Monad in functional programming

Summary

In functional programming, a monad is a type constructor $M$ with two operations, $\mathsf{return} : A \to M\, A$ and $\mathsf{bind} : M\, A \to (A \to M\, B) \to M\, B$, that satisfy three laws. A value of type $M\, A$ is read as a computation that produces a value of type $A$, possibly with an effect. Typical effects are failure, state, input and output, and nondeterminism. Eugenio Moggi used monads of category theory to structure the semantics of effects. Philip Wadler brought them into programming, where they are central to Haskell. The laws are the laws of a Kleisli triple, an equivalent form of a monad on the category of types and functions.