Английская Википедия:Functor (functional programming)
Шаблон:Short description Шаблон:About
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 :: (a -> b) -> f a -> f b
This declaration says that any type of Functor must support a method fmap, which maps a function over the element(s) of the Functor.
Functors in Haskell should also obey functor laws,[1] which state that the mapping operation preserves the identity function and composition of functions:
fmap id = id
fmap (g . h) = (fmap g) . (fmap h)
(where . stands for function composition).
trait Functor[F[_]] {
def map[A,B](a: F[A])(f: A => B): F[B]
}
Functors form a base for more complex abstractions like Applicative Functor, Monad, and Comonad, 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 (which might yet to be run).
Examples
In Haskell, lists are a simple example of a functor. We may implement Шаблон:Code as
fmap f [] = []
fmap f (x:xs) = (f x) : fmap f xs
A binary tree may similarly be described as a functor:
data Tree a = Leaf | Node a (Tree a) (Tree a)
instance Functor Tree where
fmap f Leaf = Leaf
fmap f (Node x l r) = Node (f x) (fmap f l) (fmap f r)
If we have a binary tree Шаблон:Code and a function Шаблон:Code, the function Шаблон:Code will apply Шаблон:Code to every element of Шаблон:Code. For example, if Шаблон:Code is Шаблон:Code, adding 1 to each element of Шаблон:Code can be expressed as Шаблон:Code.[2]
See also
- Functor in category theory
- Applicative functor, a special type of functor
References
External links
- Section about Functor in Haskell Typeclassopedia
- Chapter 11 Functors, Applicative Functors and Monoids in Learn You a Haskell for Great Good!
- Documentation for Functor in Cats library
- Section about Functor in lemastero/scala_typeclassopedia
Шаблон:Design Patterns Patterns
