如何更改真值表中的运算符符号

Question 1

周围不需要的间距\sim来自于这样一个事实：它被定义为使用内核中的\sim关系符号；：\mathrel

\DeclareMathSymbol{\sim}{\mathrel}{symbols}{"18}

您可以使用以下方法将该空格\sim视为普通符号\mathord{\sim}：

\cs_new_protected:Npn \__tt_build_header:
    {
        \seq_set_from_clist:NN \l__tt_header_seq \l__tt_vars_clist
        \seq_concat:NNN \l__tt_header_seq \l__tt_header_seq \l__tt_exprs_seq
        \tl_set:Nx \l_tmpa_tl {\seq_use:Nnnn \l__tt_header_seq {&}{&}{&}}
        \tl_replace_all:Nnn \l_tmpa_tl {*} {\cdot}
        \tl_replace_all:Nnn \l_tmpa_tl {+} {+}
        \tl_replace_all:Nnn \l_tmpa_tl {->} {\to}
        \tl_replace_all:Nnn \l_tmpa_tl {-} {\mathord{\sim}}
        \tl_use:N \l_tmpa_tl
    }

完成代码：

\documentclass{article}
\usepackage{xparse}

\begingroup
  \catcode`\%=12\relax
  \gdef\patmatch{"(%b())->(%b())","!%1||%2"}
\endgroup

\def\setimpaux#1{%
  \directlua{
    local s, _ = string.gsub("\luatexluaescapestring{#1}",\patmatch)
    tex.sprint(s)
  }
}

\ExplSyntaxOn
\int_new:N \l__tt_num_rows_int
\int_new:N \l__tt_num_cols_int
\int_new:N \l__tt_num_vars_int
\clist_new:N \l__tt_vars_clist
\seq_new:N \l__tt_exprs_seq
\seq_new:N \l__tt_header_seq

\NewDocumentCommand {\truthtable}{ m m }
    {
        \truth_table:nn {#1}{#2}
    }

\cs_new_protected:Npn \truth_table:nn #1#2
    {
        \clist_set:Nn \l__tt_vars_clist {#1}
        \seq_set_split:Nnn \l__tt_exprs_seq {;} {#2}
        \int_set:Nn \l__tt_num_vars_int {\clist_count:N \l__tt_vars_clist}
        \int_set:Nn \l__tt_num_rows_int {\fp_to_int:n {2^{\l__tt_num_vars_int}-1}}
        \int_set:Nn \l__tt_num_cols_int {\clist_count:N \l__tt_vars_clist +\seq_count:N \l__tt_exprs_seq}
        \__tt_gen_bins:
        \seq_map_function:NN \l__tt_exprs_seq \__tt_eval_bools:n
        \__tt_build_table:
    }

\cs_new_protected:Npn \__tt_build_header:
    {
        \seq_set_from_clist:NN \l__tt_header_seq \l__tt_vars_clist
        \seq_concat:NNN \l__tt_header_seq \l__tt_header_seq \l__tt_exprs_seq
        \tl_set:Nx \l_tmpa_tl {\seq_use:Nnnn \l__tt_header_seq {&}{&}{&}}
        \tl_replace_all:Nnn \l_tmpa_tl {*} {\cdot}
        \tl_replace_all:Nnn \l_tmpa_tl {+} {+}
        \tl_replace_all:Nnn \l_tmpa_tl {->} {\to}
        \tl_replace_all:Nnn \l_tmpa_tl {-} {\mathord{\sim}}
        \tl_use:N \l_tmpa_tl
    }

\cs_generate_variant:Nn \seq_use:Nnnn {cnnn}
\cs_new_protected:Npn \__tt_build_table:
    {
        \begin{array}{*{\int_use:N \l__tt_num_cols_int}{c}}
            \__tt_build_header:\\\hline
            \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
                {
                    \seq_use:cnnn {l__tt_row_{##1}_seq}{&}{&}{&}\\
                }
        \end{array}
    }

\cs_new_protected:Npn \__tt_set_imp:n #1
    {
        \tl_if_in:nnT {#1} {->}
            {
                \tl_set:Nx \l_tmpb_tl {\setimpaux{#1}}
                \exp_args:NV \__tt_set_imp:n \l_tmpb_tl
            }
    }
\cs_generate_variant:Nn \__tt_set_imp:n {V}

\cs_generate_variant:Nn \tl_replace_all:Nnn {Nnx}
\cs_new_protected:Npn \__tt_eval_bools:n #1
    {
        \tl_set:Nn \l_tmpa_tl {#1}
        \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
            {
                \int_set:Nn \l_tmpa_int {1}
                \tl_set_eq:NN \l_tmpb_tl \l_tmpa_tl
                \__tt_set_imp:V \l_tmpb_tl
                \tl_replace_all:Nnn \l_tmpb_tl {*}{&&}
                \tl_replace_all:Nnn \l_tmpb_tl {+}{||}
                \tl_replace_all:Nnn \l_tmpb_tl {-}{!}
                \clist_map_inline:Nn \l__tt_vars_clist
                    {
                        \tl_replace_all:Nnx \l_tmpb_tl {####1} {\seq_item:cn {l__tt_row_{##1}_seq} {\l_tmpa_int}}
                        \int_incr:N \l_tmpa_int
                    }
                \seq_put_right:cx {l__tt_row_{##1}_seq} {\fp_eval:n \l_tmpb_tl}
            }
    }

\cs_generate_variant:Nn \seq_set_split:Nnn {cnx}
\cs_new_protected:Npn \__tt_gen_bins:
    {
        \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
            {
                \seq_clear_new:c {l__tt_row_{##1}_seq}
                \seq_set_split:cnx {l__tt_row_{##1}_seq} {} {\int_to_binary:n {##1}}
                \int_while_do:nn {\seq_count:c {l__tt_row_{##1}_seq} < \l__tt_num_vars_int}
                    {
                        \seq_put_left:cn {l__tt_row_{##1}_seq} {0}
                    }
            }
    }

\ExplSyntaxOff
\begin{document}

\[
\truthtable{a,b,c}{a+b;b*(-c);-(a+b)+(b*(-c))}
\]

\end{document}

在此处输入图片描述

\mathord关于、\mathrel和类似词的解释\mathbin可以在TeX 按主题分类或电子书。

Answer

周围不需要的间距\sim来自于这样一个事实：它被定义为使用内核中的\sim关系符号；：\mathrel

\DeclareMathSymbol{\sim}{\mathrel}{symbols}{"18}

您可以使用以下方法将该空格\sim视为普通符号\mathord{\sim}：

\cs_new_protected:Npn \__tt_build_header:
    {
        \seq_set_from_clist:NN \l__tt_header_seq \l__tt_vars_clist
        \seq_concat:NNN \l__tt_header_seq \l__tt_header_seq \l__tt_exprs_seq
        \tl_set:Nx \l_tmpa_tl {\seq_use:Nnnn \l__tt_header_seq {&}{&}{&}}
        \tl_replace_all:Nnn \l_tmpa_tl {*} {\cdot}
        \tl_replace_all:Nnn \l_tmpa_tl {+} {+}
        \tl_replace_all:Nnn \l_tmpa_tl {->} {\to}
        \tl_replace_all:Nnn \l_tmpa_tl {-} {\mathord{\sim}}
        \tl_use:N \l_tmpa_tl
    }

完成代码：

\documentclass{article}
\usepackage{xparse}

\begingroup
  \catcode`\%=12\relax
  \gdef\patmatch{"(%b())->(%b())","!%1||%2"}
\endgroup

\def\setimpaux#1{%
  \directlua{
    local s, _ = string.gsub("\luatexluaescapestring{#1}",\patmatch)
    tex.sprint(s)
  }
}

\ExplSyntaxOn
\int_new:N \l__tt_num_rows_int
\int_new:N \l__tt_num_cols_int
\int_new:N \l__tt_num_vars_int
\clist_new:N \l__tt_vars_clist
\seq_new:N \l__tt_exprs_seq
\seq_new:N \l__tt_header_seq

\NewDocumentCommand {\truthtable}{ m m }
    {
        \truth_table:nn {#1}{#2}
    }

\cs_new_protected:Npn \truth_table:nn #1#2
    {
        \clist_set:Nn \l__tt_vars_clist {#1}
        \seq_set_split:Nnn \l__tt_exprs_seq {;} {#2}
        \int_set:Nn \l__tt_num_vars_int {\clist_count:N \l__tt_vars_clist}
        \int_set:Nn \l__tt_num_rows_int {\fp_to_int:n {2^{\l__tt_num_vars_int}-1}}
        \int_set:Nn \l__tt_num_cols_int {\clist_count:N \l__tt_vars_clist +\seq_count:N \l__tt_exprs_seq}
        \__tt_gen_bins:
        \seq_map_function:NN \l__tt_exprs_seq \__tt_eval_bools:n
        \__tt_build_table:
    }

\cs_new_protected:Npn \__tt_build_header:
    {
        \seq_set_from_clist:NN \l__tt_header_seq \l__tt_vars_clist
        \seq_concat:NNN \l__tt_header_seq \l__tt_header_seq \l__tt_exprs_seq
        \tl_set:Nx \l_tmpa_tl {\seq_use:Nnnn \l__tt_header_seq {&}{&}{&}}
        \tl_replace_all:Nnn \l_tmpa_tl {*} {\cdot}
        \tl_replace_all:Nnn \l_tmpa_tl {+} {+}
        \tl_replace_all:Nnn \l_tmpa_tl {->} {\to}
        \tl_replace_all:Nnn \l_tmpa_tl {-} {\mathord{\sim}}
        \tl_use:N \l_tmpa_tl
    }

\cs_generate_variant:Nn \seq_use:Nnnn {cnnn}
\cs_new_protected:Npn \__tt_build_table:
    {
        \begin{array}{*{\int_use:N \l__tt_num_cols_int}{c}}
            \__tt_build_header:\\\hline
            \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
                {
                    \seq_use:cnnn {l__tt_row_{##1}_seq}{&}{&}{&}\\
                }
        \end{array}
    }

\cs_new_protected:Npn \__tt_set_imp:n #1
    {
        \tl_if_in:nnT {#1} {->}
            {
                \tl_set:Nx \l_tmpb_tl {\setimpaux{#1}}
                \exp_args:NV \__tt_set_imp:n \l_tmpb_tl
            }
    }
\cs_generate_variant:Nn \__tt_set_imp:n {V}

\cs_generate_variant:Nn \tl_replace_all:Nnn {Nnx}
\cs_new_protected:Npn \__tt_eval_bools:n #1
    {
        \tl_set:Nn \l_tmpa_tl {#1}
        \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
            {
                \int_set:Nn \l_tmpa_int {1}
                \tl_set_eq:NN \l_tmpb_tl \l_tmpa_tl
                \__tt_set_imp:V \l_tmpb_tl
                \tl_replace_all:Nnn \l_tmpb_tl {*}{&&}
                \tl_replace_all:Nnn \l_tmpb_tl {+}{||}
                \tl_replace_all:Nnn \l_tmpb_tl {-}{!}
                \clist_map_inline:Nn \l__tt_vars_clist
                    {
                        \tl_replace_all:Nnx \l_tmpb_tl {####1} {\seq_item:cn {l__tt_row_{##1}_seq} {\l_tmpa_int}}
                        \int_incr:N \l_tmpa_int
                    }
                \seq_put_right:cx {l__tt_row_{##1}_seq} {\fp_eval:n \l_tmpb_tl}
            }
    }

\cs_generate_variant:Nn \seq_set_split:Nnn {cnx}
\cs_new_protected:Npn \__tt_gen_bins:
    {
        \int_step_inline:nnnn {0}{1}{\l__tt_num_rows_int}
            {
                \seq_clear_new:c {l__tt_row_{##1}_seq}
                \seq_set_split:cnx {l__tt_row_{##1}_seq} {} {\int_to_binary:n {##1}}
                \int_while_do:nn {\seq_count:c {l__tt_row_{##1}_seq} < \l__tt_num_vars_int}
                    {
                        \seq_put_left:cn {l__tt_row_{##1}_seq} {0}
                    }
            }
    }

\ExplSyntaxOff
\begin{document}

\[
\truthtable{a,b,c}{a+b;b*(-c);-(a+b)+(b*(-c))}
\]

\end{document}

在此处输入图片描述

\mathord关于、\mathrel和类似词的解释\mathbin可以在TeX 按主题分类或电子书。

Question 2

兼容性更新

release1.2l (2017/07/26)删除了我在这里使用的内部宏 ( \xint_gob_til_xint_relax)。因此我添加了定义以使代码再次编译。
（2015/03/07）自发布1.1 (2014/10/28)以来信特\xintNewExpr这个答案的原始代码被破坏了。用户手册中提到了的全面修改，但它应该被列入的“重大更改”列表中CHANGES.html。实际上，只有的一个非常深奥的功能的\xintNew(Bool)Expr更改影响了这里的代码，我忘了世界上存在这种用途！

xint < 1.1 对于使用旧代码的人来说，代码还在那里，但是被注释掉了。

顺便说一下，我提到现在逻辑运算&&符“和”比“与”更|| 受欢迎，但后者仍然被接受，尽管也许它们将来会用于其他用途：也许是按位运算。xint&|

这是该方法的一个（适度的）替代方案LaTeX3+lualatex。它使用xintexpr。它要求用户在逻辑表达式中使用\AND、\OR、。其他关键字有、、。\NOT\XOR\ALL\ANY

最新更新：变量的数量无论如何都限制为9，因为每个表达式都将转换为具有那么多参数的宏。因此，第一个带有嵌套的答案\xintFor，其拼写为最多5变量，在这种情况下具有完全通用的潜力。但是在我的第二个答案（这个答案的底部）中，我以类似于我在代码中看到的方法的方式生成行LaTeX3+lualatex，通过对整数进行二进制扩展0，1...最多为2^n-1，n变量数量。这使得编码更紧凑（效率也更低，但这并不重要）。

第二个答案另外添加了一个可选参数，允许用户直接指定表达式在标题行中的显示方式。

此外，它也允许最后的表达式以结尾;。

而且，星号变体使用\halign而不是array环境来允许分页。对于9变量，会512生成行，因此这是必要的。图像只是包含行的文档的第一页12。

更新：使用;（如 OP 中所示）而不是,分隔表达式。

布尔表达式使用\AND、来输入\OR，\NOT还有\XOR、\ALL、\ANY（它们有多个参数，以分隔,）。然后可以在宏中自定义如何排版它们。

布尔表达式被分隔（如在 OP 中一样）分号：我最初的答案使用了逗号，因为\xintexpr解析器本身可以处理这个问题，当在其他地方使用逗号分隔函数参数时也是如此。但是，为了排版第一行，必须用括号（例如）或隐藏这些逗号，\XOR({a,b,c})不太\XOR(a\SEP b\SEP c)方便\def\SEP{,}。因此，用户输入中的表达式现在使用分隔;。

可以看出，这里的代码很短。最后我有点精疲力竭，也许有办法将其缩短一点，避免使用大\ifcase。就目前而言，代码允许构建一个表，其中最多有5表示为字母的不确定项（扩大\ifcase可能最多有9；5字母已经有32行）和任意多个用逗号分隔的布尔表达式（实际上，就目前而言，表达式的 nb 加上不确定项的 nb 最多应保持为10，请参阅*{10}c数组前言）[我没有时间检查是否可以10用动态的东西替换，在这种情况下，从两个参数计算它没有问题\truthtable]

真值表

另外两个真值表：

更多真值表

\documentclass{article}
\usepackage{xintexpr}

\catcode`_ 11

\newcount \tt_varcnt

% this internal macro was suppressed in xint 1.2l (2017/07/26)
% but is used in this answer
\long\def\xint_gob_til_xint_relax #1\xint_relax {}%
\let\xint_relax\relax

% auxiliary macro to handle things separated by semi-colons
\def\truthtable_scanexprs #1;{%
    \xint_gob_til_xint_relax #1\truthtable_scan_done\xint_relax
    \odef\tt_exprlist {\tt_exprlist{#1}}%
    \truthtable_scanexprs
}%
\def\truthtable_scan_done #1\truthtable_scanexprs {}                           

\newcommand\truthtable [2]{%
% example of use :
% \truthtable{a,b,c}{a\OR b; b\AND\NOT(c)}
%
% The first argument lists the used indeterminates, they must be lowercase or
% uppercase Latin letters.
% 
% The second argument is a ; separated list of logical expressions.
  \begingroup
    \endlinechar-1 \everyeof{\noexpand }% for use of \scantokens
    % initializing
    \tt_varcnt 0
    \def\tt_exprlist {}% will be {exprA}{exprB}{exprC}...
    % scan #2 for ; separated expressions and fill \tt_exprlist:
    \truthtable_scanexprs #2;\xint_relax;%
    %
    % PREPARATION FOR DEFINING THE BOOLEAN EXPRESSIONS
% MODIFIED FOR COMPATIBILITY WITH xint 1.1 OR LATER
%%%% | and & are still accepted but the manual recommend || and &&
%%%%  (2015/03/07)
    \def\OR{||}\def\AND{&&}\def\NOT{!}% needed for \xintNewBoolExpr
% original was
    % \def\OR{|}\def\AND{&}\def\NOT{!}% needed for \xintNewBoolExpr
% END
    % the negation ! must be applied to a parenthesized expression
    % 
    % extra strange set-up before \edef and then \scantokens
    % the idea is too allow, X, O, R, A, L, L, A, N, Y as indeterminates...
    % ... and for this as we will need to make them active, thus
    %     we must first replace \XOR for example by \1.
    \def\XOR{\1}\def\ALL{\2}\def\ANY{\3}%
    \let\1\relax\let\2\relax\let\3\relax
    %
    \edef\tt_x {\tt_exprlist}% replaces \XOR by \1, \ALL by \2, \ANY by \3
    %
% ORIGINAL VERSION:
    % % we now make active the indeterminates to replace them by {$1}, {$2}, ..
    % % place holders (cf.  xintexpr manual)
    % \xintFor ##1 in {#1} \do 
    %   {\catcode`##1\active
    %    \advance\tt_varcnt 1
    %    \lccode`~=`##1\relax
    %    \lowercase{\edef~}{{$\the\tt_varcnt}}%$1, $2, $3, as in xintexpr manual
    % }%
% NEW VERSION FOR COMPATIBILITY WITH xint 1.1 OR LATER  (2015/03/07)
    % we now make active the indeterminates to replace them by {#1}, {#2}, ..
    % place holders (with a catcode 12 # as it simplifies things here, and
    % the \xintNewExpr scanner does not mind)
    \xintFor ##1 in {#1} \do% 
    % I should have defined a sub-macro for this, code would be clearer
        {\catcode`##1\active
         \advance\tt_varcnt 1
         \lccode`~=`##1\relax
         \lowercase{\edef~}{{\string####\the\tt_varcnt}}}%
% END OF MODIFICATION
    %
    % Now \scantokens to replace the now active letters by the braced
    % macro parameters (I don't recall exactly why I wanted them braced,
    % these braces will get removed during \xintNewExpr scan)
    %
    \edef\tt_x {\scantokens\expandafter{\tt_x}}%
    %
    % For use of \xintNewBoolExpr (which again does some \scantokens), 
    % the letters *must* be reset to their standard catcodes.
    %
    \xintFor ##1 in {#1} \do {\catcode`##1 11 }% 
    %
    % Definition of the boolean expressions. Using ; as separator for
    % user input was only in order to ease up
% NOTE: (2015/03/07)
% for simplicity I stick here to the originally used ; as expression separator
% on input, but xint 1.1 has macros which can be used, out of \xintexpr
% context to identify (expandably) comma separated things, even themselves
% containing commas if they are in parentheses
    % finding the correct
    % expressions for typesetting the head-row of the table, we need to
    % re-install here the , as separator, this allows to do only one
    % \xintNewBoolExpr, as it knows how to identify the various 
    % comma separated sub-expressions.
    %
    \def\1{xor}\def\2{all}\def\3{any}%
    \xintNewBoolExpr\tt_y[\tt_varcnt]{\xintListWithSep{,}{\tt_x}}%
    % 
    % CUSTOMIZE HERE:
    % For typesetting the head row, customize as desired:
    \def\OR{+}\def\AND{\cdot}\def\NOT{\mathord{\sim}}%
    \def\XOR{\mbox{\texttt{xor}}}%
    \def\ALL{\mbox{\texttt{all}}}%
    \def\ANY{\mbox{\texttt{any}}}%
    %
    % the table. Up to five variables, extensible up to use of nine variables
    \begin{array}{*{10}c}
       \xintListWithSep{&}{\xintCSVtoList{#1}}&%
                                 \xintListWithSep{&}{\tt_exprlist}\\
       \hline
       \ifcase\tt_varcnt
       \or
       \xintFor* ##1 in {01}\do
       {##1 & \xintListWithSep{&}{\xintCSVtoList{\tt_y {##1}}}\\ }
       \or
       \xintFor* ##1 in {01}\do
       {\xintFor* ##2 in {01}\do
        {##1 & ##2& 
           \xintListWithSep{&}{\xintCSVtoList{\tt_y {##1}{##2}}}\\ }}
       \or
       \xintFor* ##1 in {01}\do
       {\xintFor* ##2 in {01}\do
        {\xintFor* ##3 in {01}\do
         {##1 & ##2 & ##3& \xintListWithSep{&}%
                           {\xintCSVtoList{\tt_y {##1}{##2}{##3}}}\\ }}}
       \or
       \xintFor* ##1 in {01}\do
       {\xintFor* ##2 in {01}\do
        {\xintFor* ##3 in {01}\do
         {\xintFor* ##4 in {01}\do
          {##1 & ##2 & ##3& ##4&\xintListWithSep{&}%
                           {\xintCSVtoList{\tt_y {##1}{##2}{##3}{##4}}}\\ }}}}
       \or
       \xintFor* ##1 in {01}\do
       {\xintFor* ##2 in {01}\do
        {\xintFor* ##3 in {01}\do
         {\xintFor* ##4 in {01}\do
          {\xintFor* ##5 in {01}\do
          {##1 & ##2 & ##3& ##4& ##5&\xintListWithSep{&}%
                      {\xintCSVtoList{\tt_y {##1}{##2}{##3}{##4}{##5}}}\\ }}}}}
       \fi
       \hline 
    \end{array}
    \endgroup
}
\catcode`_ 8   

\begin{document}

\[
\truthtable{a,b,c}{a\OR b; b\AND\NOT(c); \NOT (a\OR b)\OR (b\AND\NOT(c))}
\]

\[
\truthtable{X,Y,Z}{Z\AND X \OR Y \AND X}
\]

\[
\truthtable{X,Y,Z,T}{Z\AND X \OR Y \AND X \AND T}
\]

\[
\truthtable{a, b}{\XOR (a,b)}
\]

\[
\truthtable {p, q, r, s, t}{\ANY(p,q,r,s,t); \XOR(p,q,r,s,t); \ALL(p,q,r,s,t)}
\]

\[
\truthtable{a, b, c, d}{\XOR (a,b,c,d); \XOR(a,\XOR(b,c,d)); \XOR(\XOR(a,b),\XOR(c,d))}
\]

\[
\truthtable{A,D,N}{A\AND D \OR N \AND D; A\OR D \AND N \OR D}
\]

\end{document}

这是第二个答案的代码：

\documentclass[a4paper]{article}
\usepackage{geometry}
\usepackage{xintexpr}
% in order to convert from decimal to binary using \xintDecBin
\usepackage{xintbinhex}

\catcode`_ 11
\makeatletter

% to count the number of variables:
\newcount \tt_varcnt
% The number of variables is at most 9 (leading to 512 rows...)

% to count the number of expressions (in order to choose dynamically
% a large enough number of columns for the array environment)
\newcount \tt_exprcnt

% to handle things separated by semi-colons

% we add some extra to allow empty expressions to be skipped, and also to allow
% the user to terminate the last expression by a ; 

% [if the optional parameter is used, use \space to get something empty in the
% header row cell]

% this internal macro was suppressed in xint 1.2l (2017/07/26)
% but is used in this answer
\long\def\xint_gob_til_xint_relax #1\xint_relax {}%
\let\xint_relax\relax

\def\truthtable_scanexprs #1;{%
    \if\relax\detokenize{#1}\relax\expandafter\truthtable_scan_skip\fi
    \xint_gob_til_xint_relax #1\truthtable_scan_done\xint_relax
    \odef\tt_exprlist {\tt_exprlist{#1}}%
    \advance \tt_exprcnt 1
    \truthtable_scanexprs
}%
\def\truthtable_scan_done #1\truthtable_scanexprs {}%                     
\def\truthtable_scan_skip #1\truthtable_scanexprs {\truthtable_scanexprs}%

% we now have an optional parameter to provide a custom typesetting
% of the expressions in the head row

% and we have furthermore a star variant to use \halign rather than array

\newcommand*\truthtable {%
   \begingroup
     \endlinechar-1 \everyeof{\noexpand }% for use of \scantokens
     \tt_varcnt 0
     \tt_exprcnt 0
     \def\tt_exprlist {}%
     \def\tt_headexprlist {\tt_exprlist}%
     \def\tt_usearray {1}%
     \@ifstar{\def\tt_usearray {0}\truthtable@chkopt}\truthtable@chkopt
}%

\def\truthtable@chkopt {\@ifnextchar[{\truthtable@opt}{\truthtable@}%]
                       }

\def\truthtable@opt [#1]{%
      % we first scan the optional argument for the header row.
      % it will be printed as is, only need to transform the ;'s into &'s
      \truthtable_scanexprs #1;\xint_relax;%
      \let\tt_headexprlist\tt_exprlist
      \tt_exprcnt 0
      \def\tt_exprlist {}%
      \truthtable@
      % *NO* check is done that #1 defines the same number of expressions
      % as the last mandatory argument to \truthtable !
}

\def\truthtable@ #1#2{%
    % convert the comma separated indeterminates into a list
    \oodef\tt_varlist{\xintCSVtoListNoExpand {#1}}%
    % scan #2 for ; separated expressions and fill \tt_exprlist:
    \truthtable_scanexprs #2;\xint_relax;%
    % PREPARATION FOR DEFINING THE BOOLEAN EXPRESSIONS
% MODIFIED FOR COMPATIBILITY WITH xint 1.1 OR LATER
%%%% | and & are still accepted but the manual recommend || and &&
%%%%  (2015/03/07)
    \def\OR{||}\def\AND{&&}\def\NOT{!}% needed for \xintNewBoolExpr
% original was
    % \def\OR{|}\def\AND{&}\def\NOT{!}% needed for \xintNewBoolExpr
% END
    % the negation ! must be applied to a parenthesized expression
    % 
    % extra strange set-up before \edef and then \scantokens
    % the idea is too allow, X, O, R, A, L, L, A, N, Y as indeterminates...
    % ... and for this as we will need to make them active, thus
    %     we must first replace \XOR for example by \1.
    \def\XOR{\1}\def\ALL{\2}\def\ANY{\3}%
    \let\1\relax\let\2\relax\let\3\relax
    %
    \edef\tt_x {\tt_exprlist}%  replaces \XOR by \1, \ALL by \2, \ANY by \3
    %
% ORIGINAL VERSION:
    % % we now make active the indeterminates to replace them by {$1}, {$2}, ..
    % % place holders (cf.  xintexpr manual)
    % \xintFor ##1 in {#1} \do 
    %   {\catcode`##1\active
    %    \advance\tt_varcnt 1
    %    \lccode`~=`##1\relax
    %    \lowercase{\edef~}{{$\the\tt_varcnt}}%$1, $2, $3, as in xintexpr manual
    % }%
% NEW VERSION FOR COMPATIBILITY WITH xint 1.1 OR LATER  (2015/03/07)
    % we now make active the indeterminates to replace them by {#1}, {#2}, ..
    % place holders (with a catcode 12 # as it simplifies things here, and
    % the \xintNewExpr scanner does not mind)
    \xintFor ##1 in {#1} \do% 
    % I should have defined a sub-macro for this, code would be clearer
        {\catcode`##1\active
         \advance\tt_varcnt 1
         \lccode`~=`##1\relax
         \lowercase{\edef~}{{\string####\the\tt_varcnt}}}%
% END OF MODIFICATION
    % Now the \scantokens with active letters. 
    \edef\tt_x {\scantokens\expandafter{\tt_x}}%
    %
    % For use of \xintNewBoolExpr (which again does some \scantokens), 
    % the letters *must* recover their standard catcodes
    %
    \xintFor* ##1 in \tt_varlist \do {\catcode`##1 11 }% 
    %
    % Definition of the boolean expressions. Using ; as separator for
    % user input was only in order to ease up finding the correct
    % expressions for typesetting the head-row of the table, we need to
    % re-install here the , as separator, this allows to do only one
    % \xintNewBoolExpr, it knows how to identify the various sub-expressions.
    \def\1{xor}\def\2{all}\def\3{any}%
    \xintNewBoolExpr\tt_y[\tt_varcnt]{\xintListWithSep{,}{\tt_x}}%
    % 
    % CUSTOMIZE HERE:
    % For typesetting the head row, customize as desired:
    % (*not* relevant in case of use of the optional parameter)
    \def\OR{+}\def\AND{\cdot}\def\NOT{\mathord{\sim}}%
    \def\XOR{\mbox{\texttt{xor}}}%
    \def\ALL{\mbox{\texttt{all}}}%
    \def\ANY{\mbox{\texttt{any}}}%
    %
    \if\tt_usearray 1\expandafter\truthtable_array\else
                     \expandafter\truthtable_halign
    \fi
    \endgroup
}

\def\truthtable_array {%
    % (we have the count of variables in \tt_varcnt and the count of 
    %  expressions in \tt_exprcnt)
    \begin{array}{*{\numexpr\tt_varcnt+\tt_exprcnt\relax}c}
       % generate the header-row, 
         \xintListWithSep{&}{\tt_varlist}
       &
         \xintListWithSep{&}{\tt_headexprlist}\\
       \hline
       % calculate 2^n, n is nb of variables
       \tt_varcnt \xintiiPow {2}{\tt_varcnt} 
       % generate integers from 2^n  to 2*2^n -1, then binary notation
       % will always start by a 1 which we can gobble
       \xintFor* ##1 in {\xintSeq {\tt_varcnt}{2*\tt_varcnt-1}}
       \do
       %    (the problem is that \xintDecToBin always trims leading zeros...
       %     hence we resort to this to always have a leading 1)
       {\edef\tt_temp{\expandafter\expandafter\expandafter
                      \xint_gobble_i\xintDecToBin {##1}}%
        \edef\tt_temp{\tt_temp\xintCSVtoList{\expandafter\tt_y\tt_temp}}%
        \xintListWithSep {&}{\tt_temp}\\}
       \hline 
    \end{array}
}

\newtoks\tt_toks

% The \halign variant (should *not* be put inside \[..\])
\def\truthtable_halign {%
    % This is variant using \halign to allow break accross pages.
    % I use some tricks to center it (whow! incredibly it works)
    % (I initially used a repeatable preamble, but following TeX by Topic
    %  25.5, to center the alignment, I need to insert some \tabskip
    %  at the LAST column, hence here I follow a more complicated approach
    %  constructing the preamble first.)
    %  
    % but then I don't know how to have horizontal rules limited to
    % the width covered by the actual contents... 
    %
    \tt_toks {\hfil$\mathstrut##$\hfil\tabskip 2\arraycolsep}%
    \xintiloop [{\tt_varcnt+\tt_exprcnt-1}+-1]
    \ifnum\xintiloopindex>0
      \tt_toks \expandafter{\the\tt_toks &\hfil$##$\hfil}%
    \repeat
    %\showthe\tt_toks
    \tabskip 0pt plus 1000pt minus 1000pt 
    \halign to \hsize
    {\span\the\tt_toks\tabskip 0pt plus 1000pt minus 1000pt \cr
     % first row
     \xintListWithSep{&}{\tt_varlist}&\xintListWithSep{&}{\tt_headexprlist}\cr
     % however the rule extends across the full page
     %     \hline
     \tt_varcnt \xintiiPow {2}{\tt_varcnt} 
     \xintFor* ##1 in {\xintSeq {\tt_varcnt}{2*\tt_varcnt-1}}
       \do
       {\edef\tt_temp{\expandafter\expandafter\expandafter
                      \xint_gobble_i\xintDecToBin {##1}}%
        \edef\tt_temp{\tt_temp\xintCSVtoList{\expandafter\tt_y\tt_temp}}%
        \xintListWithSep {&}{\tt_temp}\cr }%
     %      \hline 
    }%
}

\catcode`_ 8   
\makeatother

\pagestyle{empty}
\begin{document}\thispagestyle{empty}

\[
\truthtable{a,b,c}{a\OR b; b\AND\NOT(c); \NOT (a\OR b)\OR (b\AND\NOT(c));}
\]


\textbf{Exercise:~} fill in the header row:

\[% in the optional argument, \AND, \NOT, are not mandatory but optional
  % on can use whatever one wants.
\truthtable [a?b; ?\cdot\NOT(c); \NOT(a+?)?(b\AND\NOT(?));]% trailing ; allowed
            {a, b, c}
            {a\OR b; b\AND\NOT(c); \NOT (a\OR b)\OR (b\AND\NOT(c))}
\]


% maximal number of variables is 9

% \truthtable* {a, b, c}{\XOR(a, b, c)}
\bigskip
\hrule
\medskip
An example with the maximal number of variables (9, hence 512 rows) using
\verb|\halign| to allow breaking accross pages:\medskip

\truthtable* [\XOR(a,\cdots,i); ?(a,\cdots,d)\AND\NOT(?(e,\cdots,i));]
             {a, b , c, d, e, f, g, h, i}
             {\XOR(a, b , c, d, e, f, g, h, i); 
              \ALL(a,b,c,d)\AND\NOT(\ANY(e,f,g,h,i))
            }

\end{document}

真值表...

Answer