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Lambda calculus/PL LaTeX macros
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%% 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{1} | |
\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{\VoidT}{}{\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 | |
%% \Lam*{x}[t]{e} produces λx : t. (e) | |
\NewDocumentCommand{\Lam}{smom}{% | |
\lambda #2 \IfValueT{#3}{: #3} .\, \IfBooleanTF{#1}{\DelimPrn{#4}}{#4} | |
} | |
%% \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{-}} |
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).
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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.