1 %\documentclass{svjour3}

     2 \documentclass{llncs}

     3 \usepackage{times}

     4 \usepackage{isabelle}

     5 \usepackage{isabellesym}

     6 \usepackage{amsmath}

     7 \usepackage{amssymb}

     8 \usepackage{pdfsetup}

     9 \usepackage{tikz}

    10 \usepackage{pgf}

    11 \usepackage{verbdef}

    12 \usepackage{longtable}

    13 \usepackage{mathpartir}

    14 

    15 \urlstyle{rm}

    16 \isabellestyle{it}

    17 \renewcommand{\isastyle}{\isastyleminor}

    18 

    19 \def\dn{\,\stackrel{\mbox{\scriptsize def}}{=}\,}

    20 \verbdef\singlearr|--->|

    21 \verbdef\doublearr|===>|

    22 \verbdef\tripple|###|

    23 

    24 \renewcommand{\isasymequiv}{$\dn$}

    25 \renewcommand{\isasymemptyset}{$\varnothing$}

    26 \renewcommand{\isacharunderscore}{\mbox{$\_\!\_$}}

    27 \renewcommand{\isasymUnion}{$\bigcup$}

    28 

    29 \newcommand{\isasymsinglearr}{\singlearr}

    30 \newcommand{\isasymdoublearr}{\doublearr}

    31 \newcommand{\isasymtripple}{\tripple}

    32 

    33 \newcommand{\numbered}[1]{\refstepcounter{equation}{\rm(\arabic{equation})}\label{#1}}

    34 

    35 \begin{document}

    36 

    37 \title{Quotients Revisited for Isabelle/HOL}

    38 \author{Cezary Kaliszyk$^*$ and Christian Urban$^*$}

    39 \institute{$^*$ Technical University of Munich, Germany}

    40 \maketitle

    41 

    42 \begin{abstract}

    43 Higher-Order Logic (HOL) is based on a small logic kernel, whose only

    44 mechanism for extension is the introduction of safe definitions and of

    45 non-empty types. Both extensions are often performed in quotient

    46 constructions. To ease the work involved with such quotient constructions, we

    47 re-implemented in Isabelle/HOL the quotient package by Homeier. In doing so we

    48 extended his work in order to deal with compositions of quotients. Like his

    49 package, we designed our quotient package so that every step in a quotient construction

    50 can be performed separately and as a result we are able to specify completely

    51 the procedure of lifting theorems from the raw level to the quotient level.

    52 The importance for programming language research is that many properties of

    53 programming language calculi are easier to verify over $\alpha$-equated, or

    54 $\alpha$-quotient, terms, than over raw terms.

    55 \end{abstract}

    56 

    57 % generated text of all theories

    58 \input{session}

    59 

    60 % optional bibliography

    61 \bibliographystyle{abbrv}

    62 \bibliography{root}

    63 

    64 \end{document}

    65 

    66 %%% Local Variables:

    67 %%% mode: latex

    68 %%% TeX-master: t

    69 %%% End: