doc-src/TutorialI/Inductive/inductive.tex

Reintroduce set_interpreter for Collect and op :.
I removed them by accident when removing old code that dealt with the "set" type.
Incidentally, there is still some broken "set" code in Refute that should be fixed (see TODO in refute.ML).

\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.

\begin{warn}
Predicates can also be defined inductively.
See {\S}\ref{sec:ind-predicates}.
\end{warn}

\input{Inductive/document/Even}
\input{Inductive/document/Mutual}
\input{Inductive/document/Star}

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

\input{Inductive/document/AB}

\index{inductive definitions|)}