Hello,

I would like to know how to currify a partial mapping $A \times B \to_p C$?

Here, by "partial mapping from $X$ to $Y$", I mean a function from a subset of $X$ to $Y$, as explained here Partial Function.

It is known that $(A \times B) \to C$ is isomorphic to $A \to B \to C$. The isomorphism is known as "currying".

My question is about the relation between $A \times B \to_p C$ and $A \to_p B \to_p C$, where ${\to_p}$ denotes a partial function. Apparently, they are not isomorphic. But I would like to know how we can currify $A \times B \to_p C$?

Thanks.

Edit: My question was really, can we say that $A \to_p (B \to C) )$ is isomorphic to $A \times B \to_p C$? (I think no.) Which set would then be isomorphic to $(A \to_p (B \to C))$ (except itself)?