author | nipkow |
Tue, 05 Nov 2019 14:57:41 +0100 | |
changeset 71033 | c1b63124245c |
parent 58879 | 143c85e3cdb5 |
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permissions | -rw-r--r-- |
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\documentclass[11pt,a4paper]{article} |
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\usepackage{isabelle,isabellesym,pdfsetup} |
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\usepackage[only,bigsqcap]{stmaryrd} |
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\urlstyle{rm}\isabellestyle{it} |
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\pagestyle{headings} |
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\hyphenation{Isabelle} |
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\hyphenation{Isar} |
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\begin{document} |
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\title{Lattices and Orders in Isabelle/HOL} |
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\author{Markus Wenzel \\ TU M\"unchen} |
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\maketitle |
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|
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\begin{abstract} |
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We consider abstract structures of orders and lattices. Many fundamental |
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concepts of lattice theory are developed, including dual structures, |
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properties of bounds versus algebraic laws, lattice operations versus |
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set-theoretic ones etc. We also give example instantiations of lattices and |
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orders, such as direct products and function spaces. Well-known properties |
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are demonstrated, like the Knaster-Tarski Theorem for complete lattices. |
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|
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This formal theory development may serve as an example of applying |
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Isabelle/HOL to the domain of mathematical reasoning about ``axiomatic'' |
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structures. Apart from the simply-typed classical set-theory of HOL, we |
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employ Isabelle's system of axiomatic type classes for expressing structures |
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and functors in a light-weight manner. Proofs are expressed in the Isar |
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language for readable formal proof, while aiming at its ``best-style'' of |
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representing formal reasoning. |
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\end{abstract} |
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\tableofcontents |
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\newpage |
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{ |
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\parindent 0pt\parskip 0.7ex |
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\pagestyle{myheadings} |
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\renewcommand{\setisabellecontext}[1]{\markright{THEORY~``#1''}} |
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\input{session} |
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} |
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\nocite{Wenzel:1999:TPHOL} |
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\nocite{Wenzel:2000:isar-ref} |
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\nocite{Wenzel:2000:axclass} |
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\nocite{Bauer-Wenzel:2000:HB} |
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\bibliographystyle{abbrv} |
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\bibliography{root} |
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\end{document} |