I explained it like this elsewhere: The functional programming paradigm models computation as a relation between sets, and is thus inherently declarative. Howe

I explained it like this elsewhere: The functional programming paradigm models computation as a relation between sets, and is thus inherently declarative. However, in practice, we often think of functions as imperative, ie you put in an input value and get out an output value, same as with a procedure. From this point of view, the characteristic property of a function is that it has no side-effects. Because of ambiguity of the terms, we call such a function pure, and a language which only has pure functions would be a purely functional language. However, not all functional languages are pure: A functional language is a language with syntax and semantics which allows the programmer to use the functional paradigm efficiently. Some of the concepts which make using the paradigm feasible include - among others - lambda expressions with lexical closure, higher-order functions, variant types and pattern matching, lazy evaluation, type-inference (in case of statically-typed languages). This is by no means an authorative list, and a language can very well be functional without providing all or even most of them, but if a language does - ie makes them usable without having to jump through major hoops - their presence is a strong indicator that the language should be considered functional.