Functor (functional programming)
In functional programming, a functor is a design pattern inspired by the definition from category theory that allows one to apply a function to values inside a generic type without changing the structure of the generic type. In Haskell this idea can be captured in a type class:
class Functor f where
fmap :: -> f a -> f b
This declaration says that any instance of
Functor must support a method fmap, which maps a function over the elements of the instance.Functors in Haskell should also obey the so-called functor laws, which state that the mapping operation preserves the identity function and composition of functions:
fmap id = id
fmap = .
where
. stands for function composition.In Scala a trait can instead be used:
trait Functor
Functors form a base for more complex abstractions like [Applicative functor">applicative functors, monads, and comonads, all of which build atop a canonical functor structure. Functors are [useful">_
Functors form a base for more complex abstractions like [Applicative functor">applicative functors, monads, and comonads, all of which build atop a canonical functor structure. Functors are [useful in modeling functional effects by values of parameterized data types. Modifiable computations are modeled by allowing a pure function to be applied to values of the "inner" type, thus creating the new overall value which represents the modified computation.
Examples
In Haskell, lists are a simple example of a functor. We may implement asfmap f =
fmap f = : fmap f xs
A binary tree may similarly be described as a functor:
data Tree a = Leaf | Node a
instance Functor Tree where
fmap f Leaf = Leaf
fmap f = Node
If we have a binary tree and a function, the function will apply to every element of. For example, if is, adding 1 to each element of can be expressed as.