doc-src/Logics/preface.tex
 author haftmann Wed Dec 27 19:10:06 2006 +0100 (2006-12-27) changeset 21915 4e63c55f4cb4 parent 9695 ec7d7f877712 child 42637 381fdcab0f36 permissions -rw-r--r--
different handling of type variable names
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     2 \chapter*{Preface}

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

     4 to serve as comfortable reasoning environments.  They are also good

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

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

     7

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

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

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

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

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

    13 is also a comprehensive tutorial on Isabelle/HOL available.

    14

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

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

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

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

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

    20 in a separate manual \emph{Isabelle's Logics: FOL and ZF}~\cite{isabelle-ZF}.

    21

    22 \medskip There are some further logics distributed with Isabelle:

    23 \begin{ttdescription}

    24 \item[\thydx{CCL}] is Martin Coen's Classical Computational Logic,

    25   which is the basis of a preliminary method for deriving programs from

    26   proofs~\cite{coen92}.  It is built upon classical~FOL.

    27

    28 \item[\thydx{LCF}] is a version of Scott's Logic for Computable

    29   Functions, which is also implemented by the~{\sc lcf}

    30   system~\cite{paulson87}.  It is built upon classical~FOL.

    31

    32 \item[\thydx{HOLCF}] is a version of {\sc lcf}, defined as an extension of

    33   \texttt{HOL}\@. See \cite{MuellerNvOS99} for more details on \texttt{HOLCF}.

    34

    35 \item[\thydx{CTT}] is a version of Martin-L\"of's Constructive Type

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

    37 included.

    38

    39 \item[\thydx{Cube}] is Barendregt's $\lambda$-cube.

    40  \end{ttdescription}

    41

    42 The directory \texttt{Sequents} contains several logics based

    43   upon the sequent calculus.  Sequents have the form $A@1,\ldots,A@m\turn   44 B@1,\ldots,B@n$; rules are applied using associative matching.

    45 \begin{ttdescription}

    46 \item[\thydx{LK}] is classical first-order logic as a sequent calculus.

    47

    48 \item[\thydx{Modal}] implements the modal logics $T$, $S4$, and~$S43$.

    49

    50 \item[\thydx{ILL}] implements intuitionistic linear logic.

    51 \end{ttdescription}

    52

    53 The logics \texttt{CCL}, \texttt{LCF}, \texttt{Modal}, \texttt{ILL} and {\tt

    54   Cube} are undocumented.  All object-logics' sources are distributed with

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

    56 browsing on the WWW at

    57

    58 \begin{center}\small

    59   \begin{tabular}{l}

    60     \url{http://www.cl.cam.ac.uk/Research/HVG/Isabelle/library/} \\

    61     \url{http://isabelle.in.tum.de/library/} \\

    62   \end{tabular}

    63 \end{center}

    64

    65 Note that this is not necessarily consistent with your local sources!

    66

    67 \medskip Do not read the \emph{Isabelle's Logics} manuals before reading

    68 \emph{Isabelle/HOL --- The Tutorial} or \emph{Introduction to Isabelle}, and

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

    70 information on tactics, packages, etc.

    71

    72

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