%%% Macros %%%

%% % Values

%% %Variant Values
%% \newcommand{\plainvval}[4]
%% {\ensuremath{#1_{#2}[#3_{#4}] }}

%% \newcommand{\plainvvalindex}[1]
%% {\ensuremath{C_{#1}[v_{#1}]}}

%% \def\commonvval{\plainvval{C}{i}{v}{i}}


%% Dependency macros

%% \addto\captionsenglish{
%% \renewcommand{\tablename}{Figure}
%% }
\newcolumntype{L}[1]{>{\raggedright}m{#1}}
%misc macros
\newcommand{\comment}[1]{\ifdraft{\small\textbf{#1}}{}}

\def\inputs{\ensuremath{\mathcal{I}}}
\def\writ{\mathscr{V}^{+}}

\newcommand\mmyrbox[2][fill=red!20]{%
    \tikz[baseline]\node[%
        inner ysep=0pt, 
        inner xsep=2pt, 
        anchor=text, 
        rectangle, 
        rounded corners=1mm,
        #1] {\strut#2};%
}

\newcommand\mmygbox[2][fill=lightgray!30]{%
    \tikz[baseline]\node[%
        inner ysep=0pt, 
        inner xsep=2pt, 
        anchor=text, 
        rectangle, 
        rounded corners=1mm,
        #1] {\strut#2};%
}

\def\everything{\ensuremath \top}
\def\nothing{\ensuremath \oslash}
\def\impossible{\ensuremath \bot}

%dependency domain macros
\def\udep{\mathcal{D}}
\def\dom{\mathit{\delta}}
\newcommand{\structdom}[2]{\{#1; \ldots; #2\}}
\newcommand{\vardom}[2]{[#1; \ldots; #2]}
\newcommand{\adom}[1]{\langle #1 \rangle} 
\newcommand{\aexcdom}[3]{\langle #1 \triangleright #2: \; #3 \rangle}
\newcommand{\adomusual}{\langle \dom_{\mathit{def}} \triangleright i \;: \; \dom_{\mathit{exc}} \rangle}
\newcommand{\addef}{\langle \dom_{\mathit{def}} \triangleright i \;: \; \dom_{\mathit{exc}} \rangle}

\newcommand{\dstruct}[1]{f_{#1} \mapsto \dom_{#1}}
\newcommand{\dostruct}[1]{f_{#1} \mapsto \dom'_{#1}}
\newcommand{\djstruct}[1]{f_{#1} \mapsto \dom_{#1} \vee \dom'_{#1}}
\newcommand{\djnothingstruct}[1]{f_{#1} \mapsto \oslash \vee \dom_{#1}}
\newcommand{\dmstruct}[1]{f_{#1} \mapsto \dom_{#1} \oplus \dom'_{#1}}


\newcommand{\dvar}[1]{C_{#1} \mapsto \dom_{#1}}
\newcommand{\dovar}[1]{C_{#1} \mapsto \dom'_{#1}}
\newcommand{\djvar}[1]{C_{#1} \mapsto \dom_{#1} \vee \dom'_{#1}}
\newcommand{\djnothingvar}[1]{C_{#1} \mapsto \oslash \vee \dom_{#1}}
\newcommand{\dmvar}[1]{C_{#1} \mapsto \dom_{#1} \oplus \dom'_{#1}}

\newcommand{\deferred}[1]{\textrm{\textbf{\textsf{Deferred}}}(#1)}


\newcommand{\subst}{\blacktriangleleft(\sigma, \phi)}

\def\ddef {\ensuremath{\mathit{\dom_{def}}}}
\def\dexc {\ensuremath{\mathit{\dom_{exc}}}}
\def\dodef{\ensuremath{\mathit{\dom'_{def}}}}
\def\doexc{\ensuremath{\mathit{\dom'_{exc}}}}

\def\dleq{\sqsubseteq}

%intra macros
\def\intra{\Delta}

%inter macro
\def\inter{\mathscr{D}}
%% \def\defstruct{ \{.f_1\pi_1, \; \ldots, \; .f_n\pi_n\} }
%% \def\defstructo{ \{.f_1\pi'_1, \; \ldots, \; .f_n\pi'_n\} }
%% \def\defvar{[@C_1\pi_1, \; \ldots, \;@C_n\pi_n]}
%% \def\defvaro{[@C_1\pi'_1, \; \ldots, \;@C_n\pi'_n]}
%% \def\defcell{\langle i \rangle \pi_{\mathit{exc}}}
%% \def\defcello{\langle i \rangle \pi'_{\mathit{exc}}}
%% \def\defout{\langle * \setminus i \rangle \pi_{\mathit{out}}}
%% \def\defouto{\langle * \setminus i \rangle \pi'_{\mathit{out}}}
%% \def\defarr{\langle * \rangle \pi_{\mathit{def}}}
%% \def\defarro{\langle * \rangle \pi'_{\mathit{def}}}
%% \def\pexc{\pi_{\mathit{exc}}}
%% \def\pdef{\pi_{\mathit{def}}}
%% \def\piout{\pi_{\mathit{out}}}
%% \def\pleq{\underset{\circ}{\dleq}}
%% \def\pjoin{\underset{\circ}{\vee}}
%% \def\pf{\underset{\circ}{.f}}
%% \def\pc{\underset{\circ}{@C}}
%% \def\pind{\underset{\circ}{\langle i \rangle}}
%% \def\pout{\underset{\circ}{\langle * \setminus i \rangle}}
%% \def\parr{\underset{\circ}{\langle * \rangle}}
%% \def\wtpath{\underset{\circ}{\vdash}}
%% \def\wfpath{\underset{\circ}{\vDash}}
%% \def\app{\mathit{::}\pi_a }
%% \def\appf{\mathit{::}.f }
%% \def\appc{\mathit{::}@C }
%% \def\appa{\mathit{::}\langle * \rangle}
%% \def\appo{\mathit{::}\langle * \setminus i \rangle}
%% \def\appi{\mathit{::}\langle i \rangle}

%equations macros
\newcommand{\transfer}[3]{\llbracket#2\rrbracket_{#3}(#1)}
\newcommand{\killo}[2]{(\intra_{#1} \setminus #2)}
\def\binlabels{
 \begin{tabular}{@{}l@{}}
$\lambda_{true}$ \\\\
$\lambda_{false}$ \\
\end{tabular} }
\def\ltrue{\lambda_{true}}

%join comment macros
\def\veps{\varepsilon}
\def\vepsi{\varepsilon_i}
\def\eei{(\varepsilon \vee \varepsilon_i)}
\def\ddj{(\delta \vee \delta_j)}

%projection macros
\newcommand{\projcell}[1][i]{\langle#1\rangle}
\newcommand{\projext}[1][i]{\langle * \setminus#1\rangle}
\def\projarr{\langle * \rangle}

%paths macros
%% \def\arrpath{\langle * \rangle}
%% \def\cellpath{\langle i \rangle}
%% \def\outpath{\langle * \setminus i \rangle}

%wf
\def\inps{\mathcal{I}}
\def\outs{\mathcal{O}}

% tabular column
\newcolumntype{L}[1]{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{#1}}


% tikz figures for example
% Preparation for Variant, Structure and Array diagrams with arrows and red and green

\def\tmul{*1mm}
\def\dtriangle#1#2#3#4#5{%
  \tikz[remember picture, baseline={(dottriangle-x#1.base)}]{%
    \node[inner sep=0pt] (dottriangle-x#1) {\phantom{$x$}};%
    \node[dot,#2] (dottriangle-dot#1) at ($(dottriangle-x#1.base)!.5!(dottriangle-x#1.north)$) {};%
    %% The anchors and size of the isosceles triangle are not well positionned.
    % \node[draw, shape=isosceles triangle, shape border rotate=90, anchor=north,#2,isosceles triangle stretches,inner sep=0pt,minimum width=#3\tmul,minimum height=#4\tmul] (t) at (dot.center) {};
    \draw[#2] (dottriangle-dot#1.center) -- ++(.5*#3\tmul,-#4\tmul) coordinate (dottriangle-te#1) -- ++(-#3\tmul,0) coordinate (dottriangle-tw#1) -- cycle;
    \coordinate (dottriangle-tc#1) at (barycentric cs:dottriangle-dot#1=1,dottriangle-te#1=1,dottriangle-tw#1=1);
    \begin{pgfonlayer}{background}
    \node[fit=(dottriangle-dot#1) (dottriangle-te#1) (dottriangle-tw#1),#5] (dottriangle-bg#1) {};
    \end{pgfonlayer}
  }%
}

\def\defaultinnersep{1.3mm}
\tikzset{
  resetinnersep/.style={inner sep=\defaultinnersep,},
}

\def\dottriangle#1#2#3#4#5#6{%
  \node[resetinnersep,inner sep=0pt,anchor=base west,opacity=0] (predottriangle-x-#2) at #1 {\phantom{$x$}};%
  \node[resetinnersep,dot,anchor=south,#3,xshift=.5*#4\tmul,opacity=0] (predottriangle-dot-#2) at (predottriangle-x-#2.base west) {};%
  %% The anchors and size of the isosceles triangle are not well positionned.
  % \node[draw, shape=isosceles triangle, shape border rotate=90, anchor=north,#3,isosceles triangle stretches,inner sep=0pt,minimum width=#4\tmul,minimum height=#5\tmul] (t) at (dot.center) {};
  \draw[resetinnersep,#3,opacity=0] (predottriangle-dot-#2.center) -- ++(.5*#4\tmul,-#5\tmul) coordinate (predottriangle-te-#2) -- ++(-#4\tmul,0) coordinate (predottriangle-tw-#2) -- cycle;
%%%%%%%%%%%%
  % \begin{pgfonlayer}{background}
    \node[resetinnersep,fit=(predottriangle-dot-#2) (predottriangle-te-#2) (predottriangle-tw-#2)] (dottriangle-isep-#2) {};
    \node[inner sep=.7mm,fit=(predottriangle-dot-#2) (predottriangle-te-#2) (predottriangle-tw-#2),#6] (dottriangle-bg-#2) {};
  % \end{pgfonlayer}
%%%%%%%%%%%% same as above, but put above the background.
  \node[resetinnersep,inner sep=0pt,anchor=base west] (dottriangle-x-#2) at #1 {\phantom{$x$}};%
  \node[resetinnersep,dot,anchor=south,#3,xshift=.5*#4\tmul] (dottriangle-dot-#2) at (dottriangle-x-#2.base west) {};%
  %% The anchors and size of the isosceles triangle are not well positionned.
  % \node[draw, shape=isosceles triangle, shape border rotate=90, anchor=north,#3,isosceles triangle stretches,inner sep=0pt,minimum width=#4\tmul,minimum height=#5\tmul] (t) at (dot.center) {};
  \draw[resetinnersep,#3] (dottriangle-dot-#2.center) -- ++(.5*#4\tmul,-#5\tmul) coordinate (dottriangle-te-#2) -- ++(-#4\tmul,0) coordinate (dottriangle-tw-#2) -- cycle;
%%%%%%%%%%%%
  \coordinate (dottriangle-tc-#2) at (barycentric cs:dottriangle-dot-#2=1,dottriangle-te-#2=1,dottriangle-tw-#2=1);
  \node[inner sep=0pt,fit=(predottriangle-dot-#2) (predottriangle-te-#2) (predottriangle-tw-#2)] (dottriangle-boundingbox-#2) {};
}

%Some colors
\definecolor{coolgrey}{rgb}{0.55, 0.57, 0.67}
\definecolor{fgred}{rgb}{0.66, 0.13, 0.24}
\definecolor{yonder}{rgb}{0.64, 0.68, 0.82}
\definecolor{tangerine}{rgb}{1.0, 0.6, 0.4}
\definecolor{salmon}{rgb}{1.0, 0.63, 0.48}
\definecolor{caribbeangreen}{rgb}{0.0, 0.8, 0.6}
\definecolor{cream}{rgb}{1.0, 0.99, 0.82}
\definecolor{deepchampagne}{rgb}{0.98, 0.84, 0.65}
\definecolor{burntsienna}{rgb}{0.91, 0.45, 0.32}


% This is the definition of join_k
\def\bigijoin{%
  \alignedmathop{%
    \bigvee%
  }{%
    \mathchoice%
    {\bigvee\mkern-8mu\smash{\raisebox{-0.9ex}{$\resetstyle\mathlarger{\mathlarger{{}_{\intra}}}$}}}%
    {\bigvee\mkern-7mu\smash{\raisebox{-0.6ex}{$\resetstyle\mathlarger{\mathlarger{{}_{\intra}}}$}}}%
    {\bigvee\mkern-2.25mu\smash{\raisebox{-0.3ex}{$\resetstyle\mathlarger{\mathlarger{{}_{\intra}}}$}}}%
    {\bigvee\mkern-2.5mu\smash{\raisebox{-0.35ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
  }%
}
\def\largeijoin{%
  \alignedmathop{%
    \bigvee%
  }{%
    \mathchoice%
    {\bigvee\mkern-8mu\smash{\raisebox{-0.6ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
    {\bigvee\mkern-5mu\smash{\raisebox{-0.6ex}{$\resetstyle\mathlarger{\mathlarger{{}_{\intra}}}$}}}%
    {\bigvee\mkern-2.25mu\smash{\raisebox{-0.3ex}{$\resetstyle\mathlarger{\mathlarger{{}_{\intra}}}$}}}%
    {\bigvee\mkern-2.5mu\smash{\raisebox{-0.35ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
  }%
}
\def\ijoin{%
  \alignedmathop{%
    \vee%
  }{%
    \mathchoice%
    {\vee\mkern-4mu\smash{\raisebox{-0.3ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
    {\vee\mkern-3mu\smash{\raisebox{-0.1ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
    {\vee\mkern-2.25mu\smash{\raisebox{-0.3ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
    {\vee\mkern-2.5mu\smash{\raisebox{-0.35ex}{$\resetstyle\mathlarger{{}_{\intra}}$}}}%
  }%
}