\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-example}

\input{Inductive/document/Mutual}

\input{Inductive/document/Star}

\section{Advanced inductive definitions}

\input{Inductive/advanced-examples}

\input{Inductive/document/AB}

\index{inductive definition|)}

\index{*inductive|)}