Functional Programming
Functional programming is a programming paradigm where programs are constructed
by applying and composing/chaining functions. Functional programming is
based on the mathematical definition of a
function f(), which
applies a transformation to some input data giving us some other data as a
result (i.e. a mapping from input x to output f(x)). Thus, a program written
in a functional style becomes a series of transformations on data which are
performed to produce a desired output. Each function (transformation) taken by
itself is simple and straightforward to understand; complexity is handled by
composing functions in various ways.
Often when we use the term function we are referring to a construct containing a block of code which performs a particular task and can be reused. We have already seen this in procedural programming - so how are functions in functional programming different? The key difference is that functional programming is focussed on what transformations are done to the data, rather than how these transformations are performed (i.e. a detailed sequence of steps which update the state of the code to reach a desired state).
In his introduction to functional programming in Advanced R, Hadley Wickham gives a good summary of the style:
It’s hard to describe exactly what a functional style is, but generally I think it means decomposing a big problem into smaller pieces, then solving each piece with a function or combination of functions. When using a functional style, you strive to decompose components of the problem into isolated functions that operate independently. Each function taken by itself is simple and straightforward to understand; complexity is handled by composing functions in various ways.
-- Hadley Wickham - Functional Style