\newcommand{\sum}{2 + 3}
\sum

\renewcommand{\sum}[1]{2 #1 3}
\sum{*}

\renewcommand{\sum}[1][+]{2 #1 3}
\sum
\sum[*]

\renewcommand{\sum}[2][+]{2 #1 3 #2 4}
\sum{+}
\sum[*]{+}


\newenvironment{myHeartEnv}
  {\color{purple}{\heartsuit}\kern-2.5pt\color{green}{\heartsuit}}
  {\text{ forever}}

\begin{myHeartEnv}
\end{myHeartEnv}

\begin{myHeartEnv}
  2+3
\end{myHeartEnv}


\newenvironment{proof}
{\textbf{Proof:}}
{\begin{align} \blacksquare \end{align}}
\begin{proof}a=b\end{proof}

\newenvironment{proof}
{\begin{align}\textbf{Proof:}}
{\end{align}}
\begin{proof}a=b\end{proof}

\newenvironment{proof}
{\begin{align}\textbf{Proof:}&}
{ \begin{split} 5 \end{split}&& \blacksquare\end{align}}
\begin{proof}a&=b\end{proof}


\newenvironment{argument}[1][a]{\textbf{Argument #1:}}{aa}
\begin{argument}[c]b\end{argument}

\renewenvironment{argument}[2][a]{\textbf{Argument #1(#2):}}{aa}
\begin{argument}[c]{3}b\end{argument}

\def\bar{h}
\let\fooi\bar
\def\fooii{\bar}
\fooi +\fooii
\def\bar{g}
\fooi +\fooii

\def\foo{a + b}
\foo
\def\foo#1{a #1 b}
\foo{-}
\def\foo#1#2{#2 #1 b}
\foo{-}{x}

\let\b\lvert
\let\lvert\langle
\vert
\b
\lvert
\left\b q \right\lvert


\let\be={

  \be a}

\let\be={

  \be a}

\let\car^

a\car b

\let\lb=\{
\lb \frac{1}{2} \}
\left\lb \frac{1}{2} \right\}

\let\lb(
\lb \frac{1}{2})
\left\lb \frac{1}{2} \right)


\let\al\alpha
\al\alpha
\let\al\aleph
\al\alpha

\let\al\alpha
\al\alpha
\let\alpha\beta
\al\alpha


----------- TODO  ------------------

\def\bar[#1]#2{#1 + #2}
\bar[a]{b}
\let\foo\bar
\foo[c]{d}

\newcommand{\bar}[2][1]{#1 + #2}
\bar[a]{b}
\let\foo\bar
\foo[c]{d}


// Recognise if it is a newly created command (or created with let).

\let\kk\alpha
\kk
\let\rr\beta
\rr
\let\rr\kk
\let\kk\beta
\kk\rr

// The following do not work as expected in MJ2.

\let\ll\sin
\ll(x)
\let\rr\ll
\let\ll\cos
\rr(x)
\ll(x)

\let\save\sin
\let\sin\cos
\let\cos\tan
\let\tan\save
\sin(x)\cos(x)\tan(x)


// Delimiters:
\let\lp(
\let\rp)
\let\mp\rp
\left\lp \frac{a}{b}\middle\mp c \right\rp

\let\lp\langle
\let\rp\rangle
\let\mp\rp
\left\lp \frac{a}{b}\middle\mp c \right\rp


\let\a a
\let\b b
\a \b
\let\c\a
\let\a c
\c \a
\let\d=\c
\let\c \b
\d \c


// Macros of macros:
\let\sqrt\choose a\sqrt b

// Why does that not work?
\newenvironment{proof}{\textbf{Proof:}}{}
\begin{proof}a=b\end{proof}
\renewenvironment{proof}{\begin{align}\textbf{Proof:}&}{ \begin{split} 5 \end{split}&& \blacksquare\end{align}}\begin{proof}a&=b\end{proof}
\newenvironment{proof}{\textbf{Nix:}}{}
\begin{proof}a=b\end{proof}
\renewenvironment{proof}{\begin{equation}\textbf{Proof:}}{ 5 \blacksquare\end{equation}}\begin{proof}a=b\end{proof}