Create an environment/counter named with a given macro

Question

I'm trying to create an environment with a given macro as name:

\newcommand{\newproblemset}[1]{\newenvironment{#1}{}}
\newproblemset{problem}

However, the compiler gives the following error, though I don't define \problem directly:

LaTeX Error: Command \problem already defined.

The purpose is that I want to create a command, that supports creating an environment with a user-specified environment name.

Another issue arises when I want to define a counter with user-specified name. Although I managed to create the counter successfully, I don't how to refer to that counter, since the counter name should be in the form of \the followed by the counter name.

It seems the issue lies in the way how LaTeX does macro expansion. In fact, what I want to do is exactly what \newtheorm does, which creates an environment with user-given names.

Update: a full example

\documentclass{article}

\newcommand{\newproblemset}[1]{\newenvironment{#1}{c1}{c2}}
\newproblemset{aa}

\begin{document}

    \begin{aa}
        content
    \end{aa}

\end{document}

Compiler's error:

root.tex
LaTeX Error: Command \aa already defined.

For defining a counter:

\documentclass{article}

\newcommand{\newproblemset}[1]{\newcounter{#1}[section]\renewenvironment{#1}{c1 \refstepcounter{#1} \the#1 }{c2}}
\newproblemset{aa}

\begin{document}

    \begin{aa}
        aa
    \end{aa}

\end{document}

It gives an error:

root.tex (line 8)
You can't use `the letter a' after \the. (  \begin{aa} ...)

Answer 1

In your specific example, defining a new environment like aa won't work since the environment aa is defined by \aa and \endaa, and the former (\aa) is already defined by default as Angstrom.

You could create \newproblemset to completely ignore whether a command is already defined using the following definition:

\newcommand{\newproblemset}[1]{%
  \expandafter\let\csname #1\endcsname\relax% Remove definition of \<#1>
  \newenvironment{#1}{c1}{c2}}% Define new environment

The above definition sets \<#1> to \relax - one of the conditions used to check whether something already exists or not. Of course, you can go that one step further and issue a warning if the command already exists (but define the environment anyway):

\documentclass{article}

\makeatletter
\newcommand{\newproblemset}[1]{%
  \ifcsname #1\endcsname
    \@latex@warning{Environment `#1' will overwrite `\expandafter\string\csname #1\endcsname'.}%
    \expandafter\let\csname #1\endcsname\relax % Make sure \<#1> is available for (re)definition
  \fi
  \newenvironment{#1}{c1}{c2}}% Define new environment
\makeatother

\newproblemset{aa}

\begin{document}

\begin{aa}
content
\end{aa}

\end{document}

This outputs

LaTeX Warning: Environment aa' will overwrite\aa'. on input line 11.

in the .log.

For printing the counter, instead of \the#1, you need \csname the#1\endcsname to properly constructing something that resembles \the#1:

\documentclass{article}

\makeatletter
\newcommand{\newproblemset}[1]{%
  \ifcsname #1\endcsname
    \@latex@warning{Environment `#1' will overwrite `\expandafter\string\csname #1\endcsname'.}%
    \expandafter\let\csname #1\endcsname\relax % Make sure \<#1> is available for (re)definition
  \fi
  \newcounter{#1}[section]% Define a new counter
  \newenvironment{#1}{c1 \refstepcounter{#1}\csname the#1\endcsname}{c2}}
\makeatother

\newproblemset{aa}

\begin{document}

\begin{aa}
aa
\end{aa}

\end{document}

Answer 2

\newcommand{\newproblemset}[1]{\newenvironment{#1}{}}

is missing the third argument to \newenvironment which isn't necessarily an error if you provide the argument when calling \newproblemset (although odd that you just supply the end code not the start code).

This runs without error and produces

\documentclass{article}

    \newcommand{\newproblemset}[1]{\newenvironment{#1}{}}

\begin{document}

\newproblemset{zz}{end code}

\begin{zz}
  abc
\end{zz}
\end{document}

It also runs without error with your suggested name problem

\documentclass{article}

    \newcommand{\newproblemset}[1]{\newenvironment{#1}{}}

\begin{document}

\newproblemset{problem}{end code}

\begin{problem}
  abc
\end{problem}
\end{document}

If you get the error shown then you have previously already defined a problem environment or (equivalently) a \problem command, in which case you will need \renewenvironment not \newenvironment.