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MonadPlus

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The '''MonadPlus''' class is defined like this:
 
The '''MonadPlus''' class is defined like this:
   
class (Monad m) => MonadPlus m where
+
<haskell>
  +
class (Monad m) => MonadPlus m where
 
mzero :: m a
 
mzero :: m a
 
mplus :: m a -> m a -> m a
 
mplus :: m a -> m a -> m a
  +
</haskell>
   
 
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.
   
* '''Monoid''' &mdash; <tt>mplus</tt> and <tt>mzero</tt> form a monoid:
+
* '''Monoid''' &mdash; <hask>mplus</hask> and <hask>mzero</hask> form a monoid:
mplus mzero a = a
+
<haskell>
mplus a mzero = a
+
mplus mzero a = a
mplus (mplus a b) c = mplus a (mplus b c)
+
mplus a mzero = a
  +
mplus (mplus a b) c = mplus a (mplus b c)
  +
</haskell>
   
* '''Left Zero''' &mdash; <tt>mzero</tt> is a left zero for <tt>&gt;&gt;=</tt>:
+
* '''Left Zero''' &mdash; <hask>mzero</hask> is a left zero for <tt>&gt;&gt;=</tt>:
mzero >>= k = mzero
+
<haskell>
  +
mzero >>= k = mzero
  +
</haskell>
   
 
* '''Left Distribution''':
 
* '''Left Distribution''':
mplus a b >>= k = mplus (a >>= k) (b >>= k)
+
<haskell>
  +
mplus a b >>= k = mplus (a >>= k) (b >>= k)
  +
</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'''.
mplus (return a) b = return a
+
<haskell>
  +
mplus (return a) b = return a
  +
</haskell>
  +
  +
=== Which satisfies what? ===
  +
  +
<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'''.
   
 
== 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 <tt>[]</tt> a MonadPlus, but not <tt>Maybe</tt> or <tt>IO</tt>.
+
[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>.
  +
  +
== What should be done? ==
   
[[Category:Standard Classes]]
+
It is proposed that the class be separated into <hask>MonadZero</hask>, <hask>MonadPlus</hask>, <hask>MonadOr</hask>. See [[MonadPlus reform proposal]].

Latest revision as of 02:40, 31 July 2008

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.

  • Monoid
    mplus
    and
    mzero
    form a monoid:
mplus mzero a = a
mplus a mzero = a
mplus (mplus a b) c = mplus a (mplus b c)
  • Left Zero
    mzero
    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

[edit] 1 Which satisfies what?

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

[edit] 2 Which rules?

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

[edit] 3 What should be done?

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