module L02B where -- Examples from Week 2, lecture B -- Higher-Order Functions -- dave 2012-11-08 import Data.List(sort,group) import Data.Char(isSpace) import Test.QuickCheck import Test.QuickCheck.Function -- for testing HO functions ------------------------------------------ verse = "A dying mosquito exclaimed,\nA chemist has poisoned my brain!\nThe cause of his sorrow\nWas para-dichloro-\nDiphenyl-trichloroethane\n" -- map examples, abs, shout -- def with list comprehensions map' f xs = [f x | x <- xs] filter' p xs = [x | x <- xs, p x] sum' [] = 0 sum' (n:ns) = n + sum' ns and' [] = True and' (b:bs) = b && and' bs foldr' op b [] = b foldr' op b (x:xs) = x `op` foldr' op b xs -- foldr -- foldr op z xs -- foldl op z [a,b,c,d] == ((z `op` a) `op` b) ... unlines' ss = foldr joinNl "" ss where joinNl s1 s2 = s1 ++ "\n" ++ s2 -- takeLine, takeWord takeLine "" = "" takeLine (c:cs) | c /= '\n' = c:takeLine cs | otherwise = "" takeWord "" = "" takeWord (c:cs) | not(isSpace c) = c:takeWord cs | otherwise = "" takeWhile' :: (a -> Bool) -> [a] -> [a] takeWhile' p [] = [] takeWhile' p (x:xs) | p x = x:takeWhile' p xs | otherwise = [] -- takeLine'' cs = takeWhile' (\x -> x /= '\n') cs takeLine'' = takeWhile' (/= '\n') -- Another pattern: lines, commaSep lines' [] = [] lines' css = takeWhile (/= '\n') css : lines' (drop 1 (dropWhile (/= '\n') css)) nosh = "spam,eggs,chips,spam" commSep [] = [] commSep css = takeWhile (/= ',') css : commSep (drop 1 \$ dropWhile (/= ',') css) -- segments -- see slides ------------------------------------- -- More ways to build functions: Partial application -- redundant brackets in the type help explain partial application: -- meaningless function f :: Char -> (Bool -> (String -> String)) -- redundant brackets f c b s = c:s ++ show (not b) ++ s -- Eta reduction -- f x = e x can be rewritten as f = e -- f y x = e x --> f y = e -- use hlint to find this kind of thing -- Aside -- Fixity. How do you know when to skip brackets? -- \$ -- Example Design (Slides) -- Function composition wordCount = unlines . map (\(w,n) -> w ++ ": " ++ show n) . map (\ws -> (head ws,length ws)) . group . sort . words prop_mapmap (Fun _ f) (Fun _ g) xs = map f (map g xs) == map (f.g) xs where types = (f :: Int -> Int, g :: Int -> Int) -- foldr puzzles -- foldr (:) ys xs -- foldr atEndOf [] xs where y `atEndof` ys = ys ++ [y] -- foldr (\y ys -> f y : ys) [] xs