doc-src/TutorialI/Inductive/inductive.tex
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Sun Nov 26 10:48:38 2000 +0100 (2000-11-26)
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     1 \chapter{Inductively Defined Sets}
     2 \index{inductive definition|(}
     3 \index{*inductive|(}
     4 
     5 This chapter is dedicated to the most important definition principle after
     6 recursive functions and datatypes: inductively defined sets.
     7 
     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.
    15 
    16 \input{Inductive/Even}
    17 \input{Inductive/document/Star}
    18 
    19 \section{Advanced inductive definitions}
    20 \input{Inductive/Advanced}
    21 
    22 \input{Inductive/document/AB}
    23 
    24 \index{inductive definition|)}
    25 \index{*inductive|)}