(x >>= f) >>= g == x >>= (\v -> f v >>= g)
However, this seems to me a kind of mathematical identity. If it is mathematical identity, a programmer need not care about this law to implement a monad. Can anyone give me an example implementation of monad that violate this law ?
It's well known that "ListT m" monad violates this law in general (though it satisfies it for some particular monads m). For example, Prelude Control.Monad.List> runListT ((ListT [[(),()]] >> ListT [[()], [()]]) >> ListT [[1],[2]]) [[1,1],[1,2],[2,1],[2,2],[1,1],[1,2],[2,1],[2,2],[1,1],[1,2],[2,1], [2,2],[1,1],[1,2],[2,1],[2,2]] Prelude Control.Monad.List> runListT (ListT [[(),()]] >> (ListT [[()], [()]] >> ListT [[1],[2]])) [[1,1],[1,2],[1,1],[1,2],[2,1],[2,2],[2,1],[2,2],[1,1],[1,2],[1,1], [1,2],[2,1],[2,2],[2,1],[2,2]]