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+%title%
+Isabelle's Logics
+
+%body%
+<h3>What is Isabelle?</h3>
+
+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/">Isabelle theory
+library</a>).
+
+<dl>
+
+<dt><a href="library/HOL/"><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.html">HOL
+System</A>.
+
+<dt><a href="library/HOLCF/"><strong>Isabelle/HOLCF</strong></a><dd>
+adds Scott's Logic for Computable Functions (domain theory) to HOL.
+
+<dt><a href="library/FOL/"><strong>Isabelle/FOL</strong></a><dd>
+provides basic classical and intuitionistic first-order logic.  It is
+polymorphic.
+
+<dt><a href="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="library/HOL/Auth/">HOL/Auth</a>) or
+communication protocols (<a href="library/HOLCF/IOA/">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/">CTT</a> is an extensional version of
+Martin-L&ouml;f's Type Theory, <a href="library/Cube/">Cube</a> is
+Barendregt's Lambda Cube.  There are also some sequent calculus
+examples under <a href="library/Sequents/">Sequents</a>, including
+modal and linear logics.  Again see the <a href="library/">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).