Recursion recursion recursion recursion
Edge conditions are elements defined non recursively and allow the recursion to terminate. The best way to understand recursion is to try the example below:
Maximum
maximum' :: (Ord a) => [a] -> a
maximum' [] = error "maximum of empty list"
maximum' [x] = x
maximum' (x:xs)
| x > maxTail = x
| otherwise = maxTail
where maxTail = maximum' xs
Or better
maximum' :: (Ord a) => [a] -> a
maximum' [] = error "maximum of empty list"
maximum' [x] = x
maximum' (x:xs) = max x (maximum' xs)
Replicate
replicate' :: (Num i, Ord i) => i -> a -> [a]
replicate' n x
| n <= 0 = []
| otherwise = x:replicate' (n-1) x
Take
take' :: (Num i, Ord i) => i -> [a] -> [a]
take' n _
| n <= 0 = []
take' _ [] = []
take' n (x:xs) = x : take' (n-1) xs
Reverse
reverse' :: [a] -> [a]
reverse' [] = []
reverse' (x:xs) = reverse' xs ++ [x]
Repeat, here we don't have any edge condition. Ther result will be an infinite list
repeat' :: a -> [a]
repeat' x = x:repeat' x
Zip
zip' :: [a] -> [b] -> [(a,b)]
zip' _ [] = []
zip' [] _ = []
zip' (x:xs) (y:ys) = (x,y):zip' xs ys
Elem
elem' :: (Eq a) => a -> [a] -> Bool
elem' a [] = False
elem' a (x:xs)
| a == x = True
| otherwise = a `elem'` xs
Quick sort
quicksort :: (Ord a) => [a] -> [a]
quicksort [] = []
quicksort (x:xs) =
let smallerSorted = quicksort [a | a <- xs, a <= x]
biggerSorted = quicksort [a | a <- xs, a > x]
in smallerSorted ++ [x] ++ biggerSorted