</para>
</sect2>
+ <!-- ===================== MONAD COMPREHENSIONS ===================== -->
+
+<sect2 id="monad-comprehensions">
+ <title>Monad comprehensions</title>
+ <indexterm><primary>monad comprehensions</primary></indexterm>
+
+ <para>
+ Monad comprehesions generalise the list comprehension notation,
+ including parallel comprehensions
+ (<xref linkend="parallel-list-comprehensions"/>) and
+ transform comprenensions (<xref linkend="generalised-list-comprehensions"/>)
+ to work for any monad.
+ </para>
+
+ <para>Monad comprehensions support:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>
+ Bindings:
+ </para>
+
+<programlisting>
+[ x + y | x <- Just 1, y <- Just 2 ]
+</programlisting>
+
+ <para>
+ Bindings are translated with the <literal>(>>=)</literal> and
+ <literal>return</literal> functions to the usual do-notation:
+ </para>
+
+<programlisting>
+do x <- Just 1
+ y <- Just 2
+ return (x+y)
+</programlisting>
+
+ </listitem>
+ <listitem>
+ <para>
+ Guards:
+ </para>
+
+<programlisting>
+[ x | x <- [1..10], x <= 5 ]
+</programlisting>
+
+ <para>
+ Guards are translated with the <literal>guard</literal> function,
+ which requires a <literal>MonadPlus</literal> instance:
+ </para>
+
+<programlisting>
+do x <- [1..10]
+ guard (x <= 5)
+ return x
+</programlisting>
+
+ </listitem>
+ <listitem>
+ <para>
+ Transform statements (as with <literal>-XTransformListComp</literal>):
+ </para>
+
+<programlisting>
+[ x+y | x <- [1..10], y <- [1..x], then take 2 ]
+</programlisting>
+
+ <para>
+ This translates to:
+ </para>
+
+<programlisting>
+do (x,y) <- take 2 (do x <- [1..10]
+ y <- [1..x]
+ return (x,y))
+ return (x+y)
+</programlisting>
+
+ </listitem>
+ <listitem>
+ <para>
+ Group statements (as with <literal>-XTransformListComp</literal>):
+ </para>
+
+<programlisting>
+[ x | x <- [1,1,2,2,3], then group by x ]
+[ x | x <- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
+[ x | x <- [1,1,2,2,3], then group using myGroup ]
+</programlisting>
+
+ <para>
+ The basic <literal>then group by e</literal> statement is
+ translated using the <literal>mgroupWith</literal> function, which
+ requires a <literal>MonadGroup</literal> instance, defined in
+ <ulink url="&libraryBaseLocation;/Control-Monad-Group.html"><literal>Control.Monad.Group</literal></ulink>:
+ </para>
+
+<programlisting>
+do x <- mgroupWith (do x <- [1,1,2,2,3]
+ return x)
+ return x
+</programlisting>
+
+ <para>
+ Note that the type of <literal>x</literal> is changed by the
+ grouping statement.
+ </para>
+
+ <para>
+ The grouping function can also be defined with the
+ <literal>using</literal> keyword.
+ </para>
+
+ </listitem>
+ <listitem>
+ <para>
+ Parallel statements (as with <literal>-XParallelListComp</literal>):
+ </para>
+
+<programlisting>
+[ (x+y) | x <- [1..10]
+ | y <- [11..20]
+ ]
+</programlisting>
+
+ <para>
+ Parallel statements are translated using the
+ <literal>mzip</literal> function, which requires a
+ <literal>MonadZip</literal> instance defined in
+ <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
+ </para>
+
+<programlisting>
+do (x,y) <- mzip (do x <- [1..10]
+ return x)
+ (do y <- [11..20]
+ return y)
+ return (x+y)
+</programlisting>
+
+ </listitem>
+ </itemizedlist>
+
+ <para>
+ All these features are enabled by default if the
+ <literal>MonadComprehensions</literal> extension is enabled. The types
+ and more detailed examples on how to use comprehensions are explained
+ in the previous chapters <xref
+ linkend="generalised-list-comprehensions"/> and <xref
+ linkend="parallel-list-comprehensions"/>. In general you just have
+ to replace the type <literal>[a]</literal> with the type
+ <literal>Monad m => m a</literal> for monad comprehensions.
+ </para>
+
+ <para>
+ Note: Even though most of these examples are using the list monad,
+ monad comprehensions work for any monad.
+ The <literal>base</literal> package offers all necessary instances for
+ lists, which make <literal>MonadComprehensions</literal> backward
+ compatible to built-in, transform and parallel list comprehensions.
+ </para>
+<para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
+to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
+<programlisting>
+Expressions: e
+Declarations: d
+Lists of qualifiers: Q,R,S
+
+-- Basic forms
+D[ e | ] = return e
+D[ e | p <- e, Q ] = e >>= \p -> D[ e | Q ]
+D[ e | e, Q ] = guard e >> \p -> D[ e | Q ]
+D[ e | let d, Q ] = let d in D[ e | Q ]
+
+-- Parallel comprehensions (iterate for multiple parallel branches)
+D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] >>= \(Qv,Rv) -> D[ e | S ]
+
+-- Transform comprehensions
+D[ e | Q then f, R ] = f D[ Qv | Q ] >>= \Qv -> D[ e | R ]
+
+D[ e | Q then f by b, R ] = f b D[ Qv | Q ] >>= \Qv -> D[ e | R ]
+
+D[ e | Q then group using f, R ] = f D[ Qv | Q ] >>= \ys ->
+ case (fmap selQv1 ys, ..., fmap selQvn ys) of
+ Qv -> D[ e | R ]
+
+D[ e | Q then group by b using f, R ] = f b D[ Qv | Q ] >>= \ys ->
+ case (fmap selQv1 ys, ..., fmap selQvn ys) of
+ Qv -> D[ e | R ]
+
+where Qv is the tuple of variables bound by Q (and used subsequently)
+ selQvi is a selector mapping Qv to the ith component of Qv
+
+Operator Standard binding Expected type
+--------------------------------------------------------------------
+return GHC.Base t1 -> m t2
+(>>=) GHC.Base m1 t1 -> (t2 -> m2 t3) -> m3 t3
+(>>) GHC.Base m1 t1 -> m2 t2 -> m3 t3
+guard Control.Monad t1 -> m t2
+fmap GHC.Base forall a b. (a->b) -> n a -> n b
+mgroupWith Control.Monad.Group forall a. (a -> t) -> m1 a -> m2 (n a)
+mzip Control.Monad.Zip forall a b. m a -> m b -> m (a,b)
+</programlisting>
+The comprehension should typecheck when its desugaring would typecheck.
+</para>
+<para>
+Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
+Without rebindable
+syntax, the operators from the "standard binding" module are used; with
+rebindable syntax, the operators are looked up in the current lexical scope.
+For example, parallel comprehensions will be typechecked and desugared
+using whatever "<literal>mzip</literal>" is in scope.
+</para>
+<para>
+The rebindable operators must have the "Expected type" given in the
+table above. These types are surprisingly general. For example, you can
+use a bind operator with the type
+<programlisting>
+(>>=) :: T x y a -> (a -> T y z b) -> T x z b
+</programlisting>
+In the case of transform comprehensions, notice that the groups are
+parameterised over some arbitrary type <literal>n</literal> (provided it
+has an <literal>fmap</literal>, as well as
+the comprehension being over an arbitrary monad.
+</para>
+</sect2>
+
<!-- ===================== REBINDABLE SYNTAX =================== -->
<sect2 id="rebindable-syntax">
g (x:xs) = xs ++ [ x :: a ]
</programlisting>
This program will be rejected, because "<literal>a</literal>" does not scope
-over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
+over the definition of "<literal>g</literal>", so "<literal>x::a</literal>"
means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
quantification rules.
</para></listitem>
<programlisting>
f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
</programlisting>
-Here, the type signature <literal>forall a. ST s Bool</literal> brings the
+Here, the type signature <literal>forall s. ST s Bool</literal> brings the
type variable <literal>s</literal> into scope, in the annotated expression
<literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
</para>
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