[Haskell-cafe] What is MonadPlus good for?
ajb at spamcop.net
ajb at spamcop.net
Mon Feb 14 19:01:53 EST 2005
G'day all.
Quoting Josef Svenningsson <josef.svenningsson at gmail.com>:
> You're of course absolutely right that it doesn't make sense to talk
> about mzero being a right-identity for bind if the monad doesn't
> support mzero. I should have been more clear. Let me have another try
> at explaining myself.
OK.
> Let's consider a specific monad transformer, say (ReaderT r). What I
> hope to convince you of is that (ReaderT r) cannot be said break the
> mzero-is-right-identity-for-bind law.
Yep, I'd agree with that. The important thing is this instance:
instance (MonadPlus m) => MonadPlus (ReaderT r m)
This says that if m is a MonadPlus (we'll assume for a moment that this
includes the "mzero is a right zero for bind" law), then ReaderT r m
is a MonadPlus (including the same law).
I was thinking more along the lines of Ralf Hinze's nondeterminism
transformer monad:
http://haskell.org/hawiki/NonDeterminism
The relevant instance is this:
instance (Monad m) => MonadPlus (NondetT m)
That is, if m is a Monad, then NondetT m is a MonadPlus. This is not
true if a requirement for MonadPlus is that it include the "mzero is a
right zero for bind" law. Indeed, such a transformer is impossible to
write if that law is a requirement.
> You claimed that monad transformers break the
> mzero-is-right-identity-for-bind law because they can be applied to
> IO. I say, it's not the monad transformers fault. They cannot possibly
> be expected to repair the law if they are given a faulty monad.
IO is not a faulty monad. It satisfies all of the laws that a monad is
supposed to satisfy.
Cheers,
Andrew Bromage
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