Jonathan Cast wrote:
I see... I was under the impression that "mplus" is just any arbitrary binary operation over a given monad. How do you know what it does for a specific monad?
Process of elimination. Sometimes, this doesn't narrow things down to a single operation, but it gives you a good idea of what you're supposed to expect.
Firstly, mplus and mzero form a (natural) monoid, put together. That rules out a number of binary operations right there.
Secondly, mzero has a null law with (>>=):
mzero >>= f = mzero
So, if you have
a `mplus` b
and a calls mzero at some point (not inside another call to mplus --- nice and informal, that description :), then you know b will be executed instead. (Maybe b will be executed *anyway*. I didn't say anything about that).
So mplus and mzero are basically suitable for three kinds of things:
* Exception handling * Back-tracking * Parallelism
Usually, when you see a MonadPlus instance, you expect one or more of these.
That's in the general case.
ListT is a special case; the (somewhat idealized) specification of ListT (what people want to happen when they use ListT) is that ListT m in some sense `adds back-tracking' to m. Where back-tracking choice is implemented by mplus.
Right. OK. So... isn't there a class somewhere called MonadChoice or similar, which defines (<|>)?