In the last episode on algebraic data types we started to get a glimpse of what it means to see algebraic structure in the Swift type system. We saw that forming structs corresponds to a kind of multiplication of the types inside the struct. Then we saw that forming enums corresponded to a kind of summation of all the types on the inside. And finally we used this intuition to figure how to properly model a datatype so that impossible states are not representable, and enforced by the compiler.

In this episode we are we are going to look at the next piece of algebra that is not captured by just plain sums and products: exponentiation. We will see that it helps build our intuition for how function arrows act with respect to other constructions, and even allow us to understand what makes a function more or less complicated.