Functional programming

A functional programming language is a language modeled after mathematical functions. Non-functional computer programs allow state changes.

First class data types

Functional programs typically make functions first class data types. This allows functions to be passes as arguments to other functions and allows for the creation of higher order functions(functions of functions).

Input/Output

In functional programming state is not saved outside of function calls due to restrictions on io(input:output calls). State may not change during a function call. Restricting i/o protects agaist side effects(bad distant changes(i/o) caused by local computation).

Single assignment and proofs

Single assignment makes a computation into a dataflow. Dataflows are easy for compilers to understand. When state is fixed, functions can be treated similar to mathematical functions and facts can be proved about such functions. Some functional programs can be proved to be equal to each other or proved to be stable under certain conditions. Such proofs can aid the efforts of software engineers and computer scientists. See (Hutton, 1999) for an example.

Ref 1: Graham Hutton, 1999, [1]

      A tutorial on the universality and expressiveness of fold
      J. Functional Programming 9 (4): 355–372, July 1999,     
      Cambridge University Press.

Some examples of functional programming languages are:

scheme, 
erlang, (excluding all parallel functions)
haskel.

If a functional language is eager then all values are fully computed in the order that they are encountered. In a lazy language like haskel some arguments are allowed to have delayed evaluation.