Haskell

Question 1

What function has this type signature?

(b -> b -> c) -> (a -> b) -> a -> a -> c

Answer 1

on found in Data.Function

Question 2

How can you use the on function from Data.Function?

Answer 2

((+) `on` f) x y = f x + f y
To sort by the second value in a list of pairs - sortBy (compare `on` snd)
This is also equivalent to sortOn snd

Question 3

What is a more optimal version of nub and where is it found?

Answer 3

nubOrd in Data.Containers.ListUtils

Question 4

What functions are available in Data.Set?

Answer 4

empty :: Set a - Returns empty set of any type
singleton :: a -> Set a - Returns a set containing a singular value
fromList :: Ord a => [a] -> Set a - Creates a list from a list
insert :: Ord a => a -> Set a -> Set a - Inserts a new value in the set
member :: Ord a => a -> Set a -> Bool - Checks if a value is in a set

Question 5

What functions are available in Data.Map?

Answer 5

(!) :: Ord k => Map k a -> k -> a - Returns the value at a key (partial)
lookup :: Ord k => Map k a -> k -> Maybe a - Returns a maybe of the value at a key
empty :: Map k a - Returns empty map of any type
singleton :: k -> a -> Map k a - Returns a map containing a single key and value
insert :: Ord k => k -> a -> Map k a -> Map k a - Return a new map with a new key and value inserted

Question 6

What function has this type signature?

Foldable t => (a -> b -> b) -> b -> t a -> b

Hint: A List is an example of a foldable structure

Answer 6

foldr and foldl

Question 7

What function has this type signature?

(a -> b) -> [a] -> [b]

Answer 7

map and fmap

Question 8

What function has this type signature?

Functor t => (a -> b) -> t a -> t b

Answer 8

fmap and <$>

Question 9

How is Functor and . linked?

Answer 9

. is equivalent to fmap in the Functor (x ->) definition

Question 10

What are the fmap laws?

Answer 10

fmap id = id
fmap f . fmap g = fmap (f . g)

Question 11

What function has this type signature?

Applicative t => (a -> b -> c) -> t a -> t b -> t c

Answer 11

liftA2

Question 12

What is the applicative version of fmap

Answer 12

liftA from Control.Applicative

Question 13

What function has this type signature?

Applicative t => a -> t a

Answer 13

pure

Question 14

What function has this type signature?

(a -> b) -> a -> b

Answer 14

$

Question 15

What is the liftA definition using liftA2?

Answer 15

liftA f mx = liftA2 ($) (pure f) mx

Question 16

What function has this type signature?

Applicative t => t (a -> b) -> t a -> t b

Answer 16

<*>

Question 17

What is the definition of <*> using liftA2?

Answer 17

liftA2 ($)

Question 18

What is the liftA definition using <*>?

Answer 18

liftA f mx = pure f <*> mx

Question 19

What is the liftA2 definition using <*>?

Answer 19

liftA2 f mx my = f <$> mx <*> my

Question 20

What are the two ways that a Monad can be implemented?

Answer 20

join and >>=

Question 21

What function has this type signature?

Monad m => m (m a) -> m a

Answer 21

join

Question 22

What is join equivalent to in Monad []?

Answer 22

concat

Question 23

What function has this type signature?

Monad m => m a -> (a -> m b) -> m b

Answer 23

>>=

Question 24

What is the >>= definition using join?

Answer 24

mx >>= f = join (fmap f mx)

Question 25

What is the `join` definition using `>>=`?

Answer 25

`join mmx = mmx >>= id`

Question 26

What is the `liftM` definition?

Answer 26

`liftM f mx = mx >>= (\x -> pure (f x))`

Question 27

# What function has this type signature? `Monad m => (a -> b) -> m a -> m b`

Answer 27

`liftM`

Question 28

# What function has this type signature? `Monad m => (a -> b -> c) -> m a -> m b -> m c`

Answer 28

`liftM2`

Question 29

What is the `liftM2` definition?

Answer 29

`liftM2 f mx my = mx >>= (\x -> fmap (f x) my)`