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This is a preliminary draft of the book. The final book will appear with MIT Press in 2001 and will move to its permanent Web site sometime in the fall of 2000.

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The Design Recipe for Functions
Problem Analysis & Data Definition
Contract, Purpose & Effect Statements, Header
Examples
Functiona Template
Function Definition
Tests

#3# The dependence graph has to be translated into an HTML-suitable format. #4#

	This marker refers to teacher hints, which suggest strategies on how to present a section, on how to approach an exercise, or on how to supplement some material.
	This marker refers to DrScheme hints. The programming environment has been designed with students in mind. The hints suggest how to use it at various stages of the learning process.
	This marker, placed at the end of exercises, links to on-line solutions. Solutions are available to registered teachers. To find out more about registration, see the book's registration site (not available yet).

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 ;; dimensions of traffic light (define WIDTH 50) (define HEIGHT 160) (define BULB-RADIUS 20) (define BULB-DISTANCE 10) ;; the positions of the bulbs  (define X-BULBS (quotient WIDTH 2)) (define Y-RED (+ BULB-DISTANCE BULB-RADIUS)) (define Y-YELLOW (+ Y-RED BULB-DISTANCE (* 2 BULB-RADIUS))) (define Y-GREEN (+ Y-YELLOW BULB-DISTANCE (* 2 BULB-RADIUS))) ;; draw the light with the red bulb turned on (start WIDTH HEIGHT) (draw-solid-disk (make-posn X-BULBS Y-RED) BULB-RADIUS RED) (draw-circle (make-posn X-BULBS Y-YELLOW) BULB-RADIUS YELLOW) (draw-circle (make-posn X-BULBS Y-GREEN) BULB-RADIUS GREEN)

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(cons 'Mercury empty)

'Mercury

empty

(cons 'Venus (cons 'Mercury empty))

'Venus

'Mercury

empty

(cons 'Earth (cons 'Venus (cons 'Mercury empty)))

'Earth

'Venus

'Mercury

empty

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Item	Price	Image
robot	29.95
robot	29.95
robot	29.95

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Tree A:	Tree B:

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Scheme expression representation of Scheme expression

3 3

x 'x

(* 3 10) (make-mul 3 10)

(+ (* 3 3) (* 4 4)) (make-add (make-mul 3 3) (make-mul 4 4))

(+ (* x x) (* y y)) (make-add (make-mul 'x 'x) (make-mul 'y 'y))

(* 1/2 (* 3 3)) (make-mul 1/2 (make-mul 3 3))

Scheme expression	representation of Scheme expression
`3`	`3`
`x`	`'x`
`(* 3 10)`	`(make-mul 3 10)`
`(+ (* 3 3) (* 4 4))`	`(make-add (make-mul 3 3) (make-mul 4 4))`
`(+ (* x x) (* y y))`	`(make-add (make-mul 'x 'x) (make-mul 'y 'y))`
`(* 1/2 (* 3 3))`	`(make-mul 1/2 (make-mul 3 3))`

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`(listof number)`	`->`	`(listof number)`
`(listof IR)`	`->`	`(listof symbol)`

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`(number -> number)`	`(listof number)`	`->`	`(listof number)`
`(IR -> symbol)`	`(listof IR)`	`->`	`(listof symbol)`

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`number`	`(listof number)`	`->`	`(listof number)`
`number`	`(listof IR)`	`->`	`(listof IR)`

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`(number number -> boolean)`	`number`	`(listof number)`	`->`	`(listof number)`
`(number IR -> boolean)`	`number`	`(listof IR)`	`->`	`(listof IR)`

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`(number X -> boolean)`	`number`	`(listof X)`	`->`	`(listof X)`
`(number X -> boolean)`	`number`	`(listof X)`	`->`	`(listof X)`

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(list 11 8 14 7)

(list 8 7)

(list 7)

empty

7

empty

(list 7)

8

empty

(list 7 8)

11

(list 14)

empty

14

empty

(list 14)

(list 7 8 11 14)

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list to be sorted

sort process for partition with items smaller than pivot

pivot item

sort process for partition with items larger than pivot

sorted list

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(define hand0 (create-hand 13 spades))

rank	suit	next
13		empty

(add-at-end! diamonds 1 hand0)

rank

suit

rank	suit	next
13		empty

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i-1

a

left right

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a vector fragment with pivot item p:

left right

p sm-1 la-1 sm-2 sm-3 la-2

partitioning the vector fragment into two regions, separated by p

left1 right1 left2 right2

sm-2 sm-1 sm-3 p la-1 la-2

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finding the swapping points for partition:

left right

p sm-1 la-1 sm-2 sm-3 la-2

new-left new-right

swapping the items and recuring on a new interval:

left right

p sm-1 sm-3 sm-2 la-1 la-2

stopping the generative recursion and clean-up:

left right

p sm-1 sm-3 sm-2 la-1 la-2

new-right new-left

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left1		right1		left2	right2
sm-2	sm-1	sm-3	p	la-1	la-2

left					right
p	sm-1	la-1	sm-2	sm-3	la-2
new-left			new-right