Functor (functional programming)

In functional programming, a functor is a design pattern inspired by the definition from category theory, that allows for a generic type to apply a function inside without changing the structure of the generic type.

This idea is encoded in Haskell using type class

class Functor f where
  fmap :: (a -> b) -> f a -> f b

with conditions called functor laws

fmap id = id
fmap (g . h) = (fmap g) . (fmap h)

In Scala higher kinded types are used

trait Functor[F[_]] {
  def map[A,B](a: F[A])(f: A => B): F[B]
}

Simple examples of this are Option and collection types. Functors are very useful in modeling functional effects to apply a function to computations that did not yet finish.

Functors form a base for more complex abstractions like Applicative, Monad, Comonad.

In C++, the name functor refers to a function object instead of this definition.

External links

Software design patterns
Creational	Abstract factory Builder Dependency injection Factory method Lazy initialization Multiton Object pool Prototype RAII Singleton
Structural	Adapter Bridge Composite Decorator Delegation Facade Flyweight Front controller Marker interface Module Proxy Twin
Behavioral	Blackboard Chain of responsibility Command Interpreter Iterator Mediator Memento Null object Observer Servant Specification State Strategy Template method Visitor
Functional	Monoid Functor Applicative Monad Comonad Free monad HOF Currying Function composition Closure Generator
Concurrency	Active object Actor Balking Barrier Binding properties Coroutine Compute kernel Double-checked locking Event-based asynchronous Fiber Futex Futures and promises Guarded suspension Immutable object Join Lock Messaging Monitor Nuclear Proactor Reactor Read write lock Scheduler STM Thread pool Thread-local storage
Architectural	ADR Active record Broker Client–server CBD DAO DTO DDD ECB ECS EDA Front controller Identity map Interceptor Implicit invocation Inversion of control Model 2 MOM Microservices MVA MVC MVP MVVM Monolithic Multitier Naked objects ORB P2P Publish–subscribe PAC REST SOA Service locator Specification
Cloud Distributed	Ambassador Anti-Corruption Layer Bulkhead Cache-Aside Circuit Breaker CQRS Compensating Transaction Competing Consumers Compute Resource Consolidation Event Sourcing External Configuration Store Federated Identity Gatekeeper Index Table Leader Election MapReduce Materialized View Pipes Filters Priority Queue Publisher-Subscriber Queue-Based Load Leveling Retry Scheduler Agent Supervisor Sharding Sidecar Strangler Throttling Valet Key
Other	Business delegate Composite entity Intercepting filter Lazy loading Mangler Mock object Type tunnel Method chaining
Books	Design Patterns Enterprise Integration Patterns Code Complete POSA
People	Christopher Alexander Erich Gamma Ralph Johnson John Vlissides Grady Booch Kent Beck Ward Cunningham Martin Fowler Robert Martin Jim Coplien Douglas Schmidt Linda Rising
Communities	The Hillside Group The Portland Pattern Repository

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