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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 (polymorphic)
logic.
<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.
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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.
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There are also 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-Löf'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 or linear logics. There are a few more examples,
again see the <a
href="http://www.in.tum.de/~isabelle/library/">Isabelle theory
library</a>.
<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 3 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
"LCF system approach" to achieve a secure system).
<h2>Further information</h2>
<a href="http://www.cl.cam.ac.uk/Research/HVG/isabelle.html"><img
src="cambridge.gif" width=144 align=right alt="[Cambridge]"></a> <a
href="http://www.in.tum.de/~isabelle/"><img src="munich.gif" width=47
align=right alt="[Munich]"></a> The local Isabelle pages at <a
href="http://www.cl.cam.ac.uk/Research/HVG/isabelle.html">Cambridge</a>
and <a href="http://www.in.tum.de/~isabelle/">Munich</a> provide
further information on Isabelle and related projects.
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