[Haskell-cafe] Re: Request to review my attempt at understanding Monads

[Thomas Danecker]

> imo, the most import ingredient to understand monads, is to understand
> lazy evaluation. In Haskell, everything is about values. If you have a
> function f :: a -> b, then f x stands for a value of type b (nothing
> is evaluated yet).
> Now, if you have another function g :: a -> M b, then g x stands for a
> value of type M b, that is, a value of type b requiring something more
> (encoded by the monad M). Depending on which Monad you used, you need
> to do something the the value M b to get to the actual value b. In the
> case of the State monad, you have to run it with an initial state. In
> the case of IO, you can't do anything and so you have to give the
> value to the runtime-system (via the main-function). In the case of
> the List monad (which represents non-determinism), you can choose any
> element of the resulting list, or, more commonly, use every possible
> result (i.e. the whole list).

One thing is missing here: The interesting aspect of a monad is, that
it always allows you to "compose". Via the bind function (>>=) :: m b
-> (b -> m c) -> m c, you can take a value of M b and derive from it a
new value of M c by using the previously encapsulated value b.

--
Thomas Danecker