Functional programming

Functional programming is a style of programming which unlike imperative programming models computations as the evaluation of expressions. This article is meant to describe it briefly, however the best way to understand functional programming is to learn the basics of one of the functional programming languages (learn Haskell).

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What is functional programming?

Functional programming means that programs are executed by evaluating expressions. This contrasts with imperative programming where programs are composed of statements which change global state when executed. Functional programming, on the other hand, avoids using state and mutable data.

Functional programming requires that functions are first-class, which means that they are treated like any other values and can be passed as arguments to other functions or be returned as a result of a function. Being first-class also means that it is possible to define and manipulate functions nested in code blocks. Special attention needs to be given to nested functions, called closures, that reference local variables from their scope. If such a function escapes their block after being returned from it, the local variables must be retained in memory as they might be needed later when the function is called. Usually it is not possible to determine the moment of release statically which means that an automatic memory management technique has to be used.

Functional vs imperative languages

Many programming languages support programming in both functional and imperative styles, however each language has syntax and facilities that are optimised only for one of these styles. Often, code written in one particular style and not the other is executed efficiently by the implementations. In addition to that, coding conventions and libraries often force the programmer to use one of the styles. Therefore, programming languages are categorized into functional and imperative ones.

Following table shows which languages support functional programming (by supporting closures) and for which the functional style is the dominant one.

Language	Closures	Functional
C/C++	No	No
Pascal	No	No
Java	?	No
Python	Yes	No
Ruby	Yes	No
Ocaml	Yes	Yes
Haskell	Yes	Yes

Features of functional languages

Higher-order functions

Higher-order functions are functions that take other functions as their arguments. Basic example of a HOF is map which takes a function and a list as its arguments, applies the function to all elements of the list and returns a list of its results. For instance, we can write a function that subtracts 2 from all elements of a list without using loops or recursion:

subtractTwoFromList l = map (\x -> x - 2) l

We can generalize this function to subtract any given number:

subtractFromList l y = map (\x -> x - y) l

The function given to map then becomes a closure because \x -> x - y references a local variable (y) from the outside of its body.

Higher-order functions are very useful for refactoring the code and reduce the amount of repetitition. example needed

Add reference to functional objects?

Purity

Some functional languages allow expressions to yield actions in addition to return values. These actions are called side effects to stress out that the return value is the most important outcome of a function (as opposed to imperative programming). Languages that prohibit side effects are called pure. Even though some functional languages are impure they often contain a pure subset that is a also useful as a programming language. It is usually beneficial to write a significant part of a functional program in a purely functional fashion and keep the code involving state and I/O to the minimum as it is more prone to errors.

Immutable data

Purely functional programms operate only on immutable data. This is possible because on each modification a new version of a data structure is created and the old one is preserved. Therefore, data structures are persistent as it is possible to refer also to old versions of them. If there are no more references to the old version the unreferred data can be collected by automatic memory management, such as a garbage collector. Often, bigger data structures share their parts between versions and do not consume as much memory as all versions separately.

Referential transparency

Pure computations yield the same value each time they are invoked. This property is called referential transparency and makes possible to conduct equational reasoning on the code. For instance if y = f x and g = h y y then we should be able to replace the definition of g with g = h (f x) (f x) and get the same result, only the efficiency might change.

Lazy evaluation

Since pure compuations are referentially transparent they can be performed at any time and still yield the same result. This makes it possible to defer the computation of values until they are needed, that is to compute them lazily. Lazy evaluation avoids unnecessary computations and allows for instance to create lazy data structures that are built on the fly.

Purity and effects

Even though purely functional programming is very beneficial, the programmer might want to use features that are not available in pure programs, like efficient mutable arrays or convenient I/O. There are two approaches to this problem.

Side effects in the language

Some functional languages extend their purely functional core with side effects. The programmer must distinguish between pure and impure functions.

Side effects through monads

Another way of introducing side effects to a pure language is to simulate them using monads. While the language remain pure and referentially transparent monads can provide implicit state by threading it inside them. The compiler does not even have to 'know' about the imperative features because the language itself remains pure, however usually the implementations do 'know' about them due to the efficiency reasons, for instance to provide $O(1)$ mutable arrays.

Allowing side effects only through monads and keeping the language pure makes it possible to have lazy evaluation that does not conflict with the effects of impure code. Even though the expressions are evaluated only when their values are needed the effects are properly sequenced.

Recursion

Recursion is heavily used in functional programming as it is the canonical and often the only way to iterate. Loops are naturally expressed using tail recursion.

Benefits of functional programming

Functional programs are often shorter and easier to understand than their imperative counterparts. Since various studies have shown that the average programmers' productivity in terms of lines of code is more or less the same for any programming language, this translates also to higher productivity.