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The wikipedia article [1] is a decent introduction. Functional programming is loosely-defined as a style of programming that involves using some subset of:

* Higher-order functions

* Pure functions / referential transparency

* Immutability

* A powerful type system

* A declarative style (expression-based)

(Some of the above concepts are closely related, and some people may feel there are other important ones I left out)

A functional programming language is loosely-defined as a language which makes programming in the above style possible, feasible, or easy.

[1] http://en.wikipedia.org/wiki/Functional_programming



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