Lecture 15-2

COMP105 Lectures 2020-11-12

filter

filterkeeps only the elements for which f returns True.

filter' :: (a -> Bool) -> [a] -> [a]
filter' _ [] = []
filter' f (x:xs)
	| f x 		= x : rest
	| otherwise	= rest
	where rest 	= filter' f xs
	
filter' even [1..10]
> [2,4,6,8,10]

In comparison to map which applies a function to each element in a list. filter will apply a boolean test to each element in the list and if it fails it will remove the element from the list.

Combining map & filter

square_even :: [Int] -> [Int]
square_even list = map (^2) (filter even list)

square_even [1..10]
> [4,16,36,64,100]

Higher Order Programming

map and filter are examples of higher order programming. This style:

• De-emphasises recursion.
• Focuses on applying functions to lists.
• Are available in imperative languages (Python C++).

There is a whole family of higher order programming functions available in Haskell.

Exercises

1. onlyDiv3 = filter (\x -> mod x 3 == 0)
2. onlyLower = filter (\x -> elem x ['a'..'z'])
3. noEven = map (filter odd)