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<HTML><HEAD><TITLE>HOL/ex/README</TITLE></HEAD><BODY>
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<H2>ex--Miscellaneous Examples</H2>
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<P>This directory presents a number of small examples, illustrating various
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features of Isabelle/HOL.
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<UL>
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<LI>Files <KBD>cla.ML</KBD> demonstrates the
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power of Isabelle's classical reasoner.
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<LI>Files <KBD>meson.ML</KBD> and <KBD>mesontest.ML</KBD> present an
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implementation of the Model Elimination (ME) proof procedure, which is even
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more powerful than the classical reasoner but not generic.
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<LI><KBD>InSort</KBD> and <KBD>Qsort</KBD> are correctness proofs for sorting
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functions.
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<LI><KBD>Primes</KBD> is a theory of the <EM>divides</EM> relation, the
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greatest common divisor and Euclid's algorithm.
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<LI><KBD>Fib</KBD> proves some theorems (some rather difficult) about the
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Fibonacci function.
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<LI><KBD>Tarski</KBD> is a proof of Tarski's fixedpoint theorem: the full
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version, which states that the fixedpoints of a complete lattice themselves
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form a complete lattice. The example demonstrates first-class reasoning about theories.
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<LI><KBD>NatSum</KBD> demonstrates the power of permutative rewriting.
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Well-known identities about summations are proved using just induction and
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rewriting.
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<LI><KBD>MT</KBD> is a preliminary version of Jacob Frost's coinduction
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example. The full version is on the directory <KBD>ZF/Coind</KBD>.
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</UL>
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<HR>
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<P>Last modified on $Date$
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<ADDRESS>
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<A NAME="lcp@cl.cam.ac.uk" HREF="mailto:lcp@cl.cam.ac.uk">lcp@cl.cam.ac.uk</A>
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</ADDRESS>
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</BODY></HTML>
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