Haskell Monads Cheat Sheet

class Applicative m => Monad m where  (>>=)  :: m a -> (a -> m b) -> m b  return :: a -> m a  return = pure-- Monad laws (must hold for any correct instance):-- Left identity:  return a >>= f  ==  f a-- Right identity: m >>= return    ==  m-- Associativity:  (m >>= f) >>= g ==  m >>= (\x -> f x >>= g)

safeDivide :: Int -> Int -> Maybe IntsafeDivide _ 0 = NothingsafeDivide x y = Just (x `div` y)compute :: Maybe Intcompute = do  a <- safeDivide 10 2  b <- safeDivide a 0   -- Nothing short-circuits the rest  return (a + b)-- Desugars to:compute2 :: Maybe Intcompute2 =  safeDivide 10 2 >>= \a ->  safeDivide a 0  >>= \b ->  return (a + b)

-- Maybe: optional/failable computationlookupUser :: Int -> Maybe StringlookupUser 1 = Just "Ada"lookupUser _ = Nothing-- Either: failable computation carrying an error valueparseAge :: String -> Either String IntparseAge s = case reads s of  [(n, "")] -> Right n  _         -> Left ("invalid age: " ++ s)-- List: nondeterministic computation (all combinations)pairs :: [(Int, Int)]pairs = do  x <- [1, 2]  y <- [10, 20]  return (x, y)  -- [(1,10),(1,20),(2,10),(2,20)]-- IO: sequencing side effectsmain :: IO ()main = do  putStrLn "What's your name?"  name <- getLine  putStrLn ("Hello, " ++ name)

import Control.Monad.Readerimport Control.Monad.Writerimport Control.Monad.State-- Reader: implicit read-only environmentgreeting :: Reader String Stringgreeting = do  name <- ask  return ("Hello, " ++ name)-- Writer: accumulate a log alongside a resultlogStep :: Writer [String] IntlogStep = do  tell ["starting"]  tell ["computing"]  return 42-- State: threaded mutable-looking statecounter :: State Int Intcounter = do  n <- get  put (n + 1)  return nrunState counter 0 -- (0, 1)