;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-advanced-reader.ss" "lang")((modname |31.3|) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #t #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp") (lib "gui.ss" "teachpack" "htdp")))))
;product : (listof numbers) -> numbers
;Computes the product of alon0.

(define (product alon0)
  (local ;; the accumulator represents the product of all the numbers preceding alon1 in alon0,
    ;; ie, it represents the product of (alon1,alon0]
    ((define (product-accu alon1 accumulator)
       (cond
         [(empty? alon1) accumulator]
         [else (product-accu (rest alon1) (* (first alon1) accumulator))])))
    (product-accu alon0 1)))

(equal? (product '(1 2 3 4 5 6)) 720)

;how-many : (listof X) -> number
;Determines how many items there are in alox0.

(define (how-many alox0)
  (local ;;the accumulator represents the number of items preceding alox1 in alox0
    ((define (how-many-accu alox1 accumulator)
       (cond
         [(empty? alox1) accumulator]
         [else (how-many-accu (rest alox1) (+ 1 accumulator))])))
    (how-many-accu alox0 0)))

(equal? (how-many '(5 hey joe 5 1 0 true true false)) 9)

;add-to-pi : N -> number
;Adds pi to n.

(define (add-to-pi n0)
  (local ;; the accumulator represents n0-n1+pi.
    ((define (add-to-pi-accu n1 accumulator)
       (cond
         [(zero? n1) accumulator]
         [else (add-to-pi-accu (sub1 n1) (add1 accumulator))])))
    (add-to-pi-accu n0 pi)))

;add-to-x : N -> number
;Adds x to n.

(define (add-to-x n0 x)
  (local ;; the accumulator represents n0-n1+x.
    ((define (add-to-x-accu n1 accumulator)
       (cond
         [(zero? n1) accumulator]
         [else (add-to-x-accu (sub1 n1) (add1 accumulator))])))
    (add-to-x-accu n0 x)))

(equal? (add-to-x 5 6) 11)

;make-palindrome : (listof X) -> (listof X)
;Creates a palindrome from alox (non-empty list).

(define (make-palindrome alox0)
  (local ;The accumulator represents the items in alox0 preceding alox1
         ;in reverse order as in alox0.
    ((define (make-palindrome-accu alox1 accumulator)
       (cond
         [(empty? alox1) empty]
         [(empty? (rest alox1)) (cons (first alox1) accumulator)]
         [else (cons (first alox1)
                     (make-palindrome-accu (rest alox1) (cons (first alox1) accumulator)))])))
    (make-palindrome-accu alox0 empty)))

(make-palindrome '(a b c 1 5 3))

;is-prime? : N -> boolean
;Determines if n is a prime number.

(define (is-prime? n0)
  (local ;;accumulator i represents the numbers tested from [2,i) in order to
         ;;determine if n1 is prime
    ((define (is-prime?-accu n1 i)
       (cond
         [(= n1 i) true]
         [(= (remainder n1 i) 0) false]
         [else (is-prime?-accu n1 (add1 i))])))
    (is-prime?-accu n0 2)))

(and (is-prime? 2)
     (is-prime? 3)
     (not (is-prime? 4))
     (is-prime? 5)
     (not (is-prime? 6))
     (is-prime? 7))