CHAPTER 7 - Rule Based Programming

Abstract

This chapter discusses rule-based programming. Paragraphs in Mathematica are constructed in essentially three ways: 1) by remaining in the functional programming paradigm and constructing nested sequences of one liners, each of which uses some of the functions defined in the previous one liners; 2) by defining a function by an expression of the form f [ x_] := body, which is just a special case of a rewrite rule of the form f [pattern] := body; and 3) by using Mathematica as a block structured language with the usual control structures of an imperative language. Establishing rewrite rules in Mathematica is done in two primary fashions: through following global rules and local rules. Global rules are rules that are applied whenever the appropriate left-hand side is encountered. There are two kinds of user-defined global rewrite rules: those using “=” and those using “:=”. While local rewrite rules are rules that are applied only to a single expression, the basic syntactical ingredient of a local rewrite rule is an arrow. Pattern matching is a basic ingredient of rule-based programming. A compound pattern is an expression with zero or more of simple patterns as subexpressions. Patterns play an important role in both global and local rules.