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hdtt2020.sty
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hdtt2020.sty
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\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{hdtt2020}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Other Packages
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{amsmath,amsthm,amssymb}
\RequirePackage{mathtools}
\RequirePackage{microtype}
\RequirePackage{xparse}
\RequirePackage{mathpartir}
\RequirePackage{ebproof}
\RequirePackage{booktabs}
\RequirePackage[usenames,svgnames]{xcolor}
\RequirePackage{mleftright}
\RequirePackage{adjustbox}
\RequirePackage[natbib=true]{biblatex}
\RequirePackage{hyperref}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Start of the Content
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\ProcessOptions\relax
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Bibilography
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\addbibresource{references.bib}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Basic Stuff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mathchardef\mhyphen="2D
\NewDocumentCommand{\defeq}{}{\coloneqq}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Delimiters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand\NewPairedDelimiter{mmmmO{0mu}O{0mu}}{%
\NewDocumentCommand#2{mmm}{%
\IfNoValueTF{##2}
{\IfBooleanTF{##1}
{\mskip#6\mleft#3\mskip#5##3\mskip#5\mright#4\mskip#6}
{\mskip#6#3\mskip#5##3\mskip#5#4\mskip#6}}
{\mskip#6\mathopen{##2#3}\mskip#5##3\mskip#5\mathclose{##2#4}\mskip#6}%
}
\NewDocumentCommand#1{som}{#2{##1}{##2}{##3}}
}
\NewDocumentCommand\NewTripleDelimiter{mmmmmO{0mu}O{0mu}O{0mu}}{%
\NewDocumentCommand#2{mmmm}{%
\IfNoValueTF{##2}
{\IfBooleanTF{##1}
{\mskip#8\mleft#3\mskip#7##3\mskip#6\middle#4\mskip#6##4\mskip#7\mright#5\mskip#8}
{\mskip#8#3\mskip#7##3\mskip#6#4\mskip#6##4\mskip#7#5\mskip#8}}
{\mskip#8\mathopen{##2#3}\mskip#7##3\mskip#6{##2#4}\mskip#6##4\mskip#7\mathclose{##2#5}\mskip#8}%
}
\NewDocumentCommand#1{somm}{#2{##1}{##2}{##3}{##4}}
}
\NewPairedDelimiter{\parens}{\rawparens}{\lparen}{\rparen}
\NewPairedDelimiter{\brackets}{\rawbrackets}{[}{]}
\NewPairedDelimiter{\braces}{\rawbraces}{\lbrace}{\rbrace}
\NewPairedDelimiter{\angles}{\rawangles}{\langle}{\rangle}
\NewPairedDelimiter{\bbrackets}{\rawbbrackets}{\llbracket}{\rrbracket}
\NewTripleDelimiter{\subst}{\rawsubst}{[}{/}{]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Theorem-like environments
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newtheorem{lemma}{Lemma}[section]
\NewDocumentEnvironment{hint}{}{\noindent{\bf (Hint)}}{}
\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}
\newtheorem{definition}{Definition}
\newtheorem{remark}{Remark}
\newtheorem{task}{Task}
\newtheorem{bonus}{Bonus Task}
\renewenvironment{proof}{\trivlist \item[\hskip \labelsep{\bf Proof:}]}{\hfill$\Box$ \endtrivlist}
\NewDocumentEnvironment{solution}{}{\trivlist \item[\hskip \labelsep{\bf Solution:}]}{\endtrivlist}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Type Theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand{\ctx}{}{\Gamma}
\NewDocumentCommand{\DD}{}{\mathcal{D}}
\NewDocumentCommand{\II}{}{\mathcal{I}}
\NewDocumentCommand{\emptyctx}{}{\cdot}
\NewDocumentCommand{\entails}{gg}{\IfValueTF{#2}{\IfValueTF{#1}{#1\vdash#2}{\vdash#1}}{\vdash}}
\NewDocumentCommand{\postfixjudgment}{m}{%
\relax\ifnum\lastnodetype>0\mskip\medmuskip\fi
\mathtt{#1}%
}
\NewDocumentCommand{\istype}{mg}{\IfValueTF{#2}{#1\vdash#2\postfixjudgment{type}}{#1\postfixjudgment{type}}}
\NewDocumentCommand{\eqtype}{mmg}{\IfValueTF{#3}{#1\vdash#2\equiv#3}{#1\equiv#2}}
\NewDocumentCommand{\oftype}{mmg}{\IfValueTF{#3}{#1\vdash#2:#3}{#1:#2}}
\NewDocumentCommand{\eqterm}{mmmg}{\IfValueTF{#4}{#1\vdash#2\equiv#3:#4}{#1\equiv#2:#3}}
\NewDocumentCommand{\unittype}{}{\top}
\NewDocumentCommand{\unitelem}{}{\diamond}
\NewDocumentCommand{\booltype}{}{\varmathbb{2}}
\NewDocumentCommand{\dpairtype}{sggg}{\IfValueTF{#2}{\sum\limits_{\IfBooleanTF{#1}{\parens{#2{:}#3}}{#2{:}#3}}#4}{\sum}}
% \dpairtype*{x}{A}{B} adds the parentheses around 'x:A'
\NewDocumentCommand{\pairtype}{gg}{\IfValueTF{#1}{#1\times#2}{\mathbin{\times}}}
\NewDocumentCommand{\pair}{mm}{\angles{#1 , #2}}
\NewDocumentCommand{\pairfst}{g}{\pi_1\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\pairsnd}{g}{\pi_2\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\emptytype}{}{\bot}
\NewDocumentCommand{\emptyabort}{g}{\mathtt{abort}\IfValueT{#1}{(#1)}}
\NewDocumentCommand{\sumtype}{gg}{\IfValueTF{#1}{#1+#2}{\mathbin{+}}}
\NewDocumentCommand{\suminl}{g}{\mathtt{inl}\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\suminr}{g}{\mathtt{inr}\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\sumcase}{ooggggg}{%
\mathtt{case}%
\IfValueT{#1}{\brackets{#1\IfValueT{#2}{.#2}}}%
\IfValueT{#3}{\parens{#3.#4; #5.#6\IfValueT{#7}{; #7}}}}
\NewDocumentCommand{\dfuntype}{sggg}{\IfValueTF{#2}{\prod\limits_{\IfBooleanTF{#1}{\parens{#2{:}#3}}{#2{:}#3}}#4}{\prod}}
% \dfuntype*{x}{A}{B} adds the parentheses around 'x:A'
\NewDocumentCommand{\funtype}{gg}{\IfValueTF{#1}{#1\to#2}{\mathbin{\to}}}
\NewDocumentCommand{\lam}{gog}{\IfValueTF{#1}{\IfValueTF{#2}{\lambda\parens{#1{:}#2}.#3}{\lambda#1.#3}}{\lambda}}
\NewDocumentCommand{\app}{smm}{\IfBooleanTF{#1}{#2\parens{#3}}{#2\;#3}}
\NewDocumentCommand{\nattype}{}{\varmathbb{N}}
\NewDocumentCommand{\idtype}{ggg}{\IfValueTF{#3}{\mathtt{Id}_{#1}\parens{#2; #3}}{\IfValueTF{#1}{\mathtt{Id}\parens{#1; #2}}{\mathtt{Id}}}}
\NewDocumentCommand{\idrefl}{g}{\mathtt{refl}\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\idJ}{ooooggg}{%
\mathtt{J}%
\IfValueT{#1}{\brackets{#1\IfValueT{#2}{.#2\IfValueT{#3}{.#3\IfValueT{#4}{.#4}}}}}%
\IfValueT{#5}{\parens{#5.#6\IfValueT{#7}{; #7}}}}
\NewDocumentCommand{\univ}{g}{\IfValueTF{#1}{\mathcal{U}_{#1}}{\mathcal{U}}}
\NewDocumentCommand{\pathtype}{gggg}{%
\IfValueTF{#4}{\mathtt{Path}_{#1.#2}\parens{#3; #4}}{%
\IfValueTF{#3}{\mathtt{Path}_{\dummy.#1}\parens{#2; #3}}{%
\mathtt{Path}\IfValueT{#1}\parens{#1; #2}}}}
\NewDocumentCommand{\pathlam}{gg}{\IfValueTF{#1}{\lambda#1.#2}{\lambda}}
\NewDocumentCommand{\pathapp}{gg}{\IfValueTF{#2}{#1 \@ #2}{\@}}
\NewDocumentCommand{\spheretype}{m}{\mathcal{S}^{#1}}
\NewDocumentCommand{\spherebase}{}{\mathtt{base}}
\NewDocumentCommand{\sphereloop}{}{\mathtt{loop}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Macros for Logic / Lattice
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand{\zero}{}{\varmathbb{0}}
\NewDocumentCommand{\one}{}{\varmathbb{1}}
\NewDocumentCommand{\meet}{}{\wedge}
\NewDocumentCommand{\join}{}{\vee}
\RenewDocumentCommand{\exp}{}{\supset}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Macros for Path Operations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Definition modified from github:HoTT/book.
%%% Path concatenation (used infix, in diagrammatic order) %%%
\NewDocumentCommand{\idconcat}{gg}{%
\IfValueT{#1}{#1}%
\mathchoice{\mathbin{\raisebox{0.5ex}{$\displaystyle\centerdot$}}}%
{\mathbin{\raisebox{0.5ex}{$\centerdot$}}}%
{\mathbin{\raisebox{0.25ex}{$\scriptstyle\,\centerdot\,$}}}%
{\mathbin{\raisebox{0.1ex}{$\scriptscriptstyle\,\centerdot\,$}}}%
\IfValueT{#1}{#2}%
}
% Definition copied from github:HoTT/book.
%%% Path reversal %%%
\NewDocumentCommand{\idsym}{m}{\mathord{{#1}^{-1}}}
%%% Loop spaces!
\NewDocumentCommand{\looptype}{ogg}{\IfValueTF{#1}{\Omega^{#1}}{\Omega}\IfValueT{#2}{\parens{#2\IfValueT{#3}{;#3}}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Macros for Truncation Levels
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\NewDocumentCommand{\isset}{g}{\mathtt{is\mhyphen{}set}\IfValueT{#1}{\parens{#1}}}
\NewDocumentCommand{\haslevel}{gg}{\IfValueTF{#1}{\mathtt{has\mhyphen{}level}_{#1}}{\mathtt{has\mhyphen{}level}}\IfValueT{#2}{\parens{#2}}}
\NewDocumentCommand{\ntypes}{m}{#1\mathtt{\mhyphen{}types}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The End
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\endinput