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<TITLE>HOL/ex/README</TITLE>
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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><A HREF="Classical.thy"><KBD>Classical</KBD></A> demonstrates the power
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of Isabelle's classical reasoner.
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<LI>Files <A HREF="mesontest.ML"><KBD>mesontest.ML</KBD></A> and
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<A HREF="mesontest2.ML"><KBD>mesontest2.ML</KBD></A> 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><A HREF="InSort.thy"><KBD>InSort</KBD></A> and <A HREF="Qsort.thy"><KBD>Qsort</KBD></A> are correctness proofs for sorting
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functions.
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<LI><A HREF="Primrec.thy"><KBD>Primrec</KBD></A> proves that Ackermann's
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function is not primitive recursive.
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<LI><A HREF="Tarski.thy"><KBD>Tarski</KBD></A> 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><A HREF="NatSum.thy"><KBD>NatSum</KBD></A> 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><A HREF="MT.thy"><KBD>MT</KBD></A> 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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