Notation for a placeholder function that maps to other functions I'm trying to write a very general equation to calculate some $Value$ which relies on a context-dependent function $g$.
How do I concisely communicate that $g$ maps to different functions under different  contexts?
So far I have:
\begin{gather}
&\text{Value (a, b, c)} = {g(a,b)} + 10\\
\
\text{where:}&\\
g \mapsto\\
& A(i,j) = \begin{cases}
 1 ,& \text{if some condition}\\
 0 ,& \text{otherwise}
  \end{cases}\\
\nonumber\
& B(i,j) = \begin{cases}
 1 ,& \text{if some condition}\\
 0 ,& \text{otherwise}
  \end{cases}\\
\nonumber
& C(i,j) = \begin{cases}
 1 ,& \text{if some condition}\\
 0 ,& \text{otherwise}
  \end{cases}\\
\nonumber
\end{gather}

The  Iverson    brackets   could be useful    in this   case. Let $P$ be a proposition. We write
\begin{align*}
[[P]]=
\begin{cases}
1&\qquad  \text{if $P$ is true}\\
0&\qquad \text{if $P$ is false}
\end{cases}
\end{align*}

This way we can write
  \begin{align*}
g(a,b)=A(a,b)[[X(a,b)]]+B(a,b)[[Y(a,b)]]+C(a,b)[[Z(a,b)]]
\end{align*}

