macros.sty

\DeclarePairedDelimiter{\set}{\{}{\}}
\DeclarePairedDelimiter{\pa}{(}{)}

\newcommand{\pto}{\rightharpoonup}
\newcommand{\defeq}{\coloneq}

\newcommand{\singleton}{\star}

\newcommand{\ZFC}{\mathrm{ZFC}}
\newcommand{\Nat}{\mathbb N}

%\newcommand{\lambdadot}[2]{\mathop{\lambda}{#1}\mathrel{.}#2}

\newcommand{\pcafont}{\mathtt}
\newcommand{\pcacomb}[1]{\operatorname{\mathbf{#1}}}
% \DeclareMathOperator{\kcomb}{\mathtt{\mathbf{k}}}
%\DeclareMathOperator{\scomb}{\mathbf{s}}%{\pcafont{s}}
% {\mathbf{i}}%{\textbf{\texttt{i}}}
\newcommand{\pca}[1]{\operatorname{\pcafont{#1}}}
\newcommand{\numeral}[1]{\operatorname{\overline{\pcafont{#1}}}}

\renewcommand{\AA}{\mathcal A}
\newcommand{\BB}{\mathcal B}

\newcommand{\prenum}[1]{\varphi_{#1}}

\newcommand{\Kone}{\mathcal{K}_1}
\newcommand{\Ktwo}{\mathcal{K}_2}
\newcommand{\Ktworec}{\Ktwo^\textup{rec}}

\newcommand{\var}{}
\newcommand{\lambdapca}[2]{\langle{\var{#1}}\rangle.\,{#2}}
\newcommand{\Var}[1]{\mathcal{V}(#1)}

\newcommand{\kcomb}{\pcacomb{K}}
\newcommand{\scomb}{\pcacomb{S}}
\newcommand{\icomb}{\pcacomb{I}}

\newcommand{\pcatrue}{\pcacomb{true}}
\newcommand{\pcafalse}{\pcacomb{false}}
\newcommand{\pcaif}{\pcacomb{if}}

\newcommand{\pcapair}{\pcacomb{pair}}
\newcommand{\pcafst}{\pcacomb{fst}}
\newcommand{\pcasnd}{\pcacomb{snd}}

\newcommand{\pcaleft}{\pcacomb{left}}
\newcommand{\pcaright}{\pcacomb{right}}

\newcommand{\pcay}{\pcacomb{Y}}
\newcommand{\pcaw}{\pcacomb{W}}
\newcommand{\pcaz}{\pcacomb{Z}}
\newcommand{\pcau}{\pcacomb{U}}

\newcommand{\pcaiszero}{\pcacomb{iszero}}
\newcommand{\pcasucc}{\pcacomb{succ}}
\newcommand{\pcapred}{\pcacomb{pred}}
\newcommand{\pcarec}{\pcacomb{primrec}}

\newcommand{\powerset}{\mathcal P}
\newcommand{\PN}{\powerset(\Nat)}
\newcommand{\Scott}{\mathcal S}
\newcommand{\Scottre}{\Scott^\textup{re}}
\newcommand{\enum}{\operatorname{enum}}
\DeclarePairedDelimiter{\pairing}{[}{]}
\newcommand{\inputnum}{n_{\operatorname{in}}}
\newcommand{\outputnum}{n_{\operatorname{out}}}

\newcommand{\realizes}{\Vdash}

\newcommand{\catfont}{\mathsf}
\newcommand{\Set}{\catfont{Set}}
\newcommand{\Asm}[1]{\catfont{Asm}_{#1}}
\DeclarePairedDelimiter{\carrier}{|}{|}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\inl}{inl}
\DeclareMathOperator{\inr}{inr}

\newcommand{\Zero}{\mathbf 0}
\newcommand{\One}{\mathbf 1}
\newcommand{\Two}{\mathbf 2}
\newcommand{\NatAsm}{\mathbf N}

\DeclareMathOperator{\im}{im}

\DeclarePairedDelimiter{\sem}{\llbracket}{\rrbracket}

% Tikz
\newcommand*{\pbcorner}[1][dr]{\ar[#1,phantom,"\lrcorner" , very near start]}

\newcommand{\PA}{\powerset(\AA)}
\newcommand{\predleq}{\preceq}
\newcommand{\realpred}{\mathbb P}

\newcommand{\CC}{\mathsf{C}}
\newcommand{\CE}{\mathsf{CE}}

\DeclareMathOperator{\Mono}{Mono}