Understanding Recursion in Haskell: Functions, Base Cases, and Examples

1. Haskell Chapter 4

2. Recursion • Like other languages • Base case • Recursive call • Author programs a number of built-in functions as examples

3. Maximum maximum' :: (Ord a) => [a] -> a maximum' [] = error "can't take maximum of empty list“ -- base case, if only one item, return it maximum' [x] = x -- else return max of first element or recursive call maximum' (x:xs) = max x (maximum' xs)

4. Replicate replicate' :: Int -> a -> [a] replicate' n x -- base case returns empty list | n <= 0 = [] -- else cons element to result of recursive call | otherwise = x : replicate' (n-1) x • Used guards because boolean condition, not a pattern • replicate' 3 5 • 5 : replicate’ 2 5 => [5,5,5] • 5 : replicate’ 1 5 => [5, 5] • 5: replicate’ 0 5 => [5] • n == 0, => []

5. Take • Two base cases (n=0, or empty list) • Guard without otherwise will fall through to patterns take' :: (Num i, Ord i) => i -> [a] -> [a] take' n _ | n <= 0 = [] take' _ [] = [] take' n (x:xs) = x : take' (n-1) xs

6. Reverse • Note ++ rather than : because both are lists • : works at front of list, not back reverse' :: [a] -> [a] reverse' [] = [] reverse' (x:xs) = reverse' xs ++ [x]

7. Repeat • Haskell supports infinite lists repeat' :: a -> [a] repeat' x = x:repeat' x • repeat 3 • 3: repeat 3 • 3: repeat 3 • etc,

8. Zip zip' :: [a] -> [b] -> [(a,b)] zip' _ [] = [] zip' [] _ = [] zip' (x:xs) (y:ys) = (x,y):zip' xsys

9. Quick Exercise • With a partner, trace this code with this list of numbers: • [5,2,6,7,1,3,9,4] quicksort :: (Ord a) => [a] -> [a] quicksort [] = [] quicksort (x:xs) = let smallerOrEqual = [a | a <- xs, a <= x] larger = [a | a <- xs, a > x] in quicksortsmallerOrEqual ++ [x] ++ quicksort larger Turn in for class participation credit

10. Play and Share? • No, let’s start on the homework.