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Admin/page/index.html

author | wenzelm |

Mon, 02 Nov 1998 21:36:48 +0100 | |

changeset 5793 | 9ef3db99f24a |

parent 5792 | 4fe5d5aff4df |

child 5794 | e1aac05fe537 |

permissions | -rw-r--r-- |

Id;

<html> <head> <-- $Id$ --> <title>Isabelle</title> <body> <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. </dl> <p> 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. <p> 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. Again see the <a href="http://www.in.tum.de/~isabelle/library/">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: <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 <em>LCF system approach</em> to achieve a secure system). <h2>Further information</h2> <a href="http://www.cl.cam.ac.uk/Research/HVG/cambridge.html"><img src="cambridge.gif" width=144 align=right alt="[Cambridge]"></a> <a href="http://www.in.tum.de/~isabelle/munich.html"><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/cambridge.html">Cambridge</a> and <a href="http://www.in.tum.de/~isabelle/munich.html">Munich</a> provide further information on Isabelle and related projects. </html>