maflatMapf

MAflatMapf is a higher-order function used in functional programming to apply an effectful function to a value contained in a monad and then flatten the resulting nested monadic structure. It is the standard way to sequence computations where the function you apply returns a monadic value.

Formally, for any monad m, MAflatMapf takes a function f: a -> m b and a value ma: m a, and returns m b. It is commonly defined as MAflatMapf f ma = ma >>= f, or equivalently fmap f ma >>= join. This shows its nature as a bind operation that combines mapping with flattening, and it requires a Monad constraint rather than just a Functor or Applicative.

In practical terms, MAflatMapf chains computations that may each produce their own computational context (such as possible failure, asynchronous results, or optional values). The result propagates failure or absence automatically, without needing explicit checks after each step. If the function returns a non-empty monad, MAflatMapf flattens the nested structure so the outer monad carries a single, concrete result.

Examples: in Haskell, MAflatMapf (\x -> Just (x+1)) (Just 2) yields Just 3; if the function yields Nothing, the overall result is Nothing. In JavaScript, a similar pattern appears as ma.then(f) when ma is a Promise and f returns a Promise. In Scala, it appears as ma.flatMap(f) for monadic values.

See also monads, bind, flatMap, join.