[ocl] OCL 2017 workshop Short Circuit Operators (camera ready
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+/ShortCircuits.aux
+/ShortCircuits.log
+/ShortCircuits.synctex.gz
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+% This is LLNCS.DEM the demonstration file of
+% the LaTeX macro package from Springer-Verlag
+% for Lecture Notes in Computer Science,
+% version 2.4 for LaTeX2e as of 16. April 2010
+%
+\documentclass{llncs}
+%
+\usepackage{makeidx} % allows for indexgeneration
+\usepackage[pdftex]{graphicx}
+%
+\begin{document}
+%
+\mainmatter % start of the contributions
+%
+\title{Commutative Short Circuit Operators}
+%
+\titlerunning{Commutative Short Circuit Operators} % abbreviated title (for running head)
+% also used for the TOC unless
+% \toctitle is used
+%
+\author{Edward D. Willink}
+%
+\authorrunning{Edward Willink} % abbreviated author list (for running head)
+%
+%%%% list of authors for the TOC (use if author list has to be modified)
+\tocauthor{Edward Willink}
+%
+\institute{Willink Transformations Ltd, Reading, England,\\
+\email{ed\_at\_willink.me.uk}}
+
+
+\maketitle % typeset the title of the contribution
+Lightning presentation at the 17th International Workshop in OCL and Textual Modeling, July 20, 2017, Marburg, Germany.
+%
+\pagebreak
+%
+\section{Commutative Short Circuit Operators - E.D.Willink}
+OCL's 4-level logic has been a source of much unhappiness and while various solutions have been suggested, none have met with enthusiasm. We look at where the unhappiness comes from and thereby suggest a new solution.
+
+The OCL designers defined an underlying model in which all expressions have types. Consequently the mathematical concept of truth was reified by a \texttt{Boolean} type with associated Boolean library operations. The designers chose to avoid exceptions. This in combination with UML conformance required a \texttt{null} value for the missing value of properties with optional multiplicity, and an \texttt{invalid} value for everything bad that might be evaluated.
+
+Unfortunately \texttt{null} and \texttt{invalid} pollute the simplicity of truths and so the Amsterdam Manifesto~\cite{amsterdam} elaborates Boolean operators with short-circuit like functionality for problems such as:
+
+\texttt{a <> null and a.doSomething()}
+
+However the operators remain commutative and so it is suggested that all terms are evaluated in parallel until the result is knowable. A Karnaugh Map defines the mapping from the \texttt{true} (T), \texttt{false} (F), \texttt{null} ($\epsilon$) and \texttt{invalid} ($\perp$) values of \texttt{Left} and \texttt{Right} inputs to the \texttt{and} output.
+
+\begin{center}
+ \begin{tabular}{|c|c||c|c|c|}
+ \hline
+ Left & Right & and & requires & `and2' \\ [0.5ex]
+ \hline
+ T & T & T & T & T \\
+ T & F & F & F & F \\
+ T & $\perp$,$\epsilon$ & $\perp$ & $\perp$ & $\perp$ \\
+ F & - & & F & \\
+ F & T,F & F & & F \\
+ F & $\perp$,$\epsilon$ & F & & $\perp$ \\
+ $\perp$,$\epsilon$ & - & & $\perp$ & \\
+ $\perp$,$\epsilon$ & T,F,$\perp$,$\epsilon$ & $\perp$ & & $\perp$ \\
+ \hline
+ \end{tabular}
+\end{center}
+
+Parallel execution is an implementation nightmare and the intermediate \texttt{invalid} results can be inefficient. If we eliminate commutative short circuits, we find that \texttt{invalid} results are exceptional rather than normal.
+
+\texttt{a <> null requires a.doSomething()}
+
+A new \texttt{requires} operator imposes a left argument first evaluation order for \texttt{and}. This avoids the spurious \texttt{invalid} results from the right argument and clearly indicates the intent to handle non-truths. The \texttt{and} operator can then be used for truths only. Once static analysis verifies that neither left nor right input of an \texttt{and} operator can be \texttt{null} or \texttt{invalid}, an implementation may implement a regular \texttt{`and2'} operation that returns \texttt{invalid} for any \texttt{null} or \texttt{invalid} input.
+
+A new \texttt{obviates} operator is also needed to regularize \texttt{or} short circuiting.
+
+
+%Providing commutative short-circuits may have seemed like a good way to allow \texttt{undefined} and truths to co-exist, but experience has shown that truths are subverted. Exploratory evaluation of Boolean operator arguments in parallel is an implementation nightmare.
+
+%If we separate the distinct requirements for truth and \texttt{undefined} reasoning by eliminating the crazy commutative short-circuits.
+
+%Truth reasoning requires 2-valued \texttt{and}, \texttt{implies}, \texttt{not}, \texttt{or}, \texttt{xor} operators.
+
+%Undefined reasoning requires selectively 4-valued \texttt{and}, \texttt{implies}, \texttt{or} operators. Only \texttt{implies} is not commutative and easy to read. Replacing commutative 4-valued \texttt{and}, \texttt{or} by not-commutative selectively 4-valued \texttt{requires}, \texttt{obviates} can make them easier to read: \texttt{a <> null requires a.doSomething()}.
+
+%The selectively 4-valued functionality evaluates the first argument, if \texttt{null} or \texttt{invalid} execution terminates with an \texttt{invalid} result.
+
+
+
+
+\begin{thebibliography}{}
+ %
+ \bibitem{amsterdam}
+ Cook, s., Kleppe, A., Mitchell, R., Rumpe, B., Warmer, j., Wills, A.:
+ The Amsterdam Manifesto on OCL. December 1999.
+ \url{http://www4.informatik.tu-muenchen.de/publ/papers/CKR+99.pdf}
+
+\end{thebibliography}
+\end{document}
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+\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
+Q$}\hbox{\raise
+0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
+{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
+0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
+0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
+0.15\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.7\ht0\hss}\box0}}}}
+\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
+T$}\hbox{\hbox to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
+{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
+to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
+to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
+to0pt{\kern0.3\wd0\vrule height0.9\ht0\hss}\box0}}}}
+\def\bbbs{{\mathchoice
+{\setbox0=\hbox{$\displaystyle \rm S$}\hbox{\raise0.5\ht0\hbox
+to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
+to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
+{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox
+to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\hbox
+to0pt{\kern0.55\wd0\vrule height0.5\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox
+to0pt{\kern0.35\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
+to0pt{\kern0.5\wd0\vrule height0.45\ht0\hss}\box0}}
+{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
+to0pt{\kern0.4\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
+to0pt{\kern0.55\wd0\vrule height0.45\ht0\hss}\box0}}}}
+\def\bbbz{{\mathchoice {\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}}
+{\hbox{$\mathsf\textstyle Z\kern-0.4em Z$}}
+{\hbox{$\mathsf\scriptstyle Z\kern-0.3em Z$}}
+{\hbox{$\mathsf\scriptscriptstyle Z\kern-0.2em Z$}}}}
+
+\let\ts\,
+
+\setlength\leftmargini {17\p@}
+\setlength\leftmargin {\leftmargini}
+\setlength\leftmarginii {\leftmargini}
+\setlength\leftmarginiii {\leftmargini}
+\setlength\leftmarginiv {\leftmargini}
+\setlength \labelsep {.5em}
+\setlength \labelwidth{\leftmargini}
+\addtolength\labelwidth{-\labelsep}
+
+\def\@listI{\leftmargin\leftmargini
+ \parsep 0\p@ \@plus1\p@ \@minus\p@
+ \topsep 8\p@ \@plus2\p@ \@minus4\p@
+ \itemsep0\p@}
+\let\@listi\@listI
+\@listi
+\def\@listii {\leftmargin\leftmarginii
+ \labelwidth\leftmarginii
+ \advance\labelwidth-\labelsep
+ \topsep 0\p@ \@plus2\p@ \@minus\p@}
+\def\@listiii{\leftmargin\leftmarginiii
+ \labelwidth\leftmarginiii
+ \advance\labelwidth-\labelsep
+ \topsep 0\p@ \@plus\p@\@minus\p@
+ \parsep \z@
+ \partopsep \p@ \@plus\z@ \@minus\p@}
+
+\renewcommand\labelitemi{\normalfont\bfseries --}
+\renewcommand\labelitemii{$\m@th\bullet$}
+
+\setlength\arraycolsep{1.4\p@}
+\setlength\tabcolsep{1.4\p@}
+
+\def\tableofcontents{\chapter*{\contentsname\@mkboth{{\contentsname}}%
+ {{\contentsname}}}
+ \def\authcount##1{\setcounter{auco}{##1}\setcounter{@auth}{1}}
+ \def\lastand{\ifnum\value{auco}=2\relax
+ \unskip{} \andname\
+ \else
+ \unskip \lastandname\
+ \fi}%
+ \def\and{\stepcounter{@auth}\relax
+ \ifnum\value{@auth}=\value{auco}%
+ \lastand
+ \else
+ \unskip,
+ \fi}%
+ \@starttoc{toc}\if@restonecol\twocolumn\fi}
+
+\def\l@part#1#2{\addpenalty{\@secpenalty}%
+ \addvspace{2em plus\p@}% % space above part line
+ \begingroup
+ \parindent \z@
+ \rightskip \z@ plus 5em
+ \hrule\vskip5pt
+ \large % same size as for a contribution heading
+ \bfseries\boldmath % set line in boldface
+ \leavevmode % TeX command to enter horizontal mode.
+ #1\par
+ \vskip5pt
+ \hrule
+ \vskip1pt
+ \nobreak % Never break after part entry
+ \endgroup}
+
+\def\@dotsep{2}
+
+\let\phantomsection=\relax
+
+\def\hyperhrefextend{\ifx\hyper@anchor\@undefined\else
+{}\fi}
+
+\def\addnumcontentsmark#1#2#3{%
+\addtocontents{#1}{\protect\contentsline{#2}{\protect\numberline
+ {\thechapter}#3}{\thepage}\hyperhrefextend}}%
+\def\addcontentsmark#1#2#3{%
+\addtocontents{#1}{\protect\contentsline{#2}{#3}{\thepage}\hyperhrefextend}}%
+\def\addcontentsmarkwop#1#2#3{%
+\addtocontents{#1}{\protect\contentsline{#2}{#3}{0}\hyperhrefextend}}%
+
+\def\@adcmk[#1]{\ifcase #1 \or
+\def\@gtempa{\addnumcontentsmark}%
+ \or \def\@gtempa{\addcontentsmark}%
+ \or \def\@gtempa{\addcontentsmarkwop}%
+ \fi\@gtempa{toc}{chapter}%
+}
+\def\addtocmark{%
+\phantomsection
+\@ifnextchar[{\@adcmk}{\@adcmk[3]}%
+}
+
+\def\l@chapter#1#2{\addpenalty{-\@highpenalty}
+ \vskip 1.0em plus 1pt \@tempdima 1.5em \begingroup
+ \parindent \z@ \rightskip \@tocrmarg
+ \advance\rightskip by 0pt plus 2cm
+ \parfillskip -\rightskip \pretolerance=10000
+ \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
+ {\large\bfseries\boldmath#1}\ifx0#2\hfil\null
+ \else
+ \nobreak
+ \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
+ \@dotsep mu$}\hfill
+ \nobreak\hbox to\@pnumwidth{\hss #2}%
+ \fi\par
+ \penalty\@highpenalty \endgroup}
+
+\def\l@title#1#2{\addpenalty{-\@highpenalty}
+ \addvspace{8pt plus 1pt}
+ \@tempdima \z@
+ \begingroup
+ \parindent \z@ \rightskip \@tocrmarg
+ \advance\rightskip by 0pt plus 2cm
+ \parfillskip -\rightskip \pretolerance=10000
+ \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
+ #1\nobreak
+ \leaders\hbox{$\m@th \mkern \@dotsep mu.\mkern
+ \@dotsep mu$}\hfill
+ \nobreak\hbox to\@pnumwidth{\hss #2}\par
+ \penalty\@highpenalty \endgroup}
+
+\def\l@author#1#2{\addpenalty{\@highpenalty}
+ \@tempdima=15\p@ %\z@
+ \begingroup
+ \parindent \z@ \rightskip \@tocrmarg
+ \advance\rightskip by 0pt plus 2cm
+ \pretolerance=10000
+ \leavevmode \advance\leftskip\@tempdima %\hskip -\leftskip
+ \textit{#1}\par
+ \penalty\@highpenalty \endgroup}
+
+\setcounter{tocdepth}{0}
+\newdimen\tocchpnum
+\newdimen\tocsecnum
+\newdimen\tocsectotal
+\newdimen\tocsubsecnum
+\newdimen\tocsubsectotal
+\newdimen\tocsubsubsecnum
+\newdimen\tocsubsubsectotal
+\newdimen\tocparanum
+\newdimen\tocparatotal
+\newdimen\tocsubparanum
+\tocchpnum=\z@ % no chapter numbers
+\tocsecnum=15\p@ % section 88. plus 2.222pt
+\tocsubsecnum=23\p@ % subsection 88.8 plus 2.222pt
+\tocsubsubsecnum=27\p@ % subsubsection 88.8.8 plus 1.444pt
+\tocparanum=35\p@ % paragraph 88.8.8.8 plus 1.666pt
+\tocsubparanum=43\p@ % subparagraph 88.8.8.8.8 plus 1.888pt
+\def\calctocindent{%
+\tocsectotal=\tocchpnum
+\advance\tocsectotal by\tocsecnum
+\tocsubsectotal=\tocsectotal
+\advance\tocsubsectotal by\tocsubsecnum
+\tocsubsubsectotal=\tocsubsectotal
+\advance\tocsubsubsectotal by\tocsubsubsecnum
+\tocparatotal=\tocsubsubsectotal
+\advance\tocparatotal by\tocparanum}
+\calctocindent
+
+\def\l@section{\@dottedtocline{1}{\tocchpnum}{\tocsecnum}}
+\def\l@subsection{\@dottedtocline{2}{\tocsectotal}{\tocsubsecnum}}
+\def\l@subsubsection{\@dottedtocline{3}{\tocsubsectotal}{\tocsubsubsecnum}}
+\def\l@paragraph{\@dottedtocline{4}{\tocsubsubsectotal}{\tocparanum}}
+\def\l@subparagraph{\@dottedtocline{5}{\tocparatotal}{\tocsubparanum}}
+
+\def\listoffigures{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
+ \fi\section*{\listfigurename\@mkboth{{\listfigurename}}{{\listfigurename}}}
+ \@starttoc{lof}\if@restonecol\twocolumn\fi}
+\def\l@figure{\@dottedtocline{1}{0em}{1.5em}}
+
+\def\listoftables{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
+ \fi\section*{\listtablename\@mkboth{{\listtablename}}{{\listtablename}}}
+ \@starttoc{lot}\if@restonecol\twocolumn\fi}
+\let\l@table\l@figure
+
+\renewcommand\listoffigures{%
+ \section*{\listfigurename
+ \@mkboth{\listfigurename}{\listfigurename}}%
+ \@starttoc{lof}%
+ }
+
+\renewcommand\listoftables{%
+ \section*{\listtablename
+ \@mkboth{\listtablename}{\listtablename}}%
+ \@starttoc{lot}%
+ }
+
+\ifx\oribibl\undefined
+\ifx\citeauthoryear\undefined
+\renewenvironment{thebibliography}[1]
+ {\section*{\refname}
+ \def\@biblabel##1{##1.}
+ \small
+ \list{\@biblabel{\@arabic\c@enumiv}}%
+ {\settowidth\labelwidth{\@biblabel{#1}}%
+ \leftmargin\labelwidth
+ \advance\leftmargin\labelsep
+ \if@openbib
+ \advance\leftmargin\bibindent
+ \itemindent -\bibindent
+ \listparindent \itemindent
+ \parsep \z@
+ \fi
+ \usecounter{enumiv}%
+ \let\p@enumiv\@empty
+ \renewcommand\theenumiv{\@arabic\c@enumiv}}%
+ \if@openbib
+ \renewcommand\newblock{\par}%
+ \else
+ \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
+ \fi
+ \sloppy\clubpenalty4000\widowpenalty4000%
+ \sfcode`\.=\@m}
+ {\def\@noitemerr
+ {\@latex@warning{Empty `thebibliography' environment}}%
+ \endlist}
+\def\@lbibitem[#1]#2{\item[{[#1]}\hfill]\if@filesw
+ {\let\protect\noexpand\immediate
+ \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
+\newcount\@tempcntc
+\def\@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi
+ \@tempcnta\z@\@tempcntb\m@ne\def\@citea{}\@cite{\@for\@citeb:=#2\do
+ {\@ifundefined
+ {b@\@citeb}{\@citeo\@tempcntb\m@ne\@citea\def\@citea{,}{\bfseries
+ ?}\@warning
+ {Citation `\@citeb' on page \thepage \space undefined}}%
+ {\setbox\z@\hbox{\global\@tempcntc0\csname b@\@citeb\endcsname\relax}%
+ \ifnum\@tempcntc=\z@ \@citeo\@tempcntb\m@ne
+ \@citea\def\@citea{,}\hbox{\csname b@\@citeb\endcsname}%
+ \else
+ \advance\@tempcntb\@ne
+ \ifnum\@tempcntb=\@tempcntc
+ \else\advance\@tempcntb\m@ne\@citeo
+ \@tempcnta\@tempcntc\@tempcntb\@tempcntc\fi\fi}}\@citeo}{#1}}
+\def\@citeo{\ifnum\@tempcnta>\@tempcntb\else
+ \@citea\def\@citea{,\,\hskip\z@skip}%
+ \ifnum\@tempcnta=\@tempcntb\the\@tempcnta\else
+ {\advance\@tempcnta\@ne\ifnum\@tempcnta=\@tempcntb \else
+ \def\@citea{--}\fi
+ \advance\@tempcnta\m@ne\the\@tempcnta\@citea\the\@tempcntb}\fi\fi}
+\else
+\renewenvironment{thebibliography}[1]
+ {\section*{\refname}
+ \small
+ \list{}%
+ {\settowidth\labelwidth{}%
+ \leftmargin\parindent
+ \itemindent=-\parindent
+ \labelsep=\z@
+ \if@openbib
+ \advance\leftmargin\bibindent
+ \itemindent -\bibindent
+ \listparindent \itemindent
+ \parsep \z@
+ \fi
+ \usecounter{enumiv}%
+ \let\p@enumiv\@empty
+ \renewcommand\theenumiv{}}%
+ \if@openbib
+ \renewcommand\newblock{\par}%
+ \else
+ \renewcommand\newblock{\hskip .11em \@plus.33em \@minus.07em}%
+ \fi
+ \sloppy\clubpenalty4000\widowpenalty4000%
+ \sfcode`\.=\@m}
+ {\def\@noitemerr
+ {\@latex@warning{Empty `thebibliography' environment}}%
+ \endlist}
+ \def\@cite#1{#1}%
+ \def\@lbibitem[#1]#2{\item[]\if@filesw
+ {\def\protect##1{\string ##1\space}\immediate
+ \write\@auxout{\string\bibcite{#2}{#1}}}\fi\ignorespaces}
+ \fi
+\else
+\@cons\@openbib@code{\noexpand\small}
+\fi
+
+\def\idxquad{\hskip 10\p@}% space that divides entry from number
+
+\def\@idxitem{\par\hangindent 10\p@}
+
+\def\subitem{\par\setbox0=\hbox{--\enspace}% second order
+ \noindent\hangindent\wd0\box0}% index entry
+
+\def\subsubitem{\par\setbox0=\hbox{--\,--\enspace}% third
+ \noindent\hangindent\wd0\box0}% order index entry
+
+\def\indexspace{\par \vskip 10\p@ plus5\p@ minus3\p@\relax}
+
+\renewenvironment{theindex}
+ {\@mkboth{\indexname}{\indexname}%
+ \thispagestyle{empty}\parindent\z@
+ \parskip\z@ \@plus .3\p@\relax
+ \let\item\par
+ \def\,{\relax\ifmmode\mskip\thinmuskip
+ \else\hskip0.2em\ignorespaces\fi}%
+ \normalfont\small
+ \begin{multicols}{2}[\@makeschapterhead{\indexname}]%
+ }
+ {\end{multicols}}
+
+\renewcommand\footnoterule{%
+ \kern-3\p@
+ \hrule\@width 2truecm
+ \kern2.6\p@}
+ \newdimen\fnindent
+ \fnindent1em
+\long\def\@makefntext#1{%
+ \parindent \fnindent%
+ \leftskip \fnindent%
+ \noindent
+ \llap{\hb@xt@1em{\hss\@makefnmark\ }}\ignorespaces#1}
+
+\long\def\@makecaption#1#2{%
+ \small
+ \vskip\abovecaptionskip
+ \sbox\@tempboxa{{\bfseries #1.} #2}%
+ \ifdim \wd\@tempboxa >\hsize
+ {\bfseries #1.} #2\par
+ \else
+ \global \@minipagefalse
+ \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
+ \fi
+ \vskip\belowcaptionskip}
+
+\def\fps@figure{htbp}
+\def\fnum@figure{\figurename\thinspace\thefigure}
+\def \@floatboxreset {%
+ \reset@font
+ \small
+ \@setnobreak
+ \@setminipage
+}
+\def\fps@table{htbp}
+\def\fnum@table{\tablename~\thetable}
+\renewenvironment{table}
+ {\setlength\abovecaptionskip{0\p@}%
+ \setlength\belowcaptionskip{10\p@}%
+ \@float{table}}
+ {\end@float}
+\renewenvironment{table*}
+ {\setlength\abovecaptionskip{0\p@}%
+ \setlength\belowcaptionskip{10\p@}%
+ \@dblfloat{table}}
+ {\end@dblfloat}
+
+\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
+ ext@#1\endcsname}{#1}{\protect\numberline{\csname
+ the#1\endcsname}{\ignorespaces #2}}\begingroup
+ \@parboxrestore
+ \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
+ \endgroup}
+
+% LaTeX does not provide a command to enter the authors institute
+% addresses. The \institute command is defined here.
+
+\newcounter{@inst}
+\newcounter{@auth}
+\newcounter{auco}
+\newdimen\instindent
+\newbox\authrun
+\newtoks\authorrunning
+\newtoks\tocauthor
+\newbox\titrun
+\newtoks\titlerunning
+\newtoks\toctitle
+
+\def\clearheadinfo{\gdef\@author{No Author Given}%
+ \gdef\@title{No Title Given}%
+ \gdef\@subtitle{}%
+ \gdef\@institute{No Institute Given}%
+ \gdef\@thanks{}%
+ \global\titlerunning={}\global\authorrunning={}%
+ \global\toctitle={}\global\tocauthor={}}
+
+\def\institute#1{\gdef\@institute{#1}}
+
+\def\institutename{\par
+ \begingroup
+ \parskip=\z@
+ \parindent=\z@
+ \setcounter{@inst}{1}%
+ \def\and{\par\stepcounter{@inst}%
+ \noindent$^{\the@inst}$\enspace\ignorespaces}%
+ \setbox0=\vbox{\def\thanks##1{}\@institute}%
+ \ifnum\c@@inst=1\relax
+ \gdef\fnnstart{0}%
+ \else
+ \xdef\fnnstart{\c@@inst}%
+ \setcounter{@inst}{1}%
+ \noindent$^{\the@inst}$\enspace
+ \fi
+ \ignorespaces
+ \@institute\par
+ \endgroup}
+
+\def\@fnsymbol#1{\ensuremath{\ifcase#1\or\star\or{\star\star}\or
+ {\star\star\star}\or \dagger\or \ddagger\or
+ \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
+ \or \ddagger\ddagger \else\@ctrerr\fi}}
+
+\def\inst#1{\unskip$^{#1}$}
+\def\fnmsep{\unskip$^,$}
+\def\email#1{{\tt#1}}
+\AtBeginDocument{\@ifundefined{url}{\def\url#1{#1}}{}%
+\@ifpackageloaded{babel}{%
+\@ifundefined{extrasenglish}{}{\addto\extrasenglish{\switcht@albion}}%
+\@ifundefined{extrasfrenchb}{}{\addto\extrasfrenchb{\switcht@francais}}%
+\@ifundefined{extrasgerman}{}{\addto\extrasgerman{\switcht@deutsch}}%
+\@ifundefined{extrasngerman}{}{\addto\extrasngerman{\switcht@deutsch}}%
+}{\switcht@@therlang}%
+\providecommand{\keywords}[1]{\par\addvspace\baselineskip
+\noindent\keywordname\enspace\ignorespaces#1}%
+}
+\def\homedir{\~{ }}
+
+\def\subtitle#1{\gdef\@subtitle{#1}}
+\clearheadinfo
+%
+%%% to avoid hyperref warnings
+\providecommand*{\toclevel@author}{999}
+%%% to make title-entry parent of section-entries
+\providecommand*{\toclevel@title}{0}
+%
+\renewcommand\maketitle{\newpage
+\phantomsection
+ \refstepcounter{chapter}%
+ \stepcounter{section}%
+ \setcounter{section}{0}%
+ \setcounter{subsection}{0}%
+ \setcounter{figure}{0}
+ \setcounter{table}{0}
+ \setcounter{equation}{0}
+ \setcounter{footnote}{0}%
+ \begingroup
+ \parindent=\z@
+ \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
+ \if@twocolumn
+ \ifnum \col@number=\@ne
+ \@maketitle
+ \else
+ \twocolumn[\@maketitle]%
+ \fi
+ \else
+ \newpage
+ \global\@topnum\z@ % Prevents figures from going at top of page.
+ \@maketitle
+ \fi
+ \thispagestyle{empty}\@thanks
+%
+ \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
+ \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
+ \instindent=\hsize
+ \advance\instindent by-\headlineindent
+ \if!\the\toctitle!\addcontentsline{toc}{title}{\@title}\else
+ \addcontentsline{toc}{title}{\the\toctitle}\fi
+ \if@runhead
+ \if!\the\titlerunning!\else
+ \edef\@title{\the\titlerunning}%
+ \fi
+ \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}%
+ \ifdim\wd\titrun>\instindent
+ \typeout{Title too long for running head. Please supply}%
+ \typeout{a shorter form with \string\titlerunning\space prior to
+ \string\maketitle}%
+ \global\setbox\titrun=\hbox{\small\rm
+ Title Suppressed Due to Excessive Length}%
+ \fi
+ \xdef\@title{\copy\titrun}%
+ \fi
+%
+ \if!\the\tocauthor!\relax
+ {\def\and{\noexpand\protect\noexpand\and}%
+ \protected@xdef\toc@uthor{\@author}}%
+ \else
+ \def\\{\noexpand\protect\noexpand\newline}%
+ \protected@xdef\scratch{\the\tocauthor}%
+ \protected@xdef\toc@uthor{\scratch}%
+ \fi
+ \addtocontents{toc}{\noexpand\protect\noexpand\authcount{\the\c@auco}}%
+ \addcontentsline{toc}{author}{\toc@uthor}%
+ \if@runhead
+ \if!\the\authorrunning!
+ \value{@inst}=\value{@auth}%
+ \setcounter{@auth}{1}%
+ \else
+ \edef\@author{\the\authorrunning}%
+ \fi
+ \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip}%
+ \ifdim\wd\authrun>\instindent
+ \typeout{Names of authors too long for running head. Please supply}%
+ \typeout{a shorter form with \string\authorrunning\space prior to
+ \string\maketitle}%
+ \global\setbox\authrun=\hbox{\small\rm
+ Authors Suppressed Due to Excessive Length}%
+ \fi
+ \xdef\@author{\copy\authrun}%
+ \markboth{\@author}{\@title}%
+ \fi
+ \endgroup
+ \setcounter{footnote}{\fnnstart}%
+ \clearheadinfo}
+%
+\def\@maketitle{\newpage
+ \markboth{}{}%
+ \def\lastand{\ifnum\value{@inst}=2\relax
+ \unskip{} \andname\
+ \else
+ \unskip \lastandname\
+ \fi}%
+ \def\and{\stepcounter{@auth}\relax
+ \ifnum\value{@auth}=\value{@inst}%
+ \lastand
+ \else
+ \unskip,
+ \fi}%
+ \begin{center}%
+ \let\newline\\
+ {\Large \bfseries\boldmath
+ \pretolerance=10000
+ \@title \par}\vskip .8cm
+\if!\@subtitle!\else {\large \bfseries\boldmath
+ \vskip -.65cm
+ \pretolerance=10000
+ \@subtitle \par}\vskip .8cm\fi
+ \setbox0=\vbox{\setcounter{@auth}{1}\def\and{\stepcounter{@auth}}%
+ \def\thanks##1{}\@author}%
+ \global\value{@inst}=\value{@auth}%
+ \global\value{auco}=\value{@auth}%
+ \setcounter{@auth}{1}%
+{\lineskip .5em
+\noindent\ignorespaces
+\@author\vskip.35cm}
+ {\small\institutename}
+ \end{center}%
+ }
+
+% definition of the "\spnewtheorem" command.
+%
+% Usage:
+%
+% \spnewtheorem{env_nam}{caption}[within]{cap_font}{body_font}
+% or \spnewtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
+% or \spnewtheorem*{env_nam}{caption}{cap_font}{body_font}
+%
+% New is "cap_font" and "body_font". It stands for
+% fontdefinition of the caption and the text itself.
+%
+% "\spnewtheorem*" gives a theorem without number.
+%
+% A defined spnewthoerem environment is used as described
+% by Lamport.
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\def\@thmcountersep{}
+\def\@thmcounterend{.}
+
+\def\spnewtheorem{\@ifstar{\@sthm}{\@Sthm}}
+
+% definition of \spnewtheorem with number
+
+\def\@spnthm#1#2{%
+ \@ifnextchar[{\@spxnthm{#1}{#2}}{\@spynthm{#1}{#2}}}
+\def\@Sthm#1{\@ifnextchar[{\@spothm{#1}}{\@spnthm{#1}}}
+
+\def\@spxnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
+ {\@definecounter{#1}\@addtoreset{#1}{#3}%
+ \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
+ \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
+ \expandafter\xdef\csname #1name\endcsname{#2}%
+ \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
+ \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+ {\@definecounter{#1}%
+ \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
+ \expandafter\xdef\csname #1name\endcsname{#2}%
+ \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#3}{#4}}%
+ \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@spothm#1[#2]#3#4#5{%
+ \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2' defined}\@eha}%
+ {\expandafter\@ifdefinable\csname #1\endcsname
+ {\newaliascnt{#1}{#2}%
+ \expandafter\xdef\csname #1name\endcsname{#3}%
+ \global\@namedef{#1}{\@spthm{#1}{\csname #1name\endcsname}{#4}{#5}}%
+ \global\@namedef{end#1}{\@endtheorem}}}}
+
+\def\@spthm#1#2#3#4{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\refstepcounter{#1}%
+\@ifnextchar[{\@spythm{#1}{#2}{#3}{#4}}{\@spxthm{#1}{#2}{#3}{#4}}}
+
+\def\@spxthm#1#2#3#4{\@spbegintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
+ \ignorespaces}
+
+\def\@spythm#1#2#3#4[#5]{\@spopargbegintheorem{#2}{\csname
+ the#1\endcsname}{#5}{#3}{#4}\ignorespaces}
+
+\def\@spbegintheorem#1#2#3#4{\trivlist
+ \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4}
+
+\def\@spopargbegintheorem#1#2#3#4#5{\trivlist
+ \item[\hskip\labelsep{#4#1\ #2}]{#4(#3)\@thmcounterend\ }#5}
+
+% definition of \spnewtheorem* without number
+
+\def\@sthm#1#2{\@Ynthm{#1}{#2}}
+
+\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
+ {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
+ \expandafter\xdef\csname #1name\endcsname{#2}%
+ \global\@namedef{end#1}{\@endtheorem}}}
+
+\def\@Thm#1#2#3{\topsep 7\p@ \@plus2\p@ \@minus4\p@
+\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}
+
+\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}
+
+\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
+ {#4}{#2}{#3}\ignorespaces}
+
+\def\@Begintheorem#1#2#3{#3\trivlist
+ \item[\hskip\labelsep{#2#1\@thmcounterend}]}
+
+\def\@Opargbegintheorem#1#2#3#4{#4\trivlist
+ \item[\hskip\labelsep{#3#1}]{#3(#2)\@thmcounterend\ }}
+
+\if@envcntsect
+ \def\@thmcountersep{.}
+ \spnewtheorem{theorem}{Theorem}[section]{\bfseries}{\itshape}
+\else
+ \spnewtheorem{theorem}{Theorem}{\bfseries}{\itshape}
+ \if@envcntreset
+ \@addtoreset{theorem}{section}
+ \else
+ \@addtoreset{theorem}{chapter}
+ \fi
+\fi
+
+%definition of divers theorem environments
+\spnewtheorem*{claim}{Claim}{\itshape}{\rmfamily}
+\spnewtheorem*{proof}{Proof}{\itshape}{\rmfamily}
+\if@envcntsame % alle Umgebungen wie Theorem.
+ \def\spn@wtheorem#1#2#3#4{\@spothm{#1}[theorem]{#2}{#3}{#4}}
+\else % alle Umgebungen mit eigenem Zaehler
+ \if@envcntsect % mit section numeriert
+ \def\spn@wtheorem#1#2#3#4{\@spxnthm{#1}{#2}[section]{#3}{#4}}
+ \else % nicht mit section numeriert
+ \if@envcntreset
+ \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
+ \@addtoreset{#1}{section}}
+ \else
+ \def\spn@wtheorem#1#2#3#4{\@spynthm{#1}{#2}{#3}{#4}
+ \@addtoreset{#1}{chapter}}%
+ \fi
+ \fi
+\fi
+\spn@wtheorem{case}{Case}{\itshape}{\rmfamily}
+\spn@wtheorem{conjecture}{Conjecture}{\itshape}{\rmfamily}
+\spn@wtheorem{corollary}{Corollary}{\bfseries}{\itshape}
+\spn@wtheorem{definition}{Definition}{\bfseries}{\itshape}
+\spn@wtheorem{example}{Example}{\itshape}{\rmfamily}
+\spn@wtheorem{exercise}{Exercise}{\itshape}{\rmfamily}
+\spn@wtheorem{lemma}{Lemma}{\bfseries}{\itshape}
+\spn@wtheorem{note}{Note}{\itshape}{\rmfamily}
+\spn@wtheorem{problem}{Problem}{\itshape}{\rmfamily}
+\spn@wtheorem{property}{Property}{\itshape}{\rmfamily}
+\spn@wtheorem{proposition}{Proposition}{\bfseries}{\itshape}
+\spn@wtheorem{question}{Question}{\itshape}{\rmfamily}
+\spn@wtheorem{solution}{Solution}{\itshape}{\rmfamily}
+\spn@wtheorem{remark}{Remark}{\itshape}{\rmfamily}
+
+\def\@takefromreset#1#2{%
+ \def\@tempa{#1}%
+ \let\@tempd\@elt
+ \def\@elt##1{%
+ \def\@tempb{##1}%
+ \ifx\@tempa\@tempb\else
+ \@addtoreset{##1}{#2}%
+ \fi}%
+ \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
+ \expandafter\def\csname cl@#2\endcsname{}%
+ \@tempc
+ \let\@elt\@tempd}
+
+\def\theopargself{\def\@spopargbegintheorem##1##2##3##4##5{\trivlist
+ \item[\hskip\labelsep{##4##1\ ##2}]{##4##3\@thmcounterend\ }##5}
+ \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
+ \item[\hskip\labelsep{##3##1}]{##3##2\@thmcounterend\ }}
+ }
+
+\renewenvironment{abstract}{%
+ \list{}{\advance\topsep by0.35cm\relax\small
+ \leftmargin=1cm
+ \labelwidth=\z@
+ \listparindent=\z@
+ \itemindent\listparindent
+ \rightmargin\leftmargin}\item[\hskip\labelsep
+ \bfseries\abstractname]}
+ {\endlist}
+
+\newdimen\headlineindent % dimension for space between
+\headlineindent=1.166cm % number and text of headings.
+
+\def\ps@headings{\let\@mkboth\@gobbletwo
+ \let\@oddfoot\@empty\let\@evenfoot\@empty
+ \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}%
+ \leftmark\hfil}
+ \def\@oddhead{\normalfont\small\hfil\rightmark\hspace{\headlineindent}%
+ \llap{\thepage}}
+ \def\chaptermark##1{}%
+ \def\sectionmark##1{}%
+ \def\subsectionmark##1{}}
+
+\def\ps@titlepage{\let\@mkboth\@gobbletwo
+ \let\@oddfoot\@empty\let\@evenfoot\@empty
+ \def\@evenhead{\normalfont\small\rlap{\thepage}\hspace{\headlineindent}%
+ \hfil}
+ \def\@oddhead{\normalfont\small\hfil\hspace{\headlineindent}%
+ \llap{\thepage}}
+ \def\chaptermark##1{}%
+ \def\sectionmark##1{}%
+ \def\subsectionmark##1{}}
+
+\if@runhead\ps@headings\else
+\ps@empty\fi
+
+\setlength\arraycolsep{1.4\p@}
+\setlength\tabcolsep{1.4\p@}
+
+\endinput
+%end of file llncs.cls
