fmap

Fmap is a function in functional programming, most closely associated with Haskell's Functor type class, that applies a function to the value inside a container or context without changing the container’s structure. It allows you to lift a plain function to operate on values wrapped in a functor.

In Haskell, fmap has the type fmap :: Functor f => (a -> b) -> f a -> f b. A functor is a type constructor that supports mapping a function over its contents, returning a new functor with the transformed values while preserving the original layout.

Common examples illustrate its behavior. For Maybe a, fmap f Nothing = Nothing and fmap f (Just x) = Just (f x). For lists, fmap f xs applies f to every element, effectively the same as map f xs. For IO, fmap f action applies f to the result produced by the IO action, i.e., fmap f action = action >>= (return . f). Other standard instances include Either e, and various user-defined containers.

Fmap is governed by functor laws. The identity law states that fmap id = id, meaning mapping the identity function leaves the structure unchanged. The composition law states fmap (g . h) = (fmap g) . (fmap h), ensuring that successive mappings compose correctly. These laws ensure predictability when chaining mappings.

Beyond Haskell, the concept appears in other languages via map-like operations on container types, such as List.map, Option/Maybe.map, or similar abstractions in Scala, Rust, and languages with functor-like interfaces. The operator form of fmap in Haskell is often written as <$>, providing an infix alternative to fmap.