In functional programming, monads are a way to build computer programs by joining simple components in predictable and robust ways. A monad encapsulates values of a particular data type, creating a new type associated with a specific computation; this computation follows a set of mathematical axioms called monad laws. The monad represents computations with a sequential structure: a monad defines what it means to chain operations together, or nest functions of the type defined by the monad. This allows the programmer to build pipelines that process data in a series of steps (i.e. a series of actions applied to the data), in which each action is decorated with the additional processing rules provided by the monad.[1] A monad is defined by a return operator that creates values, and a bind operator used to link the actions in the pipeline.
Monads allow a programming style where programs are written by putting together highly composable parts, combining in flexible ways the possible actions that can work on a particular type of data. As such, monads have been described as "programmable semicolons"; a semicolon is the operator used to chain together individual statements in many imperative programming languages, thus the expression implies that extra code will be executed between the actions in the pipeline. Monads have also been explained with a physical metaphor as assembly lines, where a conveyor belt transports data between functional units that transform it one step at a time. They can also be seen as a functional design pattern to build generic types.
Purely functional programs can use monads to structure procedures that include sequenced operations like those found in structured programming. Many common programming concepts can be described in terms of a monad structure without losing the beneficial property of referential transparency, including side effects such as input/output, variable assignment, exception handling, parsing, nondeterminism, concurrency, continuations, or domain-specific languages. This allows these concepts to be defined in a purely functional manner, without major extensions to the language's semantics. Languages like Haskell provide monads in the standard core, allowing programmers to reuse large parts of their formal definition and apply in many different libraries the same interfaces for combining functions.
The name and concept comes from category theory, where monads are one particular kind of functor, a mapping between categories; although the term monad in functional programming contexts is usually used with a meaning corresponding to that of the term strong monad in category theory.
