MonadPlus

MonadPlus class (base)

import Control.Monad

The MonadPlus class is defined like this:

class (Monad m) => MonadPlus m where
  mzero :: m a
  mplus :: m a -> m a -> m a

The precise set of rules that MonadPlus should obey is not agreed upon.

• Monoid — mplus and mzero form a monoid:

mplus mzero a = a
mplus a mzero = a
mplus (mplus a b) c = mplus a (mplus b c)

• Left Zero — mzero is a left zero for >>=:

mzero >>= k = mzero

• Left Distribution:

mplus a b >>= k = mplus (a >>= k) (b >>= k)

• Left Catch — this is rarely advocated, but Maybe and IO satisfy this as an alternative to Left Distribution.

mplus (return a) b = return a

Which satisfies what?

[] satisfies Monoid, Left Zero, and Left Distribution.

Maybe, IO and STM satisfy Monoid, Left Zero, and Left Catch.

Which rules?

Martin & Gibbons choose Monoid, Left Zero, and Left Distribution. This makes [] a MonadPlus, but not Maybe or IO.

What should be done?

It is proposed that the class be separated into MonadZero, MonadPlus, MonadOr. See MonadPlus reform proposal.