author wenzelm
Mon, 02 Nov 1998 21:36:48 +0100
changeset 5793 9ef3db99f24a
parent 5792 4fe5d5aff4df
child 5794 e1aac05fe537
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<-- $Id$ -->


<h1>Isabelle </h1> <a href=""><img
src="isabelle.gif" width=100 align=right alt="[Isabelle logo]"></a>


<strong>Isabelle</strong> is a popular generic theorem proving
environment developed at Cambridge University (<a
href="">Larry Paulson</a>) and TU
Munich (<a href="">Tobias Nipkow</a>).
The latest version is <strong>Isabelle98-1</strong>. It is available
from several <a href="dist/">mirror sites</a>.


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="">Isabelle theory


is a version of classical higher-order logic, similar to Gordon's HOL
(it is related to Church's Simple Theory of Types).

adds a considerably amount of Scott's domain theory to HOL.

provides basic classical and intuitionistic first-order (polymorphic)

offers a formulation of Zermelo-Fraenkel set theory on top of FOL.



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


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.


There are also a few minor object logics that may serve as further
examples: <a
href="">CTT</a> is an
extensional version of Martin-L&ouml;f's Type Theory, <a
href="">Cube</a> is
Barendregt's Lambda Cube.  There are also some sequent calculus
examples under <a
including modal or linear logics.  Again see the <a
href="">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:


<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).


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
<em>LCF system approach</em> to achieve a secure system).

<h2>Further information</h2>

<a href=""><img
src="cambridge.gif" width=144 align=right alt="[Cambridge]"></a> <a
src="munich.gif" width=47 align=right alt="[Munich]"></a> The local
Isabelle pages at <a
and <a href="">Munich</a>
provide further information on Isabelle and related projects.