[Haskell-cafe] Explaining monads

[Jeff Polakow]

Hello,

> On 8/14/07, Jeff Polakow <jeff.polakow at db.com> wrote:
> > One general intuition about monads is that they represent computations
> > rather than simple (already computed) values:
> 
> >     x :: Int               -- x is an Int
> >     x :: Monad m => m Int  -- x is a computation of an Int
> 
> What's a "computation"? It seems to me that in a lazy language, x::Int
> represents a computation of an int, not an "already computed" value.
>
This intuition for monads as "computations" is independent of operational 
semantics.

> x::[Int] is a computation that returns multiple values. x::(Int,Int)
> is a computation that returns a pair of values. x::() is a computation
> that returns nothing. x::Map a b is a computation that gives a way to
> associate values of type a with values of type b. Some of these are
> monads, some are not. What's the difference between them? Why are you
> calling certain values "computations"?
>
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. 
However, I do not mean to imply that everything which can be viewed as a 
computation of something is a monad. 

In any case, this is only meant to be a general (i.e. high-level) 
intuition. BTW, this intuition was, more or less, the one used by Moggi 
when describing how monads can be used to describe denotational models for 
languages.

-Jeff


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