mflatMapt

mflatMapt is a hypothetical higher‑order function used in functional programming to map a function over the contents of a monadic container and then flatten the resulting structure. It combines ideas from flatMap, sequence, and traverse and is defined in terms of a monad m and a container of elements a.

In a Haskell‑like type system, its standard form is:

mflatMapt :: Monad m => m [a] -> (a -> m [b]) -> m [b]

The function takes a monadic value containing a list of a, and a function f that maps each a to a monadic list of b. The result is a monadic list of b. The intended behavior is to apply f to every a inside the inner list, gather the resulting monadic lists, and concatenate them into a single list inside the outer monad.

A common implementation pattern is:

mflatMapt mas f = mas >>= \xs -> mapM f xs >>= join

Equivalently, using sequence and fmap:

mflatMapt mas f = mas >>= \xs -> fmap concat (sequence (fmap f xs))

Observation: If the outer monad or the inner results can fail (for example, Maybe or Either), mflatMapt propagates failure, as in other monadic compositions.

Relation and variations: mflatMapt is related to flatMap, bind, and traversals over monadic containers. In languages with traversable structures, a version can operate over a generic traversable t, using type constraints to reflect the nested mapping and flattening.

Notes: The suffix t in mflatMapt commonly signals a variant involving traversal through a container or a transformer and is used in documentation as a naming convention rather than a formal standard.