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- <title>Overview</title>
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- <h2>What is Isabelle?</h2>
- <p>
- Isabelle is a generic proof assistant. It allows mathematical
- formulas to be expressed in a formal language and provides tools
- for proving those formulas in a logical calculus. The main
- application is the formalization of mathematical proofs and in
- particular <em>formal verification</em>, which includes proving
- the correctness of computer hardware or software and proving
- properties of computer languages and protocols.</p>
-
- <p>Compared with similar tools, Isabelle's distinguishing feature is its
- flexibility. Most proof assistants are built around a single formal calculus,
- typically higher-order logic. Isabelle has the capacity to accept a variety
- of formal calculi. The distributed version supports higher-order logic but
- also axiomatic set theory and several other formalisms. See
- <a href="logics.html">logics</a> for more details.</p>
-
- <p>Isabelle is a joint project between Lawrence C. Paulson
- (University of Cambridge, UK) and Tobias Nipkow (Technical
- University of Munich, Germany).</p>
-
- <p>Isabelle is distributed <em>freely</em> as Open Source
- Software <!--a href="//dist/Isabelle/COPYRIGHT"-->BSD
- license<!--/a-->; see the <a
- href="installation.html">installation instructions</a>.</p>
-
- <h2>Preview of Isabelle</h2>
-
- <a href="//media/pg_preview.mov">
- <img class="left" src="//img/screenshot_isabelle_pg.png" alt="Isabelle Screenshot"
- width="250" height="277" />
- </a>
-
- <p>Here is a <a href="//media/pg_preview.mov">hyperlinked preview</a> demonstrating
- Isabelle and ProofGeneral, in <a href="http://www.apple.com/quicktime/download/">QuickTime
- format</a> and in <a href="//media/pg_preview.pdf">PDF</a>.</p>
- <br clear="all"/>
-
- <h2>What Isabelle offers</h2>
-
- <p>Isabelle provides excellent notational support: new notations
- can be introduced, using normal mathematical symbols. Proofs can
- be written in a structured notation based upon traditional proof
- style, or more straightforwardly as sequences of
- commands. Definitions and proofs may include TeX source, from
- which Isabelle can automatically generate typeset documents.</p>
-
- <p>The main limitation of all such proof systems is that proving
- theorems requires much effort from an expert user. Isabelle
- incorporates some tools to improve the user's productivity by
- automating some parts of the proof process. In particular,
- Isabelle's <em>classical reasoner</em> can perform long chains
- of reasoning steps to prove formulas. The <em>simplifier</em>
- can reason with and about equations. Linear <em>arithmetic</em>
- facts are proved automatically.</p>
-
- <p>Isabelle comes with a large theory library of formally
- verified mathematics, including elementary number theory (for
- example, Gauss's law of quadratic reciprocity), analysis (basic
- properties of limits, derivatives and integrals), algebra (up to
- Sylow's theorem) and set theory (the relative consistency of the
- Axiom of Choice). Also provided are numerous examples arising
- from research into formal verification.</p>
-
- <p>With <em>Isar</em>, Isabelle offers a concise proof formulation language
- which enables a user to write proof scripts naturally understandable for
- both humans <em>and</em> computers.</p>
-
- <p>Isabelle is closely integrated with the <a href=
- "http://proofgeneral.inf.ed.ac.uk/">ProofGeneral</a> user interface, which
- eases the task of writing and maintaining proof scripts.</p>
-
- <p>Ample <a href="documentation.html">documentation</a> is available
- about using Isabelle and its inner concepts, including a
- <a href="http://www4.in.tum.de/~nipkow/LNCS2283/">Tutorial</a> published by
- Springer-Verlag.</p>
-
- </div>
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