Convert token to string in LaTeX3

Further thinking along with @egreg's comments have led me to do things in a slightly different way and use an inline map. It's not quite as compact as I might have hoped to achieve with \str_if_in:nnTF, but at least it doesn't involve nested boolean checks.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\bool_new:N \l__dcp_punct_found_bool
\cs_new_protected:Nn \__dcp_test_punct:
  {
    \bool_set_false:N \l__dcp_punct_found_bool
    \str_map_inline:nn { .,:;!? }
      {
        \token_if_eq_meaning:NNT \l_peek_token ##1
          {
            ~Punctuation~found:~
            \bool_set_true:N \l__dcp_punct_found_bool
            \str_map_break:
          }
      }
    \bool_if:NF \l__dcp_punct_found_bool
      { ~Punctuation~not~found~ }
  }
\cs_new_protected:Nn \__dcp_test_punct:n
  {
    \peek_after:Nw \__dcp_test_punct:
  }
\DeclareDocumentCommand {\testpunct} { +m }
  {
    \__dcp_test_punct:n {#1}
  }
\ExplSyntaxOff
\begin{document}
\testpunct{A}.

\testpunct{A},

\testpunct{A}:

\testpunct{A};

\testpunct{A}!

\testpunct{A}?

\testpunct{A}
\end{document}