7. Higher-order functions

Question 1

Function for applying a function to every item in a list

Answer 1

map :: (a -> b) -> [a] -> [b]
map f [ ] = [ ]
map f (x:xs) = f x : map f xs

Question 2

Function for filtering elements of a list with a specific property

Answer 2

filter :: (a -> Bool) -> [a] -> [a]
filter p [ ] = [ ]
filter p (x:xs) | p x = x : filter p xs
| otherwise = filter p xs

Question 3

What is the syntax of foldr (recursive)

Answer 3

foldr :: (a -> b -> b) -> b -> [a] -> b
foldr f v [ ] = v
foldr f v (x:xs) = f x (foldr f v xs)

Question 4

what is the order of execution given:
foldr (#) v [x0, x1, .. , xn] =

Answer 4

x0 # (x1 # (… (xn # v) … ))

Question 5

what is the syntax of foldl (recursive)

Answer 5

foldl :: (a -> b -> a) -> a -> [b] -> a
fold f v [ ] = v
foldl f v (x:xs) = foldl f (f v x) xs

Question 6

what is the order of execution given:
foldl (#) v [x0, x1, … , xn]

Answer 6

(… ((v # x0) # x1 …) # xn

Question 7

describe the composition function

Answer 7

(.) :: (b -> c) -> (a -> b) -> (a -> c)
f . g = \x -> f (g x)