14. Foldables and friends

Question 1

What is a Monoid?

Answer 1

A set together with an associative operator that combines 2 elements from the set, and an identity element for the operator.

Question 2

What are Monoids used for?

Answer 2

As a way to define algebraic structures and provide a way to reason about and manipulate values of that structure

Question 3

Give the declaration of a Monoid

Answer 3

class Monoid a where
mempty :: a
mappend :: a -> a -> a
mconcat :: [a] -> a
mconcat = foldr mappend mempty

Question 4

Give the 3 rules of the Monoid class

Answer 4

1. mempty ‘mappend’ x = x
2. x ‘mappend’ mempty = x
3. x ‘mappend’ (y ‘mappend’ z) = (x ‘mappend’ y) ‘mappend’ z

Question 5

What is a Foldable?

Answer 5

A way to fold a data structure to a single value.

Question 6

What is the foldable declaration

Answer 6

class Foldable t where
fold :: Monoid a => t a -> a
foldMap :: Monoid b => (a -> b) -> t a -> b
foldr :: (a -> b -> b) -> b -> t a -> b
foldl :: (a -> b -> a) -> a -> t b -> a

Question 7

What is a Traversable?

Answer 7

A typeclass that defines a way to traverse a data structure, performing some operation on each element.

Question 8

Give the Traversable definition

Answer 8

class (Functor t, Foldable t) => Traversable t where
traverse :: Applicative f => (a -> f b) -> t a -> f (t b)

Question 9

describe the sequenceA function and an example

Answer 9

sequenceA :: Applicative f => t (f a) -> f (t a)
sequenceA = traverse id

> sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]