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coqmacros.tex
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\definecolor{termcolor}{rgb}{0.1,0.1,0.9}
\definecolor{prooftermcolor}{rgb}{0.3,0.1,1.0}
\definecolor{metavarcolor}{rgb}{0.5,0.0,1.0}
\definecolor{darkgreen}{rgb}{0.1,0.7,0.1}
\definecolor{answercolor}{rgb}{.8,.15,.08}
\definecolor{sourcecolor}{rgb}{.07,.1,.7}
\definecolor{normalcolor}{rgb}{0.0,0.0,0.0}
\definecolor{exbluecolor}{rgb}{0.1,0.1,0.9}
\definecolor{dontlookcolor}{rgb}{0.5,0.5,0.5}
\definecolor{termcolor}{rgb}{0.05,0.05,0.4}
\definecolor{lookcolor}{rgb}{0.9,0.1,0.0}
\definecolor{darklookcolor}{rgb}{0.5,0.1,0.0}
\definecolor{prooftermcolor}{rgb}{0.3,0.1,1.0}
\definecolor{typecolor}{rgb}{1.0,0.4,0.0}
\definecolor{taccolor}{rgb}{0.1,0.10,0.0}
\definecolor{pink}{rgb}{0.8,0.6,0.6}
\definecolor{darkmagenta}{rgb}{0.4,0.0,0.6}
\definecolor{darkblue}{rgb}{0.0,0.0,0.6}
%\newcommand{\todo}{\textbf{To do}}
%%% MMCG symbols
\newcommand{\idot}[1]{\mbox{$\bullet_{#1}$}}
\newcommand{\baredot}{\mbox{$\bullet$}}
\newcommand{\iback}[1]{\mbox{$\backslash_{#1}$}}
\newcommand{\back}{\mbox{$\backslash$}}
\newcommand{\islash}[1]{\mbox{$/_{#1}$}}
\newcommand{\icomma}[3]{\mbox{$(#1\,,\,#2)_{#3}$}}
%\newcommand{\icomma}[3]{\mbox{$#1\,\mathbin{\circ}_{#3}\,#2$}}
%\newcommand{\comma}{\mbox{$\mathbin{\circ}$}}
\newcommand{\comma}{\mbox{,}}
\newcommand{\slashe}{\mbox{\textbf{$/_{\textbf{E}}$}}}
\newcommand{\slashi}{\mbox{\textbf{$/_{\textbf{I}}$}}}
\newcommand{\backe}{\mbox{\textbf{$\backslash_{\textbf{E}}$}}}
\newcommand{\backi}{\mbox{\textbf{$\backslash_{\textbf{I}}$}}}
\newcommand{\dote}{\mbox{\textbf{$\baredot_{\textbf{E}}$}}}
\newcommand{\doti}{\mbox{\textbf{$\baredot_{\textbf{I}}$}}}
\newcommand{\diame}{\mbox{\textbf{$\Diamond_{\textbf{E}}$}}}
\newcommand{\diami}{\mbox{\textbf{$\Diamond_{\textbf{I}}$}}}
\newcommand{\struct}{\mbox{\textbf{struct}}}
\newcommand{\axrule}{\mbox{\textbf{Ax}}}
\newcommand{\boxe}{\mbox{\textbf{$\Box_{\textbf{E}}$}}}
\newcommand{\boxi}{\mbox{\textbf{$\Box_{\textbf{I}}$}}}
\newcommand{\AssD}{\textbf{L$_\Diamond$}}
\newcommand{\ComD}{\textbf{P$_\Diamond$}}
\newcommand{\marginok}[1]{\marginpar{\raggedright OK:#1}}
\newcommand{\tab}{{\null\hskip1cm}}
\newcommand{\Ltac}{\mbox{{$\cal L$}tac}}
%\newcommand{\coq}{\mbox{{Coq}}}
\newcommand{\compcert}{\mbox{{CompCert}}}
\newcommand{\pcoq}{\mbox{{Pcoq}}}
\newcommand{\grail}{\mbox{{Grail}}}
\newcommand{\lcf}{\mbox{{LCF}}}
\newcommand{\hol}{\mbox{{HOL}}}
\newcommand{\pvs}{\mbox{{PVS}}}
\newcommand{\icharate}{\mbox{{Icharate}}}
\newcommand{\isabelle}{\mbox{{Isabelle}}}
%\newcommand{\coq}{\mbox{{Coq}}}
\newcommand{\prolog}{\mbox{{Prolog}}}
\newcommand{\goalbar}{\tt{}{\color{black}------------------------------------}\it}
\newcommand{\gallina}{Gallina\xspace}
\newcommand{\joker}{\texttt{\_}}
\newcommand{\eprime}{\(\e^{\prime}\)}
\newcommand{\Ztype}{\textbf{Z}}
\newcommand{\propsort}{\textbf{Prop}}
\newcommand{\setsort}{\textbf{Set}}
\newcommand{\typesort}{\textbf{Type}}
\newcommand{\ocaml}{\mbox{{OCaml}}}
\newcommand{\haskell}{\mbox{{Haskell}}}
\newcommand{\why}{\mbox{{Why}}}
\newcommand{\Pascal}{\mbox{{Pascal}}}
\newcommand{\ml}{\mbox{{ML}}}
\newcommand{\scheme}{\mbox{{Scheme}}}
\newcommand{\lisp}{\mbox{{Lisp}}}
\newcommand{\implarrow}{\mbox{$\Rightarrow$}}
\newcommand{\metavar}[1]{?#1}
\newcommand{\notincoq}[1]{#1}
\newcommand{\coqscope}[1]{\%#1}
\newcommand{\arrow}{\mbox{$\rightarrow$}}
\newcommand{\fleche}{\arrow}
\newcommand{\funarrow}{\mbox{$\Rightarrow$}}
\newcommand{\ltacarrow}{\funarrow}
\newcommand{\coqand}{\mbox{\(\wedge\)}}
\newcommand{\coqor}{\mbox{\(\vee\)}}
\newcommand{\coqnot}{\mbox{\(\neg\)}}
\newcommand{\hide}[1]{}
\newcommand{\hidedots}[1]{...}
\newcommand{\sig}[3]{\texttt{\{}#1\texttt{:}#2 \texttt{|} #3\texttt{\}}}
\renewcommand{\neg}{\mbox{$\sim$}}
%%% Operateurs, etc.
\newcommand{\impl}{\mbox{$\rightarrow$}}
\newcommand{\appli}[2]{\mbox{\tt{#1 #2}}}
\newcommand{\applis}[1]{\mbox{\texttt{#1}}}
\newcommand{\abst}[3]{\mbox{\tt{fun #1:#2 \funarrow #3}}}
\newcommand{\coqle}{\mbox{$\leq$}}
\newcommand{\coqge}{\mbox{$\geq$}}
\newcommand{\coqdiff}{\mbox{$\neq$}}
\newcommand{\coqiff}{\mbox{$\leftrightarrow$}}
\newcommand{\prodsym}{\mbox{\(\forall\,\)}}
\newcommand{\exsym}{\mbox{\(\exists\,\)}}
\newcommand{\included}{\mbox{\(\subseteq\)}}
\newcommand{\substsign}{/}
\newcommand{\subst}[3]{\mbox{#1\{#2\substsign{}#3\}}}
\newcommand{\anoabst}[2]{\mbox{\tt[#1]#2}}
\newcommand{\letin}[3]{\mbox{\tt let #1:=#2 in #3}}
\newcommand{\prodep}[3]{\mbox{\tt \(\forall\,\)#1:#2,$\,$#3}}
\newcommand{\prodplus}[2]{\mbox{\tt\(\forall\,\)$\,$#1,$\,$#2}}
\newcommand{\dom}[1]{\textrm{dom}(#1)} % domaine d'un contexte (log function)
\newcommand{\norm}[1]{\textrm{n}(#1)} % forme normale (log function)
\newcommand{\coqZ}[1]{\mbox{\tt{`#1`}}}
\newcommand{\coqnat}[1]{\mbox{\tt{#1}}}
\newcommand{\coqcart}[2]{\mbox{\tt{#1*#2}}}
\newcommand{\alphacong}{\mbox{$\,\cong_{\alpha}\,$}} % alpha-congruence
\newcommand{\betareduc}{\mbox{$\,\rightsquigarrow_{\!\beta}$}\,} % beta reduction
%\newcommand{\betastar}{\mbox{$\,\Rightarrow_{\!\beta}^{*}\,$}} % beta reduction
\newcommand{\deltareduc}{\mbox{$\,\rightsquigarrow_{\!\delta}$}\,} % delta reduction
\newcommand{\dbreduc}{\mbox{$\,\rightsquigarrow_{\!\delta\beta}$}\,} % delta,beta reduction
\newcommand{\ireduc}{\mbox{$\,\rightsquigarrow_{\!\iota}$}\,} % delta,beta reduction
\newcommand{\slam}[2] {\mbox{$\lambda_#1\;#2$}}
\newcommand{\srho}[2] {\mbox{$\rho_#1\;#2$}}
\newcommand{\Vforall}[2] {\mbox{$\forall\,#1\,\in\,V(#2)$}}
\newcommand{\Eforall}[2] {\mbox{$\forall\,#1\,\in\,E(#2)$}}
\newcommand{\Vforone}[2] {\mbox{$\exists!\,#1\,\in\,V(#2)$}}
\newcommand{\Eforone}[2] {\mbox{$\exists!\,#1\,\in\,E(#2)$}}
\newcommand{\Vforsome}[2] {\mbox{$\exists\,#1\,\in\,V(#2)$}}
\newcommand{\Eforsome}[2] {\mbox{$\exists\,#1\,\in\,E(#2)$}}
% jugement de typage
\newcommand{\these}{\mbox{$\boldsymbol{\large \vdash}$}}
\newcommand{\rthese}[1]{\mbox{$\boldsymbol{\vdash_{#1}}$}}
\newcommand{\replace}[2]{\mbox{$#1[#2]$}}
\newcommand{\msubst}[2]{\mbox{$#1\{#2\}$}}
\newcommand{\disj}{\mbox{$\backslash/$}}
\newcommand{\conj}{\mbox{$/\backslash$}}
\newcommand{\deriv}[2]{\mbox{$#1\;\these\;#2$}}
\newcommand{\smalljuge}[3]{\mbox{$#1 \these #2 \boldsymbol{:} #3 $}}
%\newcommand{\juge}[3]{\mbox{$#1 \these #2 \boldsymbol{:} #3 $}}
\newcommand{\goal}[3]{\mbox{$#1,#2 \these^{\!\!\!?} #3 $}}
\newcommand{\sgoal}[2]{\mbox{$#1\,\these^{\!\!\!\!?}\, #2 $}}
\newcommand{\sequent}[2]{\mbox{$#1\;\these\; #2 $}}
\newcommand{\reduc}[5]{\mbox{$#1,#2 \these #3 \rhd_{#4}#5 $}}
\newcommand{\convert}[5]{\mbox{$#1,#2 \these #3 =_{#4}#5 $}}
\newcommand{\convorder}[5]{\mbox{$#1,#2 \these #3\leq _{#4}#5 $}}
\newcommand{\wouff}[2]{\mbox{$\emph{WF}(#1)[#2]$}}
\newcommand{\type}{\boldsymbol{:}}
% jugement absolu
%\newcommand{\ajuge}[2]{\mbox{$ \boldsymbol{\vdash} #1 : #2 $}}
\newcommand{\ajuge}[2]{\mbox{$\these #1 \boldsymbol{:} #2 $}}
\newcommand{\coqsimple}[1]{\mbox{\textbf{#1}}}
\newcommand{\cons}{\mbox{\tt\,::\,}}
\newcommand{\nil}{\mbox{\tt\,[\,]\,}}
%%% Colors
\definecolor{mintedbgcolor}{rgb}{0.95,0.95,1.0}
\definecolor{badcoqcolor}{rgb}{0.8,0.8,0.8}
\definecolor{altcoqcolor}{rgb}{0.7,1.0,0.8}
\definecolor{mathcolor}{rgb}{0.95,0.90,0.85}
\definecolor{vertfluo}{rgb}{0.623, 0.94, 0.886}
\definecolor{lightred}{rgb}{1.0, 0.74, 0.7}
\definecolor{lightgray}{rgb}{0.7, 0.7, 0.7}
\definecolor{lookcolor}{rgb}{0.9,0.2,0.0}
\definecolor{darkred}{rgb}{.3,.0,.0}
\definecolor{sourcecolor}{rgb}{.07,.1,.7}
\definecolor{cyan}{rgb}{.0,1.0,1.0}
\newunicodechar{𝟙}{\ensuremath{\mathds{1}}}
\newunicodechar{ℤ}{\ensuremath{\mathds{Z}}}
\newcommand{\rounds}{\mbox{\,\texttt{-+->}\,}}
\newcommand{\round}{\mbox{\,\texttt{-1->}\,}}
\newcommand{\rplus}[1]{\mbox{$\,\underset{#1}{\longrightarrow}\,$}}
\newcommand{\canonseq}[2]{\mbox{$\{#1\}(#2)$}}
\newcommand{\showmath}[1]{\mathcolor{\mbox{$#1$}}}
\newcommand{\bigmath}[1]{\textcolor{blue}{\mbox{\[#1\]}}}
\newcommand{\myemph}[1]{\textcolor{lookcolor}{\,\it{#1}\,}}
%%% Coq and libraries
\newcommand{\coq}{Coq\xspace}
\newcommand{\community}{Coq-community\xspace}
\newcommand{\gaia}{Gaia\xspace}
\newcommand{\alectr}{Alectryon\xspace}
\newcommand{\equations}{Equations\xspace}
\newcommand{\Hydras}{Hydras \& Co$\text.$\xspace}
\newcommand{\HydrasLib}{Hydra-battles\xspace}
\newcommand{\gaiaHydras}{Gaia-hydras\xspace}
\newcommand{\ssreflect}{SSReflect\xspace}
\newcommand{\stdpp}{Stdpp\xspace}
\newcommand{\mathcomp}{MathComp\xspace}
\newcommand{\additions}{Addition-chains\xspace}
%%% Gaia sign
\newcommand{\mycircled}[2][none]{%
\tikz[baseline=(a.base)]\node[draw,circle,inner sep=1pt, outer sep=0pt,fill=#1](a){\ensuremath{\scriptsize #2}\strut};
}
{\theorembodyfont{\upshape}
\newtheorem{exercise}{Exercise}[chapter]
\newtheorem{project}{Project}[chapter]
\newtheorem{remark}{Remark}[chapter]
}
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{proposition}{Proposition}[chapter]
\newtheorem{lemma}{Lemma}[chapter]
\newtheorem{conjecture}{Conjecture}[chapter]
\newtheorem{definition}{Definition}[chapter]
\newtheorem{todo}{To do}[chapter]
\newmdenv[linecolor=red]{mathframe}
\newcommand{\mathcolor}[1]{\colorbox{mathcolor}{\mbox{#1}}}
%% ajoute des parenthèses légères aux expressions de la forme "f x y"
\newcommand{\kscite}[1]{\texttt{#1} {of} KS~\cite{KS81}}
\newcommand{\kpcite}[1]{\texttt{#1} {of} KP~\cite{KP82}}
\newcommand{\slcite}[1]{\texttt{#1} {of} TT~\cite{Sladek07thetermite}}
%% KS eaters
\newcommand{\gnaw}[2]{\mbox{$\{#1\}\langle #2 \rangle $}}
%\input{setup-latex}
\DefineVerbatimEnvironment%
{Coqsrc}{Verbatim}
{fontsize=\small, frame=single,rulecolor=\color{blue},fillcolor=\color{blue!05}}
\DefineVerbatimEnvironment%
{Coqanswer}{Verbatim}
{fontsize=\small, frame=single,fontshape=it,rulecolor=\color{red},fillcolor=\color{red!05}}
\DefineVerbatimEnvironment%
{Coqbad}{Verbatim}
{fontsize=\small, frame=single,rulecolor=\color{black},fillcolor=\color{black!05}}
\DefineVerbatimEnvironment%
{Coqalt}{Verbatim}
{fontsize=\small, frame=single,rulecolor=\color{green},fillcolor=\color{green!05}}
\setcounter{secnumdepth}{5}
\DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}