MapflatMap

MapflatMap is a higher-order operation on a container (such as a list, option, or future) that applies a function returning a container and then flattens the result. It is essentially the combination of mapping and flattening, and in many languages this is more commonly called flatMap or bind. The name mapflatMap emphasizes the two steps: map a value to a container, then flatten the nested container into a single level.

Formal definition and signature

For a generic container M with types A and B, mapflatMap has the type

M[A] -> (A -> M[B]) -> M[B].

It takes a container of A and a function that maps A to a container of B, producing a container of B. Operationally, it applies the function to each element and then concatenates or flattens the inner containers.

Relation to map and flatten

MapflatMap is equivalent to applying map with a function that returns a container, followed by flatten. In languages with explicit flatMap, the same effect is achieved by M[A].flatMap(f). It is central to monadic sequencing, allowing chaining of computations that themselves yield containers.

Examples

- List: [1, 2, 3].mapFlatMap(n => [n, n+1]) yields [1, 2, 2, 3, 3, 4].

- Option/Maybe: Some(2).mapFlatMap(x => Some(x+3)) yields Some(5); None.mapFlatMap(...) yields None.

- Asynchronous contexts: futures or promises use mapflatMap to chain operations that return futures.

Notes

Naming varies by library; some call it flatMap or bind. The concept remains a way to compose operations that produce nested containers into a single container, avoiding nested structures.

See also: map, flatten, flatMap, bind, monad.