Total functions

A function is said to be total if it’s defined for it’s entire domain. That is, A => B is total if there is a B for every possible A.

A function that is not total is said to be partial.

For example, in the following code:

def int2str(i: Int): String = i.toString

def str2int(s: String): Int = Integer.parseInt(s)

• int2str is total because there exists no Int for which it’s not defined.
• str2int is partial because there exists many Strings for which it isn’t defined.