Are these pairs equivalent?

Stream: new members

[Mr Proof]

If a have a type that takes in two values I could define it either as A->B->Type or (AxB)->Type
e.g. I have encountered this when thinking about defining vector spaces like R^2.
Is there advantages/disadvantages to each approach?
This is similar to the problem you have in programming APIs, where a function could take coordinates as separate parameters or a tuple and you end up having to make about 6 different functions to cover all cases.

[Marcus Rossel]

What you're describing is called currying. Here's a whole thread on its up- and downsides: https://softwareengineering.stackexchange.com/questions/185585/what-is-the-advantage-of-currying

[Mark Fischer]

They're isomorphic (Prod.forall). Which is better is often an aesthetic choice.

My rule of thumb is to prefer A → B → C over A × B → C since you can easily partially apply the first. If I'm temped to use A × B, then I tend to first consider creating a structure instead so that each projection has a nice name.