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<title>Isabelle</title>
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<h1>Isabelle</h1>
<p><a href="http://isabelle.in.tum.de/">Isabelle</a> 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 potential application in industry is <em>formal verification</em>, which includes proving the correctness of computer hardware or software and proving properties of computer languages and protocols. Among its research applications are the formalization of mathematical proofs. </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 <a href="http://isabelle.in.tum.de/logics.html">other formalisms</a>. 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 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 prove certain arithmetic facts and can reason about equations. Isabelle is closely integrated with the <a href="http://www.cl.cam.ac.uk/users/lcp/papers/protocols.html">Proof General</a> user interface, which eases the task of writing and maintaining proof scripts.. </p>
<p>Isabelle includes with large theories 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. Isabelle is <a href="http://isabelle.in.tum.de/dist/">distributed</a> free of charge to academic users.</p>
<p>Ample <a href="http://isabelle.in.tum.de/dist/docs.html">documentation</a> is available, including a <a href="http://www4.in.tum.de/%7enipkow/LNCS2283/">Tutorial</a> published by Springer-Verlag. Several <a href="http://www.cl.cam.ac.uk/users/lcp/papers/isabelle.html">papers</a> on the design of Isabelle are available. There is also a list of past and present <a href="http://www.cl.cam.ac.uk/Research/HVG/Isabelle/projects.html">projects</a> undertaken using Isabelle. </p>
<p>Isabelle is a joint project between <a href="http://www.cl.cam.ac.uk/users/lcp/">Lawrence C. Paulson</a> (University of Cambridge, UK) and <a href="http://www.in.tum.de/%7enipkow/">Tobias Nipkow</a> (Technical University of Munich, Germany).</p>
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