On Wed, 2009-02-04 at 22:16 +0200, Tymur Porkuian wrote:
For me, the key to understanding monads was that monad is "a value that know how to apply functions to itself". Or, more correctly, a container that knows how to apply functions to whatever is inside it.
Close. (Monads are not `values' but types, but I'll let that slide). Remembering that all Haskell functions take a single argument, but we use currying to support an arbitrary number of arguments, we can arrange the Monad type class hierarchy like this: * Functor: A functor F allows a single function to be applied to a single F value. Multiple arguments (or none) are not supported; the definition of application does what you probably *don't* want if the function returns an F value itself. * Applicative: An applicative functor A allows a function of n arguments (for n >= 0) to be applied to n A values. However, the definition of application does what you probably *don't* want if the function returns an A value itself. * Monad: A monad M allows a function of n arguments (for n >= 0) to be applied to n M values; in addition, if the function returns an M value itself, you can combine that result with the arguments in a sensible way. jcc