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September 10, 2017 00:51
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Lambda Calculus in TeX
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\documentclass[a4paper]{article} | |
\usepackage[T1]{fontenc} | |
\usepackage{geometry} | |
\usepackage{fancyvrb} | |
\fvset{tabsize=2} | |
\title{Lambda Calculus in \TeX} | |
\author{Camil Staps} | |
\makeatletter | |
% TeX for loop | |
\def\for#1=#2:#3{\ifor{#1}{#3}#2} | |
\def\ifor#1#2#3{% | |
\xdef#1{#3}% | |
#2% | |
\kernel@ifnextchar,{\iforcomma{#1}{#2}}\relax} | |
\def\iforcomma#1#2,{\ifor{#1}{#2}} | |
% IKS | |
\def\i#1{\csname#1\endcsname} | |
\def\k#1#2{#1} | |
\def\s#1#2#3{\csname#1\endcsname{#3}{\csname#2\endcsname{#3}}} | |
% Booleans | |
\def\True#1#2{#1} | |
\def\False#1#2{#2} | |
\def\And#1#2{\csname#1\endcsname{#2}{#1}} | |
\def\Ior#1#2{\csname#1\endcsname{#1}{#2}} | |
\def\Not#1{\csname#1\endcsname{False}{True}} | |
\def\Xor#1#2{\And{\Ior{#1}{#2}}{\Not{\And{#1}{#2}}}} | |
% Numbers (Barendregt numerals) | |
\def\Zero#1{} | |
\def\Succ#1#2{\csname#2\endcsname{False}{#1}} | |
% Printing numbers | |
\def\@print#1#2{#2{@print}{\global\advance\count255 by 1}}% | |
\def\print#1{% | |
\count255=0 | |
#1{@print}% | |
\number\count255} | |
\makeatother | |
\begin{document} | |
\maketitle | |
\thispagestyle{empty} | |
\section*{Booleans} | |
\VerbatimInput[firstline=27,lastline=32]{lambda.tex} | |
\VerbatimInput[firstline=55,lastline=60]{lambda.tex} | |
\begin{center} | |
\begin{tabular}{llllll} | |
$p$ & $q$ & $\lnot p$ & $p \land q$ & $p \lor q$ & $p \oplus q$ \\\hline | |
\for\p={False},{True}:{% | |
\for\q={False},{True}:{% | |
\p & \q & \Not{\p} & \And{\p}{\q} & \Ior{\p}{\q} & \Xor{\p}{\q}\\}} | |
\end{tabular} | |
\end{center} | |
\section*{Barendregt numerals} | |
\VerbatimInput[firstline=35,lastline=36]{lambda.tex} | |
\VerbatimInput[firstline=39,lastline=43]{lambda.tex} | |
\VerbatimInput[firstline=70,lastline=70]{lambda.tex} | |
\begin{center} | |
\print{\Succ{\Succ{\Succ{\Zero}}}} | |
\end{center} | |
\end{document} |
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