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Elements of Programming

Год: 2009
Автор: Alexander Stepanov, Paul McJones
Издательство: Addison-Wesley
ISBN: 032163537X
Язык: Английский
Формат: CHM
Качество: Изначально компьютерное (eBook)
Количество страниц: 288

Описание: "Ask a mechanical, structural, or electrical engineer how far they would get without a heavy reliance on a firm mathematical foundation, and they will tell you, 'not far.' Yet so-called software engineers often practice their art with little or no idea of the mathematical underpinnings of what they are doing. And then we wonder why software is notorious for being delivered late and full of bugs, while other engineers routinely deliver finished bridges, automobiles, electrical appliances, etc. on time and with only minor defects. This book sets out to redress this imbalance. Members of my advanced development team at Adobe who took the course based on the same material all benefited greatly from the time invested. It may appear as a highly technical text intended only for computer scientists, but it should be required reading for all practicing software engineers."
—Martin Newell, Adobe Fellow

"The book contains some of the most beautiful code I have ever seen."
— Bjarne Stroustrup, Designer of C++

"I am happy to see Alex's course, development and teaching of which I strongly supported as the CTO of Silicon Graphics, to be now available to all programmers in this elegant little book."
—Forest Baskett, General Partner, New Enterprise Associates

"Paul's patience and architectural experience helped to organize Alex's mathematical approach into a tightly-structured edifice—an impressive feat!"
—Robert W. Taylor, Founder of Xerox PARC CSL and DEC Systems Research Center

Elements of Programming provides a different understanding of programming than is presented elsewhere. Its major premise is that practical programming, like other areas of science and engineering, must be based on a solid mathematical foundation. The book shows that algorithms implemented in a real programming language, such as C++, can operate in the most general mathematical setting. For example, the fast exponentiation algorithm is defined to work with any associative operation. Using abstract algorithms leads to efficient, reliable, secure, and economical software.

This is not an easy book. Nor is it a compilation of tips and tricks for incremental improvements in your programming skills. The book's value is more fundamental and, ultimately, more critical for insight into programming. To benefit fully, you will need to work through it from beginning to end, reading the code, proving the lemmas, doing the exercises. When finished, you will see how the application of the deductive method to your programs assures that your system's software components will work together and behave as they must.

Following key definitions, the book describes a number of algorithms and requirements for types on which they are defined that exemplify its abstract mathematical approach. The code for these descriptions—also available on the Web—is written in a small subset of C++ meant to be accessible to any experienced programmer. This subset is defined in a special language appendix coauthored by Sean Parent and Bjarne Stroustrup.

Whether you are a software developer, or any other professional for whom programming is an important activity, or a committed student, you will come to understand what the book's experienced authors have been teaching and demonstrating for years—that mathematics is good for programming, that theory is good for practice.


Copyright
Preface
About the Authors
Chapter 1. Foundations
Section 1.1. Categories of Ideas: Entity, Species, Genus
Section 1.2. Values
Section 1.3. Objects
Section 1.4. Procedures
Section 1.5. Regular Types
Section 1.6. Regular Procedures
Section 1.7. Concepts
Section 1.8. Conclusions
Chapter 2. Transformations and Their Orbits
Section 2.1. Transformations
Section 2.2. Orbits
Section 2.3. Collision Point
Section 2.4. Measuring Orbit Sizes
Section 2.5. Actions
Section 2.6. Conclusions
Chapter 3. Associative Operations
Section 3.1. Associativity
Section 3.2. Computing Powers
Section 3.3. Program Transformations
Section 3.4. Special-Case Procedures
Section 3.5. Parameterizing Algorithms
Section 3.6. Linear Recurrences
Section 3.7. Accumulation Procedures
Section 3.8. Conclusions
Chapter 4. Linear Orderings
Section 4.1. Classification of Relations
Section 4.2. Total and Weak Orderings
Section 4.3. Order Selection
Section 4.4. Natural Total Ordering
Section 4.5. Clusters of Derived Procedures
Section 4.6. Extending Order-Selection Procedures
Section 4.7. Conclusions
Chapter 5. Ordered Algebraic Structures
Section 5.1. Basic Algebraic Structures
Section 5.2. Ordered Algebraic Structures
Section 5.3. Remainder
Section 5.4. Greatest Common Divisor
Section 5.5. Generalizing gcd
Section 5.6. Stein gcd
Section 5.7. Quotient
Section 5.8. Quotient and Remainder for Negative Quantities
Section 5.9. Concepts and Their Models
Section 5.10. Computer Integer Types
Section 5.11. Conclusions
Chapter 6. Iterators
Section 6.1. Readability
Section 6.2. Iterators
Section 6.3. Ranges
Section 6.4. Readable Ranges
Section 6.5. Increasing Ranges
Section 6.6. Forward Iterators
Section 6.7. Indexed Iterators
Section 6.8. Bidirectional Iterators
Section 6.9. Random-Access Iterators
Section 6.10. Conclusions
Chapter 7. Coordinate Structures
Section 7.1. Bifurcate Coordinates
Section 7.2. Bidirectional Bifurcate Coordinates
Section 7.3. Coordinate Structures
Section 7.4. Isomorphism, Equivalence, and Ordering
Section 7.5. Conclusions
Chapter 8. Coordinates with Mutable Successors
Section 8.1. Linked Iterators
Section 8.2. Link Rearrangements
Section 8.3. Applications of Link Rearrangements
Section 8.4. Linked Bifurcate Coordinates
Section 8.5. Conclusions
Chapter 9. Copying
Section 9.1. Writability
Section 9.2. Position-Based Copying
Section 9.3. Predicate-Based Copying
Section 9.4. Swapping Ranges
Section 9.5. Conclusions
Chapter 10. Rearrangements
Section 10.1. Permutations
Section 10.2. Rearrangements
Section 10.3. Reverse Algorithms
Section 10.4. Rotate Algorithms
Section 10.5. Algorithm Selection
Section 10.6. Conclusions
Chapter 11. Partition and Merging
Section 11.1. Partition
Section 11.2. Balanced Reduction
Section 11.3. Merging
Section 11.4. Conclusions
Chapter 12. Composite Objects
Section 12.1. Simple Composite Objects
Section 12.2. Dynamic Sequences
Section 12.3. Underlying Type
Section 12.4. Conclusions
Afterword
Regularity
Concepts
Algorithms and Their Interfaces
Programming Techniques
Meanings of Pointers
Conclusions
Appendix A. Mathematical Notation
Appendix B. Programming Language
Section B.1. Language Definition
Section B.2. Macros and Trait Structures
Bibliography
Index
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