What is the difference between functors and applicatives in functional programming?

What is the difference between functors and applicatives in functional programming?

Functors and applicatives are both concepts in functional programming that deal with how functions can be applied to wrapped values. A functor allows you to apply a function to a value inside a context (like a list or an option) using the map function. An applicative, on the other hand, allows you to apply functions that are also wrapped in a context to values that are wrapped in a context, using the apply function.

Can you give me an example of a functor?

Sure! In Haskell, a common example of a functor is the Maybe type. If you have a Maybe Int, you can use fmap to apply a function to the Int inside it, if it exists. For example, fmap (+1) (Just 2) results in Just 3, while fmap (+1) Nothing results in Nothing.

What about an example of an applicative?

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

How do functors and applicatives relate to monads?

Great question! Functors, applicatives, and monads are all part of the same hierarchy in functional programming. Functors are the most basic, allowing you to map functions over wrapped values. Applicatives build on functors by allowing you to apply wrapped functions to wrapped values. Monads extend this further by allowing for chaining operations that depend on the results of previous computations.