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-Isabelle's Logics
-
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-
-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 existing logics like
-<strong>Isabelle/HOL</strong> provide a theorem proving environment
-ready to use for sizable applications.
-
-
-<h2>Isabelle's Logics</h2>
-
-The Isabelle distribution includes a large body of object logics and
-other examples (see the <a href="library/index.html">Isabelle theory
-library</a>).
-
-<dl>
-
-<dt><a
-href="library/HOL/index.html"><strong>Isabelle/HOL</strong></a><dd> is
-a version of classical higher-order logic resembling that of the <A
-HREF="http://www.cl.cam.ac.uk/Research/HVG/HOL/">HOL System</A>. The
-main libraries of the HOL 4 System are now <a
-href="library/HOL/HOL-Complex/HOL4/index.html">available in
-Isabelle</a>.
-
-<dt><a
-href="library/HOLCF/index.html"><strong>Isabelle/HOLCF</strong></a><dd>
-adds Scott's Logic for Computable Functions (domain theory) to HOL.
-
-<dt><a
-href="library/FOL/index.html"><strong>Isabelle/FOL</strong></a><dd>
-provides basic classical and intuitionistic first-order logic. It is
-polymorphic.
-
-<dt><a
-href="library/ZF/index.html"><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="library/HOL/Auth/index.html">HOL/Auth</a>) or communication
-protocols (<a href="library/HOLCF/IOA/index.html">HOLCF/IOA</a>).
-
-<p>
-
-Isabelle/ZF provides another starting point for applications, with a
-slightly less developed library. 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 a few minor object logics that may serve as further
-examples: <a href="library/CTT/index.html">CTT</a> is an extensional
-version of Martin-Löf's Type Theory, <a
-href="library/Cube/index.html">Cube</a> is Barendregt's Lambda Cube.
-There are also some sequent calculus examples under <a
-href="library/Sequents/index.html">Sequents</a>, including modal and
-linear logics. Again see the <a href="library/index.html">Isabelle
-theory library</a> for other examples.
-
-
-<h3>Defining Logics</h3>
-
-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 automatic proof tools (simplifier, classical
-tableau prover etc.),
-
-<li>manually code special proof procedures (via tacticals or
-hand-written ML).
-
-</ol>
-
-The first three 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).