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From Mathematics to Generic Programming, by Alexander A. Stepanov, Daniel E. Rose
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In this substantive yet accessible book, pioneering software designer Alexander Stepanov and his colleague Daniel Rose illuminate the principles of generic programming and the mathematical concept of abstraction on which it is based, helping you write code that is both simpler and more powerful.
If you’re a reasonably proficient programmer who can think logically, you have all the background you’ll need. Stepanov and Rose introduce the relevant abstract algebra and number theory with exceptional clarity. They carefully explain the problems mathematicians first needed to solve, and then show how these mathematical solutions translate to generic programming and the creation of more effective and elegant code. To demonstrate the crucial role these mathematical principles play in many modern applications, the authors show how to use these results and generalized algorithms to implement a real-world public-key cryptosystem.
As you read this book, you’ll master the thought processes necessary for effective programming and learn how to generalize narrowly conceived algorithms to widen their usefulness without losing efficiency. You’ll also gain deep insight into the value of mathematics to programming—insight that will prove invaluable no matter what programming languages and paradigms you use.
You will learn about
- How to generalize a four thousand-year-old algorithm, demonstrating indispensable lessons about clarity and efficiency
- Ancient paradoxes, beautiful theorems, and the productive tension between continuous and discrete
- A simple algorithm for finding greatest common divisor (GCD) and modern abstractions that build on it
- Powerful mathematical approaches to abstraction
- How abstract algebra provides the idea at the heart of generic programming
- Axioms, proofs, theories, and models: using mathematical techniques to organize knowledge about your algorithms and data structures
- Surprising subtleties of simple programming tasks and what you can learn from them
- How practical implementations can exploit theoretical knowledge
- Sales Rank: #107707 in Books
- Published on: 2014-11-17
- Original language: English
- Number of items: 1
- Dimensions: 9.30" h x .70" w x 6.20" l, .0 pounds
- Binding: Paperback
- 320 pages
Most helpful customer reviews
51 of 53 people found the following review helpful.
Great illustration of the core ideas in Generic Programming
By kurseewalla
This is a remarkable book. It vividly illustrates the relationship of abstract mathematics to generic programming, and I don't know of any other book that gets to the heart of generic programming the way this one does.
It starts by describing two algorithms which have been known for millennia - the Egyptian multiplication algorithm, and Euclid's greatest common measure algorithm - and then traces their evolution through history, describing how the algorithms were extended by successive generations of mathematicians. At each step, the authors implement the algorithm in C++, illustrating the process of taking a concrete algorithm and successively generalizing it. These two parallel threads of algorithm evolution and implementation generalization run throughout the book, providing a very compelling demonstration that the process of generalizing an algorithm is precisely the same as the process that mathematics has followed through the ages.
Along the way, we meet many great figures from mathematics, which turns what could have been a dry theoretical text into an absorbing story of the evolution of mathematical thought and the remarkable people that led it. This is an informal book, designed to be easy to read (in stark contrast to "Elements of Programming" by Stepanov and McJones), and any competent programmer with an understanding of high school math should be able to follow it comfortably.
24 of 26 people found the following review helpful.
Great Resource for Designing Reusable Code
By Andrew Norton
I am currently an undergraduate CS student, and I really like using math to solve programming problems. In this book, the authors present mathematical approaches to generalization that would be extremely useful to anyone designing libraries of code.
This book applies abstract algebra to the problem of designing reusable program code. (If you're not familiar with abstract algebra already, don't worry--the authors introduce and explain the relevant concepts as needed.) It proposes a paradigm of studying operations on data types separately from the types themselves. One can then categorize these operations--for instance, whether or not the associative/commutative/distributive laws hold--and then use the templates/generics feature of a programming language to create methods that work on many different data types (sometimes these types are so far separated that one wouldn't think that the same code would work for both).
Throughout the book, the authors use the Euclidean algorithm (for computing the greatest common divisor) as an example of the flexibility of an algorithm. After analyzing what properties the related operations and data types must satisfy, they show how the *same code* for the Euclidean algorithm on integers can be used to determine the GCD of two polynomials, two complex numbers, and more. I like writing and maintaining some personal libraries of code, and I believe that the techniques that the authors cover in this book will help me write better code.
Although the primary focus of this book is on the use of Generic Programming, one part of the book that I really appreciated was the time the authors spent taking note of the efficiency of each method. Since this book is describing techniques that are to be used when designing library functions that may be called millions of times a second, every iteration of a loop matters. The authors' careful description of how they take the naive approach and pare it down to the minimum number of operations helped improve my own coding style.
The authors also provide biographical information on the people whose work greatly affected the concepts in this book. This gives the reader a sense of how this topic progressed through history. Some people may not like this (some people want to know only what is immediately useful to them right now), but I enjoyed seeing the progression and refinement of generic mathematics followed by generic programming.
This book uses C++ for all its examples (which shouldn't be unexpected--after all, Stepanov did design the STL), but the book includes a really helpful "C++ for non-C++ Programmers" section in the appendices. (My "primary language" is Java, but using that appendix made all of the code in the book quite understandable.)
18 of 19 people found the following review helpful.
Another masterpiece from Alex Stepanov
By Fernando Pelliccioni
Another masterpiece from Alex Stepanov.
I had the honor of reviewing the draft version, and I can say it is a wonderful book!
It combines mathematics, programming and history in a gorgeous and unique way.
Contains ancient geometric algorithms, abstract algebra, and generic programming.
A journey through history, visiting the most prominent figures of mathematics, whose influence can be seen in Generic Programming.
It is a pleasure to read.
Strongly recommended for all programmers who love their profession.
Thanks Alex for improving our discipline.
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