src/ZF/README.html
author wenzelm
Thu Sep 02 00:48:07 2010 +0200 (2010-09-02)
changeset 38980 af73cf0dc31f
parent 36862 952b2b102a0a
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turned show_question_marks into proper configuration option;
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tuned;
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    12 <H2>ZF: Zermelo-Fraenkel Set Theory</H2>
    13 
    14 This directory contains the ML sources of the Isabelle system for
    15 ZF Set Theory, based on FOL.<p>
    16 
    17 There are several subdirectories of examples:
    18 <DL>
    19 <DT>AC
    20 <DD>subdirectory containing proofs from the book "Equivalents of the Axiom
    21 of Choice, II" by H. Rubin and J.E. Rubin, 1985.  Thanks to Krzysztof
    22 Gr`abczewski.<P>
    23 
    24 <DT>Coind
    25 <DD>subdirectory containing a large example of proof by co-induction.  It
    26 is by Jacob Frost following a paper by Robin Milner and Mads Tofte.<P>
    27 
    28 <DT>IMP
    29 <DD>subdirectory containing a semantics equivalence proof between
    30 operational and denotational definitions of a simple programming language.
    31 Thanks to Heiko Loetzbeyer & Robert Sandner.<P>
    32 
    33 <DT>Resid
    34 <DD>subdirectory containing a proof of the Church-Rosser Theorem.  It is
    35 by Ole Rasmussen, following the Coq proof by G´┐Żard Huet.<P>
    36 
    37 <DT>ex
    38 <DD>subdirectory containing various examples.
    39 </DL>
    40 
    41 Isabelle/ZF formalizes the greater part of elementary set theory,
    42 including relations, functions, injections, surjections, ordinals and
    43 cardinals.  Results proved include Cantor's Theorem, the Recursion
    44 Theorem, the Schroeder-Bernstein Theorem, and (assuming AC) the
    45 Wellordering Theorem.<P>
    46 
    47 Isabelle/ZF also provides theories of lists, trees, etc., for
    48 formalizing computational notions.  It supports inductive definitions
    49 of infinite-branching trees for any cardinality of branching.<P>
    50 
    51 Useful references for Isabelle/ZF:
    52 
    53 <UL>
    54 <LI>	Lawrence C. Paulson,<BR>
    55 	Set theory for verification: I. From foundations to functions.<BR>
    56 	J. Automated Reasoning 11 (1993), 353-389.
    57 
    58 <LI>	Lawrence C. Paulson,<BR>
    59 	Set theory for verification: II. Induction and recursion.<BR>
    60 	Report 312, Computer Lab (1993).<BR>
    61 
    62 <LI>	Lawrence C. Paulson,<BR>
    63 	A fixedpoint approach to implementing (co)inductive definitions. <BR> 
    64 	In: A. Bundy (editor),<BR>
    65 	CADE-12: 12th International Conference on Automated Deduction,<BR>
    66 	(Springer LNAI 814, 1994), 148-161.
    67 </UL>
    68 
    69 Useful references on ZF set theory:
    70 
    71 <UL>
    72 <LI>	Paul R. Halmos, Naive Set Theory (Van Nostrand, 1960)
    73 
    74 <LI>	Patrick Suppes, Axiomatic Set Theory (Dover, 1972)
    75 
    76 <LI>	Keith J. Devlin,<BR>
    77 	Fundamentals of Contemporary Set Theory (Springer, 1979)
    78 
    79 <LI>	Kenneth Kunen<BR>
    80 	Set Theory: An Introduction to Independence Proofs<BR>
    81 	(North-Holland, 1980)
    82 </UL>
    83 
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