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Concepts of the functional programming

Functional programming

A programming paradigm is a fundamental style of computer programming. (Compare with a methodology, which is a style of solving specific software engineering problems.) Paradigms differ in the concepts and abstractions used to represent the elements of a program (such as objects, functions, variables, constraints, etc.) and the steps that compose a computation (assignation, evaluation, continuations, data flows, etc.).

In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state. Functional programming has its roots in the lambda calculus, a formal system developed in the 1930s to investigate function definition, function application, and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus.

Functional programming languages, especially purely functional ones, have largely been emphasized in academia rather than in commercial software development. However, prominent functional programming languages such as Scheme, Erlang, OCaml and Haskell have been used in industrial and commercial applications by a wide variety of organizations. Functional programming also finds use in industry through domain-specific programming languages like R (statistics), Mathematica (symbolic math), J and K (financial analysis), and XSLT (XML). Widespread declarative domain specific languages like SQL and Lex/Yacc, use some elements of functional programming, especially in eschewing mutable values. Spreadsheets can also be viewed as functional programming languages.

Programming in a functional style can also be accomplished in languages that aren't specifically designed for functional programming. For example, the imperative Perl programming language has been the subject of a book describing how to apply functional programming concepts. Javascript, one of the most widely employed languages today, incorporates functional programming capabilities.

Concepts of the functional programming

A number of concepts and paradigms are specific to functional programming, and generally foreign to imperative programming (including object oriented programming). However, programming languages are often hybrids of several programming paradigms so programmers using "mostly imperative" languages may have utilized some of these concepts.

Higher-order functions

Functions are higher-order when they can take other functions as arguments, and return them as results. (Operators in mathematics, such as the differential operator d / dx that produces the derivative in calculus when applied to a function f, are examples of this.)

Higher-order functions enable currying, a technique in which a function is applied to its arguments one at a time, with each application returning a new function that accepts the next argument.



Pure functions

Purely functional functions (or expressions) have no memory or I/O side effects, unless the computation of the result in itself is counted as a side-effect. This means that pure functions have several useful properties, many of which can be used to optimize the code:

If the result of a pure expression is not used, it can be removed without affecting other expressions.

If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list (sometimes called referential transparency), i.e. if the pure function is again called with the same parameters, the same result will be returned (this can enable caching optimisations such as memoization).

If there is no data dependency between two pure expressions, then their order can be reversed, or they can be performed in parallel and they cannot interfere with one another (in other terms, the evaluation of any pure expression is thread-safe).

If the entire language does not allow side-effects, then any evaluation strategy can be used; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program (for example, using deforestation).

Recursion

Iteration (looping) in functional languages is usually accomplished via recursion. Recursive functions invoke themselves, allowing an operation to be performed over and over. Recursion may require maintaining a stack, but tail recursion can be recognized and optimized by a compiler into the same code used to implement iteration in imperative languages.

Common patterns of recursion can be factored out using higher order functions, catamorphisms and anamorphisms (or "folds" and "unfolds") being the most obvious examples. Such higher order functions play a role analogous to built-in control structures such as loops in imperative languages.

Strict versus non-strict evaluation

Functional languages can be categorized by whether they use strict (eager) or non-strict (lazy) evaluation, concepts that refer to how function arguments are processed when an expression is being evaluated. The technical difference is in the denotational semantics of expressions containing failing or divergent computations. Under strict evaluation, the evaluation of any term containing a failing subterm will itself fail.

For example, the expression

print length([2+1, 3*2, 1/0, 5-4])

will fail under strict evaluation because of the division by zero in the third element of the list. Under nonstrict evaluation, the length function will return the value 4, since evaluating it will not attempt to evaluate the terms making up the list. In brief, strict evaluation always fully evaluates function arguments before invoking the function. Non-strict evaluation does not evaluate function arguments unless their values are required to evaluate the function call itself.

The usual implementation strategy for non-strict evaluation in functional languages is graph reduction. Non-strict evaluation is used by default in several pure functional languages, including Miranda, Clean and Haskell.

Functional programming in non-functional languages

It is possible to employ a functional style of programming in languages that are not traditionally considered functional languages. Some non-functional languages have borrowed features such as higher-order functions, and list comprehensions from functional programming languages. This makes it easier to adopt a functional style when using these languages. Functional constructs such as higher-order functions and lazy lists can be obtained in C++ via libraries. In C, function pointers can be used to get some of the effects of higher-order functions. For example the common function map can be implemented using function pointers. In C# version 3.0 and higher, lambda functions can be employed to write programs in a functional style. In Java, anonymous classes can sometimes be used to simulate closures, however anonymous classes are not always proper replacements to closures because they have more limited capabilities.

Many object-oriented design patterns are expressible in functional programming terms: for example, the Strategy pattern simply dictates use of a higher-order function.

Comparison of functional and imperative programming

Functional programming is very different from imperative programming. The most significant differences stem from the fact that functional programming avoids side effects, which are used in imperative programming to implement state and I/O. Pure functional programming disallows side effects completely. Disallowing side effects provides for referential transparency, which makes it easier to verify, optimize, and parallelize programs, and easier to write automated tools to perform those tasks.

Higher order functions are rarely used in older imperative programming. Where a traditional imperative program might use a loop to traverse a list, a functional style would often use a higher-order function, map, that takes as arguments a function and a list, applies the function to each element of the list, and returns a list of the results.

Simulating state

There are tasks (for example, maintaining a bank account balance) that often seem most naturally implemented with state. Pure functional programming performs these tasks, and I/O tasks such as accepting user input and printing to the screen, in a different way.

The pure functional programming language Haskell implements them using monads, derived from category theory. Monads are powerful and offer a way to abstract certain types of computational patterns, including (but not limited to) modeling of computations with mutable state (and other side effects such as I/O) in an imperative manner without losing purity. While existing monads may be easy to apply in a program, given appropriate templates and examples, many find them difficult to understand conceptually, e.g., when asked to define new monads (which is sometimes needed for certain types of libraries).

Alternative methods such as Hoare logic and uniqueness have been developed to track side effects in programs. Some modern research languages use effect systems to make explicit the presence of side effects.

Efficiency issues

Functional programming languages have been perceived as less efficient in their use of CPU and memory than imperative languages such as C and Pascal. However, for programs that perform intensive numerical computations, functional languages such as OCaml and Clean are similar in speed to C. For programs that handle large matrices and multidimensional databases, array functional languages (such as J and K) were designed with speed optimization in mind.

Further, immutability of data can, in many cases, lead to execution efficiency in allowing the compiler to make assumptions that are unsafe in an imperative language, vastly increasing opportunities for inlining.

Lazy evaluation may also speed up the program, even asymptotically, whereas it may slow it down at most by a constant factor (however, it may introduce memory leaks when used improperly).

 


Date: 2015-12-11; view: 620


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