[Haskell-cafe] Explaining monads

[Jeff Polakow]

Hello,

> On 14/08/07, Jeff Polakow <jeff.polakow at db.com> 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


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