doc-src/Logics/preface.tex
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1.4 +%% $Id$
1.5 +\chapter*{Preface}
1.6 +Several logics come with Isabelle.  Many of them are sufficiently developed
1.7 +to serve as comfortable reasoning environments.  They are also good
1.8 +starting points for defining new logics.  Each logic is distributed with
1.9 +sample proofs, some of which are described in this document.
1.10 +
1.11 +The logics \texttt{FOL} (first-order logic) and \texttt{ZF} (axiomatic set
1.12 +theory) are described in a separate manual~\cite{isabelle-ZF}.  Here are the
1.13 +others:
1.14 +
1.15 +\begin{ttdescription}
1.16 +\item[\thydx{CCL}] is Martin Coen's Classical Computational Logic,
1.17 +  which is the basis of a preliminary method for deriving programs from
1.18 +  proofs~\cite{coen92}.  It is built upon classical~\FOL{}.
1.19 +
1.20 +\item[\thydx{LCF}] is a version of Scott's Logic for Computable
1.21 +  Functions, which is also implemented by the~{\sc lcf}
1.22 +  system~\cite{paulson87}.  It is built upon classical~\FOL{}.
1.23 +
1.24 +\item[\thydx{HOL}] is the higher-order logic of Church~\cite{church40},
1.25 +which is also implemented by Gordon's~{\sc hol} system~\cite{mgordon-hol}.
1.26 +This object-logic should not be confused with Isabelle's meta-logic, which is
1.27 +also a form of higher-order logic.
1.28 +
1.29 +\item[\thydx{HOLCF}] is a version of {\sc lcf}, defined as an
1.30 +  extension of \texttt{HOL}\@.
1.31 +
1.32 +\item[\thydx{CTT}] is a version of Martin-L\"of's Constructive Type
1.33 +Theory~\cite{nordstrom90}, with extensional equality.  Universes are not
1.34 +included.
1.35 +
1.36 +\item[\thydx{Cube}] is Barendregt's $\lambda$-cube.
1.37 + \end{ttdescription}
1.38 +
1.39 +The directory \texttt{Sequents} contains several logics based
1.40 +  upon the sequent calculus.  Sequents have the form $A@1,\ldots,A@m\turn 1.41 +B@1,\ldots,B@n$; rules are applied using associative matching.
1.42 +\begin{ttdescription}
1.43 +\item[\thydx{LK}] is classical first-order logic as a sequent calculus.
1.44 +
1.45 +\item[\thydx{Modal}] implements the modal logics $T$, $S4$, and~$S43$.
1.46 +
1.47 +\item[\thydx{ILL}] implements intuitionistic linear logic.
1.48 +\end{ttdescription}
1.49 +
1.50 +The logics \texttt{CCL}, \texttt{LCF}, \texttt{HOLCF}, \texttt{Modal}, \texttt{ILL} and {\tt
1.51 +  Cube} are undocumented.  All object-logics' sources are
1.52 +distributed with Isabelle (see the directory \texttt{src}).  They are
1.53 +also available for browsing on the WWW at
1.54 +\begin{ttbox}
1.55 +http://www4.informatik.tu-muenchen.de/~nipkow/isabelle/
1.56 +\end{ttbox}
1.57 +Note that this is not necessarily consistent with your local sources!
1.58 +