retired Ben Porter's DenumRat in favour of the shorter proof in
Real/Rational.thy
%% $Id$\chapter*{Preface}Several logics come with Isabelle. Many of them are sufficiently developedto serve as comfortable reasoning environments. They are also goodstarting points for defining new logics. Each logic is distributed withsample proofs, some of which are described in this document.\texttt{HOL} is currently the best developed Isabelle object-logic, includingan extensive library of (concrete) mathematics, and various packages foradvanced definitional concepts (like (co-)inductive sets and types,well-founded recursion etc.). The distribution also includes some largeapplications. See the separate manual \emph{Isabelle's Logics: HOL}. Thereis also a comprehensive tutorial on Isabelle/HOL available.\texttt{ZF} provides another starting point for applications, with a slightlyless developed library than \texttt{HOL}. \texttt{ZF}'s definitional packagesare similar to those of \texttt{HOL}. Untyped \texttt{ZF} set theory providesmore advanced constructions for sets than simply-typed \texttt{HOL}.\texttt{ZF} is built on \texttt{FOL} (first-order logic), both are describedin a separate manual \emph{Isabelle's Logics: FOL and ZF}~\cite{isabelle-ZF}.\medskip There are some further logics distributed with Isabelle:\begin{ttdescription}\item[\thydx{CCL}] is Martin Coen's Classical Computational Logic, which is the basis of a preliminary method for deriving programs from proofs~\cite{coen92}. It is built upon classical~FOL.\item[\thydx{LCF}] is a version of Scott's Logic for Computable Functions, which is also implemented by the~{\sc lcf} system~\cite{paulson87}. It is built upon classical~FOL.\item[\thydx{HOLCF}] is a version of {\sc lcf}, defined as an extension of \texttt{HOL}\@. See \cite{MuellerNvOS99} for more details on \texttt{HOLCF}.\item[\thydx{CTT}] is a version of Martin-L\"of's Constructive TypeTheory~\cite{nordstrom90}, with extensional equality. Universes are notincluded.\item[\thydx{Cube}] is Barendregt's $\lambda$-cube. \end{ttdescription}The directory \texttt{Sequents} contains several logics based upon the sequent calculus. Sequents have the form $A@1,\ldots,A@m\turnB@1,\ldots,B@n$; rules are applied using associative matching.\begin{ttdescription}\item[\thydx{LK}] is classical first-order logic as a sequent calculus.\item[\thydx{Modal}] implements the modal logics $T$, $S4$, and~$S43$. \item[\thydx{ILL}] implements intuitionistic linear logic.\end{ttdescription}The logics \texttt{CCL}, \texttt{LCF}, \texttt{Modal}, \texttt{ILL} and {\tt Cube} are undocumented. All object-logics' sources are distributed withIsabelle (see the directory \texttt{src}). They are also available forbrowsing on the WWW at\begin{center}\small \begin{tabular}{l} \url{http://www.cl.cam.ac.uk/Research/HVG/Isabelle/library/} \\ \url{http://isabelle.in.tum.de/library/} \\ \end{tabular}\end{center}Note that this is not necessarily consistent with your local sources!\medskip Do not read the \emph{Isabelle's Logics} manuals before reading\emph{Isabelle/HOL --- The Tutorial} or \emph{Introduction to Isabelle}, andperforming some Isabelle proofs. Consult the {\em Reference Manual} for moreinformation on tactics, packages, etc.%%% Local Variables: %%% mode: latex%%% TeX-master: "logics"%%% End: