1.3.1 (对过程的抽象)

(define (sum-integers a b)
  (if (> a b)
      0
      (+ a (sum-integers (+ a 1) b))))

(sum-integers 1 10)

(define (sum-cubes a b)
  (define (cube x)
    (* x x x))
  (if (> a b)
      0
      (+ (cube a) (sum-cubes (+ a 1) b))))

(sum-cubes 1 10)

(define (pi-sum a b)
  (if (> a b)
      0
      (+ (/ 1.0 (* a (+ a 2))) (pi-sum (+ a 4) b))))

(* 8 (pi-sum 1 1000000))

　　对过程的抽象:

(define (sum term a next b)
  (if (> a b)
      0
      (+ (term a)
         (sum term (next a) next b))))

　　填充:

(define (inc n)
  (+ n 1))

(define (cube n)
  (* n n n))

(define (sum-cubes a b)
  (sum cube a inc b))
(sum-cubes 1 10)

　　

(define (inc n)
  (+ n 1))

(define (identity x) x)

(define (sum-integers a b)
  (sum identity a inc b))

(sum-integers 1 10)

　　

(define (pi-next n)
  (+ n 4))

(define (pi-term x)
  (/ 1.0 (* x (+ x 2))))

(define (pi-sum a b)
  (sum pi-term a pi-next b))

(* 8 (pi-sum 1 10000))

　　拓展:

(define (integral f a b dx)  ;积分
  (define (add-dx x) (+ x dx))
  (* (sum f (+ a (/ dx 2.0)) add-dx b)
     dx))

  (define (cube x) (* x x x))
  
(integral cube 0 1 0.0001)