Understand Functor, Applicative and Monad

weaming (25)in #haskell • 6 years ago (edited)

Functor

A Functor is any data type that defines how fmap applies to it.
Lists are functors too!
Functions are Functors too. When you use fmap on a function, you're just doing function composition!
Functors apply a function to a wrapped value

Applicatives take it to the next level. With an applicative, our values are wrapped in a context.
Applicative pushes Functor aside.
Control.Applicative defines <*>
Applicatives apply a wrapped function to a wrapped value

Monads apply a function that returns a wrapped value to a wrapped value.
Monads have a function >>= (pronounced "bind") to do this.
Monad is another typeclass.
Maybe is a Functor, an Applicative, and a Monad
Haskell also provides us with some syntactical sugar for monads, called do notation

Functor, Applicative, Monad are typeclass, the value implements them is one Functor or Applicative or Monad
A functor is a data type that implements the Functor typeclass.
An applicative is a data type that implements the Applicative typeclass.
A monad is a data type that implements the Monad typeclass.
A Maybe implements all three, so it is a functor, an applicative, and a monad.
syntax sugar
1. functors: you apply a function to a wrapped value using fmap or <$>
2. applicatives: you apply a wrapped function to a wrapped value using <*> or liftA
3. monads: you apply a function that returns a wrapped value, to a wrapped value using >>= or liftM

# normal
f a -> b
# functor: <a>
f <a> -> <b>
# applicative: <b>
<f> <a> -> <b>
# monad: f a -> <b>
<a> (f a -> <b>) -> <b>

所以

另外一种视角

所以可以把这个 container 看作“更多数量的元素”，把monad看做可中断的流水线。