MonadPlus

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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

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

IO

3 What should be done?

It is proposed that the class be separated into

MonadZero

MonadPlus

MonadOr

. See MonadPlus reform proposal.

Retrieved from "http://www.haskell.org/haskellwiki/MonadPlus"

Category: Standard classes

@@ Line 2: / Line 2: @@
 The '''MonadPlus''' class is defined like this:
- class (Monad m) => MonadPlus m where
+<haskell>
+class (Monad m) => MonadPlus m where
    mzero :: m a
    mplus :: m a -> m a -> m a
+</haskell>
 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''':
- 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'''.
- 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? ==
-[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? ==
-It is proposed that the class be separated into MonadZero, MonadPlus, MonadOr. See [[MonadPlus reform proposal]].
+It is proposed that the class be separated into <hask>MonadZero</hask>, <hask>MonadPlus</hask>, <hask>MonadOr</hask>. See [[MonadPlus reform proposal]].
-[[Category:Standard classes]]

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