Monad

In functional programming, a monad is a programming structure that represents computations. Monads are a kind of abstract data type constructor that encapsulate program logic instead of data in thedomain model. A defined monad allows the programmer to chain actions together and build different pipelines that process data in various steps, in which each action is decorated with additional processing rules provided by the monad; for example a sequence of arithmetic operations can be controlled to avoid division by zero in intermediate results. Programs written in functional style can make use of monads to structure procedures that include sequenced operations,^[1][2] or to define some arbitrary control flows (like handling concurrency, continuations, side effects such asinput/output, or exceptions).

Formally, a monad is constructed by defining two operations (bind and return) and a type constructor M that must fulfill several properties to allow the correct composition of monadic functions (i.e. functions that use values from the monad as their arguments). The return operation takes a value from a plain type and puts it into a monadic container of type M. The bind operation performs the reverse process, extracting the original value from the container and passing it to the associated next function in the pipeline.

A programmer uses an existing monad by composing monadic functions to define a new data-processing pipeline. The monad acts as a framework, as it's a reusable behavior that decides the order in which the specific monadic functions in the pipeline are called, and manages all the undercover work required by the computation.^[3] The bind and return operators interleaved in the pipeline will be executed after each monadic function returns control, and will take care of the particular aspects handled by the monad.

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