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Example Picture

Example Picture. type Picture = [[Char]] horse :: Picture horse = [[’.’,’.’,’.’,’.’,’.’,’.’,’.’,’#’,’#’,’.’,’.’,’.’], [’.’,’.’,’.’,’.’,’.’,’#’,’#’,’.’,’.’,’#’,’.’,’.’], [’.’,’.’,’.’,’#’,’#’,’.’,’.’,’.’,’.’,’.’,’#’,’.’], [’.’,’.’,’#’,’.’,’.’,’.’,’.’,’.’,’.’,’.’,’#’,’.’],

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Example Picture

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  1. Example Picture type Picture = [[Char]] horse :: Picture horse = [[’.’,’.’,’.’,’.’,’.’,’.’,’.’,’#’,’#’,’.’,’.’,’.’], [’.’,’.’,’.’,’.’,’.’,’#’,’#’,’.’,’.’,’#’,’.’,’.’], [’.’,’.’,’.’,’#’,’#’,’.’,’.’,’.’,’.’,’.’,’#’,’.’], [’.’,’.’,’#’,’.’,’.’,’.’,’.’,’.’,’.’,’.’,’#’,’.’], [’.’,’.’,’#’,’.’,’.’,’.’,’#’,’.’,’.’,’.’,’#’,’.’], [’.’,’.’,’#’,’.’,’.’,’.’,’#’,’#’,’#’,’.’,’#’,’.’], [’.’,’#’,’.’,’.’,’.’,’.’,’#’,’.’,’.’,’#’,’#’,’.’], [’.’,’.’,’#’,’.’,’.’,’.’,’#’,’.’,’.’,’.’,’.’,’.’], [’.’,’.’,’.’,’#’,’.’,’.’,’.’,’#’,’.’,’.’,’.’,’.’], [’.’,’.’,’.’,’.’,’#’,’.’,’.’,’#’,’.’,’.’,’.’,’.’], [’.’,’.’,’.’,’.’,’.’,’#’,’.’,’#’,’.’,’.’,’.’,’.’], [’.’,’.’,’.’,’.’,’.’,’.’,’#’,’#’,’.’,’.’,’.’,’.’]]

  2. Example Picture (cont’d) printPicture :: Picture -> IO () printPicture = putStr . concat . map (++"\n") printPicture horse .......##... .....##..#.. ...##.....#. ..#.......#. ..#...#...#. ..#...###.#. .#....#..##. ..#...#..... ...#...#.... ....#..#.... .....#.#.... ......##....

  3. Example Picture (cont’d) printPicture :: Picture -> IO () printPicture = putStr . concat . map (++"\n") rotate90 :: Picture -> Picture rotate90 pic = [ [ line !! i | line <- reverse pic ] | i <- [0..length pic - 1] ] scale :: Picture -> Int -> Picture scale pic n | n <= 0 = [[]] | otherwise = map (concat . map (replicate n)) pic

  4. Local definitions There are two syntactic constructions for local definitions • let … in … • … where … doubleSquare :: Int -> Int doubleSquare x = let sqx = x*x in sqx + sqx strange :: Int -> Int -> Int strange x y = let diff = x – y sum = x + y in diff^2 – diff + sum^2 - sum strange x y = let diff = x – y; sum = x + y in …

  5. maxsq :: Int -> Int -> Int maxsq x y | sqx > sqy = sqx | otherwise = sqy where sqx = sq x sqy = sq y sq :: Int -> Int sq z = z*z maxsq x y | sqx > sqy = sqx | otherwise = sqy where sqx = sq x sqy = sq y sq :: Int -> Int sq x = x*x

  6. Example: Supermarket billing List of bar codes: [1234,4719,3814,1112,1113,1234] Produce a bill: Haskell Stores Dry Sherry, 1lt...........5.40 Fish Fingers..............1.21 Orange Jelly..............0.56 Hula Hoops (Giant)........1.33 Unknown Item..............0.00 Dry Sherry, 1lt...........5.40 Total....................13.90

  7. Example: Supermarket billing (cont’d) type Name = String type Price = Int type BarCode = Int type Database = [(BarCode,Name,Price)] codeIndex = [ (4719,”Fish Fingers”,121), (5643,”Nappies”,1010), (3814,”Orange Jelly”,56), (1111,”Hula Hoops”,21), (1112,”Hula Hoops (Giant)”,133), (1234,”Dry Sherry, 1lt”,540)]

  8. Example: Supermarket billing (cont’d) type TillType = [BarCode] type BillType = [(Name,Price)] makeBill :: TillType -> BillType formatBill :: BillType -> String produceBill :: TillType -> String lineLength :: Int lineLength = 30

  9. Example: Supermarket billing (cont’d) look :: Database -> BarCode -> (Name,Price) look db b = if res == [] then ("Unknown Item",0) else head res where res = [ (n,p) | (bn,n,p) <- db, b == bn ] lookup :: BarCode -> (Name,Price) lookup = look codeIndex makeBill :: TillType -> BillType makeBill = map lookup formatPence :: Price -> String formatPence price = show d ++ "." ++ if p < 10 then "0" ++ show p else show p where d = price `div` 100 p = price `mod` 100

  10. Example: Supermarket billing (cont’d) formatLine :: (Name,Price) -> String formatLine (name,price) = name ++ replicate n '.' ++ ps ++ "\n" where ps = formatPence price n = lineLength - length name - length ps formatLines :: BillType -> String formatLines = concat . map formatLine makeTotal :: BillType -> Price makeTotal = sum . map snd formatTotal :: Price -> String formatTotal price = "\nTotal" ++ replicate n '.' ++ ps where ps = formatPence price n = lineLength - 5 - length ps

  11. Example: Supermarket billing (cont’d) formatBill :: BillType -> String formatBill bill = title ++ formatLines bill ++ formatTotal (makeTotal bill) where title = replicate sp ' ' ++ "Haskell Stores\n\n" sp = (lineLength - 14) `div` 2 produceBill :: TillType -> String produceBill = formatBill . makeBill printBill :: TillType -> IO () printBill = putStr . produceBill

  12. Case Construction firstDigit :: String -> Char firstDigit st = case (digits st) of [] -> ’\0’ (x:_) -> x General form: case e of p1 -> e1 p2 -> e2 ... pk -> ek

  13. Primitive recursion over lists sum :: [Int] -> Int sum [] = 0 sum (x:xs) = x + sum xs General pattern: fun [] = … fun (x:xs) = … x … xs … fun xs … iSort :: [Int] -> [Int] iSort [] = [] iSort (x:xs) = ins x (iSort xs) where ins x [] = [x] ins x z@(y:ys) = if x<=y then x:z else y:ins x ys

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