Thank you for clarifying. I was familiar with the notation A^B for the set of all f: A -> B, but this seemed like something more (and it does appear to be).
I'm not sure if the notation you'd encountered differed, but in this case the equivalence is between A^B and B -> A (note the order).
Interestingly, every identity you learned in grade school algebra which involved only addition, multiplication, and exponentiation holds here as an isomorphism. It can be a fun exercise to write the functions that take you back and forth. For instance:
A^(B+C) = A^B * A^C
to: (Either b c -> a) -> (b -> a, c -> a)
to f = (f . Left, f . Right)
fro: (b -> a, c -> a) -> (Either b c -> a)
fro (f, g) = \case
Left b -> f b
Right c -> g c
Interestingly, every identity you learned in grade school algebra which involved only addition, multiplication, and exponentiation holds here as an isomorphism. It can be a fun exercise to write the functions that take you back and forth. For instance: