Meaning of double colon $::$ I've came across this expression regarding function composition in some notes by people from computer science, and I don't know what the notation "$::$" means.

\begin{equation}
g \circ f : A \rightarrow C :: a \mapsto g(f(a))
\end{equation}

I get what this expression is trying to tell me, but I am pretty disturbed by the fact that I don't know what "$::$" means exactly and how to read it. Can anyone tell me what is "$::$"?
It stands for "given by" or "defined by". The function $g \circ f$ is a function from $A$ to $C$ which maps $a$ to $g(f(a))$.