author | Christian Urban <urbanc@in.tum.de> |
Thu, 18 Aug 2011 14:10:52 +0200 | |
changeset 2993 | 38147e67196e |
parent 2991 | 8146b0ad8212 |
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permissions | -rw-r--r-- |
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\documentclass{lmcs} |
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%%\usepackage{times} |
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\usepackage{isabelle} |
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\usepackage{isabellesym} |
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\usepackage{amsmath} |
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\usepackage{amssymb} |
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%%\usepackage{amsthm} |
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\usepackage{tikz} |
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\usepackage{pgf} |
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\usepackage{pdfsetup} |
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\usepackage{ot1patch} |
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\usepackage{times} |
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\usepackage{boxedminipage} |
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\usepackage{proof} |
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\usepackage{setspace} |
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\allowdisplaybreaks |
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\urlstyle{rm} |
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\isabellestyle{it} |
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\renewcommand{\isastyleminor}{\it}% |
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\renewcommand{\isastyle}{\normalsize\it}% |
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\DeclareRobustCommand{\flqq}{\mbox{\guillemotleft}} |
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\DeclareRobustCommand{\frqq}{\mbox{\guillemotright}} |
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\renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}} |
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\renewcommand{\isasymbullet}{{\raisebox{-0.4mm}{\Large$\boldsymbol{\hspace{-0.5mm}\cdot\hspace{-0.5mm}}$}}} |
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\def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,} |
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\renewcommand{\isasymequiv}{$\dn$} |
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%%\renewcommand{\isasymiota}{} |
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\renewcommand{\isasymxi}{$..$} |
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\renewcommand{\isasymemptyset}{$\varnothing$} |
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\newcommand{\isasymnotapprox}{$\not\approx$} |
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\newcommand{\isasymLET}{$\mathtt{let}$} |
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\newcommand{\isasymAND}{$\mathtt{and}$} |
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\newcommand{\isasymIN}{$\mathtt{in}$} |
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\newcommand{\isasymEND}{$\mathtt{end}$} |
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\newcommand{\isasymBIND}{$\mathtt{bind}$} |
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\newcommand{\isasymANIL}{$\mathtt{anil}$} |
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\newcommand{\isasymACONS}{$\mathtt{acons}$} |
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\newcommand{\isasymCASE}{$\mathtt{case}$} |
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\newcommand{\isasymOF}{$\mathtt{of}$} |
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\newcommand{\isasymAL}{\makebox[0mm][l]{$^\alpha$}} |
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\newcommand{\isasymPRIME}{\makebox[0mm][l]{$'$}} |
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\newcommand{\isasymFRESH}{\#} |
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\newcommand{\LET}{\;\mathtt{let}\;} |
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\newcommand{\IN}{\;\mathtt{in}\;} |
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\newcommand{\END}{\;\mathtt{end}\;} |
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\newcommand{\AND}{\;\mathtt{and}\;} |
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\newcommand{\fv}{\mathit{fv}} |
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\newcommand{\numbered}[1]{\refstepcounter{equation}{\rm(\arabic{equation})}\label{#1}} |
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%----------------- theorem definitions ---------- |
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%%\theoremstyle{plain} |
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%%\spnewtheorem{thm}[section]{Theorem} |
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%%\newtheorem{property}[thm]{Property} |
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%%\newtheorem{lemma}[thm]{Lemma} |
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%%\spnewtheorem{defn}[theorem]{Definition} |
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%%\spnewtheorem{exmple}[theorem]{Example} |
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%%\spnewtheorem{myproperty}{Property}{\bfseries}{\rmfamily} |
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%-------------------- environment definitions ----------------- |
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\newenvironment{proof-of}[1]{{\em Proof of #1:}}{} |
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%\addtolength{\textwidth}{2mm} |
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\addtolength{\parskip}{-0.33mm} |
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\begin{document} |
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\title[Genral Bindings]{General Bindings and Alpha-Equivalence in Nominal |
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Isabelle$^\star$} |
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\author{Christian Urban} |
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\address{Technical University of Munich, Germany} |
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\email{urbanc@in.tum.de} |
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\author{Cezary Kaliszyk} |
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\address{University of Tsukuba, Japan} |
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\email{kaliszyk@score.cs.tsukuba.ac.jp} |
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\thanks{$^\star$~This is a revised and expanded version of~\cite{UrbanKaliszyk11}} |
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\keywords{Nominal Isabelle, variable convention, formal reasoning} |
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\subjclass{F.3.1} |
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\begin{abstract} |
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Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem |
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prover. It provides a proving infrastructure for reasoning about |
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programming language calculi involving named bound variables (as |
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opposed to de-Bruijn indices). In this paper we present an extension of |
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Nominal Isabelle for dealing with general bindings, that means |
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term-constructors where multiple variables are bound at once. Such general |
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bindings are ubiquitous in programming language research and only very |
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poorly supported with single binders, such as lambda-abstractions. Our |
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extension includes new definitions of alpha-equivalence and establishes |
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automatically the reasoning infrastructure for alpha-equated terms. We |
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also prove strong induction principles that have the usual variable |
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convention already built in. |
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\end{abstract} |
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\maketitle |
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\input{session} |
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\bibliographystyle{plain} |
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\bibliography{root} |
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%\pagebreak |
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%\input{Appendix} |
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\end{document} |
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%%% Local Variables: |
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%%% mode: latex |
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%%% TeX-master: t |
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%%% End: |