concatMap

concatMap is a higher-order function used in functional programming to map a function over a collection where the function itself returns a collection, and then concatenate the results into a single collection. It combines mapping and flattening in one step, effectively performing a one-level join after the map. For lists, the typical signature is concatMap :: (a -> [b]) -> [a] -> [b], and it can be defined as concatMap f xs = concat (map f xs) or equivalently as join . map f. This means: apply f to each element of xs to obtain a list of lists, then concatenate those lists in order.

In the list monad, concatMap corresponds to the list-specific form of bind: it is the same as using (>>=) with f, where f returns a list. For example, in Haskell: concatMap (\x -> [x, x+1]) [1,2,3] yields [1,2,2,3,3,4].

Other languages use similar constructs with varying names: Scala uses flatMap, JavaScript uses Array.prototype.flatMap, and ReactiveX libraries offer a concatMap operator for observable streams (often aliasing map followed by concatenation). The concept generalizes to any structure that supports mapping to a collection and concatenation, such as vectors or streams.

Performance and memory: concatMap processes elements sequentially and produces a flattened result without creating a nested list, but the total number of produced elements depends on the function's outputs. It is useful when the mapping function generates multiple results per input and you want a single flat sequence.