doc-src/TutorialI/Inductive/inductive.tex
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     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 context-free grammars. The chapter closes with a discussion
    13 from the realm of context-free 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|)}