Problem of understanding definitions

Question

I have defined a stack structure (I found an example in the LaTeX currfile package, which I adapted to my needs):

\def\MB@modulestack{}
\def\MB@modulestack@push#1{\xdef\MB@modulestack{{#1}\MB@modulestack}}
\def\MB@modulestack@top{\expandafter\MB@modulestack@top@eat\MB@modulestack\relax\relax}
\def\MB@modulestack@top@eat#1#2\relax{#1}
\def\MB@modulestack@pop{\expandafter\MB@modulestack@pop@eat\MB@modulestack\relax\relax}
\def\MB@modulestack@pop@eat#1#2\relax{\gdef\MB@modulestack{#2}}

I understand how it works, especially those \relax. I keep a 4-tuple of parameters there:

\def\MB@modulestack@push{{a}{b}{c}{d}}
\def\MB@modulestack@push{{1}{2}{3}{4}}

Now, to parse such a 4-tuple from the top of stack I wanted to use the following code:

\def\MB@modulestack@topitemparse@eat#1#2#3#4{... here I use #1, #2, #3, #4 ...}
\def\MB@modulestack@topitemparse{
  \expandafter\MB@modulestack@topitemparse@eat\MB@modulestack@top
}

...but it didn't work. While experimenting I found that I had to do this another way:

\def\MB@modulestack@topitemparse@eat#1#2#3#4#5\relax{... here I use  #1, #2, #3, #4 ...}
\def\MB@modulestack@topitemparse{
  \edef\MB@modulestack@topitem{\MB@modulestack@top}
  \expandafter\MB@modulestack@topitemparse@eat\MB@modulestack@topitem\relax\relax
}

Why does the first doesn't work and the second does? Why do I need to get #5 and \relax in the @eat macro? Why do I need to read the top of stack into variable, instead of passing it straight to the @eat macro?

Answer 1

This is the classic difference between a macro expansion language and an function-based system. When you do

\def\MB@modulestack@topitemparse{
  \expandafter\MB@modulestack@topitemparse@eat\MB@modulestack@top
}

you expand \MB@modulestack@top exactly once, which leaves TeX reading

\MB@modulestack@topitemparse@eat\expandafter\MB@modulestack@top@eat
  \MB@modulestack\relax\relax

which does not do what you want. You could work out the exact number of expansions needed to get this to work; in this case, you'd need:

\def\MB@modulestack@topitemparse{
  \expandafter\expandafter\expandafter
    \expandafter\expandafter\expandafter
    \expandafter\MB@modulestack@topitemparse@eat\MB@modulestack@top
}

which will expand everything as you want. However, this is clearly awkward, which is where \edef comes in as it always fully-expands stuff. The only danger is that the result of

\edef\MB@modulestack@topitem{\MB@modulestack@top}

might not be what you expect if the stack items are themselves expandable.

Answer 2

Joseph already explained why and how it works. Here an alternative way to do this without using \expandafter to much:

Instead of using the @top macro as part of an argument, you can define it to "call" the parse macro with the top of the stack:

\def\MB@modulestack@top{\expandafter\MB@modulestack@top@call\MB@modulestack\relax}
\def\MB@modulestack@top@call#1#2\relax#3{#3#1}% here #1 are the four {.}{.}{.}{.} pushed on the stack

The parse macro simple receives the four arguments:

\def\MB@modulestack@topitemparse#1#2#3#4{%
  % do what you want with the four arguments
}

Usage:

\MB@modulestack@top\MB@modulestack@topitempars

The \MB@modulestack@topitempars could also be hardcoded into \MB@modulestack@top@call.