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% truthtable.sty
%% Copyright 2021 D. Flück
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status “author-maintained”.
%
% The Current Maintainer of this work is D. Flück.
%
% This work consists of the file truthtable.sty.
\NeedsTeXFormat{LaTeX2e}[1994/06/01]
\ProvidesPackage{truthtable}[2021/10/08 0.0.2 Package for generating truth tables automatically using LuaTeX]
\ProcessOptions\relax
\@ifpackageloaded{luacode}{
\PackageWarningNoLine{truthtable}{Package luacode was already loaded}
}{
\RequirePackage{luacode}
}
\begin{luacode*}
function Impl(a,b)
return (not a or b);
end
function Equiv(a,b)
return ((a and b) or ((not a) and (not b)));
end
function Xor(a,b)
return ((a or b) and (not (a and b)));
end
function Nand(a,b)
return (not (a and b));
end
function ComputeRows(header)
return 2^header
end
function Split(s, delimiter)
local result = {};
for match in (s..delimiter):gmatch("(.-)"..delimiter) do
table.insert(result, match);
end
return result;
end
function EvaluateFormula(formula)
local parsedFormula = "function res() return( " .. string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(string.gsub(formula, " ", ""),">>","Impl"),"__","Equiv"),"<>","Equiv"),"%^","Xor"),"!&","Nand"),"!","not "),"&" ," and "),"|"," or "),";",",") .. " ) end";
chunk = load(parsedFormula);
chunk();
local result = res();
return result;
end
function toBits(num)
local t = "" -- will contain the bits
while num>0 do
local rest = math.fmod(num,2)
if (rest == 1) then
t = "1" .. t
else
t = "0" .. t
end
num=(num-rest)/2
end
return t;
end
function printTruthValue(expr, dTrue, dFalse)
local returnVal = ""
if (expr) then
returnVal = dTrue;
else
returnVal = dFalse;
end
return returnVal;
end
function parse(commaSepVariables, commaSepDisplayVariables, commaSepResultRows, commaSepResultDisplayRows, displayTrue, displayFalse)
print("\n\ntruthtable v0.0.2\n")
local vrbls = Split(commaSepVariables, ",");
local numberOfColumns = #(vrbls);
local rows = ComputeRows(numberOfColumns);
local dVrbls = Split(commaSepDisplayVariables, ",");
local resRows = Split(commaSepResultRows, ",");
local dResRows = Split(commaSepResultDisplayRows, ",");
local dHeader = string.gsub(commaSepDisplayVariables, ",", " & ") .. " & " .. string.gsub(commaSepResultDisplayRows, ",", " & ") .. " \\\\ \\hline";
if (#(dVrbls) ~= #(vrbls)) then
print("Error: The number of variables does not match the number of display variables.");
return
end
if (#(dResRows) ~= #(resRows)) then
print("Error: The number of statements does not match the number of display statements.");
return
end
local tableContent = dHeader;
for i = (rows - 1),0,-1
do
local bitString = toBits(i);
while #bitString < numberOfColumns do
bitString = "0" .. bitString
end
local wVrbls = commaSepVariables;
local wCommaSepRows = commaSepResultRows
for ii = 1,numberOfColumns
do
wVrbls = string.gsub(wVrbls, vrbls[ii], (string.sub(bitString,ii,ii) == "1" ) and "+" or "-" )
wCommaSepRows = string.gsub(wCommaSepRows, vrbls[ii], (string.sub(bitString,ii,ii) == "1" ) and "+" or "-" )
end
local aWVrbls = Split(string.gsub(string.gsub(wVrbls, "+", "true"),"-", "false"), ",");
local aWCommaSepRows = Split(string.gsub(string.gsub(wCommaSepRows, "+", "true"),"-", "false"), ",");
local row = "";
for c = 1,#(aWVrbls)
do
row = row .. printTruthValue(EvaluateFormula(aWVrbls[c]), displayTrue, displayFalse) .. " & ";
end
for c = 1,#(aWCommaSepRows)
do
row = row .. printTruthValue(EvaluateFormula(aWCommaSepRows[c]), displayTrue, displayFalse) .. " & ";
end
row = string.sub(row, 1, #row - 2) .. "\\\\"
tableContent = tableContent .. "\n" .. row
end
tex.print(tableContent);
end
\end{luacode*}
\newcommand{\truthtable}[6]{
\luadirect{parse("#1", "\luaescapestring{#2}", "\luaescapestring{#3}", "\luaescapestring{#4}", "\luaescapestring{#5}","\luaescapestring{#6}")}
}
\endinput
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