Functional programming

Computers use special rules to work.

These rules use small parts to build big ones.

Each part does one job very well.

This helps people write good code.

It can help computers work fast.

Do you like to build things with blocks?

Computers follow sets of rules to run programs. One way to do this is called functional programming. In this style, programmers build big programs using small parts. These parts are called functions. A function is like a little machine. You give it a value, and it gives you a new value back.

In functional programming, functions are very special. They are called first-class entities. This means you can treat a function just like a number. You can give a function to another function as an argument. You can even have a function give back a new function as its result. This lets people combine small parts to make complex tools.

Some people use pure functions. A pure function is very predictable. If you give it the same input, it always gives the same result. It does not cause side effects. A side effect is a change that happens somewhere else in the program. Because pure functions are so steady, they can have fewer bugs. This makes them easier to test. Many famous languages use these ideas. Examples include Haskell, Lisp, and even parts of Python and Java.

Functional programming is a special way to write computer programs. Instead of giving a computer a long list of step-by-step instructions, programmers build programs by combining small parts called functions. Think of a function like a small machine that takes an input and turns it into an output. In this style, functions are treated as "first-class entities." This means you can treat a function just like a number or a piece of text. You can name them, pass them into other functions, or even have one function create a brand new function as its result. This makes it easy to build big, complex tools by snapping together many small, simple pieces.

One of the most important ideas is using "pure functions." A pure function is very predictable and steady. If you give a pure function the same input, it will always give you the exact same result. It does not have "side effects," which are unexpected changes that happen elsewhere in the program. For example, an impure function might change a number stored in the computer's memory, but a pure function only cares about its own math. Because they are so steady, pure functions help programmers write code with fewer bugs. They are also easier to test and can often be run at the same time to make computers work faster.

This way of thinking has deep roots in math and history. In the 1930s, a mathematician named Alonzo Church created a system called lambda calculus. This system uses only functions to do math and logic. Later, in 1937, Alan Turing proved that this system was just as powerful as his own famous machines. This discovery showed that functional programming could solve almost any problem a computer can handle. Other thinkers like Moses Schönfinkel and Haskell Curry also helped build these ideas through something called combinatory logic. All of these early discoveries form the foundation for the languages we use today.

Many famous programming languages were built using these ideas. The first high-level functional language was Lisp, created by John McCarthy at MIT in the late 1950s. Since then, many other languages have appeared, such as Scheme, Haskell, and Erlang. Some languages are used for very specific jobs. For instance, the language R is used for statistics, and others are used for big financial tasks. Even some of the most popular languages today, like Python, Java, and C++, have added functional features. This shows that these old mathematical ideas are still very useful in modern technology.

You can see functional programming in action all around you. It helps run the math behind the websites you visit using JavaScript. It is used to manage large amounts of data and information. Because functional programming is so good at handling logic, it is even used to verify complex mathematical theorems with a language called Lean. Whether it is helping a bank analyze money or helping a scientist study data, these small, reliable functions work together to power our digital world. It is a way of turning math into a tool for building everything we use on our screens.

Functional programming is a specific paradigm in computer science. In this approach, programmers construct software by applying and composing functions. It is a declarative paradigm, which means it focuses on what to solve rather than how to change state. Instead of using a sequence of imperative statements to update a program's running state, functional programming uses trees of expressions. These expressions map specific input values to new output values. This style allows for a modular approach where small, manageable functions are combined to create complex systems.

A core mechanic of this paradigm is treating functions as first-class entities. This term means functions have no restrictions on their use within a program. They can be bound to names or local identifiers just like any other data type. Programmers can also pass functions as arguments to other functions. Furthermore, a function can return another function as its result. This capability leads to the use of higher-order functions. A higher-order function is a mathematical concept where a function operates on other functions. This allows for techniques like currying, which is the process of applying a function to its arguments one at a time. Each step returns a new function that accepts the next argument.

Within this field, the concept of pure functions is vital. A pure function is a deterministic mathematical function. This means that when a pure function is called with specific arguments, it will always return the same result. Pure functions are defined by their lack of side effects. A side effect is an unintended change, such as modifying the program's state or taking user input. Because pure functions do not rely on or change mutable state, they offer several technical advantages. If the result of a pure expression is not needed, a compiler can safely remove it. If there is no data dependency between two pure expressions, they can be performed in parallel. This makes the code thread-safe and easier to optimize through methods like memoization, which is a form of caching.

The history of functional programming is rooted deeply in academic mathematics. In the 1930s, Alonzo Church developed the lambda calculus. This is a formal system of computation built entirely from function application. In 1937, Alan Turing proved that lambda calculus and Turing machines are equivalent models of computation. This proved that lambda calculus is Turing complete. Other foundational work includes combinatory logic, developed by Moses Schönfinkel and Haskell Curry in the 1920s and 1930s. Church also created the simply typed lambda calculus. This system assigned data types to all terms and became the basis for statically typed functional programming.

Practical implementation began in the late 1950s with the creation of Lisp. John McCarthy developed Lisp at the Massachusetts Institute of Technology for the IBM 700/7000 series of scientific computers. Lisp functions used Church's lambda notation and included a label construct for recursive functions. Other early milestones include the Information Processing Language in 1956 and the SECD machine in the mid-1960s. In 1977, John Backus delivered a Turing Award lecture regarding a functional style. He proposed that programs could be built hierarchically through an algebra of programs. This emphasized the principle of compositionality, where complex structures are built from simpler ones.

Today, functional programming is used across many different industries and domains. There are many specialized languages, such as Haskell, which began as an open standard in 1987. Other languages like Erlang and Elixir are used in modern industry. Some languages are designed for specific tasks, such as R for statistics or JavaScript for the Web. Financial analysis often relies on languages like J, K, and Q. Even domain-specific languages like SQL and XQuery use functional elements, such as the restriction of mutable values. Furthermore, many mainstream languages have adopted functional features. These include C++ since C++11, Java since Java 8, Python, Rust, and Go.

Functional programming connects deeply to other fields like formal verification and artificial intelligence. The language Lean is used specifically to verify mathematical theorems. In the field of artificial intelligence, the Logic Theorist program used a paradigm that embeds functional programming to prove theorems from Principia Mathematica. The connection between functional programs and constructive proofs was also advanced by Per Martin-Löf through intuitionistic type theory. This work has influenced modern approaches to interactive theorem proving. By restricting side effects, proponents argue that programs become easier to debug, test, and verify formally.