Lambda calculus/PL LaTeX macros

lambda-macros.sty

%% Basic Lambda Calculus macros
%% Alex Kavvos, 2021-2023

\ProvidesPackage{lambda-macros}[2024/04/10 lambda-macros]

%% Load in your own work by putting in the same folder as your file and invoking
%%
%%   \usepackage{lambda-macros}
%%

%% We require Jon M. Sterling's delimiters package for nice parentheses.

\RequirePackage{jmsdelim}

%% THE FOLLOWING MACROS REQUIRE THE USE OF **xparse**
%% I HIGHLY RECOMMEND YOU LEARN HOW TO USE IT
%% IT IS ONE OF THE FEW PACKAGES THAT MAKE LaTeX MORE BEARABLE

\RequirePackage{xparse}

%% We also need this to make pretty colours

\RequirePackage{xcolor}

\definecolor{IdiotPurple}{RGB}{102, 51, 102}
\definecolor{FernGreen}{HTML}{467D5E}
\definecolor{ThroneBlue}{RGB}{51, 51, 102}
\definecolor{PermaRed}{RGB}{255, 102, 102}
\definecolor{DogwoodRose}{RGB}{204, 51, 102}
\definecolor{MaizeCrayola}{RGB}{255, 204, 102}
\definecolor{CommandPurple}{RGB}{135, 23, 77}
\definecolor{RegalBlue}{RGB}{3,69,117}
\definecolor{DefinitePurple}{RGB}{77,28,192}

\NewDocumentCommand{\Meta}{m}{{\color{IdiotPurple}{#1}}}
\NewDocumentCommand{\Tm}{m}{{\color{RegalBlue}{#1}}}
\NewDocumentCommand{\Deriv}{m}{{\color{DogwoodRose}{#1}}}

%% Judgements and Induction

\NewDocumentCommand{\IsNat}{m}{#1\ \textsf{nat}}
\NewDocumentCommand{\IsEven}{m}{#1\ \textsf{even}}
\NewDocumentCommand{\IsOdd}{m}{#1\ \textsf{odd}}
\NewDocumentCommand{\IsSum}{mmm}{\textsf{sum}(#1, #2, #3)}
\NewDocumentCommand{\IsList}{m}{#1\ \textsf{list}}
\NewDocumentCommand{\Nil}{}{\textsf{nil}}
\NewDocumentCommand{\Cons}{mm}{\textsf{cons}(#1, #2)}

%% Contexts
\NewDocumentCommand{\EmptyCtx}{}{\cdot}

%% Simple expressions

%% \IsTerm{M}{A}         produces Γ |- Μ : A
%% \IsTerm[\Delta]{M}{A} produces Δ |- M : A
\NewDocumentCommand{\IsTerm}{O{\Gamma}mm}{#1 \vdash \Tm{#2} : #3}

\NewDocumentCommand{\NumT}{}{\textsf{Num}}
\NewDocumentCommand{\StrT}{}{\textsf{Str}}
\NewDocumentCommand{\Num}{m}{\overline{#1}}
\NewDocumentCommand{\Str}{m}{\textsf{str}[#1]}

% Some basic operations
\NewDocumentCommand{\Plus}{mm}{\textsf{plus}(#1; #2)}
\NewDocumentCommand{\Times}{mm}{\textsf{times}(#1; #2)}
\NewDocumentCommand{\ConcatA}{mm}{\textsf{cat}(#1; #2)}
\NewDocumentCommand{\Concat}{mm}{#1 \mathbin{{+}\mspace{-8mu}{+}} #2}
\NewDocumentCommand{\Length}{m}{\textsf{len}(#1)}

\NewDocumentCommand{\Subst}{smmm}{
  \DelimMin{2}
  \IfBooleanTF{#1}{\DelimPrn{\Tm{#2}}}{\Tm{#2}}\Meta{\DelimBrk{\Tm{#3}/\Tm{#4}}}
}

%% STLC

\NewDocumentCommand{\Tuple}{mm}{\DelimGl{#1, #2}}
\NewDocumentCommand{\Proj}{O{1}m}{\pi_{#1}(#2)}
\NewDocumentCommand{\Inl}{m}{\textsf{inl}\DelimPrn{#1}}
\NewDocumentCommand{\Inr}{m}{\textsf{inr}\DelimPrn{#1}}
\NewDocumentCommand{\In}{O{i}m}{\textsf{in}_{#1}\DelimPrn{#2}}
\NewDocumentCommand{\Case}{mmmmm}{\textsf{case}\DelimPrn{#1; #2.\, #3; #4.\, #5}}

\NewDocumentCommand{\UnitT}{}{\mathbf{1}}
\NewDocumentCommand{\UnitV}{}{\langle\rangle}
\NewDocumentCommand{\Void}{}{\mathbf{0}}
\NewDocumentCommand{\Abort}{m}{\textsf{abort}(#1)}

\NewDocumentCommand{\DeclVar}{mm}{#1\mathbin{:}#2}

%% \Lam{x}{e}    produces λx. e
%% \Lam{x}[t]{e} produces λx : t. e
\NewDocumentCommand{\Lam}{mom}{\lambda \IfValueTF{#2}{\DeclVar{#1}{#2}}{#1} .\, #3}

%% \App{e}{e'}  produces e(e')
%% \App*{e}{e'} produces (e)(e')
\NewDocumentCommand{\App}{smm}{\IfBooleanTF{#1}{\DelimPrn{#2}}{#2}\DelimPrn{#3}}

%% Recursion
\NewDocumentCommand{\NatT}{}{\textsf{Nat}}
\NewDocumentCommand{\FName}{m}{\textsf{#1}}
\NewDocumentCommand{\ParTo}{}{\rightharpoonup}
\NewDocumentCommand{\Fix}{mom}{\textsf{fix}\DelimPrn{\IfValueTF{#2}{\DeclVar{#1}{#2}}{#1}.\, #3}}

%% Natural numbers 
\NewDocumentCommand{\Zero}{}{\textsf{zero}}
\NewDocumentCommand{\Succ}{m}{\textsf{succ}(#1)}
\NewDocumentCommand{\Ifz}{mmmm}{\textsf{ifz}(#1; #2; #3.\, #4)}

%% Booleans
\NewDocumentCommand{\BoolT}{}{\textsf{Bool}}
\NewDocumentCommand{\True}{}{\textsf{true}}
\NewDocumentCommand{\False}{}{\textsf{false}}
\NewDocumentCommand{\If}{mmm}{\textsf{if } #1 \textsf{ then } #2 \textsf{ else } #3}

% Let constructs
\NewDocumentCommand{\LetA}{mmm}{\textsf{let}(#1; #2.\, #3)}
\NewDocumentCommand{\Let}{mmm}{\textsf{let}\, #1 \Leftarrow #2\, \textsf{in}\, #3}


%% Operational semantics

\NewDocumentCommand{\IsVal}{m}{\Tm{#1}\ \textsf{val}}
\NewDocumentCommand{\Step}{}{\longmapsto}
\NewDocumentCommand{\StepMany}{}{\mathbin{{\Step}^\ast}}
\NewDocumentCommand{\StepsTo}{mm}{\Tm{#1} \Step \Tm{#2}}
\NewDocumentCommand{\StepsMany}{mm}{\Tm{#1} \StepMany \Tm{#2}}
\NewDocumentCommand{\Eval}{mm}{\Tm{#1} \mathbin{\Downarrow} \Tm{#2}}

%% Contexts

\NewDocumentCommand{\Ctx}{mo}{
  \mathcal{#1}\IfNoValueTF{#2}{\Hole}{\DelimBrk{#2}}
}
\NewDocumentCommand{\Hole}{}{\DelimBrk{-}}

This is great! Would you happen to know of any other packages meant for category or type theory? I'm still unfamiliar with the LaTeX packages the community uses.

Thank you. For type theory people make their own macros, mostly of the same ilk as the ones found here. (Protip: you can find what other people use by downloading the source code of papers from arXiv). For commutative diagrams it's almost exclusively tikz now (tikz-cd is easier but somewhat more cumbersome for sufficiently complicated diagrams).