How to set two tabular environments, horizontally aligned, to the width needed for the larger?

Question

As part of a larger display, I am placing two tabular environments together, one above the other. These two environments are going to appear in one column of a larger tabular, and I want the two environments to have the same width. I would prefer not to use tabular*, because I don't want to have to guess the width and keep adjusting it as the contents change.

I tried setting them in a single tabular, but then both columns got too wide, making the total both too wide and unpleasant to read. In other words, it won't do have both tables share a first column, because that column will be too wide for the first table to be readable. And they can't share a second column, because the second table won't really have room for a second column of that width.

However, if they have the same total width, everything should look good. But I don't know how to find that total width other then playing guessing games with tabular* and explicit widths.

Is there a way to change the following MWE so that the second table is set to the width of the first table? (With suitable \extracolsep).

\documentclass{article}
\usepackage{booktabs}

\begin{document}
\thispagestyle{empty}
\begin{center} 

\begin{tabular}[t]{@{}l@{}}
\begin{tabular}{@{}ll@{}}
\multicolumn2{c}{(a) Names}\\[\medskipamount]
\toprule
$x, f$&Name of a variable (or function)\\
$X$& Name of a module\\
$K$& Name of a value constructor\\
$t$& Name of a type\\
$T$& Name of a module type\\
\bottomrule
\end{tabular}
\\
\begin{tabular}{@{}ll@{}}
\strut\\
\multicolumn2{c}{(b) Declarations in the theory}\\[\medskipamount]
\toprule
\mbox{(abstype $t$)}&$t :: *$ or $t :: * \mathrel @ \pi$\\
\mbox{(type $t$ $\tau$)}&$t = \tau$\\
\mbox{(val $x$ $\tau$)}&$x : \tau$\\
\bottomrule
\end{tabular}
\end{tabular}
\end{center}
\end{document}

Answer 1

I'd set the captions and the rules in the outer (main) tabular and use two inner tabulars for the actual data:

\documentclass{article}

\usepackage{booktabs}

\begin{document}

\begin{tabular}{@{} l @{}}
  \multicolumn{1}{@{} c @{}}{(a) Names} \\[\medskipamount]
  \toprule
  \begin{tabular}{@{} l l @{}}
    $x, f$ & Name of a variable (or function) \\
    $X$    & Name of a module                 \\
    $K$    & Name of a value constructor      \\
    $t$    & Name of a type                   \\
    $T$    & Name of a module type
  \end{tabular} \\
  \bottomrule \\[\dimexpr-\normalbaselineskip+\bigskipamount]
  \multicolumn{1}{@{} c @{}}{(b) Declarations in the theory} \\[\medskipamount]
  \toprule
  \begin{tabular}{@{} l l @{}}
    (abstype $t$)     & $t :: *$ or $t :: * \mathrel{@} \pi$ \\
    (type $t$ $\tau$) & $t = \tau$                           \\
    (val $x$ $\tau$)  & $x : \tau$
  \end{tabular} \\
  \bottomrule
\end{tabular}

\end{document}

Answer 2

REVISED: Here it is, WITHOUT tabular*.

I took the OP's MWE and enclosed the larger width tabular portion in its own sub-tabular, using \multicolumn to place it.

\documentclass{article}
\usepackage{booktabs}

\begin{document}
\thispagestyle{empty}
\begin{center} 

\begin{tabular}[t]{@{}l@{}}
\begin{tabular}{@{}ll@{}}
\multicolumn2{c}{(a) Names}\\[\medskipamount]
\toprule
\multicolumn2{@{}c@{}}{\begin{tabular}{@{}ll@{}}
$x, f$&Name of a variable (or function)\\
$X$& Name of a module\\
$K$& Name of a value constructor\\
$t$& Name of a type\\
$T$& Name of a module type\\
\end{tabular}}\\
\bottomrule
\strut\\
\multicolumn2{c}{(b) Declarations in the theory}\\[\medskipamount]
\toprule
\mbox{(abstype $t$)}&$t :: *$ or $t :: * \mathrel @ \pi$\\
\mbox{(type $t$ $\tau$)}&$t = \tau$\\
\mbox{(val $x$ $\tau$)}&$x : \tau$\\
\bottomrule
\end{tabular}
\end{tabular}
\end{center}
\end{document}

Answer 3

With nested tabulars:

\documentclass{article}
\usepackage{booktabs}

\begin{document}
\thispagestyle{empty}
\begin{center} 

\begin{tabular}{@{}ll@{}}
\multicolumn2{c}{(a) Names}\\[\medskipamount]
\toprule
$x, f$&Name of a variable (or function)\\
$X$& Name of a module\\
$K$& Name of a value constructor\\
$t$& Name of a type\\
$T$& Name of a module type\\
\bottomrule
\strut\\
\multicolumn2{c}{(b) Declarations in the theory}\\[\medskipamount]
\toprule
\multicolumn{2}{@{}l@{}}{\begin{tabular}{@{}ll@{}}
\mbox{(abstype $t$)}&$t :: *$ or $t :: * \mathrel @ \pi$\\
\mbox{(type $t$ $\tau$)}&$t = \tau$\\
\mbox{(val $x$ $\tau$)}&$x : \tau$\\
\end{tabular}}\\
\bottomrule
\end{tabular}
\end{center}
\end{document}