[Haskell-cafe] What is MonadPlus good for?

[ajb at spamcop.net]

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