How to use an environment whose name comes from a reference?

Question

Suppose somewhere in my long Ph.D. thesis I use a theorem-like environment (maybe it's a theorem, maybe it's a lemma, etc.), and label it. At another place I want to have an environment which is the same as that earlier one (not with the same number though). I can get the environment's name with cleveref's \namecref - but I can't just use it:

\documentclass{article}
\usepackage{ntheorem}
\usepackage{cleveref}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
\label{myfirst}
This is the first theorem.
\end{theorem}
\begin{\namecref{myfirst}}
This is another environment of the same kind as \ref{myfirst}!.
\end{\namecref{myfirst}}
\end{document}

trying to \def or \edef something to the \namecref doesn't work either. What can I do? Of course, the environment cannot be known on the first run, so I would obviously need a macro which would expand to some 'dummy environment' on the first run and the real environment on the second (\namecref should give ?? on the first run which is not useful.)

Note: This questions is a lead-up to the question Need a 'thin', flexible, theorem restatement environment.

Answer 1

One can use either cleveref or hyperref to get the "pure" name of the environment from the aux file. Unfortunately there are no documented ways on how to do it, so one has to use internal macros (which can change in future versions) in both cases.

First a solution for cleveref. It uses two internals from the cleveref package:

1. cleveref stores an additional label preceding with "cref@" to hold the environment name
2. cleveref offers an internal macro called \cref@gettype to get the "pure" environment name

\documentclass{article}
\usepackage{ntheorem}
\usepackage{cleveref}
\newtheorem{theorem}{Theorem}

\makeatletter
\newenvironment{xxxref}[1]{%
  \@ifundefined{r@cref@#1}%
    {\def\@xxx@env{quote}}% use default environment
    {\cref@gettype{#1}{\@xxx@env}}%
  \begin{\@xxx@env}}%
{\end{\@xxx@env}}%
\makeatother

\begin{document}
\begin{theorem}
\label{myfirst}
This is the first theorem.
\end{theorem}
\begin{xxxref}{myfirst}
\label{xxxfirst}
This is another environment of the same kind as \ref{myfirst}!.
\end{xxxref}
\begin{xxxref}{myfirst}
This is another environment of the same kind as \ref{xxxfirst}!.
\end{xxxref}
\end{document}

Second, a solution for hyperref. It uses two internals from the hyperref package:

1. hyperref stores the environment name inside the 4th argument of the label
2. The environment name is limited by a period inside that argument.

See also my answer here: Get label target type

\documentclass{article}
\usepackage{ntheorem}
\usepackage{hyperref}
\newtheorem{theorem}{Theorem}

\makeatletter
\newcommand*\@myautoref[2]{% \HyPsd@@@autoref from hyperref, modified
  \expandafter\expandafter\expandafter\@@myautoref
      \csname r@#2\endcsname{}{}{}{}\@nil#1\@nil
}
\def\@@myautoref#1#2#3#4#5\@nil#6\@nil{% \HyPsd@autorefname, modified
  #6#4.\@nil}% Argument #4 = type and number, e.g. "section.1" or "subsection.1.2"
\def\@myreftype#1.#2\@nil{#1}

\newcommand*\beginref{\xxx@ref{\begin}}
\def\endref{\xxx@ref{\end}}
\newcommand*\xxx@ref[2]{%
  \@ifundefined{r@#2}%
    {\def\@tempa{quote}}% use default environment
    {\def\@tempa{\@myautoref\@myreftype{#2}}}%
  \edef\@tempa{\noexpand#1{\@tempa}}%
  \@tempa}
\makeatother

\begin{document}
\begin{theorem}
\label{myfirst}
This is the first theorem.
\end{theorem}
\beginref{myfirst}
This is another environment of the same kind as \ref{myfirst}!.
\endref{myfirst}
\beginref{xxxfirst}
This is another environment of the same kind as \ref{xxxfirst}!.
\endref{xxxfirst}
\makeatother
\end{document}

Answer 2

The following is a hack, which is based on the existing cleveref implementation, which I'm not familiar with. It seems to work, but you may have to add a bit more robustness. (The solution is similar to one of Axel's solutions.)

\documentclass{article}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}

\usepackage{cleveref}
\makeatletter

\newenvironment{reformulation}[1]
    {\expandafter\ifx\csname r@cref@#1\endcsname\relax% label undefined
         \def\my@env{theorem}% if label is undefined, assume it's a theorem
     \else%
         \cref@gettype{#1}{\my@env}%
     \fi%
     \begin{\my@env}}%
    {\end{\my@env}}

\makeatother

\begin{document}
   \begin{lemma}\label{hi}
      Lemma.
   \end{lemma}
   \begin{reformulation}{hi}
      Theorem or lemma.
   \end{reformulation}
\end{document}