2-40.scm

#lang scheme

(define nil '())

(define (square x) (* x x))

(define (smallest-divisor n)
  (find-divisor n 2))

(define (find-divisor n test-divisor)
  (cond ((> (square test-divisor) n) n)
        ((divides? test-divisor n) test-divisor)
        (else (find-divisor n (+ test-divisor 1)))))

(define (divides? a b)
  (= (remainder b a) 0))

(define (prime? n)
  (= n (smallest-divisor n)))

(define (fold-right op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (fold-right op initial (cdr sequence)))))
(define accumulate fold-right)

(define (enumerate-interval start end)
  (if (> start end)
      nil
      (cons start (enumerate-interval (+ start 1) end))))

(define (flatmap proc seq)
  (accumulate append nil (map proc seq)))

(define (prime-sum? pair)
  (prime? (+ (car pair) (cadr pair))))

(define (make-pair-sum pair)
  (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))

(define (unique-pairs n)
  (flatmap
   (lambda (i)
     (map (lambda (j) (list i j))
          (enumerate-interval 1 (- i 1))))
   (enumerate-interval 1 n)))

(define (prime-sum-pairs n)
  (map make-pair-sum
       (filter prime-sum?
               (unique-pairs n))))

(prime-sum-pairs 6)

(define (permutations s)
  (if (null? s) 
      (list nil) 
      (flatmap (lambda (x)
                 (map (lambda (p) (cons x p))
                      (permutations (remove x s))))
               s)))