Are side effects everything that cannot be found in a pure function?

Question

Is it safe to say that the following dichotomy holds:

Each given function is

• either pure
• or has side effects

If so, side effects (of a function) are anything that can't be found in a pure function.

Answer 1

This very much depends on the definitions that you choose. It is definitely fair to say that a function is pure or impure. A pure function always returns the same result and does not modify the environment. An impure function can return different results when it is executed repeatedly (which can be caused by doing something to the environment).

Are all impurities side-effects? I would not say so - a function can depend on something in the environment in which it executes. This could be reading some configuration, GPS location or reading data from the internet. These are not really "side-effects" because it does not do anything to the world.

I think there are two different kinds of impurities:

• Output impurity is when a function does something to the world. In Haskell, this is modelled using monads - an impure function a -> b is actually a function a -> M b where M captures the other things that it does to the world.

• Input impurity is when a function requires something from the environment. An impure function a -> b can be modelled as a function C a -> b where the type C captures other things from the environment that the function may access.

Monads and output impurities are certainly better known, but I think input impurities are equally important. I wrote my PhD thesis about input impurities which I call coeffects, so I this might be a biased answer though.

Answer 2

For a function to be pure it must:

1. not be affected by side-effects (i.e. always return same value for same arguments)
2. not cause side-effects

But, you see, this defines functional purity with the property or absence of side-effects. You are trying to apply backwards logic to deduct the definition of side-effects using pure functions, which logically should work, but practically the definition of a side-effect has nothing to do with functional purity.