3 \index{*inductive(} 
3 \index{*inductive(} 
4 
4 
5 This chapter is dedicated to the most important definition principle after 
5 This chapter is dedicated to the most important definition principle after 
6 recursive functions and datatypes: inductively defined sets. 
6 recursive functions and datatypes: inductively defined sets. 
7 
7 
8 We start with a simple example \ldots . A slightly more complicated example, the 
8 We start with a simple example: the set of even numbers. 

9 A slightly more complicated example, the 
9 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular, 
10 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular, 
10 some standard induction heuristics are discussed. To demonstrate the 
11 some standard induction heuristics are discussed. To demonstrate the 
11 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study 
12 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study 
12 from the realm of contextfree grammars. The chapter closes with a discussion 
13 from the realm of contextfree grammars. The chapter closes with a discussion 
13 of advanced forms of inductive definitions. 
14 of advanced forms of inductive definitions. 
14 
15 

16 \input{Inductive/Even} 
15 \input{Inductive/document/Star} 
17 \input{Inductive/document/Star} 
16 \input{Inductive/document/AB} 
18 \input{Inductive/document/AB} 
17 
19 
18 \index{inductive definition)} 
20 \index{inductive definition)} 
19 \index{*inductive)} 
21 \index{*inductive)} 