Functional programming is a programming paradigm which avoids changing or mutating states and data values over time. It is a declarative programming style, meaning the programmer defines what the program should accomplish without specifying how to achieve the desired result. Instead, the code is structured in such a way that it describes the output of a particular given input. It also seeks to minimize state changes, aiming for a deterministic, more predictable result from a given input.

Functional programming has been a part of programming for a long time, with some of the earliest implementations revealed in the 1960s. However, it only recently started to gain widespread recognition in the 21st century with the use of modern functional programming languages such as Scala, JavaScript, Haskell, and Clojure.

Functional programming languages are especially powerful and popular for developing backend microservices, as they can easily handle parallel processing and message-passing; as well as for algorithm-intensive software that require strong math support. However, due to its higher level of abstraction it is generally considered more difficult to learn and program.

Functional programming is also used in many web frameworks such as React and Angular, striving to present a more efficient form of web development while making it easier to ship changes to an existing web application.

Finally, functional programming is often combined with object-oriented programming, making it achievable to write code that is both precise and easy for other developers to read. This is especially important in asynchronous programming, where pieces of code may need to act independently of each other.

In conclusion, functional programming is a complex but powerful paradigm with popular applications in code engineering, backend microservices, web development, as well as general algorithm-intensive software. Although learning functional programming takes time and dedication, many developers now recognize the great potential that this style possesses.

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