http://stackoverflow.com/questions/16283298/haskell-pointless-performance-efficiently-map-multiple-functions-to-the-same-d

gistfile1.hs

a note on dave4420's comment: 

    sequence [a,b] 
     = a >>= (\x -> b >>= (\y -> return [x,y])) 
     = a >>= (\x -> sequence [b] >>= (\xs -> return x:xs))

For `Monad ((->) r)`,  `(f >>= k) r = k (f r) r = (k.f) r r = join (k.f) r` 
(makes sense, because in general, `f>>=k = join (fmap k f)`. 

so, `sequence [a,b] r = (a >>= k1) r = k1 (a r) r`. 
(`a :: m x ~ (r -> x)`, `k1 :: (x -> m [x]) ~ (x -> r -> [x])`, 
 `a>>=k1 :: m [x]`).  

so, `sequence :: [m a] -> m [a] ~ [r -> a] -> (r -> [a])`.