links: Software Design Patterns MOC

What is Functor

Functors are objects (Containers) that implement map method. These are the rules for a qualifying functor

Preserve function composition while mapping. It means composing two functions and then mapping the result function over a function should be the same as first mapping one function over the functor and then mapping the other one.

For example javascript Array’s map method is a functor

// fx.map(f).map(g) == fx.map(x => g(f(x)))
 
const result1 = ['Squirrels']
					.map(s => s.substr(5))
					.map(s => s.toUpperCase())
 
const result2 = ['Squirrels']
					.map(s => s.substr(5).toUpperCase())
 
console.log(result1, result2)

If we map the id function over a functor, the functor that we get back should be the same as original functor id is the identity function which just returns it’s parameter unmodified.

// fx.map(id) == id(fx)
 
const id = x => x
 
const result1 = ['Crayons'].map(id)
 
const result2 = id(['Crayons'])
 
console.log(result1, result2)

Origin

In Mathematics, a functor is a map between categories. It belongs to a category theory in Mathematics.

tags: design-pattern

sources:

Category theory