#lang sicp

; a) Define unique-pairs
(define (accumulate op initial sequence)
  (if (null? sequence)
    initial
    (op (car sequence)
        (accumulate op initial (cdr sequence)))))

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

(define (enumerate-interval a b)
  (if (> a b)
      '()
      (cons a (enumerate-interval (+ a 1) b))))

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

; b) use it to define prime-sum-pairs

(define (filter predicate sequence)
  (cond ((null? sequence) nil)
        ((predicate (car sequence))
         (cons (car sequence)
               (filter predicate (cdr sequence))))
        (else (filter predicate (cdr sequence)))))

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

(define (prime-sum-pairs n)
  (map (lambda (pair)
         (list (car pair) (cadr pair) (+ (car pair)
                                         (cadr pair))))
       (filter prime-sum?
               (unique-pairs n))))