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\chapter*{Preface}

Several logics come with Isabelle.  Many of them are sufficiently developed

to serve as comfortable reasoning environments.  They are also good

starting points for defining new logics.  Each logic is distributed with

sample proofs, some of which are described in this document.

\texttt{HOL} is currently the best developed Isabelle object-logic, including

an extensive library of (concrete) mathematics, and various packages for

advanced definitional concepts (like (co-)inductive sets and types,

well-founded recursion etc.). The distribution also includes some large

applications.  See the separate manual \emph{Isabelle's Logics: HOL}.  There

is also a comprehensive tutorial on Isabelle/HOL available.

\texttt{ZF} provides another starting point for applications, with a slightly

less developed library than \texttt{HOL}.  \texttt{ZF}'s definitional packages

are similar to those of \texttt{HOL}. Untyped \texttt{ZF} set theory provides

more advanced constructions for sets than simply-typed \texttt{HOL}.

\texttt{ZF} is built on \texttt{FOL} (first-order logic), both are described

in 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 Type

Theory~\cite{nordstrom90}, with extensional equality.  Universes are not

included.

\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\turn

B@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 with

Isabelle (see the directory \texttt{src}).  They are also available for

browsing 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}, and

performing some Isabelle proofs.  Consult the {\em Reference Manual} for more

information on tactics, packages, etc.

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