\chapter{Inductively Defined Sets} \label{chap:inductive}
\index{inductive definition|(}
\index{*inductive|(}

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. To demonstrate the
versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study
from the realm of context-free grammars. The chapter closes with a discussion
of advanced forms of inductive definitions.

\input{Inductive/Even}
\input{Inductive/document/Mutual}
\input{Inductive/document/Star}

\section{Advanced inductive definitions}
\input{Inductive/Advanced}

\input{Inductive/document/AB}

\index{inductive definition|)}
\index{*inductive|)}
