How to deal with empty values in command arguments

Question

In this MWE, a command argument is directly passed to an environment. That works fine with empty values:

\documentclass{article}

\newcommand{\minipag}[1]{%
    \begin{minipage}[b][#1][b]{6em}
    One minipage
    \end{minipage}
    }
    
\begin{document}

\minipag{2em}
\minipag{\relax}
\minipag{}

\end{document}

However, when the argument is passed using a macro, and it takes an empty value, it is not recognized by the (minipage) environment:

\documentclass{article}

\newcommand{\minipag}[1]{%
    \def\upto{#1}
    \begin{minipage}[b][\upto][b]{6em}
    One minipage
    \end{minipage}
    }
    
\begin{document}

\minipag{2em}
\minipag{\relax}
\minipag{}

\end{document}

Why does it happens? What is the way to do this?

For me, the underlying question is what are string arguments really: macros, lists of tokens, general text, registers...

Answer 1

There is no general feature here you are just seeing a lack of error checking in minipage.

In

\begin{minipage}[b][...][b]{6em}

The ... is a length so an empty argument is a syntax error. Unfortunately minipage (as space was tight in 1993 when this argument was added) does not do any real error checking and the empty argument sneaks through then finally ends up at

\ifx \relax #2\else \setlength \@tempdimb {#2}

so the \ifx test is a (overly simple) test to see if that argument was used; and when #2 is empty it does not test #2 against \relax but rather tests \relax against \else which is a nonsense test which just luckily makes it avoid the setlength with an empty length, so avoids an error.

When #2 is (any) commandname other than \relax then the intended test happens, the test is false so the length is set to the expansion of #2 which in this case is empty, so you get an error, the same as for

\setlegth\@tempdima{}