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MonadPlus reform proposal

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=== MonadZero ===
 
=== MonadZero ===
   
class Monad m => MonadZero m where
+
<haskell>
mzero :: m a
+
class Monad m => MonadZero m where
  +
mzero :: m a
  +
</haskell>
   
 
satisfying '''Left Zero''':
 
satisfying '''Left Zero''':
mzero >>= k = mzero
+
  +
<haskell>
  +
mzero >>= k = mzero
  +
</haskell>
   
 
=== MonadPlus ===
 
=== MonadPlus ===
   
class MonadZero m => MonadPlus m where
+
<haskell>
mplus :: m a -> m a -> m a
+
class MonadZero m => MonadPlus m where
  +
mplus :: m a -> m a -> m a
  +
</haskell>
   
 
satisfying '''Monoid''' and '''Left Distribution''':
 
satisfying '''Monoid''' and '''Left Distribution''':
mplus mzero b = b
+
mplus a mzero = a
+
<haskell>
mplus (mplus a b) c = mplus a (mplus b c)
+
mplus mzero b = b
mplus a b >>= k = mplus (a >>= k) (b >>= k)
+
mplus a mzero = a
  +
mplus (mplus a b) c = mplus a (mplus b c)
  +
mplus a b >>= k = mplus (a >>= k) (b >>= k)
  +
</haskell>
   
 
=== MonadOr ===
 
=== MonadOr ===
   
class MonadZero m => MonadOr m where
+
<haskell>
morelse :: m a -> m a -> m a
+
class MonadZero m => MonadOr m where
  +
morelse :: m a -> m a -> m a
  +
</haskell>
   
 
satisfying '''Monoid''' and '''Left Catch''':
 
satisfying '''Monoid''' and '''Left Catch''':
morelse mzero b = b
+
morelse a mzero = a
+
<haskell>
morelse (morelse a b) c = morelse a (morelse b c)
+
morelse mzero b = b
morelse (return a) b = return a
+
morelse a mzero = a
  +
morelse (morelse a b) c = morelse a (morelse b c)
  +
morelse (return a) b = return a
  +
</haskell>
   
 
== Instances of both ==
 
== Instances of both ==
Line 39: Line 39:
 
Some types could be made instances of both. For instance:
 
Some types could be made instances of both. For instance:
   
instance MonadOr [] where
+
<haskell>
  +
instance MonadOr [] where
 
morelse [] b = b
 
morelse [] b = b
 
morelse a b = a
 
morelse a b = a
  +
</haskell>
   
 
[[Category:Proposals]] [[Category:Monad]]
 
[[Category:Proposals]] [[Category:Monad]]

Revision as of 00:26, 4 January 2007

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.

Contents

1 Proposal

It is proposed that MonadPlus be split like this:

1.1 MonadZero

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

satisfying Left Zero:

mzero >>= k = mzero

1.2 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)

1.3 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

2 Instances of both

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

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