Composing macros

Question

I have a macro \lip defined with xparse which takes several arguments.

I would like to define some macro \slip which applies macro \eset after macro \lip.

Is there a way to define \slip without defining a new macro with as many arguments as \lip and passing them to this latter command?

\documentclass{article}

\usepackage{xparse}

\newcommand{\eset}[1]{\mathchoice{\left \{#1\right \}}{\{#1\}}{\{#1\}}{\{#1\}}}

\ExplSyntaxOn
\NewDocumentCommand \lip { D||{A} m D||{B} m } {
  #1^#2, #3^#4
}
\ExplSyntaxOff


% How can I define slip without the xparse boilerplate?
\ExplSyntaxOn
\NewDocumentCommand \slip {D||{A} m D||{B} m } {
  \eset{\lip |#1| {#2} |#3| {#4}}
}
\ExplSyntaxOff

\begin{document}

\[\lip |a| {1} |b| {2}\]

\[\slip |a| {1} |b| {2}\]

\end{document}

Answer 1

Apart from the doubts about \eset (it's wrong to begin with, in my opinion), you can incorporate it in \lip:

\documentclass{article}

\usepackage{xparse}

\newcommand{\eset}[1]{\mathchoice{\left \{#1\right \}}{\{#1\}}{\{#1\}}{\{#1\}}}

\ExplSyntaxOn
\NewDocumentCommand \lip {s D||{A} m D||{B} m }
 {
  \IfBooleanTF{#1}
   { \eset{#2^#3, #4^#5} }
   { #2^#3, #4^#5 }
 }
\NewDocumentCommand \slip {} { \lip* }
\ExplSyntaxOff

\begin{document}

\[\lip |a| {1} |b| {2}\]

\[\slip |a| {1} |b| {2}\]

\end{document}

Avoid using a wealth of optional arguments: you'll lose yourself in trying to remember them.

In this particular case I see no connection between the syntax and the output, so a simpler

\NewDocumentCommand \lip {s O{A} m O{B} m }
 {
  \IfBooleanTF{#1}
   { \eset{#2^#3, #4^#5} }
   { #2^#3, #4^#5 }
 }

with calls \lip{x}{y}, \lip[u]{x}{y}, \lip{x}[v]{y} or \lip[u]{x}[v]{y} would do better.

Why is the definition of \eset wrong? Because it's generally wrong to apply \left and \right indiscriminately.

If you want to accommodate other variants, you can use a slightly different strategy:

\documentclass{article}

\usepackage{xparse}

\newcommand{\eset}[1]{\mathchoice{\left \{#1\right \}}{\{#1\}}{\{#1\}}{\{#1\}}}
\newcommand{\bset}[1]{[#1]}

\ExplSyntaxOn
\NewDocumentCommand \lip {o D||{A} m D||{B} m }
 {
  \IfNoValueTF{#1}
   { #2^#3, #4^#5 }
   { #1{#2^#3, #4^#5} }
 }
\NewDocumentCommand \slip {} { \lip[\eset] }
\NewDocumentCommand \blip {} { \lip[\bset] }
\ExplSyntaxOff

\begin{document}

\[\lip |a| {1} |b| {2}\]

\[\slip |a| {1} |b| {2}\]

\[\blip |a| {1} |b| {2}\]

\end{document}