Recursion - splitting a group.

Question

I've been trying to understand the notion of recursion in TeX - not easy given that my background is the high-level stuff in LaTeX. The only examples I can (just about) understand are very basic for-loop constructions, but I don't really feel like I have a picture for what expansion is or how it works.

I'd like to write a function that will take as its argument a group

{{#1}{#2}...{#n}}

where n can take any positive-integer value, and return the pair of groups

{#1}{{#2}...{#n}},

when n is at least 2, and {#1} otherwise.

This seems like it should be reasonably simple to do, but I don't know how I'd go about it.

edit: I want to use this function in beamer to progressively overlay lines inside AMSMath environments such that

• Vertical spacing is preserved;
• Equation numbering (where applicable) appears in-time with the displayed lines of the equation array, and is preserved (i.e. not incremented) between overlays.

Answer 1

\catcode`@=11
\def\splitarg#1{\@splitarg#1\@nil}
\def\@splitarg#1#2\@nil{{#1}\if\relax\detokenize{#2}\relax\else{#2}\fi}
\catcode`@=12

\edef\x{\splitarg{{a}{b}{c}}}\show\x
\edef\x{\splitarg{{a}}}\show\x

Requires e-TeX, so you must process the example with pdftex, xetex, or luatex (not Knuth's tex). The test \if\relax\detokenize{#2}\relax is true when #2 is empty (that is, when there is only one element in the list you pass to \splitarg) and e-TeX finds nothing in the "true" part; otherwise e-TeX braces what remains in the original list.