Re: [Haskell-cafe] Commutative monads vs Applicative functors

On Wed, 14 May 2008, David Menendez wrote:

On Tue, May 13, 2008 at 9:06 PM, Ronald Guida wrote:

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I have a few questions about commutative monads and applicative functors.

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From what I have read about applicative functors, they are weaker than monads because with a monad, I can use the results of a computation to select between alternative future computations and their side effects, whereas with an applicative functor, I can only select between the results of computations, while the structure of those computations and their side effects are fixed in advance.

But then there are commutative monads. I'm not exactly sure what a commutative monad is, but my understanding is that in a commutative monad the order of side effects does not matter.

This leads me to wonder, are commutative monads still stronger than applicative functors, or are they equivalent?

And by the way, what exactly is a commutative monad?

Interestingly I used a Writer monad with a commutative monoid recently, which is also an example of a commutative monad.