Wrapping a length

Question

I've cobbled together the \basis macro which sets and gets a hidden/internal length \b@sis. It is meant to work as follows :

1. Calling \basis returns the value of \b@sis
2. Calling \basis{} sets \b@sis to the default value (The current font size \f@size) and
3. Calling \basis{1ex} sets the \b@sis to the specified length.

2 and 3 work but 1 does not always return the value as expected. I can't use \basis within TikZ as a length for instance nor can I show it's value using \the\basis or \showthe\basis. I also tried prefixing \expandafterto the previous two "the" commands with no effect. Below is the code I have so far

\documentclass{standalone}
\usepackage{luatex85}

\usepackage{xparse}
\usepackage{ifthen}
\usepackage{xifthen}
\usepackage{tikz}
\usepackage{booktabs}

\makeatletter
\newlength{\b@sis}
\newlength{\length}
\setlength{\length}{2pt}
\setlength{\b@sis}{2pt}
\ProvideDocumentCommand{\basis}{g}{%
 \IfNoValueTF{#1}{%
  \b@sis}{%
  \ifthenelse{\isempty{#1}}%
  {\setlength{\b@sis}{\f@size pt}%
   \setlength{\length}{\f@size pt}}%
  {\setlength{\b@sis}{#1}%
   \setlength{\length}{#1}}}}%
\newcommand{\showbasis}{\the\b@sis}
\makeatother

\begin{document}
\begin{tabular}{|l|r|c|c|}                                                   % The following calls fail
\toprule
No response  & \basis        \showbasis & \tikz \draw circle(0.5*\length);            \\%& \tikz \draw circle(0.5*\basis); \\
\midrule
Sets default & \basis{}      \showbasis & \basis{}\tikz \draw circle(0.5*\length);    \\%& \tikz \draw circle(0.5*\basis); \\
\midrule
Sets Value   & \basis{1ex}   \showbasis & \basis{1ex}\tikz \draw circle(0.5*\length); \\%& \tikz \draw circle(0.5*\basis); \\
\bottomrule
\end{tabular}
\end{document}

its output looks as follows

My belief is that the \IfNoValueTF is not being expanded when there is no argument and that the expected length not returned. Is there some means of expanding it to return the internal length or is there perhaps a better means fordoing this.

I see \ProvideDocumentCommand allows for an l argument, perhaps I should be using this within my definition ? e.g. is there a change \basis is reading ahead to the first non-whitespace character, the xparse manual implies this might be the case.

Update

Egreg clearly has the better solution but I only saw it after David Carlisle responded and I had messed about with it some more. The interface I got to used \basis and \basis[VALUE] to set the value and \basis* to retrieve it. This is really bad practice though and is certainly not what star is for.

\ProvideDocumentCommand{\basis}{s o}{%
 \IfBooleanTF{#1}
  {\the\b@sis}
  {\IfNoValueTF{#2}{%
    \setlength{\b@sis}{\f@size pt}%
    \setlength{\length}{\f@size pt}}
   {\setlength{\b@sis}{#2}%
    \setlength{\length}{#2}}}
  }%

Answer 1

The posted code runs without error and produces what I'd expect, however you do not say what you expect it to do.

The user interface using the same command to both set and retrieve is very confusing and perhaps that is the source of the confusion.

In the second column in the 2nd and 3rd rows you set the length but in the first row you have the rather odd construct

\basis        \showbasis

\basis expands to a use of the internal length and \showbasis expands to \the applied to that length.

if you change it to

\basis        \showbasis\showbasis 

so if \b@sis is 2pt as it is set initially then

\basis        \showbasis

is

\b@sis        \the\b@sis

which expands to

 \b@sis 2pt

so sets \b@sis to the value 2pt that it had already.

Adding a second \showbasis as I did prints the 2pt to the table,

then you see that the value is 2pt hence the small circle.

and if you just have \basis on the cell on its own you get a missing number error as it is the assignment of a length, with no supplied value.

Answer 2

A command defined with an optional g argument is not expandable, so you cannot use \basis without argument in an expansion context, such as

\draw circle(0.5*\basis)

It's surely better, as suggested, to split the calls between setting the variable and using it. And you can use the full power of expl3 to get more efficient code.

\documentclass[border=4pt]{standalone}
\usepackage{luatex85}

\usepackage{xparse}
\usepackage{tikz}
\usepackage{booktabs}

\ExplSyntaxOn
\dim_new:N \l_carel_basis_dim
\dim_set:Nn \l_carel_basis_dim { 2pt }

\NewDocumentCommand{\setbasis}{O{\use:c {f@size} pt}}
 {
  \dim_set:Nn \l_carel_basis_dim { #1 }
 }

\NewExpandableDocumentCommand{\basis}{}{\dim_use:N \l_carel_basis_dim}
\ExplSyntaxOff

\begin{document}
\begin{tabular}{lrcc}
\toprule
Initial value & \basis & \tikz \draw circle(0.5*\basis); \\
\midrule
Sets default & \setbasis\basis & \setbasis\tikz \draw circle(0.5*\basis); \\
\midrule
Sets Value   & \setbasis[1ex]\basis & \setbasis[1ex]\tikz \draw circle(0.5*\basis); \\
\bottomrule
\end{tabular}
\end{document}