🔍 Filter

Theory

filter bottles the selection pattern: traverse a list, keep elements that satisfy a predicate $p:a\to \text{Bool}$.

Type: $\text{filter}::(a\to \text{Bool})\to [a]\to [a]$

Semantics

filter _  []     = []
filter p (x:xs)  = if p x
		           then x : filter p xs   -- keep
                   else     filter p xs  -- skip

Examples

isEven  x = x `mod` 2 == 0
evens   xs = filter isEven xs        -- [2,4]
 
isFour  w = length w == 4
fourChr xs = filter isFour xs        -- ["must","work"]

Straight recursion as shown above is idiomatic; under the hood filter is tail‑recursive and works in tandem with list comprehensions.

evens = [ x | x <- xs, even x ]