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<HTML><HEAD><TITLE>HOL/README</TITLE></HEAD><BODY>
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<H2>HOL: Higher-Order Logic</H2>
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This directory contains the ML sources of the Isabelle system for
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Higher-Order Logic.<P>
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There are several subdirectories with examples:
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<DL>
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<DT>ex
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<DD>general examples
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<DT>Auth
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<DD>a new approach to verifying authentication protocols
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<DT>AxClasses
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<DD>a few axiomatic type class examples:
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<DL>
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<DT> Tutorial <DD> Some simple axclass demos that go along with the
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<em>axclass</em> Isabelle document (<tt>isatool doc axclass</tt>).
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<DT> Group
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<DD> Some bits of group theory.
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<DT> Lattice
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<DD> Basic theory of lattices and orders.
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</DL>
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<DT>Hoare
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<DD>verification of imperative programs; verification conditions are
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generated automatically from pre/post conditions and loop invariants.
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<DT>IMP
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<DD>mechanization of a large part of a semantics text by Glynn Winskel
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<DT>Induct
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<DD>examples of (co)inductive definitions
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<DT>Integ
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<DD>a development of the integers including efficient integer
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calculations (part of the standard HOL environment)
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<DT>IOA
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<DD>a simple theory of Input/Output Automata
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<DT>Isar_examples
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<DD>several Isabelle/Isar example proof documents
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<DT>Lambda
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<DD>a proof of the Church-Rosser theorem for lambda-calculus
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<DT>Lex
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<DD>verification of a simple lexical analyzer generator
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<DT>MiniML
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<DD>formalization of type inference for the language Mini-ML
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<DT>Real
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<DD>a development of the reals and hyper-reals, which are used in
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non-standard analysis. Also includes the positive rationals. Used to build
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the image HOL-Real.
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<DT>Real/HahnBanach
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<DD>the Hahn-Banach theorem for real vectorspaces (Isabelle/Isar).
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<DT>Subst
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<DD>defines a theory of substitution and unification.
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<DT>TLA
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<DD>Lamport's Temporal Logic of Actions
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<DT>Tools
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<DD>holds code used to provide support for records, datatypes, induction, etc.
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<DT>UNITY
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<DD>Chandy and Misra's UNITY formalism.
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<DT>W0
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<DD>a precursor of MiniML, without let-expressions
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</DL>
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Useful references on Higher-Order Logic:
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<UL>
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<LI> P. B. Andrews,<BR>
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An Introduction to Mathematical Logic and Type Theory<BR>
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(Academic Press, 1986).
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<P>
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<LI> A. Church,<BR>
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A Formulation of the Simple Theory of Types<BR>
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(Journal of Symbolic Logic, 1940).
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<P>
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<LI> M. J. C. Gordon and T. F. Melham (editors),<BR>
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Introduction to HOL: A theorem proving environment for higher order logic<BR>
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(Cambridge University Press, 1993).
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<P>
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<LI> J. Lambek and P. J. Scott,<BR>
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Introduction to Higher Order Categorical Logic<BR>
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(Cambridge University Press, 1986).
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</UL>
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</BODY></HTML>
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