Difference between revisions of "MonadPlus"

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.

mplus mzero a = a
mplus a mzero = a
mplus (mplus a b) c = mplus a (mplus b c)

mzero >>= k = mzero

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

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

@@ Line 1: / Line 1: @@
+{{Standard class|MonadPlus|module=Control.Monad|module-doc=Control-Monad|package=base}}
 The '''MonadPlus''' class is defined like this:
@@ Line 6: / Line 7: @@
 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:
+ mplus mzero a = a
+ mplus a mzero = a
+ mplus (mplus a b) c = mplus a (mplus b c)
+* '''Left Zero''' &mdash; <tt>mzero</tt> is a left zero for <tt>&gt;&gt;=</tt>:
+ mzero >>= k = mzero
+* '''Left Distribution''':
+ mplus a b >>= k = mplus (a >>= k) (b >>= k)
+* '''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
+== 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>.
+[[Category:Standard Classes]]