Re: [Haskell-cafe] Explaining monads

Hello,

On 14/08/07, Jeff Polakow wrote: Of course, the type [Int] denotes a value which is a list of Ints; additionally [Int] can be viewed as a value representing the nondeterministic computation of a single Int. Generally, the type Monad m => m Int can be viewed as a value representing the computation of an Int.

But thats not really right. What exactly m Int does /depends/ on m. It might represent 0 or more computations of Int, or computations of Int carrying some extra stuff around, or complex control logic about what the computation does when.

Perhaps the confusion is in the word computation. I'm using the word in an abstract sense. I do not mean the actual execution of Haskell code to produce a value. Thus, under this intuition: The type Int represents a value which denotes an Int. The type m Int denotes a value which is a single computation (for an unspecified notion of computation) of an Int. A specific computation of an Int might result in several, or zero, actual Ints (the list monad); a String or an Int (the Either String monad); the constant () (the trivial monad); ... The type Monad m => m Int cannot represent multiple computations of an Int. The type Monad m => [m Int] represents multiple computations of an Int (of course, any container type can be used in place of list). -Jeff --- This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error) please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden.