# MonadPlus reform proposal

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=== MonadZero === | === MonadZero === | ||

− | + | <haskell> | |

− | + | class Monad m => MonadZero m where | |

+ | mzero :: m a | ||

+ | </haskell> | ||

satisfying '''Left Zero''': | satisfying '''Left Zero''': | ||

− | + | ||

+ | <haskell> | ||

+ | mzero >>= k = mzero | ||

+ | </haskell> | ||

=== MonadPlus === | === MonadPlus === | ||

− | + | <haskell> | |

− | + | class MonadZero m => MonadPlus m where | |

+ | mplus :: m a -> m a -> m a | ||

+ | </haskell> | ||

satisfying '''Monoid''' and '''Left Distribution''': | satisfying '''Monoid''' and '''Left Distribution''': | ||

− | + | ||

− | + | <haskell> | |

− | + | 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) | ||

+ | </haskell> | ||

=== MonadOr === | === MonadOr === | ||

− | + | <haskell> | |

− | + | class MonadZero m => MonadOr m where | |

+ | morelse :: m a -> m a -> m a | ||

+ | </haskell> | ||

satisfying '''Monoid''' and '''Left Catch''': | satisfying '''Monoid''' and '''Left Catch''': | ||

− | + | ||

− | + | <haskell> | |

− | + | morelse mzero b = b | |

− | + | 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 == | ||

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

− | + | <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