Primary effect - An effect on the input arguments, who's effect is captured in the output.

Side effect - An effect on state that was not passed in as input arguments, who's effect may or may not be captured on the output.

Side effect free - Also known as pure, means the function only has a primary effect. Thus it only effects the input in a way that the output captures.

Idempotent - Applying a function to itself results in the same effects. Applies to both primary and side effects.

Where things get weird, is that there's also the following:

- An effect on implicit input state, which did not come from input arguments, who's effect is captured on the output. This would be like a HTTP GET. Or any query on a DB where the DB is an implicit input.

- An effect who's effect is captured on implicit output state, either by having its effect captured on an input (like a modification to a pointed object), or captured on output not returned by the function (like print to screen). This would be like a HTTP POST.

And now if you look at all these, there's an easy permutations of them. So you can build a table like so:

  Input | Output | Idempotent
  Arguments | Return Value | Yes
  Arguments | Return Value | No
  Arguments | Outside State | Yes
  Arguments | Outside State | No
  Arguments | Arguments | Yes
  Arguments | Arguments | No
  Outside State | Return Value | Yes
  Outside State | Return Value | No
  Outside State | Arguments | Yes
  Outside State | Arguments | No
  Outside State | Outside State | Yes
  Outside State | Outside State | No

All these combinations are possible. That's why it can be really tricky.