Problems 1

• 1 + sqrt 9 * 4 + 13 = 26.0::Double
• "asfd" ++ "dfsa" = "asfddfsa" ::String
• "a" : "dfsa type error
• [‘a’] ++ [‘d’,’f’,’s’,’a’] ="adfsa"::[Char]
• [20,30..100] = [20,30,40,50,60,70,80,90,100]::[Int]
• sum [1..10] = 1+2+3+4+5+6+7+8+9+10 = 55 :: Int
• let x = 5 in x*(x+1) = 5*6 = 30 :: Int
• 1:(take 1 [1,2]) = [1,1]::[Int]
• [[1,2],[3,4]] = [[1,2],[3,4]]::[[Int]]

1. Given the following definition of the function f, simplify the expression f (f 1 2) (f 3 4), showing all your steps.

f :: Int -> Int -> Int

f x y = 2*x + 3

1. Write a function isLetter :: Char -> Bool that determines whether its argument is a letter of the alphabet.
2. isletter x = (x>='A' && x<= 'Z') || (x>='a' && x<= 'z')
3. Write a function capitalise :: String -> String that makes all the letters upper case.

capitalise xs = map toUpper xs

4. Write a function that determines whether or not one string is the prefix of another string.

prefix [] ys = True

prefix xs [] = False

prefix (x:xs) (y:ys) = if (x==y) then prefix xs ys else False

or

prefix xs ys = (xs == take (length xs) ys)

5. Write a function that occurs :: Int -> [Int] -> Int that returns the number of times a given number occurs in a list.

occurs x xs = sum [1|y<-xs, y == x]

6. Write a function reverse that reverses a string.

reverse1 [] = []

reverse1 (x:xs) = (reverse1 xs) ++ [x]

or

reverse2 [] = []

reverse2 xs = rev (xs,[])

where

rev ([],ys) = ys

rev (x:xs,ys) = rev (xs, (x:ys))

7. Write a function palindrome :: String -> Bool that determines whether its argument is a palindrome. A palindrome is a string which is the same when you reverse it; for example, ‘abccba’ is a palindrome, but ‘abcca’ is not.