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Some Implementation in Swift.

Functor

Let $C$ be a constructor which takes a variable as parameter.

$C$ is a Functor if $C$ has the following ability.

For example, we can write such a function functor or map.

And we can chain functors like this.

We can also do it like Haskell

$C$ is a Monad if $C$ has the following ability. This is also called as flatmap.
$C$ is a Applicative if $C$ has the following ability.