Haskell does have "fail" as part of the Monad typeclass. But it is being depreciated and moved into the MonadFail class.

Haskell's Monad also has >> and >>= both defined as part of the typeclass itself; instead of making >> a normal function. The typeclass does provide a default implementation of >> in terms of >>=.

But you are correct. In general all you need for a monad is bind and return.

http://hackage.haskell.org/package/base-4.9.1.0/docs/Prelude...

The "categorical" definition of monads uses return and, instead of bind,

  join :: m(m a) -> m a

You don't need to specify it if you already have bind/>>= and return/pure, since they can be derived from each other.

For instance, purely by "following the types",

  f :: a -> m b
  fmap f :: m a -> m (m b)
  join (fmap f) :: m a -> m b

In other words,

  (>>=) :: m a -> (a -> m b) -> m b
  ma >>= f = join (fmap f ma)

is a perfectly good definition of bind I you have join.

(>>=) :: m a -> (a -> m b) -> m b

(>>) :: m a -> m b -> m b

There are two forms of bind.

The >> function is used when the function does not need the value produced by the first monadic operator.