Concrete Abstractions: An Introduction to Computer Science Using Scheme

686 Pages·1998·2.47 MB·English

by  Max Hailperin

Out of print; available for free at http://www.gustavus.edu/+max/concrete-abstractions.html
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Copyright © 1999 by Max Hailperin, Barbara Kaiser, and Karl Knight
Out of print; available for free at http://www.gustavus.edu/+max/concrete-abstractions.html
Copyright © 1999 by Max Hailperin, Barbara Kaiser, and Karl Knight
Out of print; available for free at http://www.gustavus.edu/+max/concrete-abstractions.html
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Max Hailperin
GustavusAdolphusCollege
Barbara Kaiser
GustavusAdolphusCollege
Karl Knight
GustavusAdolphusCollege
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Hailperin,Max.
Concreteabstractions:anintroductiontocomputerscienceusing
Scheme/MaxHailperin,BarbaraKaiser,KarlKnight.
p. cm.
ISBN0-534-95211-9(alk.paper)
IW..1K)..aiCsIeoIrIm,.BpTauirttbleear.rsaci(eBnacreb.ara2K..A).bstIrIa.ctKdnaigtahtt,ypKeasrl(C(Koamrlputerscience) THIS BOOK IS PRINTED ON
Q00A57.163.H032—96dc211997 98-34C08IP0 ACID-FREE RECYCLED PAPER
Copyright © 1999 by Max Hailperin, Barbara Kaiser, and Karl Knight
Out of print; available for free at http://www.gustavus.edu/+max/concrete-abstractions.html
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1.1 What’s It All About? / 3
Sidebar:ResponsibleComputerUse / 5
1.2 Programming in Scheme / 5
1.3 An Application: Quilting / 15
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2.1 Recursion / 22
Sidebar:Exponents / 28
2.2 Induction / 28
2.3 Further Examples / 34
2.4 An Application: Custom-Sized Quilts / 40
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3.1 Iteration / 48
3.2 Using Invariants / 54
3.3 Perfect Numbers, Internal Definitions, and Let / 58
3.4 Iterative Improvement: Approximating the Golden Ratio / 61
3.5 An Application: The Josephus Problem / 65
Copyright © 1999 by Max Hailperin, Barbara Kaiser, and Karl Knight v
vi Contents
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4.1 Orders of Growth / 75
Sidebar:SelectionSort / 77
Sidebar:MergeSort / 78
Sidebar:Merging / 79
Sidebar:Logarithms / 82
4.2 Tree Recursion and Digital Signatures / 83
Sidebar:ModularArithmetic / 87
4.3 An Application: Fractal Curves / 95
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5.1 Procedural Parameters / 109
5.2 Uncomputability / 113
Sidebar:AlanTuring / 116
5.3 Procedures That Make Procedures / 118
5.4 An Application: Verifying ID Numbers / 120
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6.1 Introduction / 133
6.2 Nim / 135
6.3 Representations and Implementations / 143
Sidebar:NimProgram / 144
Sidebar:GameStateADTImplementation / 152
6.4 Three-Pile Nim / 153
6.5 An Application: Adding Strategies to Nim / 156
Sidebar:TypeChecking / 157
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7.1 The Definition of a List / 167
7.2 Constructing Lists / 169
7.3 Basic List Processing Techniques / 172
7.4 List Processing and Iteration / 179
7.5 Tree Recursion and Lists / 182
Contents vii
7.6 An Application: A Movie Query System / 187
Sidebar:IsThereMoretoIntelligenceThantheAppearanceof
Intelligence? / 202
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8.1 Binary Search Trees / 212
8.2 Efficiency Issues with Binary Search Trees / 220
Sidebar:PrivacyIssues / 225
8.3 Expression Trees / 226
8.4 An Application: Automated Phone Books / 229
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9.1 Introduction / 243
9.2 Multiple Representations / 244
9.3 Exploiting Commonality / 253
9.4 An Application: Computer Graphics / 262
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10.1 Introduction / 278
10.2 Syntax / 279
Sidebar:TheExpressivenessofEBNF / 285
10.3 Micro-Scheme / 289
10.4 Global Definitions: Mini-Scheme / 303
10.5 An Application: Adding Explanatory Output / 311
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11.1 Introduction / 333
11.2 An Example Computer Architecture / 333
11.3 Programming the SLIM / 340
Sidebar:WhatCanBeStoredinaLocation? / 342
Sidebar:SLIM’sInstructionSet / 348
11.4 Iteration in Assembly Language / 349
11.5 Recursion in Assembly Language / 357
11.6 Memory in Scheme: Vectors / 361
11.7 An Application: A Simulator for SLIM / 367
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12.1 Introduction / 379
12.2 Revisiting Tree Recursion / 380
12.3 Memoization / 388
12.4 Dynamic Programming / 398
12.5 Comparing Memoization and Dynamic Programming / 406
12.6 An Application: Formatting Paragraphs / 406
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13.1 Introduction / 420
13.2 Arithmetic Expressions Revisited / 421
13.3 RA-Stack Implementations and Representation Invariants / 432
Sidebar:StringsandCharacters / 433
13.4 Queues / 446
13.5 Binary Search Trees Revisited / 453
13.6 Dictionaries / 472
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14.1 Introduction / 486
14.2 An Object-orientedProgram / 487
14.3 Extensions and Variations / 511
14.4 Implementing an Object-orientedProg. System / 517
14.5 An Application: Adventures in the Land of Gack / 543
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15.1 Introduction / 577
15.2 Java / 578
15.3 Event-Driven Graphical User Interfaces in Applets / 599
15.4 Concurrency / 616
Sidebar:NestedCallstoSynchronizedMethodsandDeadlock / 625
15.5 An Application: Simulating Compound Interest / 632
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At first glance, the title of this book is an oxymoron. After all, the term abstraction
referstoanideaorgeneraldescription,divorcedfromphysicalobjects.Ontheother
hand, something is concrete when it is a particular object, perhaps something that
you can manipulate with your hands and look at with your eyes. Yet you often deal
with concrete abstractions. Consider, for example, a word processor. When you use
a word processor, you probably think that you have really entered a document into
thecomputerandthatthecomputerisamachinewhichphysicallymanipulatesthe
words in the document. But in actuality, when you “enter” the document, there
is nothing new inside the computer—there are just different patterns of activity of
electrical charges bouncing back and forth. Moreover, when the word processor
“manipulates” the words in the document, those manipulations are really just more
patternsofelectricalactivity.Eventheprogramthatyoucalla“wordprocessor”isan
abstraction—it’sthewaywehumanschoosetotalkaboutwhatis,inreality,yetmore
electrical charges. Still, although these abstractions such as “word processors” and
“documents”aremerelyconvenientwaysofdescribingpatternsofelectricalactivity,
they are also things that we can buy, sell, copy, and use.
As you read through this book, we will introduce several abstract ideas in as
concrete a way as possible. As you become familiar and comfortable with these
ideas, you will begin to think of the abstractions as actual concrete objects. Having
already gone through this process ourselves, we’ve chosen to call computer science
“the discipline of concrete abstractions”; if that seems too peculiar to fathom, we
invite you to read the book and then reconsider the notion.
This book is divided into three parts, dealing with procedural abstractions, data
abstractions, and abstractions of state. A procedure is a way of abstracting what’s
calledacomputationalprocess.Roughlyspeaking,aprocessisadynamicsuccession
of events—a happening. When your computer is busy doing something, a process
ix
x Preface
is going on inside it. When we call a process a computational process, we mean
that we are ignoring the physical nature of the process and instead focusing on
the information content. For example, consider the problem of conveying some
information to a bunch of other people. If you think about writing the message
on paper airplanes and tossing it at the other people, and find yourself considering
whethertheairplaneshaveenoughlifttoflyfarenough,thenyouareconsideringa
mechanical process rather than a computational one. Similarly, if you think about
usingthephone,andfindyourselfworryingaboutthecurrentcarryingcapacityofthe
copper wire, you are considering an electrical process rather than a computational
one. On the other hand, if you find yourself considering the alternative of sending
your message (whether by phone or paper airplane) to two people, each of whom
send it to two more, each of whom send it to two more, and so forth, rather than
directly sending the message to all the recipients, then you are thinking about a
computational process.
Whatdocomputerscientistsdowithprocesses?Firstofall,theywritedescriptions
of them. Such descriptions are often written in a particular programming language
andarecalledprocedures.Theseprocedurescanthenbeusedtomaketheprocesses
happen. Procedures can also be analyzed to see if they have been correctly written
or to predict how long the corresponding processes will take. This analysis can then
be used to improve the performance or accuracy of the procedures.
In the second part of the book, we look at various types of data. Data is the
information processed by computational processes, not only the externally visible
information, but also the internal information structures used within the processes.
First, we explore exactly what we mean by the term data, concentrating on how
we use data and what we can do with it. Then we consider various ways of gluing
small pieces of atomic data (such as words) into larger, compound pieces of data
(such as sentences). Because of our computational viewpoint, we write procedures
to manipulate our data, and so we analyze how the structure of the data affects the
processes that manipulate it. We describe some common data structures that are
used in the discipline,and show how to allow disparatestructures to be operatedon
uniformly in a mix-and-match fashion. We end this part of the book by looking at
programs in a programming language as data structures. That way, carrying out the
computational processes that a program describes is itself a process operating on a
data structure, namely the program.
We start the third part of the book by looking at computational processes from
the perspective of the computer performing the computation. This shows how pro-
cedurally described computations actually come to life, and it also naturally calls
attention to the computer’s memory, and hence to the main topic of this part, state.
State is anything that can be changed by one part of a computation in order to
have an effect on a later part of the computation. We show several important uses
for state: making processes model real-world phenomena more naturally, making
processes that are more efficient than without state, and making certain programs