Question about macro parameter expansion

Question

This question is just for my own understanding of how expansion works.

I'm using the siunitx package in a document. In order to make sure that I'm consistant with myself, I try to write results of measurements as a macro so that I can change them globally from one place.

I noticed that adding a pair of braces {} to the end of one of these macros causes an error from siunitx. Have a look at the following MWE:

\documentclass{article}

\usepackage{siunitx}

\begin{document}

\newcommand{\aMeasurement}{0.9(1)}

% This works fine
The answer was \num{\aMeasurement}.

% This gives an error
The answer was \num{\aMeasurement{}}.

\end{document}

I thought that parameters to macros were fully expanded before the macro was run. If so, how can siunitx possibly tell any difference between these two calls?

Answer 1

Ignoring the specifics of siunitx there appear to be some misunderstandings about TeX's execution order.

Firstly macro parameters are not expanded before a macro call they are only expanded (if at all) if the parameter is met after the macro is expanded.

You can see this in

\def\foo#1{}


\foo{\somethingundefined}

\bye

\somethingundefined is not expanded before calling \foo (which would have generated an error) in fact as \foo does not use #1 the parameter is never expanded at all.

Secondly {} after a macro is not a parameter unless the macro is defined to take a parameter (the macro \aMeasurement in your question does not take a parameter)

After

\def\foo{hbox}


\foo

\foo{}

\foo and \foo{} are not at all equivalent, \foo expands to hbox and \foo{} expands to hbox{} these will take very different code paths for example

\csname\foo\endcsname

would execute the command \hbox but

\csname\foo{}\endcsname

would execute the command with name hbox{} (which being previously undefined would act like \relax)

Answer 2

You may have been misguided by the fact that when a parameterless macro has to be used in text, it should be followed by something that makes LaTeX to respect the space after it:

\LaTeX has macros

would print no space between the logo and “has”, whereas

\LaTeX{} has macros

prints correctly. However, this empty pair of braces is not swallowed as part of the macro expansion, because TeX knows \LaTeX has no argument, so it doesn't look for one.

It would be different if a macro is defined like

\newcommand{\foo}[1]{vim}

(where the argument is not used) and

\vim{} can't be escaped from

would indeed swallow the braces. For instance, \edef\VIM{\foo{}} would be equivalent to \def\VIM{vim}, because the braces disappear as part of argument substitution. On the other hand,

\vim\ can't be escaped from

would print with no space between “vim” and “can't”, because the argument is now “control space” and the macro throws its argument away.

Your input \num{\aMeasurement{}} is essentially equivalent to

\num{0.9(1){}}

and you receive the error message

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! siunitx error: "invalid-token-in-number"
! 
! Invalid token '\q_recursion_tail ' in numerical input.
! 
! See the siunitx documentation for further information.
! 
! For immediate help type H <return>.
!...............................................  

The invalid token that's referred to is the open brace {. If you scroll past the error, you'll see

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! siunitx error: "invalid-number"
! 
! Invalid numerical input '0.9(1){}'.
! 
! See the siunitx documentation for further information.
! 
! For immediate help type H <return>.
!...............................................  

that should be clear enough: \SIdoesn't like at all the tokens{}`.