Blow your mind

Helpful Idioms

 -- splitting in twos (alternating)
 -- "1234567" -> ("1357", "246")
 foldr (\a (x,y) -> (a:y,x)) ("","")

 -- splitting in N
 -- 2 -> "1234567" -> ["12", "34", "56", "7"]
 until (null . snd) (\(a,b) -> let (x,y) = splitAt 2 b in (a++[x],y)) $ ([], [1..7])

 -- split at whitespace
 -- "hello world" -> ["hello","world"]
 words
 fst . until (null . snd) 
             (\(a,b) -> let (x,y) = break (==' ') b 
                        in (a++[x], drop 1 y)) 
             $ ([], "hello world")

 -- combinations
 -- "12" -> "45" -> ["14", "15", "24", "25"]
 sequence ["12", "45"]

 -- factorial
 -- 6 -> 720
 product [1..6]
 foldl1 (*) [1..6]
 (!!6) $ unfoldr (\(n,f) -> Just (f, (n+1,f*n))) (1,1)
 fix (\f (n,g) -> if n > 6 then g else f (n+1,g*n)) (1,1)

 -- interspersing with newlines
 -- ["hello","world"] -> "hello world"
 unlines
 intersperse '\n'

 -- sorting by a custom function
 -- length -> ["abc", "ab", "a"] -> ["a", "ab", "abc"]
 sortBy length
 map snd . sortBy fst . map (length &&& id) 
 
 
 -- zweierpotenzen
 iterate (*2) 1
 unfoldr (\z -> Just (z,2*z)) 1

 -- simulating lisp's cond
 case () of () | 1 > 2     -> True
               | 3 < 4     -> False
               | otherwise -> True

 -- add indices to list for later use
 -- [3,3,3] -> [(0,3),(1,3),(2,3)]
 zip [0..]
 

 -- fibonacci series
 unfoldr (\(f1,f2) -> Just (f1,(f2,f1+f2))) (1,1)
 fibs = 1:1:zipWith (+) fibs (tail fibs)


 -- naive matrix operations
 -- m = [[1,2],[3,4],[5,6]]
 transpose
 scalMul s  = map (map (s*))
 invert     = scalMul (-1)
 matMul a b = zipWith (zipWith (*)) a (transpose b)
 matAdd     = zipWith (zipWith (+))

 -- unjust'ify list of Maybe's
 -- [Just 4, Nothing, Just 3] -> [4,3]
 catMaybes

 -- find substring
 -- "ell" -> "hello" -> True
 substr a b = any (a `elem`) $ liftM inits (tails b)

 -- apply a list of functions to an argument
 -- even -> odd -> 4 -> [True,False]
 map ($4) [even,odd]
 sequence [even,odd] 4
 
 
 -- apply a function to two other function the same argument
 -- (lifting to the function monad (->))
 -- even 4 && odd 4 -> False
 liftM2 (&&) even odd 4
 liftM2 (>>) putStrLn return "hello"    -- putStrLn "hello" >> return "hello"

 {-
 either
 maybe
 group
 fun with monad, monadPlus
 liftM
 -}