1 \chapter{Inductively Defined Sets}
2 \index{inductive definition|(}
5 This chapter is dedicated to the most important definition principle after
6 recursive functions and datatypes: inductively defined sets.
8 We start with a simple example: the set of even numbers.
9 A slightly more complicated example, the
10 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular,
11 some standard induction heuristics are discussed. To demonstrate the
12 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study
13 from the realm of context-free grammars. The chapter closes with a discussion
14 of advanced forms of inductive definitions.
16 \input{Inductive/Even}
17 \input{Inductive/document/Star}
19 \section{Advanced inductive definitions}
20 \input{Inductive/Advanced}
22 \input{Inductive/document/AB}
24 \index{inductive definition|)}