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MonadPlus

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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'''.
 
* '''Left Catch''' &mdash; this is rarely advocated, but <tt>Maybe</tt> and <tt>IO</tt> satisfy this as an alternative to '''Left Distribution'''.
 
mplus (return a) b = return a
 
mplus (return a) b = return a
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=== Which satisfies what? ===
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<tt>[]</tt> satisfies '''Monoid''', '''Left Zero''', and '''Left Distribution'''.
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<tt>Maybe</tt>, <tt>IO</tt> and <tt>STM</tt> satisfy '''Monoid''', '''Left Zero''', and '''Left Catch'''.
   
 
== Which rules? ==
 
== Which rules? ==

Revision as of 00:34, 16 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

1 Which satisfies what?

[] satisfies Monoid, Left Zero, and Left Distribution.

Maybe, IO and STM satisfy Monoid, Left Zero, and Left Catch.

2 Which rules?

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

3 What should be done?

It is proposed that the class be separated into MonadZero, MonadPlus, MonadOr. See MonadPlus reform proposal.