macros.sty

\NeedsTeXFormat{LaTeX2e}
\RequirePackage{amssymb}
%\RequirePackage{theorem}
\RequirePackage{ifthen}


%% theorem environments for amsthm
\newcommand\@thmheadfont{\bfseries}
%\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{fact}[theorem]{Fact}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{exampl}[theorem]{Example}
\newtheorem{observation}[theorem]{Observation}
\newtheorem{sublemma}{Lemma}[theorem]
\newtheorem{definition}[theorem]{Definition}

\newcommand{\myunderbrace}[2]{\underbrace{#1}_{\mathclap{\txt{\scriptsize #2}}}}
\newcommand{\myoverbrace}[2]{\overbrace{#1}^{\mathclap{\txt{\scriptsize #2}}}}




\newenvironment{example}{{\@thmheadfont Example:}}{~$\square$}
\newenvironment{remark}{{\@thmheadfont Remark:}}{}


\RequirePackage{ifthen}
\RequirePackage{amssymb}

\newcommand{\PP}{\mathbb{P}}
\newcommand{\RR}{\mathbb{R}}



\newcommand{\Land}{\bigwedge}
\newcommand{\Lor}{\bigvee}
\newcommand{\es}{\emptyset}
\newcommand{\incl}{\subseteq}
\renewcommand{\iff}{\Leftrightarrow}
\newcommand{\ci}{\circ}
\newcommand{\sat}{\vDash}
\newcommand{\notsat}{\nvDash}
\newcommand{\imp}{\Rightarrow}
\newcommand{\fleq}{\preccurlyeq}
\newcommand{\false}{\mbox{\it false}}
\newcommand{\true}{\mbox{\it true}}
\def\ff{\mbox{\it{ff}}}
%\def\tt{\mbox{\it{tt}}}
\newcommand{\ttrue}{\mathit{tt}}
\newcommand{\ffalse}{\mathit{ff}}
\newcommand{\Nat}{{\mathbb N}}
\newcommand{\Rat}{{\mathbb Q}}
\newcommand{\Int}{{\mathbb Z}}
\newcommand{\Ord}{\mbox{\textit{Ord}}}
\newcommand{\ex}{\exists}
\newcommand{\all}{\forall}
\newcommand{\Dom}{\operatorname{\mathrm{Dom}}}
\newcommand{\Ran}{\operatorname{\mathrm{Ran}}}
\newcommand{\Inf}{\operatorname{\mathrm{Inf}}}
%\newcommand{\inf}{\operatorname{\mathrm{inf}}}
\newcommand{\last}{\operatorname{\mathrm{last}}}
\newcommand{\fin}{\operatorname{\mathrm{fin}}}
\newcommand{\Un}{\operatorname{\mathrm{Un}}}
\newcommand{\Prop}{\mathit{Prop}}
\newcommand{\Act}{\mathit{Act}}
\newcommand{\LTrL}{\ensuremath{\mathit{LTrL}}}
\newcommand{\LTL}{\ensuremath{\mathit{LTL}}}

%% math operators

\newcommand{\sq}[1]{[#1]}
\newcommand{\di}[1]{\langle #1 \rangle}
\newcommand{\set}[1]{\{#1\}}

%% Calligraphic

\newcommand{\Aa}{{\mathcal A}}
\newcommand{\Bb}{{\mathcal B}}
\newcommand{\Cc}{{\mathcal C}}
\newcommand{\Dd}{{\mathcal D}}
\newcommand{\Ee}{{\mathcal E}}
\newcommand{\Ff}{{\mathcal F}}
\newcommand{\Gg}{{\mathcal G}}
\newcommand{\Hh}{{\mathcal H}}
\newcommand{\Jj}{{\mathcal J}}
\newcommand{\Kk}{{\mathcal K}}
\newcommand{\Ll}{{\mathcal L}}
\newcommand{\Mm}{{\mathcal M}}
\newcommand{\Nn}{{\mathcal N}}
\newcommand{\Oo}{{\mathcal O}}
\newcommand{\Pp}{{\mathcal P}}
\newcommand{\Qq}{{\mathcal Q}}
\newcommand{\Rr}{{\mathcal R}}
\newcommand{\Ss}{{\mathcal S}}
\newcommand{\Tt}{{\mathcal T}}
\newcommand{\Uu}{{\mathcal U}}
\newcommand{\Vv}{{\mathcal V}}
\newcommand{\Ww}{{\mathcal W}}
\newcommand{\Xx}{\mathcal X}
\newcommand{\Yy}{{\mathcal Y}}
\newcommand{\Zz}{{\mathcal Z}}




%% various text 
\newcommand{\Var}{\ensuremath{\mathit{Var}}}
\newcommand{\Val}{\ensuremath{\mathit{Val}}}

\newcommand{\I}{\ensuremath{\mathit{I}}}
\newcommand{\II}{\ensuremath{\mathit{II}}}

\newcommand{\SiS}{\mbox{$S1S$}}
\newcommand{\SiiS}{\mbox{$S2S$}}
\newcommand{\MSii}{MS${}_2$}

\newcommand{\LFP}{\operatorname{\mathsf{LFP}}}
\newcommand{\GFP}{\operatorname{\mathsf{GFP}}}
\newcommand{\LGFP}{\begin{smallmatrix}\LFP\\ \GFP\end{smallmatrix}}
\newcommand{\rt}{\text{\textit{rt}}}
%\newcommand{\qd}{\operatorname{\mathsf{qd}}}
\newcommand{\FL}{\operatorname{\mathsf{FL}}}



\newcommand{\koniec}{$\Box$}
 \newenvironment{proof}[1][!*!,!]%
 {\noindent{\@thmheadfont Proof%
     \ifthenelse{\equal{#1}{!*!,!}}{}{%
       \normalfont\ (#1)}\\}}%
 {\koniec\medskip}

\newcommand{\comment}[1]{\marginpar{\footnotesize #1}}

\newcommand{\ctlstar}{CTL$^*$ }
\newcommand{\tuple}[1]{\langle #1 \rangle}

\newcommand{\ign}[1]{}

\newcounter{ourexamplecounter}
\newenvironment{myexample}{
\medskip

\refstepcounter{ourexamplecounter}
\smallskip\noindent{\textbf{{Example \arabic{ourexamplecounter}. }}}}{
$\Box$ \smallskip 
}

\newenvironment{note}{
\medskip

\refstepcounter{ourexamplecounter}
\smallskip\noindent{\textbf{{Note \arabic{ourexamplecounter}. }}}}{
$\Box$ \smallskip 
}


\ProcessOptions


\newcommand{\mso}{{\sc mso}\xspace}
\newcommand{\sst}{{\sc sst}\xspace}
\newcommand{\slp}{{\sc slp}\xspace}
\newcommand{\msoone}{{\sc mso}$_1$\xspace}
\newcommand{\msotwo}{{\sc mso}$_2$\xspace}
\newcommand{\fo}{{\sc fo}\xspace}

\newcommand{\mypic}[1]{
	\begin{center}
		\includegraphics[page=#1,scale=0.3]{compressed}
	\end{center}
}

\newcommand{\slpa}{\mathbb A}
\newcommand{\slpb}{\mathbb B}
\newcommand{\slpc}{\mathbb C}





\newcommand{\eqdef}{\stackrel{\text{def}}=}
\newcommand{\aalg}{\mathbf A}
\newcommand{\powerset}{\mathsf P}

\newcommand{\red}[1]{{\color{red}#1}}
\newcommand{\alg}{\mathbf{A}}
\newcommand{\arity}[1]{\mathrm{ar}(#1)}

\newcommand{\nullset}{\mathrm{Null}}
\newcommand{\sumset}{\mathrm{Sum}}


\newcommand{\oneset}{\set{1^1}}
\newcommand{\rankbool}{\mathsf{Bool}}

% \newcommand{\dbw}[1]{|\!|#1|\!|}
\newcommand{\dbw}[1]{\mathrm{dbw}(#1)}
\newcommand{\downset}[1]{#1\!\downarrow}

\newcommand{\contexts}{\mathsf{C}}
\newcommand{\synch}[1]{\mathsf{Syn}(#1)}
\newcommand{\hmonad}{\mathsf{H}}
\newcommand{\pfin}{\mathsf{P}_{\mathrm{fin}}}


\newcommand{\lessk}[1]{\stackrel  {#1} \le}
\newcommand{\simk}[1]{\stackrel  {#1} \sim}

\newcommand{\equibounded}[3]
{
	#1 
	\quad \sim \quad 
	#2 
	\qquad \text{ for }#3
}
\newcommand{\bounded}[3]
{
	#1 
	\quad \le \quad 
	#2 
	\qquad \text{ for }#3
}

\newcommand{\xor}{\oplus}

\newcommand{\colcless}[1]{\stackrel {#1} \leq}
\newcommand{\colcsim}[1]{\stackrel {#1} \sim}
\newcommand{\equalbecause}[1]{ & = & \text{\small(#1)}}

\newcommand{\vectors}[2][ ]{\mathrm{Vec}_{#1}(#2)}
\newcommand{\elements}[2][ ]{\mathrm{El}_{#1}(#2)}
\newcommand{\interface}[2][ ]{\mathrm{Int}_{#1}(#2)}
\newcommand{\external}[1]{\mathrm{Ext}(#1)}


\newcommand{\algclass}{\mathscr A}
\newcommand{\langclass}{\mathscr L}

\newcommand{\atoms}{\mathbb A}

\newcommand{\queryalg}[1]{\mathsf P_{#1}}
\newcommand{\varlabel}[2]{\stackrel{#1}{#2}}

\newcommand{\setbuild}[2]{\set{#1 \ | \ \text{#2}}}
\newcommand{\vecspan}[1]{\langle #1 \rangle}
\newcommand{\vecrep}{\mathrm{vec}}
\newcommand{\trees}{\mathrm{trees}}

\newcommand{\msoto}{\rightsquigarrow}