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MonadPlus

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{{Standard class|MonadPlus|module=Control.Monad|module-doc=Control-Monad|package=base}}
 
The '''MonadPlus''' class is defined like this:
 
The '''MonadPlus''' class is defined like this:
   
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The precise set of rules that MonadPlus should obey is not agreed upon.
 
The precise set of rules that MonadPlus should obey is not agreed upon.
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* '''Monoid''' &mdash; <tt>mplus</tt> and <tt>mzero</tt> form a monoid:
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mplus mzero a = a
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mplus a mzero = a
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mplus (mplus a b) c = mplus a (mplus b c)
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* '''Left Zero''' &mdash; <tt>mzero</tt> is a left zero for <tt>&gt;&gt;=</tt>:
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mzero >>= k = mzero
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* '''Left Distribution''':
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mplus a b >>= k = mplus (a >>= k) (b >>= k)
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* '''Left Catch''' &mdash; this is rarely advocated, but <tt>Maybe</tt> and <tt>IO</tt> satisfy this as an alternative to '''Left Distribution'''.
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mplus (return a) b = return a
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== Which rules? ==
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[http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/tactics.pdf Martin & Gibbons] choose '''Monoid''', '''Left Zero''', and '''Left Distribution'''. This makes <tt>[]</tt> a MonadPlus, but not <tt>Maybe</tt> or <tt>IO</tt>.
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[[Category:Standard Classes]]

Revision as of 23:16, 15 January 2006

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.

  • Monoidmplus and mzero form a monoid:
mplus mzero a = a
mplus a mzero = a
mplus (mplus a b) c = mplus a (mplus b c)
  • Left Zeromzero 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 rules?

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