#
Introduction to Computing

Explorations in Language, Logic, and Machines

David
Evans

Computer science studies how to describe, predict properties of, and efficiently implement information processes. This book introduces the most important ideas in computing using the Scheme and Python programming languages. It focuses on how to describe information processes by defining procedures, how to analyze the costs required to carry out a procedure, and the fundamental limits of what can and cannot be computed mechanically.

Errata (last update: 13 October 2013)

## Contents

Front Matter [PDF]

Preface [PDF]

#### Introduction

Chapter 1: Computing [PDF]

1.1 Processes, Procedures, and Computers

1.2 Measuring Computing Power (Information, Representing Data, Growth of Computing Power)

1.3 Science, Engineering, and the Liberal Arts

1.4 Summary and Roadmap

1.2 Measuring Computing Power (Information, Representing Data, Growth of Computing Power)

1.3 Science, Engineering, and the Liberal Arts

1.4 Summary and Roadmap

Exercises and solutions: PDF

#### Part I: Defining Procedures

Chapter 2: Language [PDF]

2.1 Surface Forms and Meanings

2.2 Language Construction

2.3 Recursive Transition Networks

2.4 Replacement Grammars

2.5 Summary

2.2 Language Construction

2.3 Recursive Transition Networks

2.4 Replacement Grammars

2.5 Summary

Exercises and solutions: PDF

Chapter 3: Programming [PDF]

3.1 Problems with Natural Languages

3.2 Programming Languages

3.3 Scheme

3.4 Expressions (Primitives, Application Expressions)

3.5 Definitions

3.6 Procedures (Making Procedures, Substitution Model of Evaluation)

3.7 Decisions

3.8 Evaluation Rules

3.9 Summary

3.2 Programming Languages

3.3 Scheme

3.4 Expressions (Primitives, Application Expressions)

3.5 Definitions

3.6 Procedures (Making Procedures, Substitution Model of Evaluation)

3.7 Decisions

3.8 Evaluation Rules

3.9 Summary

Exercises and solutions: PDF

Chapter 4: Problems and Procedures [PDF]

4.1 Solving Problems

4.2 Composing Procedures (Procedures as Inputs and Outputs)

4.3 Recursive Problem Solving

4.4 Evaluating Recursive Applications

4.5 Developing Complex Programs (Printing. Tracing)

4.6 Summary

4.2 Composing Procedures (Procedures as Inputs and Outputs)

4.3 Recursive Problem Solving

4.4 Evaluating Recursive Applications

4.5 Developing Complex Programs (Printing. Tracing)

4.6 Summary

Exercises and solutions: PDF

Chapter 5: Data [PDF]

#### Part II: Analyzing Procedures

Chapter 6: Machines [PDF]

6.1 History of Computing Machines

6.2 Mechanizing Logic (Implementing Logic, Composing Operations, Arithmetic)

6.3 Modeling Computing (Turing Machines)

6.4 Summary

6.2 Mechanizing Logic (Implementing Logic, Composing Operations, Arithmetic)

6.3 Modeling Computing (Turing Machines)

6.4 Summary

Chapter 7: Cost [PDF]

7.1 Empirical Measurements

7.2 Orders of Growth (Big

7.3 Analyzing Procedures (Input Size, Running Time, Worst Case Input)

7.2 Orders of Growth (Big

*O*, Omega, Theta)7.3 Analyzing Procedures (Input Size, Running Time, Worst Case Input)

7.4 Growth Rates (No Growth: Constant Time, Linear Growth, Quadratic
Growth, Exponential Growth, Faster than Exponential Growth, Non-terminating Procedures)

7.5 Summary

Chapter 8: Sorting and Searching [PDF]

8.1 Sorting (Best-First Sort, Insertion Sort, Quicker
Sorting, Binary Trees, Quicksort)

8.2 Searching (Unstructured Search, Binary Search, Indexed Search)

8.3 Summary

8.2 Searching (Unstructured Search, Binary Search, Indexed Search)

8.3 Summary

#### Part III: Improving Expressiveness

Chapter 9: Mutation [PDF]

9.1 Assignment

9.2 Impact of Mutation (Names, Places, Frames, and Environments; Evaluation Rules with State)

9.3 Mutable Pairs and Lists

9.4 Imperative Programming (List Mutators, Imperative Control Structures)

9.5 Summary

9.2 Impact of Mutation (Names, Places, Frames, and Environments; Evaluation Rules with State)

9.3 Mutable Pairs and Lists

9.4 Imperative Programming (List Mutators, Imperative Control Structures)

9.5 Summary

Chapter 10: Objects [PDF]

10.1 Packaging Procedures and State (Encapsulation, Messages, Object Terminology)

10.2 Inheritance (Implementing Subclasses, Overriding Methods)

10.3 Object-Oriented Programming

10.4 Summary

10.2 Inheritance (Implementing Subclasses, Overriding Methods)

10.3 Object-Oriented Programming

10.4 Summary

Chapter 11: Interpreters [PDF]

11.1 Python (Python Programs, Data Types, Applications and Invocations, Control Statements)

11.2 Parser

11.5 Summary

11.2 Parser

11.3 Evaluator (Primitives, If Expressions, Definitions and Names,
Procedures, Application, Finishing the Interpreter)

11.4 Lazy Evaluation (Lazy Interpreter, Lazy Programming)11.5 Summary

#### Part IV: The Limits of Computing

Chapter 12: Computability [PDF]

12.1 Mechanizing Reasoning (Gödel's Incompleteness Theorem)

12.2 The Halting Problem

12.3 Universality

12.4 Proving Non-Computability

12.5 Summary

12.2 The Halting Problem

12.3 Universality

12.4 Proving Non-Computability

12.5 Summary

Indexes [PDF]

Previous versions:
**Fall 2011 Edition**,
**Spring 2010 Edition**,
**Fall 2009 Edition**,
**Spring 2009 Edition**