We can write a function $f:X\times Y\to Z$ as $\tilde f:X\to (Y\to Z)$. This is called “currying”.
We can also write an element of a power set $Y\in \mathcal P(X)$ as $Y:X\to \{0,1\}$. It’s somewhat similar to currying.
Is there a term for representing the element of a power set as a function like this? A verb, like “currrying”?