Hi Adrian,
Thanks for the explanations. Could we perhaps examine one recursive example in detail, i.e., step-by-step, as I'm still confused? Maybe the following program from chapter 2 of
http://book.realworldhaskell.org?
myDrop n xs = if n <= 0 || null xs
then xs
else myDrop (n - 1) (tail xs)
Danke,
Caitlin
--- On Wed, 3/18/09, Adrian Neumann
Hi.
As a Haskell
beginner, I was wondering if someoneone could explain how the following programs function (pardon the pun)?
This function takes some type which has an ordering defined, i.e. you can compare its elements to one another
maximum' :: (Ord a) => [a] -> a
it doesn't work for an empty list
maximum' [] = error "maximum of empty list"
the maximum of a one element list is the lone element. this is the base case which will be eventually reached by the recursion
maximum' [x] = x
should the list have more than one element
maximum' (x:xs)
compare the first element to the maximum of the other elements. if it's greater, it's the maximum
| x > maxTail = x
otherwise the maximum of the other elements is the maximum of the whole list
| otherwise = maxTail
how to compute the maximum of the other elements? just use this function again. after a while we will only have one element left and reach the base case above.
where maxTail = maximum' xs
This function takes a number and a list of some type a
take' :: (Num i, Ord i) => i -> [a] -> [a]
first, ignore the list and check whether n is <= 0. in this case return an empty list. this is the base case, that's eventually reached by the recursion
take' n _ | n <= 0 = []
otherwise, check if the list is empty. this is another base case.
take' _ [] = []
if neither n<=0 or the list empty, take the first element, x, and put it on front of the prefix of length (n-1) of the other elements. use take' again, to get that prefix. after a while either n is 0 or there are no more elements in the list and we reach the base case
take' n (x:xs) = x : take' (n-1) xs
Take two lists
zip' :: [a] -> [b] -> [(a,b)]
if either one of them is empty, stop
zip' _ [] = [] zip' [] _ = []
otherwise prepend a tuple, build from the two first elements to the zipped list of the other elements. after a while one of the lists should become empty and the base case is reached.
zip' (x:xs) (y:ys) = (x,y):zip' xs ys
quicksort :: (Ord a) => [a] -> [a]
empty list -> nothing to do
quicksort [] = [] quicksort (x:xs) =
otherwise take the first element of the list and use it to split the list in two halves. one with all the elements that are smaller or equal than x, the other one with all those that are bigger. now sort them and put x in the middle. that should give us a sorted whole. how to sort them? just use quicksort again! after some splitting the lists will become empty and the recursion stops.
let smallerSorted = quicksort [a | a <- xs, a <= x] biggerSorted = quicksort [a | a <- xs, a > x] in smallerSorted ++ [x] ++ biggerSorted
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