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\chapter{Inductively Defined Sets} \label{chap:inductive}
\index{inductive definitions|(}
This chapter is dedicated to the most important definition principle after
recursive functions and datatypes: inductively defined sets.
We start with a simple example: the set of even numbers. A slightly more
complicated example, the reflexive transitive closure, is the subject of
{\S}\ref{sec:rtc}. In particular, some standard induction heuristics are
discussed. Advanced forms of inductive definitions are discussed in
{\S}\ref{sec:adv-ind-def}. To demonstrate the versatility of inductive
definitions, the chapter closes with a case study from the realm of
context-free grammars. The first two sections are required reading for anybody
interested in mathematical modelling.
\input{Inductive/even-example}
\input{Inductive/document/Mutual}
\input{Inductive/document/Star}
\section{Advanced Inductive Definitions}
\label{sec:adv-ind-def}
\input{Inductive/advanced-examples}
\input{Inductive/document/AB}
\index{inductive definitions|)}