In Haskell, a monad is a way of structuring computations, particularly in situations where a sequence of computations may have side effects or where the order of execution matters.

A monad in Haskell is defined as a type class that provides two operations: `return` and `(>>=)` (pronounced "bind"). The `return` operation takes a value and wraps it in a monadic context, while the `(>>=)` operation takes a monadic value and a function that operates on the underlying value, and returns a new monadic value. The key feature of a monad is that it allows for sequencing of computations, where the output of one computation is passed as input to the next computation.

The mathematical concept of a monad provides a theoretical underpinning for the use of monads in functional programming. In category theory, a monad is a way of composing functors in a certain way, as I mentioned in my previous answer. This composition of functors can be thought of as a way of structuring computations in a category-theoretic setting.

In functional programming, the monad structure provides a way of structuring computations in a way that is both composable and modular. By using the operations provided by the monad, we can chain together computations in a way that is easy to reason about and that allows us to encapsulate side effects.

In essence, the Haskell concept of a monad is a concrete implementation of the abstract mathematical concept of a monad, adapted to the specific needs of functional programming.
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