Earlier quoted context omitted.
A first-order function type is already exponential. A sum type has as many possible values as the sum of its cases. E.g. `A of bool | B of bool` has 2+2=4 values. Similarly for product types and exponential types. E.g. the type bool -> bool has 2^2=4 values (id, not, const true, const false) if you don't think about side effects.
> bool -> bool has 2^2=4 values Not the best example since 2*2=4 also. How about this bit of Haskell: f :: Bool -> Maybe Bool That's 3 ^ 2 = 9, right? f False = Nothing f False = Just True f False = Just False f True = Nothing f True = Just True f True = Just False Those are 6. What would be the other 3? or should it actually be a*b=6? EDIT: Nevermind, I counted wrong. Here are the 9: f x = case x of True -> Nothing…
EDIT: now you see why I used the smallest type possible to make my point. Exponentials get big FAST (duh).