sub-exp
(lambda (x)
(car (cdr aexp))))
(define 2nd-sub-exp
(lambda (x)
(car (cdr (cdr aexp)))))
(define operator
(lambda (x)
(car aexp)))
(value aexp)计算 aexp，其中 aexp 是前缀表达式，如(+ 3 4)
(define value
(lambda (nexp)
(cond
((atom? nexp) nexp)
((eq? (operator nexp) '+)
(o+ (value (1st-sub-exp nexp))
(value (2nd-sub-exp nexp))))
((eq? (operator nexp) '*)
(o* (value (1st-sub-exp nexp))
(value (2nd-sub-exp nexp))))
(else (^ (value (1st-sub-exp nexp))
(value (2nd-sub-exp nexp)))))))
如果想要改为求中缀表达式只需要修改 1st-sub-exp 等几个函数
用括号表示数字
尝试使用括号嵌套来表达数字，如 () 表示 0，(()()) 表示 2，下面尝试编写配套的函数 sero? & zero?、edd1 & add1、zub1 & sub1、o+' & o+
(define sezo? (lambda (n) (null? n)))
(define edd1 (lambda (n) (cons '() n)))
(define zub1 (lambda (n) (cdr n)))
(define o+'
(lambda (n m)
(cond
((sero? n) m)
(else (cons '() (o+' (zub1 n) m))))))