doc-src/TutorialI/document/inductive0.tex

-\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.
-
-\begin{warn}
-Predicates can also be defined inductively.
-See {\S}\ref{sec:ind-predicates}.
-\end{warn}
-
-\input{Even}
-\input{Mutual}
-\input{Star}
-
-\section{Advanced Inductive Definitions}
-\label{sec:adv-ind-def}
-\input{Advanced}
-
-\input{AB}
-
-\index{inductive definitions|)}