Custom argument specification: Defaults of '\Foo' have circular dependency

Question

I have a command, \Baz, that takes one optional argument which must be inline code. It relies on an external variable to store the default inline code (1). As standalone it works, but it does not meet the requirement of the project I am developing (2). That's where \Foo and a meta command to define it (3), enter the picture. Problem: when I try to define \Foo, I get the error: Defaults of '\Foo' have circular dependency.

Side notes: (1) The reason for keeping the default outside is to be able to modify \Baz that way. (2) Serialize calls to \Baz: information about the default is lost. (3) The tentative solution is borrowed from that of a post asking to create a lambda function.

\documentclass{report}
\usepackage{xparse}

\ExplSyntaxOn

\cs_set:Npn \__erw_baz_default:n #1{Hello, #1!}
\cs_set:Npn \__erw_baz_set:n #1
{
  \cs_gset:Npn \__erw_baz:n ##1 {#1}
}
\DeclareDocumentCommand{\Baz}
{O{\__erw_baz_default:n{##1}}}
{
  \__erw_baz_set:n {#1}
  \__erw_baz:n{world}
}

\cs_set:Npn \__erw_foo_set:n #1
{
  \cs_gset:Npn \__erw_foo:n ##1 {#1}
}
\cs_new_protected:Npn \__erw_make_Foo:n
#1 
{
  \use:x
  {
    \exp_not:n{\DeclareDocumentCommand{\Foo}}
    {O{#1}}
  }
  {
    \__erw_foo_set:n{##1}
    \__erw_foo:n{world}
  }

}
\__erw_make_Foo:n{Hello, ##1!}

\NewDocumentCommand{\Test}
{}
{

  \noindent
  \Baz[Jello,~##1!]\\
  \Baz\\

  \Foo[Jello,~##1!]\\

  %\Foo
  % Expected:     % Hello, world!
  % Actual:       % LaTeX3 Error: Defaults of '\Foo' have circular dependency

}

\ExplSyntaxOff


\begin{document}

\Test

\end{document}

Answer 1

The TeX-equivalent for “Have you tried turning it off and on again?” is “have you tried doubling or halving the hashes?”

---

When \__erw_make_Foo:n {Hello, ##1!} expands and the argument is consumed, the hashes are halved when TeX replaces the parameters of \__erw_make_Foo:n into its definition, so you have:

\DeclareDocumentCommand \Foo { O{Hello, #1!} }
  {
    \__erw_foo_set:n {#1}
    \__erw_foo:n { world }
  }

which as xparse advertises is a circular definition. If the optional argument is not given, then the default value of #1 depends on the value of #1, which depends on the value of #1, which depends...

If you double the hashes when calling \__erw_make_Foo:n then you get:

\DeclareDocumentCommand \Foo { O{Hello, ##1!} }
  {
    \__erw_foo_set:n {#1}
    \__erw_foo:n { world }
  }

which in turn inserts a parameter #1 when you use \__erw_foo_set:n.

---

A few nicpicks on your expl3:

• Macros which are not supposed to be expandable (for instance, if they perform an assignment) must be defined with protected, so \cs_new_protected:Npn instead of \cs_new:Npn. The version without protected is strictly for expandable (by design) macros;

• Avoid \cs_set(_protected):Npn unless you really need that. One of the advantages of (properly used) expl3 is that you avoid the name clashes with other packages and accidental overwriting of macros. If you use \cs_set:Npn you are walking over that. Use \cs_new(_protected):Npn;

• \exp_args:NNx \DeclareDocumentCommand \Foo { O{#1} } is a bit easier than \use:x { \exp_not:n { \DeclareDocumentCommand \Foo } { O{#1} } };

• Indent the code :-)

Here's the code:

\documentclass{report}
\usepackage{xparse}
\ExplSyntaxOn
\cs_new:Npn \__erw_baz_default:n #1 { Hello,~#1! }
\cs_new_protected:Npn \__erw_baz_set:n #1
  { \cs_gset:Npn \__erw_baz:n ##1 {#1} }
\NewDocumentCommand \Baz { O{ \__erw_baz_default:n {##1} } }
  {
    \__erw_baz_set:n {#1}
    \__erw_baz:n { world }
  }

\cs_new_protected:Npn \__erw_foo_set:n #1
  { \cs_gset:Npn \__erw_foo:n ##1 {#1} }
\cs_new_protected:Npn \__erw_make_Foo:n #1
  {
    \exp_args:NNx \DeclareDocumentCommand \Foo { O{#1} }
      {
        \__erw_foo_set:n {##1}
        \__erw_foo:n { world }
      }
  }
\NewDocumentCommand \Test { }
  {
    \noindent
    \Baz[Jello,~##1!]\\
    \Baz\\
    \Foo[Jello,~##1!]\\
    \Foo
  }

\__erw_make_Foo:n {Hello, ####1!}
\ExplSyntaxOff
\begin{document}
\Test
\end{document}