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<html>
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<head>
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<!-- $Id$ -->
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<title>Isabelle</title>
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</head>
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<body>
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<h1>Isabelle </h1> <a href="http://www.in.tum.de/~isabelle/logo/"><img
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src="isabelle.gif" width=100 align=right alt="[Isabelle logo]"></a>
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<p>
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<strong>Isabelle</strong> is a popular generic theorem proving
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environment developed at Cambridge University (<a
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href="http://www.cl.cam.ac.uk/users/lcp/">Larry Paulson</a>) and TU
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Munich (<a href="http://www.in.tum.de/~nipkow/">Tobias Nipkow</a>).
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The latest version is <strong>Isabelle98-1</strong>. It is available
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from several <a href="dist/">mirror sites</a>.
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<p>
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Isabelle can be viewed from two main perspectives.  On the one hand it
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may serve as a generic framework for rapid prototyping of deductive
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systems.  On the other hand, major object logics like
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<strong>Isabelle/HOL</strong> provide a theorem proving environment
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ready to use for sizable applications.
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<h2>Object logics</h2>
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The Isabelle distribution includes a large body of object logics and
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other examples (see the <a
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href="http://www.in.tum.de/~isabelle/library/">Isabelle theory
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library</a>).
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<dl>
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<dt><a
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href="http://www.in.tum.de/~isabelle/library/HOL/"><strong>Isabelle/HOL</strong></a><dd>
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is a version of classical higher-order logic, similar to Gordon's HOL
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(it is related to Church's Simple Theory of Types).
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<dt><a
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href="http://www.in.tum.de/~isabelle/library/HOLCF/"><strong>Isabelle/HOLCF</strong></a><dd>
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adds a considerably amount of Scott's domain theory to HOL.
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<dt><a
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href="http://www.in.tum.de/~isabelle/library/FOL/"><strong>Isabelle/FOL</strong></a><dd>
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provides basic classical and intuitionistic first-order (polymorphic)
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logic.
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<dt><a
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href="http://www.in.tum.de/~isabelle/library/ZF/"><strong>Isabelle/ZF</strong></a><dd>
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offers a formulation of Zermelo-Fraenkel set theory on top of FOL.
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</dl>
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<p>
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Isabelle/HOL is currently the best developed object logic, including
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an extensive library of (concrete) mathematics, and various packages
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for advanced definitional concepts (like (co-)inductive sets and
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types, well-founded recursion etc.).  The distribution also includes
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some large applications, for example correctness proofs of
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cryptographic protocols (<a
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href="http://www.in.tum.de/~isabelle/library/HOL/Auth/">HOL/Auth</a>).
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<p>
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Isabelle/ZF provides another starting point for applications, with a
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slightly less developed library, though.  Its definitional packages
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are similar to those of Isabelle/HOL.  Untyped ZF provides more
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advanced constructions for sets than simply typed HOL.
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<p>
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There are also a few minor object logics that may serve as further
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examples: <a
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href="http://www.in.tum.de/~isabelle/library/CTT/">CTT</a> is an
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extensional version of Martin-L&ouml;f's Type Theory, <a
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href="http://www.in.tum.de/~isabelle/library/Cube/">Cube</a> is
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Barendregt's Lambda Cube.  There are also some sequent calculus
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examples under <a
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href="http://www.in.tum.de/~isabelle/library/Sequents/">Sequents</a>,
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including modal or linear logics.  Again see the <a
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href="http://www.in.tum.de/~isabelle/library/">Isabelle theory
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library</a> for other examples.
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<h2>Defining Logics</h2>
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Logics are not hard-wired into Isabelle, but formulated within
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Isabelle's meta logic: <strong>Isabelle/Pure</strong>.  There are
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quite a lot of syntactic and deductive tools available in generic
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Isabelle.  Thus defining new logics or extending existing ones
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basically works as follows:
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<ol>
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<li> declare concrete syntax (via mixfix grammar and syntax macros),
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<li> declare abstract syntax (as higher-order constants),
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<li> declare inference rules (as meta-logical propositions),
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<li> instantiate generic proof tools (simplifier, classical tableau
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prover etc.),
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<li> manually code special proof procedures (via tacticals or
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hand-written ML).
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</ol>
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The first 3 steps above are fully declarative and involve no ML
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programming at all.  Thus one already gets a decent deductive
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environment based on primitive inferences (by employing the built-in
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mechanisms of Isabelle/Pure, in particular higher-order unification
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and resolution).
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For sizable applications some degree of automated reasoning is
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essential.  Instantiating existing tools like the classical tableau
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prover involves only minimal ML-based setup.  One may also write
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arbitrary proof procedures or even theory extension packages in ML,
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without breaching system soundness (Isabelle follows the well-known
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<em>LCF system approach</em> to achieve a secure system).
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<h2>Further information</h2>
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<a href="http://www.cl.cam.ac.uk/Research/HVG/cambridge.html"><img
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src="cambridge.gif" width=144 align=right alt="[Cambridge]"></a> <a
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href="http://www.in.tum.de/~isabelle/munich.html"><img
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src="munich.gif" width=47 align=right alt="[Munich]"></a> The local
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Isabelle pages at <a
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href="http://www.cl.cam.ac.uk/Research/HVG/cambridge.html">Cambridge</a>
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and <a href="http://www.in.tum.de/~isabelle/munich.html">Munich</a>
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provide further information on Isabelle and related projects.
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</body>
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</html>