> The only thing we can tell from the Monad laws is that that function f should be associative.
That f is associative is a very small step away from f forming a monoid. What about listen :: m a -> m (w, a)? What laws should it hold that are compatible with those of the monad and those of tell? Reasoning about listen is enough to force the existence of a monoid identity. -- Kim-Ee On Sun, Dec 9, 2012 at 5:41 AM, Roman Cheplyaka <r...@ro-che.info> wrote: > * Edward Z. Yang <ezy...@mit.edu> [2012-12-08 14:18:38-0800] > > Excerpts from Roman Cheplyaka's message of Sat Dec 08 14:00:52 -0800 > 2012: > > > * Edward Z. Yang <ezy...@mit.edu> [2012-12-08 11:19:01-0800] > > > > 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 > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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