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src/ZF/README.html

author | clasohm |

Fri, 17 Nov 1995 13:22:50 +0100 | |

changeset 1341 | 69fec018854c |

child 3279 | 815ef5848324 |

permissions | -rw-r--r-- |

HTML version of README

<HTML><HEAD><TITLE>ZF/ReadMe</TITLE></HEAD><BODY> <H2>ZF: Zermelo-Fraenkel Set Theory</H2> This directory contains the Standard ML sources of the Isabelle system for ZF Set Theory. It is loaded upon FOL, not Pure Isabelle. Important files include <DL> <DT>Makefile <DD>compiles the files under Poly/ML or SML of New Jersey. Can also run all the tests described below.<P> <DT>ROOT.ML <DD>loads all source files. Enter an ML image containing FOL and type: use "ROOT.ML"; </DL> There are also several subdirectories of examples. To execute the examples on some directory <Dir>, enter an ML image containing ZF and type <TT>use "<Dir>/ROOT.ML";</TT> <DL> <DT>AC <DD>subdirectory containing proofs from the book "Equivalents of the Axiom of Choice, II" by H. Rubin and J.E. Rubin, 1985. Thanks to Krzysztof Gr`abczewski.<P> <DT>Coind <DD>subdirectory containing a large example of proof by co-induction. It is by Jacob Frost following a paper by Robin Milner and Mads Tofte.<P> <DT>IMP <DD>subdirectory containing a semantics equivalence proof between operational and denotational definitions of a simple programming language. Thanks to Heiko Loetzbeyer & Robert Sandner.<P> <DT>Resid <DD>subdirectory containing a proof of the Church-Rosser Theorem. It is by Ole Rasmussen, following the Coq proof by Gérard Huet.<P> <DT>ex <DD>subdirectory containing various examples. </DL> Isabelle/ZF formalizes the greater part of elementary set theory, including relations, functions, injections, surjections, ordinals and cardinals. Results proved include Cantor's Theorem, the Recursion Theorem, the Schroeder-Bernstein Theorem, and (assuming AC) the Wellordering Theorem.<P> Isabelle/ZF also provides theories of lists, trees, etc., for formalizing computational notions. It supports inductive definitions of infinite-branching trees for any cardinality of branching.<P> Useful references for Isabelle/ZF: <UL> <LI> Lawrence C. Paulson,<BR> Set theory for verification: I. From foundations to functions.<BR> J. Automated Reasoning 11 (1993), 353-389. <LI> Lawrence C. Paulson,<BR> Set theory for verification: II. Induction and recursion.<BR> Report 312, Computer Lab (1993).<BR> <LI> Lawrence C. Paulson,<BR> A fixedpoint approach to implementing (co)inductive definitions. <BR> In: A. Bundy (editor),<BR> CADE-12: 12th International Conference on Automated Deduction,<BR> (Springer LNAI 814, 1994), 148-161. </UL> Useful references on ZF set theory: <UL> <LI> Paul R. Halmos, Naive Set Theory (Van Nostrand, 1960) <LI> Patrick Suppes, Axiomatic Set Theory (Dover, 1972) <LI> Keith J. Devlin,<BR> Fundamentals of Contemporary Set Theory (Springer, 1979) <LI> Kenneth Kunen<BR> Set Theory: An Introduction to Independence Proofs<BR> (North-Holland, 1980) </UL> </BODY></HTML>