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author wenzelm
Tue, 03 Nov 1998 09:47:49 +0100 (1998-11-03)
changeset 5798 cc32a1c16710
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<title>Isabelle</title>
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<h1>Isabelle </h1> <a href="http://www.in.tum.de/~isabelle/logo/"><img
src="isabelle.gif" width=100 align=right alt="[Isabelle logo]"></a>

<p>

<strong>Isabelle</strong> is a popular generic theorem proving
environment developed at Cambridge University (<a
href="http://www.cl.cam.ac.uk/users/lcp/">Larry Paulson</a>) and TU
Munich (<a href="http://www.in.tum.de/~nipkow/">Tobias Nipkow</a>).
The latest version is <strong>Isabelle98-1</strong>, it is available
from several <a href="dist/">mirror sites</a>.

<p>

Isabelle can be viewed from two main perspectives.  On the one hand it
may serve as a generic framework for rapid prototyping of deductive
systems.  On the other hand, major object logics like
<strong>Isabelle/HOL</strong> provide a theorem proving environment
ready to use for sizable applications.


<h2>Object logics</h2>

The Isabelle distribution includes a large body of object logics and
other examples (see the <a
href="http://www.in.tum.de/~isabelle/library/">Isabelle theory
library</a>).

<dl>

<dt><a
href="http://www.in.tum.de/~isabelle/library/HOL/"><strong>Isabelle/HOL</strong></a><dd>
is a version of classical higher-order logic, similar to Gordon's HOL
(it is related to Church's Simple Theory of Types).

<dt><a
href="http://www.in.tum.de/~isabelle/library/HOLCF/"><strong>Isabelle/HOLCF</strong></a><dd>
adds a considerably amount of Scott's domain theory to HOL.

<dt><a
href="http://www.in.tum.de/~isabelle/library/FOL/"><strong>Isabelle/FOL</strong></a><dd>
provides basic classical and intuitionistic first-order logic
(polymorphic).

<dt><a
href="http://www.in.tum.de/~isabelle/library/ZF/"><strong>Isabelle/ZF</strong></a><dd>
offers a formulation of Zermelo-Fraenkel set theory on top of FOL.

</dl>

<p>

Isabelle/HOL is currently the best developed 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, for example correctness proofs of
cryptographic protocols (<a
href="http://www.in.tum.de/~isabelle/library/HOL/Auth/">HOL/Auth</a>).

<p>

Isabelle/ZF provides another starting point for applications, with a
slightly less developed library, though.  Its definitional packages
are similar to those of Isabelle/HOL.  Untyped ZF provides more
advanced constructions for sets than simply-typed HOL.

<p>

There are a few minor object logics that may serve as further
examples: <a
href="http://www.in.tum.de/~isabelle/library/CTT/">CTT</a> is an
extensional version of Martin-L&ouml;f's Type Theory, <a
href="http://www.in.tum.de/~isabelle/library/Cube/">Cube</a> is
Barendregt's Lambda Cube.  There are also some sequent calculus
examples under <a
href="http://www.in.tum.de/~isabelle/library/Sequents/">Sequents</a>,
including modal and linear logics.  Again see the <a
href="http://www.in.tum.de/~isabelle/library/">Isabelle theory
library</a> for other examples.


<h2>Defining Logics</h2>

Logics are not hard-wired into Isabelle, but formulated within
Isabelle's meta logic: <strong>Isabelle/Pure</strong>.  There are
quite a lot of syntactic and deductive tools available in generic
Isabelle.  Thus defining new logics or extending existing ones
basically works as follows:

<ol>

<li> declare concrete syntax (via mixfix grammar and syntax macros),

<li> declare abstract syntax (as higher-order constants),

<li> declare inference rules (as meta-logical propositions),

<li> instantiate generic proof tools (simplifier, classical tableau
prover etc.),

<li> manually code special proof procedures (via tacticals or
hand-written ML).

</ol>

The first three steps above are fully declarative and involve no ML
programming at all.  Thus one already gets a decent deductive
environment based on primitive inferences (by employing the built-in
mechanisms of Isabelle/Pure, in particular higher-order unification
and resolution).

For sizable applications some degree of automated reasoning is
essential.  Instantiating existing tools like the classical tableau
prover involves only minimal ML-based setup.  One may also write
arbitrary proof procedures or even theory extension packages in ML,
without breaching system soundness (Isabelle follows the well-known
<em>LCF system approach</em> to achieve a secure system).


<h2>Further information</h2>

<a href="http://www.cl.cam.ac.uk/Research/HVG/cambridge.html"><img
src="cambridge.gif" width=144 border=0 align=right
alt="[Cambridge]"></a> <a
href="http://www.in.tum.de/~isabelle/munich.html"><img
src="munich.gif" width=47 border=0 align=right alt="[Munich]"></a> The
local Isabelle pages at <a
href="http://www.cl.cam.ac.uk/Research/HVG/cambridge.html">Cambridge</a>
and <a href="http://www.in.tum.de/~isabelle/munich.html">Munich</a>
provide further information on Isabelle and related projects.

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isabelle