Difference between revisions of "MonadPlus"

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* '''Monoid''' &mdash; <hask>mplus</hask> and <hask>mzero</hask> form a monoid:
 
* '''Monoid''' &mdash; <hask>mplus</hask> and <hask>mzero</hask> form a monoid:
<haskell>
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:<haskell>
 
mplus mzero a = a
 
mplus mzero a = a
 
mplus a mzero = a
 
mplus a mzero = a
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</haskell>
 
</haskell>
   
* '''Left Zero''' &mdash; <hask>mzero</hask> is a left zero for <tt>&gt;&gt;=</tt>:
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* '''Left Zero''' &mdash; <hask>mzero</hask> is a left zero for <code>(>>=)</code>:
<haskell>
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:<haskell>
 
mzero >>= k = mzero
 
mzero >>= k = mzero
 
</haskell>
 
</haskell>
   
 
* '''Left Distribution''':
 
* '''Left Distribution''':
<haskell>
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:<haskell>
 
mplus a b >>= k = mplus (a >>= k) (b >>= k)
 
mplus a b >>= k = mplus (a >>= k) (b >>= k)
 
</haskell>
 
</haskell>
   
 
* '''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'''.
<haskell>
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:<haskell>
 
mplus (return a) b = return a
 
mplus (return a) b = return a
 
</haskell>
 
</haskell>
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=== Which satisfies what? ===
 
=== Which satisfies what? ===
   
<hask>[]</hask> satisfies '''Monoid''', '''Left Zero''', and '''Left Distribution'''.
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* <hask>[]</hask> satisfies '''Monoid''', '''Left Zero''', and '''Left Distribution'''.
   
<hask>Maybe</hask>, <hask>IO</hask> and <hask>STM</hask> satisfy '''Monoid''', '''Left Zero''', and '''Left Catch'''.
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* <hask>Maybe</hask>, <hask>IO</hask> and <hask>STM</hask> satisfy '''Monoid''', '''Left Zero''', and '''Left Catch'''.
   
 
== Which rules? ==
 
== Which rules? ==
   
[http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/tactics.pdf Martin & Gibbons] choose '''Monoid''', '''Left Zero''', and '''Left Distribution'''. This makes <hask>[]</hask> a MonadPlus, but not <hask>Maybe</hask> or <hask>IO</hask>.
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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 <hask>[]</hask> a <code>MonadPlus</code>, but not <hask>Maybe</hask> or <hask>IO</hask>.
   
 
== What should be done? ==
 
== What should be done? ==

Latest revision as of 22:55, 5 April 2021

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 satisfies what?

  • [] satisfies Monoid, Left Zero, and Left Distribution.
  • Maybe, IO and STM satisfy Monoid, Left Zero, and Left Catch.

Which rules?

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

What should be done?

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