Mathematica Cookbook

Chapter 2. Functional Programming

A man builds a city With banks and cathedrals A man melts the sand so he can See the world outside

(You’re gonna meet her there) A man makes a car (She’s your destination) And builds a road to run them on (Gotta get to her) A man dreams of leaving (She’s imagination) But he always stays behind

And these are the days When our work has come asunder

And these are the days When we look for something other

—U2, “Lemon”

2.0 Introduction

Functional Programming

Many books on Mathematica tout its capabilities as a multiparadigm language. Although it’s true that Mathematica supports procedural, recursive, rule-based, functional, and even object-oriented styles (to some degree), I believe it is the functional and rule-based styles that are most important to master. Some gurus may go a step further and say that if you do not master the functional style then you are not really programming in Mathematica and your programs will have a far greater chance of being inefficient and clumsy. I won’t be so dogmatic, but until you are an expert it’s best to stick with an approach that many Mathematica experts prefer. A practical reason to learn the functional style is that most of the recipes in this book use either functional or rule-based styles and sometimes mixtures of both. This chapter is intended as a kind of decoder key for readers who want to master the functional style and get a deeper understanding of the solutions throughout this book. There are also a few recipes ...