Functors

Functors

Recall: A functor is something we can map over, applying a function to some underlying value.

Now that you know about type classes, classes, and collections, let's talk about how functors really work.

type Functor:

def map(self, function)

Maybe Functor

Let's go back to the Maybe example, and see how we could implement it as a functor.

class Maybe:

Just(value)

None

If we have a Just(value), we should apply the function to value:

Just(value).map(f) = Just(f(value))

If we have a None, we should do nothing

None.map(f) = None

Putting these together:

instance Maybe of Functor:

def map(Just(value), f):

return Just(f(value))

def map(_, _):

return None

BTree

As promised, let's go over how to turn a BTree into a functor:

class BTree:

Node(value, left, right)

Leaf

When we call map on a Node, we want to apply a function to the value, and all values on the left and right.

When we call map on a Leaf, we want to do nothing. Exactly the same as calling None.map(f)

instance BTree:

def map(Node(value, left, right), f):

return Node(

f(value),

left.map(f),

right.map(f),

)

def map(_, _):

return Leaf

So, this isn't done automatically, but it's very simple to implement. And now, for any BTree we define, we can call map on it! Magical!