Re: [Haskell-cafe] mtl: Why there is "Monoid w" constraint in the definition of class MonadWriter?

* Edward Z. Yang [2012-12-08 14:18:38-0800]

Excerpts from Roman Cheplyaka's message of Sat Dec 08 14:00:52 -0800 2012:

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* Edward Z. Yang [2012-12-08 11:19:01-0800]

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The monoid instance is necessary to ensure adherence to the monad laws.

This doesn't make any sense to me. Are you sure you're talking about the MonadWriter class and not about the Writer monad?

Well, I assume the rules for Writer generalize for MonadWriter, no?

Here's an example. Haskell monads have the associativity law:

(f >=> g) >=> h === f >=> (g >=> h)

From this, we can see that

(m1 >> m2) >> m3 === m1 >> (m2 >> m3)

Now, consider tell. We'd expect it to obey a law like this:

tell w1 >> tell w2 === tell (w1 <> w2)

First of all, I don't see why two tells should be equivalent to one tell. Imagine a MonadWriter that additionally records the number of times 'tell' has been called. (You might argue that your last equation should be a MonadWriter class law, but that's a different story — we're talking about the Monad laws here.) Second, even *if* the above holds (two tells are equivalent to one tell), then there is *some* function f such that tell w1 >> tell w2 == tell (f w1 w2) It isn't necessary that f coincides with mappend, or even that the type w is declared as a Monoid at all. The only thing we can tell from the Monad laws is that that function f should be associative. Roman