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MonadPlus reform proposal

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The MonadPlus class is ambiguous: while all instances satisfy Monoid and Left Zero, some such as [] satisfy Left Distribution, while others such as Maybe and IO satisfy Left Catch.

It is proposed that MonadPlus be split like this:


1 MonadZero

class Monad m => MonadZero m where
   mzero :: m a

satisfying Left Zero:

mzero >>= k = mzero

2 MonadPlus

class MonadZero m => MonadPlus m where
   mplus :: m a -> m a -> m a

satisfying Monoid and Left Distribution:

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

3 MonadOr

class MonadZero m => MonadOr m where
   morelse :: m a -> m a -> m a

satisfying Monoid and Left Catch:

morelse mzero b = b
morelse a mzero = a
morelse (morelse a b) c = morelse a (morelse b c)
morelse (return a) b = return a

4 Instances of both

Some types could be made instances of both. For instance:

instance MonadOr [] where
  morelse [] b = b
  morelse a b = a