The standard criterion for distinguishing purely functional languages from others is that no operation may have any side effect, and that all functions maintain referential integrity, that is, that any function always return the same result when called with the same parameters.

To my knowledge so far, Haskell is indeed purely functional, but I'm not sure about these monads.

An example for an absolutely purely functional language by the above criteria would be Clean.

Makeshifts last the longest.