| author | wenzelm | 
| Tue, 08 Oct 2024 16:14:36 +0200 | |
| changeset 81131 | bad7156a7814 | 
| parent 73404 | 299f6a8faccc | 
| permissions | -rw-r--r-- | 
| 10157 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 1 | \documentclass[11pt,a4paper]{article}
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| 73404 | 2 | \usepackage[T1]{fontenc}
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changeset | 3 | \usepackage{isabelle,isabellesym,pdfsetup}
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changeset | 4 | \usepackage[only,bigsqcap]{stmaryrd}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 6 | \urlstyle{rm}\isabellestyle{it}
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changeset | 7 | \pagestyle{headings}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 9 | \hyphenation{Isabelle}
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changeset | 10 | \hyphenation{Isar}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 13 | \begin{document}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 14 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 15 | \title{Lattices and Orders in Isabelle/HOL}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 16 | \author{Markus Wenzel \\ TU M\"unchen}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 17 | \maketitle | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 18 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 19 | \begin{abstract}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 20 | We consider abstract structures of orders and lattices. Many fundamental | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 21 | concepts of lattice theory are developed, including dual structures, | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 22 | properties of bounds versus algebraic laws, lattice operations versus | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 23 | set-theoretic ones etc. We also give example instantiations of lattices and | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 24 | orders, such as direct products and function spaces. Well-known properties | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 25 | are demonstrated, like the Knaster-Tarski Theorem for complete lattices. | 
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changeset | 26 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 27 | This formal theory development may serve as an example of applying | 
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 28 | Isabelle/HOL to the domain of mathematical reasoning about ``axiomatic'' | 
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changeset | 29 | structures. Apart from the simply-typed classical set-theory of HOL, we | 
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changeset | 30 | employ Isabelle's system of axiomatic type classes for expressing structures | 
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changeset | 31 | and functors in a light-weight manner. Proofs are expressed in the Isar | 
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changeset | 32 | language for readable formal proof, while aiming at its ``best-style'' of | 
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changeset | 33 | representing formal reasoning. | 
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changeset | 34 | \end{abstract}
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 36 | \tableofcontents | 
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changeset | 37 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 38 | \newpage | 
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changeset | 39 | {
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changeset | 40 | \parindent 0pt\parskip 0.7ex | 
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changeset | 41 |   \pagestyle{myheadings}
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| 58879 | 42 |   \renewcommand{\setisabellecontext}[1]{\markright{THEORY~``#1''}}
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changeset | 43 |   \input{session}
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changeset | 44 | } | 
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changeset | 45 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 46 | \nocite{Wenzel:1999:TPHOL}
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changeset | 47 | \nocite{Wenzel:2000:isar-ref}
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changeset | 48 | \nocite{Wenzel:2000:axclass}
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changeset | 49 | \nocite{Bauer-Wenzel:2000:HB}
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changeset | 51 | \bibliographystyle{abbrv}
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changeset | 52 | \bibliography{root}
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changeset | 53 | |
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* HOL/Lattice: fundamental concepts of lattice theory and order structures;
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changeset | 54 | \end{document}
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