H-99: Ninety-Nine Haskell Problems

These are Haskell translations of Ninety Nine Lisp Problems.

Problem 1

(*) 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

Problem 2

(*) 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

Problem 3

(*) 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)

Problem 4

(*) 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

Problem 5

(*) Reverse a list.

This is "reverse" in Prelude, which is defined as:

reverse          :: [a] -> [a]
reverse          =  foldl (flip (:)) []

Problem 6

(*) 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)