Exception Type

Consider a simple deterministic function such as division that takes in two numbers and returns the result by dividing one over the other:

const division = (a: number, b: number): number => {
  return a / b
}

The function division is defined over a limited set of values for b. Passing b as 0 will return Infinity which is not a number thus producing an anomaly in the program at runtime.

Partial Functions

In functional programming, such functions that are not defined over the complete range of input values, are called as partial functions.

Total Functions

Functions that are defined over the complete range of input values are called as total functions.

Enriching Return Type

Using QIO we can represent the function more clearly:

class DivisionByZero extends Error {}

const division = (a: number, b: number): QIO<number, DivisionByZero> => {
  return b === 0 ? QIO.reject(new DivisionByZero()) : QIO.resolve(a / b)
}

QIO<number, DivisionByZero> is a much better representation than just number, because it clearly represents how it can succeed and how it can fail.