H-99: Ninety-Nine Haskell Problems
These are Haskell translations of Ninety Nine Lisp Problems.
(*) Find the last box of a list. Example: * (my-last '(a b c d)) (D)
This is "last" in Prelude, which is defined as:
last :: [a] -> a last [x] = x last (_:xs) = last xs
(*) Find the last but one box of a list. Example: * (my-but-last '(a b c d)) (C D)
This can be done by dropping all but the last two elements of a list:
myButLast :: [a] -> [a] myButLast list = drop ((length list) - 2) list
(*) Find the K'th element of a list. The first element in the list is number 1. Example: * (element-at '(a b c d e) 3) C
This is (almost) the infix operator !! in Prelude, which is defined as:
(!!) :: [a] -> Int -> a (x:_) !! 0 = x (_:xs) !! n = xs !! (n-1)
Except this doesn't quite work, because !! is zero-indexed, and element-at should be one-indexed. So:
elementAt :: [a] -> Int -> a elementAt list i = list !! (i-1)
(*) Find the number of elements of a list.
This is "length" in Prelude, which is defined as:
length :: [a] -> Int length  = 0 length (_:l) = 1 + length l
(*) Reverse a list.
This is "reverse" in Prelude, which is defined as:
reverse :: [a] -> [a] reverse = foldl (flip (:)) 
The standard definition is concise, but not very readable. Another way to define reverse is:
reverse :: [a] -> [a] reverse  =  reverse (x:xs) = reverse xs ++ [x]
(*) Find out whether a list is a palindrome. A palindrome can be read forward or backward; e.g. (x a m a x).
This is trivial, because we can use reverse:
isPalindrome :: (Eq a) => [a] -> Bool isPalindrome xs = xs == (reverse xs)
(**) Flatten a nested list structure. Transform a list, possibly holding lists as elements into a `flat' list by replacing each list with its elements (recursively). Example: * (my-flatten '(a (b (c d) e))) (A B C D E)
This is tricky, because lists in Haskell are homogeneous. [1, [2, [3, 4], 5]] is a type error. We have to devise some way of represent a list that may (or may not) be nested:
data NestedList a = Elem a | List [NestedList a] flatten :: NestedList a -> [a] flatten (Elem x) = [x] flatten (List ) =  flatten (List (x:xs)) = flatten x ++ flatten (List xs)
Our NestedList datatype is either a single element of some type (Elem a), or a list of NestedLists of the same type. (List [NestedList a]). Let's try it out in ghci:
*Main> flatten (Elem 5)  *Main> flatten (List [Elem 1, List [Elem 2, List [Elem 3, Elem 4], Elem 5]]) [1,2,3,4,5] *Main> flatten (List )