# MonadPlus reform proposal

### From HaskellWiki

(→Instances of both) |
|||

(6 intermediate revisions by 5 users not shown) | |||

Line 7: | Line 7: | ||

=== 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 == | ||

Line 39: | Line 54: | ||

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> | ||

+ | |||

+ | The left-biased implementation of mplus for the Maybe monad should be used as an implementation of morelse, but it is also possible to give an unbiased mplus for Maybe: | ||

+ | |||

+ | <haskell> | ||

+ | instance MonadPlus Maybe where | ||

+ | mplus (Just a) Nothing = a | ||

+ | mplus Nothing (Just a) = a | ||

+ | mplus _ _ = Nothing | ||

+ | |||

+ | instance MonadOr Maybe where | ||

+ | morelse (Just a) _ = Just a | ||

+ | morelse _ b = b | ||

+ | </haskell> | ||

+ | |||

+ | == Discussion == | ||

+ | Given that Control.Applicative(Alternative) now defines a class which seems innately bound to '''Left Catch''', at least in spirit, it seems to make sense to clean up MonadPlus such that all instances obey '''Left Distribution'''? --sclv | ||

+ | |||

+ | I'd actually suggest almost the opposite, that MonadPlus be dispensed with and merged into Monad. The (controversial) fail method looks no different than an mzero, except the string argument; indeed, so far as I know <tt>fail s</tt> is just mzero for any MonadPlus. MonadPlus is also barely made use of; just guard and msum in the standard? To be concrete, I would make the following the default definitions (in Monad): | ||

+ | |||

+ | <haskell> | ||

+ | mzero = fail "something" | ||

+ | mplus a b = a | ||

+ | </haskell> | ||

+ | |||

+ | These are thus somewhat trivial by default, but having msum=head and guard=assert (roughly; more like <tt>(`assert` return ())</tt>) for less-flexible monads doesn't seem actually wrong and could be useful fallbacks. | ||

+ | |||

+ | I also question the claim that Maybe and IO should be thought of as "left catch". IO is not even in MonadPlus, and I don't see how it can be meaningfully in any way other than the above. Maybe does satisfy Left Catch, but it seems almost like that's only because it's such a simple monad (holding only one value). It is a useful observation that it fails Left Distribution, but that may only call for weaker Monad/Plus conditions. | ||

+ | |||

+ | The MonadOr idea is a solid one, but it seems to be taking the monad in a different direction. So if there's a good match in Control.Applicative or Parsec, that might be the best place to develop that idea. -- Galen | ||

+ | |||

+ | The default <hask>mplus</hask> doesn't satisfy <hask>mplus mzero b = b</hask>, so you lose Monoid which seems to be the only thing people actually agree on :) -- [[User:Benmachine|Benmachine]] | ||

− | [[Category:Proposals]] | + | [[Category:Proposals]] [[Category:Monad]] |

## Revision as of 01:01, 18 May 2011

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

The left-biased implementation of mplus for the Maybe monad should be used as an implementation of morelse, but it is also possible to give an unbiased mplus for Maybe:

instance MonadPlus Maybe where mplus (Just a) Nothing = a mplus Nothing (Just a) = a mplus _ _ = Nothing instance MonadOr Maybe where morelse (Just a) _ = Just a morelse _ b = b

## 3 Discussion

Given that Control.Applicative(Alternative) now defines a class which seems innately bound to **Left Catch**, at least in spirit, it seems to make sense to clean up MonadPlus such that all instances obey **Left Distribution**? --sclv

I'd actually suggest almost the opposite, that MonadPlus be dispensed with and merged into Monad. The (controversial) fail method looks no different than an mzero, except the string argument; indeed, so far as I know `fail s` is just mzero for any MonadPlus. MonadPlus is also barely made use of; just guard and msum in the standard? To be concrete, I would make the following the default definitions (in Monad):

mzero = fail "something" mplus a b = a

These are thus somewhat trivial by default, but having msum=head and guard=assert (roughly; more like `(`assert` return ())`) for less-flexible monads doesn't seem actually wrong and could be useful fallbacks.

I also question the claim that Maybe and IO should be thought of as "left catch". IO is not even in MonadPlus, and I don't see how it can be meaningfully in any way other than the above. Maybe does satisfy Left Catch, but it seems almost like that's only because it's such a simple monad (holding only one value). It is a useful observation that it fails Left Distribution, but that may only call for weaker Monad/Plus conditions.

The MonadOr idea is a solid one, but it seems to be taking the monad in a different direction. So if there's a good match in Control.Applicative or Parsec, that might be the best place to develop that idea. -- Galen

The default