Learning Functional Programming in Go

Isomorphic equations

We have learned the following isomorphic equations:

• (C,A) x (C,B) = (C, AxB)
• (A,C) x (C,B) = (A+B, C)
• (C x A,B) = (C, [A⇒B])

In first equation, what does it mean to have an arrow from C to AxB?

A: We have a pair of arrows, an arrow from C to A and an arrow from C to B.

Similarly for 2 and 3.

If C is a finite set with exactly C objects in it, and A is a finite set with exactly A things in it, then how many ways are there to get from C to A?

Answer: There are A X C different ways of getting from C to A

How many functions are there from n variables onto 2?

Answer: 2ⁿ

Do you see the direct correspondence between the categorical isomorphic equations and the laws of exponents we learned in high school?