Notation for a placeholder function that maps to other functions

Question

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}

Answer 1

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*}