no program can be purely functional

Pure functional programming means building up a machine. This machine will eventually be executed by the runtime system (at which point IO will happen) but from the programmer's perspective a program can still be purely functional.

By this I mean that a function that takes an Int and outputs an Int will have type `Int -> Int`, and a function that takes an Int, does logging, and outputs an Int will have type `Int -> IO Int`. Both are purely functional -- they're pure transformations from an Int to some other thing. For the first function that other thing is another Int, for the second that other thing is an action that can be performed by the machine which will return an Int.

So from the perspective that matters to us a developers programs can be purely functional.

(This becomes even more useful with something like PureScript's granular effect tracking https://github.com/purescript/purescript/wiki/Differences-fr...)