On Thu, Aug 31, 2006 at 07:23:55PM +0200, Benjamin Franksen wrote:
I'd like to know if the following reasoning can be made more precise:
As we all know, the monadic bind operation has type:
bind :: Monad m => m a -> (a -> m b) -> m b
My intuition says that in order to apply the second argument to some non-trivial (i.e. non-bottom) value of type a, the bind operator needs to be able to somehow 'extract' a value (of type a) from the first argument (of type m a).
The bind operator doesn't have to neccesarily apply the second argument to anything. What if m is Maybe, and the first arguments is Nothing? And if the bind operator "wants" to apply the second argument to something, it doesn't have to do it only once - consider the [] monad. Other examples: get :: State s s -- from Control.Monad.State there is no way you can extract an 's' value from "get" alone - you have to supply the state to the whole computation Cont (const ()) :: Cont () a -- from Control.Monad.Cont whatever you do, you won't be able to extract an 'a' typed value, non-bottom from this computation. Cont is defined as: newtype Cont r a = Cont {runCont :: (a -> r) -> r)} Best regards Tomasz