1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
|
% 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}[2021/10/01 0.0.1 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 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(formula, " ", ""),">>","Impl"),"__","Equiv"),"!","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)
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 (not (numberOfColumns == #(vrbls) and numberOfColumns == #(dVrbls))) then
return("error");
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
|