doc-src/TutorialI/Inductive/inductive.tex
author chaieb
Wed, 19 May 2004 11:23:59 +0200
changeset 14758 af3b71a46a1c
parent 11428 332347b9b942
child 23843 4cd60e5d2999
permissions -rw-r--r--
A new implementation for presburger arithmetic following the one suggested in technical report Chaieb Amine and Tobias Nipkow. It is generic an smaller. the tactic has also changed and allows the abstaction over fuction occurences whose type is nat or int.

\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.

\input{Inductive/even-example}
\input{Inductive/document/Mutual}
\input{Inductive/document/Star}

\section{Advanced Inductive Definitions}
\label{sec:adv-ind-def}
\input{Inductive/advanced-examples}

\input{Inductive/document/AB}

\index{inductive definitions|)}