1) Am I right in thinking that any type with two elements ("m a") is always a Monad? (IO String, Maybe Int, etc).
2) When I say "m a >>= f" the >>= just pulls the "a" out of "m a" and passes it to "f". Right?
3) The last two properties are not comparing values but functions. Right? For example, reading the second-last property:
(m >>= return) :: a -> m a
Where (m >>= return) is defined by (\x -> m x >>= return). Right? And this is why you can write the last property:
(k >>= h) :: a -> h a defined by (\x -> k a >>= h) This is what allows us to make (k >>= h) the second argument of ">>=" as in the last property:
m >>= (k >>= h) == (m >>= k) >>= h
Am I right?
I am also a beginner, so you should take my words with the grain of salt. Strange enough, the monad description that helped me most is the Wikipedia article: http://en.wikipedia.org/wiki/Monad_(functional_programming) This basically answers some of your questions by defining monad as triple (type constructor, bind function and return function), with certain properties. S.