What are the differences between functors and applicatives?

What are the differences between functors and applicatives?

Functors and applicatives are both concepts in functional programming. A functor is a type that can be mapped over, allowing you to apply a function to values wrapped in a context. An applicative, on the other hand, extends this idea by allowing you to apply functions that are also wrapped in a context to values wrapped in a context.

Can you give me an example of a functor?

Sure! In Haskell, the Maybe type is a functor. You can use the fmap function to apply a function to the value inside a Maybe, if it exists. For example, fmap (+1) (Just 2) results in Just 3, while fmap (+1) Nothing remains Nothing.

What about an example of an applicative?

An example of an applicative is the Either type in Haskell. You can use the <*> operator to apply a function wrapped in an Either to a value wrapped in an Either. For instance, if you have Right (+1) and Right 2, applying them gives you Right 3. If either is Left, the result will also be Left.

How do functors relate to applicatives?

Functors are a foundational concept for applicatives. Every applicative is a functor, but not every functor is an applicative. Applicatives build on the functor's ability to map functions over wrapped values by allowing functions that are also wrapped to be applied.