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<?xml version="1.0" encoding="iso-8859-1"?>
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<para>
<indexterm><primary>language, GHC</primary></indexterm>
<indexterm><primary>extensions, GHC</primary></indexterm>
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As with all known Haskell systems, GHC implements some extensions to
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the language.  They can all be enabled or disabled by commandline flags
or language pragmas. By default GHC understands the most recent Haskell
version it supports, plus a handful of extensions.
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</para>
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<para>
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Some of the Glasgow extensions serve to give you access to the
underlying facilities with which we implement Haskell.  Thus, you can
get at the Raw Iron, if you are willing to write some non-portable
code at a more primitive level.  You need not be &ldquo;stuck&rdquo;
on performance because of the implementation costs of Haskell's
&ldquo;high-level&rdquo; features&mdash;you can always code
&ldquo;under&rdquo; them.  In an extreme case, you can write all your
time-critical code in C, and then just glue it together with Haskell!
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</para>
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<para>
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Before you get too carried away working at the lowest level (e.g.,
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sloshing <literal>MutableByteArray&num;</literal>s around your
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program), you may wish to check if there are libraries that provide a
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&ldquo;Haskellised veneer&rdquo; over the features you want.  The
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separate <ulink url="../libraries/index.html">libraries
documentation</ulink> describes all the libraries that come with GHC.
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</para>
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<!-- LANGUAGE OPTIONS -->
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  <sect1 id="options-language">
    <title>Language options</title>
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    <indexterm><primary>language</primary><secondary>option</secondary>
    </indexterm>
    <indexterm><primary>options</primary><secondary>language</secondary>
    </indexterm>
    <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
    </indexterm>
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    <para>The language option flags control what variation of the language are
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    permitted.</para>
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    <para>Language options can be controlled in two ways:
    <itemizedlist>
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      <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
        (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
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        (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
      <listitem><para>
          Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
          thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
          </listitem>
      </itemizedlist></para>
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    <para>The flag <option>-fglasgow-exts</option>
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          <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
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	  is equivalent to enabling the following extensions:
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          &what_glasgow_exts_does;
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	    Enabling these options is the <emphasis>only</emphasis>
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	    effect of <option>-fglasgow-exts</option>.
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          We are trying to move away from this portmanteau flag,
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	  and towards enabling features individually.</para>
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  </sect1>
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<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
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<sect1 id="primitives">
  <title>Unboxed types and primitive operations</title>

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<para>GHC is built on a raft of primitive data types and operations;
"primitive" in the sense that they cannot be defined in Haskell itself.
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While you really can use this stuff to write fast code,
  we generally find it a lot less painful, and more satisfying in the
  long run, to use higher-level language features and libraries.  With
  any luck, the code you write will be optimised to the efficient
  unboxed version in any case.  And if it isn't, we'd like to know
  about it.</para>

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<para>All these primitive data types and operations are exported by the
library <literal>GHC.Prim</literal>, for which there is
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<ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
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(This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
</para>
<para>
If you want to mention any of the primitive data types or operations in your
program, you must first import <literal>GHC.Prim</literal> to bring them
into scope.  Many of them have names ending in "&num;", and to mention such
names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
</para>

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<para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
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and <link linkend="unboxed-tuples">unboxed tuples</link>, which
we briefly summarise here. </para>
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<sect2 id="glasgow-unboxed">
<title>Unboxed types
</title>

<para>
<indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
</para>

<para>Most types in GHC are <firstterm>boxed</firstterm>, which means
that values of that type are represented by a pointer to a heap
object.  The representation of a Haskell <literal>Int</literal>, for
example, is a two-word heap object.  An <firstterm>unboxed</firstterm>
type, however, is represented by the value itself, no pointers or heap
allocation are involved.
</para>

<para>
Unboxed types correspond to the &ldquo;raw machine&rdquo; types you
would use in C: <literal>Int&num;</literal> (long int),
<literal>Double&num;</literal> (double), <literal>Addr&num;</literal>
(void *), etc.  The <emphasis>primitive operations</emphasis>
(PrimOps) on these types are what you might expect; e.g.,
<literal>(+&num;)</literal> is addition on
<literal>Int&num;</literal>s, and is the machine-addition that we all
know and love&mdash;usually one instruction.
</para>

<para>
Primitive (unboxed) types cannot be defined in Haskell, and are
therefore built into the language and compiler.  Primitive types are
always unlifted; that is, a value of a primitive type cannot be
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bottom.  We use the convention (but it is only a convention)
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that primitive types, values, and
operations have a <literal>&num;</literal> suffix (see <xref linkend="magic-hash"/>).
For some primitive types we have special syntax for literals, also
described in the <link linkend="magic-hash">same section</link>.
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</para>

<para>
Primitive values are often represented by a simple bit-pattern, such
as <literal>Int&num;</literal>, <literal>Float&num;</literal>,
<literal>Double&num;</literal>.  But this is not necessarily the case:
a primitive value might be represented by a pointer to a
heap-allocated object.  Examples include
<literal>Array&num;</literal>, the type of primitive arrays.  A
primitive array is heap-allocated because it is too big a value to fit
in a register, and would be too expensive to copy around; in a sense,
it is accidental that it is represented by a pointer.  If a pointer
represents a primitive value, then it really does point to that value:
no unevaluated thunks, no indirections&hellip;nothing can be at the
other end of the pointer than the primitive value.
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A numerically-intensive program using unboxed types can
go a <emphasis>lot</emphasis> faster than its &ldquo;standard&rdquo;
counterpart&mdash;we saw a threefold speedup on one example.
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</para>

<para>
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There are some restrictions on the use of primitive types:
<itemizedlist>
<listitem><para>The main restriction
is that you can't pass a primitive value to a polymorphic
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function or store one in a polymorphic data type.  This rules out
things like <literal>[Int&num;]</literal> (i.e. lists of primitive
integers).  The reason for this restriction is that polymorphic
arguments and constructor fields are assumed to be pointers: if an
unboxed integer is stored in one of these, the garbage collector would
attempt to follow it, leading to unpredictable space leaks.  Or a
<function>seq</function> operation on the polymorphic component may
attempt to dereference the pointer, with disastrous results.  Even
worse, the unboxed value might be larger than a pointer
(<literal>Double&num;</literal> for instance).
</para>
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</listitem>
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<listitem><para> You cannot define a newtype whose representation type
(the argument type of the data constructor) is an unboxed type.  Thus,
this is illegal:
<programlisting>
  newtype A = MkA Int#
</programlisting>
</para></listitem>
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<listitem><para> You cannot bind a variable with an unboxed type
in a <emphasis>top-level</emphasis> binding.
</para></listitem>
<listitem><para> You cannot bind a variable with an unboxed type
in a <emphasis>recursive</emphasis> binding.
</para></listitem>
<listitem><para> You may bind unboxed variables in a (non-recursive,
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non-top-level) pattern binding, but you must make any such pattern-match
strict.  For example, rather than:
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<programlisting>
  data Foo = Foo Int Int#
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  f x = let (Foo a b, w) = ..rhs.. in ..body..
</programlisting>
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you must write:
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<programlisting>
  data Foo = Foo Int Int#

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  f x = let !(Foo a b, w) = ..rhs.. in ..body..
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</programlisting>
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since <literal>b</literal> has type <literal>Int#</literal>.
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</para>
</listitem>
</itemizedlist>
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</para>

</sect2>

<sect2 id="unboxed-tuples">
<title>Unboxed Tuples
</title>

<para>
Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
they're available by default with <option>-fglasgow-exts</option>.  An
unboxed tuple looks like this:
</para>

<para>

<programlisting>
(# e_1, ..., e_n #)
</programlisting>

</para>

<para>
where <literal>e&lowbar;1..e&lowbar;n</literal> are expressions of any
type (primitive or non-primitive).  The type of an unboxed tuple looks
the same.
</para>

<para>
Unboxed tuples are used for functions that need to return multiple
values, but they avoid the heap allocation normally associated with
using fully-fledged tuples.  When an unboxed tuple is returned, the
components are put directly into registers or on the stack; the
unboxed tuple itself does not have a composite representation.  Many
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of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
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tuples.
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In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
tuples to avoid unnecessary allocation during sequences of operations.
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</para>

<para>
There are some pretty stringent restrictions on the use of unboxed tuples:
<itemizedlist>
<listitem>

<para>
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Values of unboxed tuple types are subject to the same restrictions as
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other unboxed types; i.e. they may not be stored in polymorphic data
structures or passed to polymorphic functions.

</para>
</listitem>
<listitem>

<para>
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No variable can have an unboxed tuple type, nor may a constructor or function
argument have an unboxed tuple type.  The following are all illegal:
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<programlisting>
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  data Foo = Foo (# Int, Int #)
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  f :: (# Int, Int #) -&#62; (# Int, Int #)
  f x = x
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  g :: (# Int, Int #) -&#62; Int
  g (# a,b #) = a
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  h x = let y = (# x,x #) in ...
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</programlisting>
</para>
</listitem>
</itemizedlist>
</para>
<para>
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The typical use of unboxed tuples is simply to return multiple values,
binding those multiple results with a <literal>case</literal> expression, thus:
<programlisting>
  f x y = (# x+1, y-1 #)
  g x = case f x x of { (# a, b #) -&#62; a + b }
</programlisting>
You can have an unboxed tuple in a pattern binding, thus
<programlisting>
  f x = let (# p,q #) = h x in ..body..
</programlisting>
If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
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the resulting binding is lazy like any other Haskell pattern binding.  The
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above example desugars like this:
<programlisting>
  f x = let t = case h x o f{ (# p,q #) -> (p,q)
            p = fst t
            q = snd t
        in ..body..
</programlisting>
Indeed, the bindings can even be recursive.
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</para>

</sect2>
</sect1>

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<!-- ====================== SYNTACTIC EXTENSIONS =======================  -->

<sect1 id="syntax-extns">
<title>Syntactic extensions</title>
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    <sect2 id="unicode-syntax">
      <title>Unicode syntax</title>
      <para>The language
      extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
      enables Unicode characters to be used to stand for certain ASCII
      character sequences.  The following alternatives are provided:</para>

      <informaltable>
	<tgroup cols="2" align="left" colsep="1" rowsep="1">
	  <thead>
	    <row>
	      <entry>ASCII</entry>
              <entry>Unicode alternative</entry>
	      <entry>Code point</entry>
	      <entry>Name</entry>
	    </row>
	  </thead>
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<!--
               to find the DocBook entities for these characters, find
               the Unicode code point (e.g. 0x2237), and grep for it in
               /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
               your system.  Some of these Unicode code points don't have
               equivalent DocBook entities.
            -->

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	  <tbody>
	    <row>
	      <entry><literal>::</literal></entry>
	      <entry>::</entry> <!-- no special char, apparently -->
              <entry>0x2237</entry>
	      <entry>PROPORTION</entry>
	    </row>
          </tbody>
	  <tbody>
	    <row>
	      <entry><literal>=&gt;</literal></entry>
	      <entry>&rArr;</entry>
	      <entry>0x21D2</entry>
              <entry>RIGHTWARDS DOUBLE ARROW</entry>
	    </row>
          </tbody>
	  <tbody>
	    <row>
	      <entry><literal>forall</literal></entry>
	      <entry>&forall;</entry>
	      <entry>0x2200</entry>
              <entry>FOR ALL</entry>
	    </row>
          </tbody>
	  <tbody>
	    <row>
	      <entry><literal>-&gt;</literal></entry>
	      <entry>&rarr;</entry>
	      <entry>0x2192</entry>
              <entry>RIGHTWARDS ARROW</entry>
	    </row>
          </tbody>
	  <tbody>
	    <row>
	      <entry><literal>&lt;-</literal></entry>
	      <entry>&larr;</entry>
	      <entry>0x2190</entry>
              <entry>LEFTWARDS ARROW</entry>
	    </row>
          </tbody>
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	  <tbody>
	    <row>
	      <entry>-&lt;</entry>
	      <entry>&larrtl;</entry>
	      <entry>0x2919</entry>
	      <entry>LEFTWARDS ARROW-TAIL</entry>
	    </row>
          </tbody>

	  <tbody>
	    <row>
	      <entry>&gt;-</entry>
	      <entry>&rarrtl;</entry>
	      <entry>0x291A</entry>
	      <entry>RIGHTWARDS ARROW-TAIL</entry>
	    </row>
          </tbody>

	  <tbody>
	    <row>
	      <entry>-&lt;&lt;</entry>
	      <entry></entry>
	      <entry>0x291B</entry>
	      <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
	    </row>
          </tbody>

	  <tbody>
	    <row>
	      <entry>&gt;&gt;-</entry>
	      <entry></entry>
	      <entry>0x291C</entry>
	      <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
	    </row>
          </tbody>

	  <tbody>
	    <row>
	      <entry>*</entry>
	      <entry>&starf;</entry>
	      <entry>0x2605</entry>
	      <entry>BLACK STAR</entry>
	    </row>
          </tbody>

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        </tgroup>
      </informaltable>
    </sect2>

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    <sect2 id="magic-hash">
      <title>The magic hash</title>
      <para>The language extension <option>-XMagicHash</option> allows "&num;" as a
	postfix modifier to identifiers.  Thus, "x&num;" is a valid variable, and "T&num;" is
	a valid type constructor or data constructor.</para>

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      <para>The hash sign does not change semantics at all.  We tend to use variable
	names ending in "&num;" for unboxed values or types (e.g. <literal>Int&num;</literal>),
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        but there is no requirement to do so; they are just plain ordinary variables.
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	Nor does the <option>-XMagicHash</option> extension bring anything into scope.
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	For example, to bring <literal>Int&num;</literal> into scope you must
	import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
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	the <option>-XMagicHash</option> extension
	then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
	that is now in scope.</para>
      <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
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	<itemizedlist>
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	  <listitem><para> <literal>'x'&num;</literal> has type <literal>Char&num;</literal></para> </listitem>
	  <listitem><para> <literal>&quot;foo&quot;&num;</literal> has type <literal>Addr&num;</literal></para> </listitem>
	  <listitem><para> <literal>3&num;</literal> has type <literal>Int&num;</literal>. In general,
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	  any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
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            <literal>-0x3A&num;</literal> as well as <literal>32&num;</literal></para>.</listitem>
	  <listitem><para> <literal>3&num;&num;</literal> has type <literal>Word&num;</literal>. In general,
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	  any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
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	      is a <literal>Word&num;</literal>. </para> </listitem>
	  <listitem><para> <literal>3.2&num;</literal> has type <literal>Float&num;</literal>.</para> </listitem>
	  <listitem><para> <literal>3.2&num;&num;</literal> has type <literal>Double&num;</literal></para> </listitem>
	  </itemizedlist>
      </para>
   </sect2>

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    <!-- ====================== HIERARCHICAL MODULES =======================  -->

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    <sect2 id="hierarchical-modules">
      <title>Hierarchical Modules</title>

      <para>GHC supports a small extension to the syntax of module
      names: a module name is allowed to contain a dot
      <literal>&lsquo;.&rsquo;</literal>.  This is also known as the
      &ldquo;hierarchical module namespace&rdquo; extension, because
      it extends the normally flat Haskell module namespace into a
      more flexible hierarchy of modules.</para>

      <para>This extension has very little impact on the language
      itself; modules names are <emphasis>always</emphasis> fully
      qualified, so you can just think of the fully qualified module
      name as <quote>the module name</quote>.  In particular, this
      means that the full module name must be given after the
      <literal>module</literal> keyword at the beginning of the
      module; for example, the module <literal>A.B.C</literal> must
      begin</para>

<programlisting>module A.B.C</programlisting>


      <para>It is a common strategy to use the <literal>as</literal>
      keyword to save some typing when using qualified names with
      hierarchical modules.  For example:</para>

<programlisting>
import qualified Control.Monad.ST.Strict as ST
</programlisting>

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      <para>For details on how GHC searches for source and interface
      files in the presence of hierarchical modules, see <xref
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      linkend="search-path"/>.</para>
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      <para>GHC comes with a large collection of libraries arranged
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      hierarchically; see the accompanying <ulink
      url="../libraries/index.html">library
      documentation</ulink>.  More libraries to install are available
      from <ulink
      url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
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    </sect2>

    <!-- ====================== PATTERN GUARDS =======================  -->

<sect2 id="pattern-guards">
<title>Pattern guards</title>

<para>
<indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
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The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
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</para>

<para>
Suppose we have an abstract data type of finite maps, with a
lookup operation:

<programlisting>
lookup :: FiniteMap -> Int -> Maybe Int
</programlisting>

The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
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where <varname>v</varname> is the value that the key maps to.  Now consider the following definition:
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</para>

<programlisting>
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clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
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| otherwise  = var1 + var2
where
  m1 = lookup env var1
  m2 = lookup env var2
  ok1 = maybeToBool m1
  ok2 = maybeToBool m2
  val1 = expectJust m1
  val2 = expectJust m2
</programlisting>

<para>
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The auxiliary functions are
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</para>

<programlisting>
maybeToBool :: Maybe a -&gt; Bool
maybeToBool (Just x) = True
maybeToBool Nothing  = False

expectJust :: Maybe a -&gt; a
expectJust (Just x) = x
expectJust Nothing  = error "Unexpected Nothing"
</programlisting>

<para>
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What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
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ok2</literal> checks that both lookups succeed, using
<function>maybeToBool</function> to convert the <function>Maybe</function>
types to booleans. The (lazily evaluated) <function>expectJust</function>
calls extract the values from the results of the lookups, and binds the
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returned values to <varname>val1</varname> and <varname>val2</varname>
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respectively.  If either lookup fails, then clunky takes the
<literal>otherwise</literal> case and returns the sum of its arguments.
</para>

<para>
This is certainly legal Haskell, but it is a tremendously verbose and
un-obvious way to achieve the desired effect.  Arguably, a more direct way
to write clunky would be to use case expressions:
</para>

<programlisting>
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clunky env var1 var2 = case lookup env var1 of
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  Nothing -&gt; fail
  Just val1 -&gt; case lookup env var2 of
    Nothing -&gt; fail
    Just val2 -&gt; val1 + val2
where
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  fail = var1 + var2
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</programlisting>

<para>
This is a bit shorter, but hardly better.  Of course, we can rewrite any set
of pattern-matching, guarded equations as case expressions; that is
precisely what the compiler does when compiling equations! The reason that
Haskell provides guarded equations is because they allow us to write down
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the cases we want to consider, one at a time, independently of each other.
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This structure is hidden in the case version.  Two of the right-hand sides
are really the same (<function>fail</function>), and the whole expression
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tends to become more and more indented.
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</para>

<para>
Here is how I would write clunky:
</para>

<programlisting>
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clunky env var1 var2
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  | Just val1 &lt;- lookup env var1
  , Just val2 &lt;- lookup env var2
  = val1 + val2
...other equations for clunky...
</programlisting>

<para>
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The semantics should be clear enough.  The qualifiers are matched in order.
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For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
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right hand side is evaluated and matched against the pattern on the left.
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If the match fails then the whole guard fails and the next equation is
tried.  If it succeeds, then the appropriate binding takes place, and the
next qualifier is matched, in the augmented environment.  Unlike list
comprehensions, however, the type of the expression to the right of the
<literal>&lt;-</literal> is the same as the type of the pattern to its
left.  The bindings introduced by pattern guards scope over all the
remaining guard qualifiers, and over the right hand side of the equation.
</para>

<para>
Just as with list comprehensions, boolean expressions can be freely mixed
with among the pattern guards.  For example:
</para>

<programlisting>
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f x | [y] &lt;- x
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    , y > 3
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    , Just z &lt;- h y
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    = ...
</programlisting>

<para>
Haskell's current guards therefore emerge as a special case, in which the
qualifier list has just one element, a boolean expression.
</para>
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</sect2>

    <!-- ===================== View patterns ===================  -->

<sect2 id="view-patterns">
<title>View patterns
</title>

<para>
View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
More information and examples of view patterns can be found on the
<ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
page</ulink>.
</para>

<para>
View patterns are somewhat like pattern guards that can be nested inside
of other patterns.  They are a convenient way of pattern-matching
against values of abstract types. For example, in a programming language
implementation, we might represent the syntax of the types of the
language as follows:

<programlisting>
type Typ
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data TypView = Unit
             | Arrow Typ Typ

view :: Type -> TypeView

-- additional operations for constructing Typ's ...
</programlisting>

The representation of Typ is held abstract, permitting implementations
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to use a fancy representation (e.g., hash-consing to manage sharing).
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Without view patterns, using this signature a little inconvenient:
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<programlisting>
size :: Typ -> Integer
size t = case view t of
  Unit -> 1
  Arrow t1 t2 -> size t1 + size t2
</programlisting>

It is necessary to iterate the case, rather than using an equational
function definition. And the situation is even worse when the matching
against <literal>t</literal> is buried deep inside another pattern.
</para>

<para>
View patterns permit calling the view function inside the pattern and
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matching against the result:
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<programlisting>
size (view -> Unit) = 1
size (view -> Arrow t1 t2) = size t1 + size t2
</programlisting>

That is, we add a new form of pattern, written
<replaceable>expression</replaceable> <literal>-></literal>
<replaceable>pattern</replaceable> that means "apply the expression to
whatever we're trying to match against, and then match the result of
that application against the pattern". The expression can be any Haskell
expression of function type, and view patterns can be used wherever
patterns are used.
</para>

<para>
The semantics of a pattern <literal>(</literal>
<replaceable>exp</replaceable> <literal>-></literal>
<replaceable>pat</replaceable> <literal>)</literal> are as follows:

<itemizedlist>

<listitem> Scoping:

<para>The variables bound by the view pattern are the variables bound by
<replaceable>pat</replaceable>.
</para>

<para>
Any variables in <replaceable>exp</replaceable> are bound occurrences,
but variables bound "to the left" in a pattern are in scope.  This
feature permits, for example, one argument to a function to be used in
the view of another argument.  For example, the function
<literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
written using view patterns as follows:

<programlisting>
clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
...other equations for clunky...
</programlisting>
</para>

<para>
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More precisely, the scoping rules are:
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<itemizedlist>
<listitem>
<para>
In a single pattern, variables bound by patterns to the left of a view
pattern expression are in scope. For example:
<programlisting>
example :: Maybe ((String -> Integer,Integer), String) -> Bool
example Just ((f,_), f -> 4) = True
</programlisting>

Additionally, in function definitions, variables bound by matching earlier curried
arguments may be used in view pattern expressions in later arguments:
<programlisting>
example :: (String -> Integer) -> String -> Bool
example f (f -> 4) = True
</programlisting>
That is, the scoping is the same as it would be if the curried arguments
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were collected into a tuple.
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</para>
</listitem>

<listitem>
<para>
In mutually recursive bindings, such as <literal>let</literal>,
<literal>where</literal>, or the top level, view patterns in one
declaration may not mention variables bound by other declarations.  That
is, each declaration must be self-contained.  For example, the following
program is not allowed:
<programlisting>
let {(x -> y) = e1 ;
     (y -> x) = e2 } in x
</programlisting>

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(For some amplification on this design choice see
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<ulink url="http://hackage.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
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</para>
</listitem>
</itemizedlist>

</para>
</listitem>

<listitem><para> Typing: If <replaceable>exp</replaceable> has type
<replaceable>T1</replaceable> <literal>-></literal>
<replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
a <replaceable>T2</replaceable>, then the whole view pattern matches a
<replaceable>T1</replaceable>.
</para></listitem>

<listitem><para> Matching: To the equations in Section 3.17.3 of the
<ulink url="http://www.haskell.org/onlinereport/">Haskell 98
Report</ulink>, add the following:
<programlisting>
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case v of { (e -> p) -> e1 ; _ -> e2 }
 =
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case (e v) of { p -> e1 ; _ -> e2 }
</programlisting>
That is, to match a variable <replaceable>v</replaceable> against a pattern
<literal>(</literal> <replaceable>exp</replaceable>
<literal>-></literal> <replaceable>pat</replaceable>
<literal>)</literal>, evaluate <literal>(</literal>
<replaceable>exp</replaceable> <replaceable> v</replaceable>
<literal>)</literal> and match the result against
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<replaceable>pat</replaceable>.
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</para></listitem>

<listitem><para> Efficiency: When the same view function is applied in
multiple branches of a function definition or a case expression (e.g.,
in <literal>size</literal> above), GHC makes an attempt to collect these
applications into a single nested case expression, so that the view
function is only applied once.  Pattern compilation in GHC follows the
matrix algorithm described in Chapter 4 of <ulink
url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
Implementation of Functional Programming Languages</ulink>.  When the
top rows of the first column of a matrix are all view patterns with the
"same" expression, these patterns are transformed into a single nested
case.  This includes, for example, adjacent view patterns that line up
in a tuple, as in
<programlisting>
f ((view -> A, p1), p2) = e1
f ((view -> B, p3), p4) = e2
</programlisting>
</para>

<para> The current notion of when two view pattern expressions are "the
same" is very restricted: it is not even full syntactic equality.
However, it does include variables, literals, applications, and tuples;
e.g., two instances of <literal>view ("hi", "there")</literal> will be
collected.  However, the current implementation does not compare up to
alpha-equivalence, so two instances of <literal>(x, view x ->
y)</literal> will not be coalesced.
</para>

</listitem>

</itemizedlist>
</para>

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</sect2>

    <!-- ===================== n+k patterns ===================  -->

<sect2 id="n-k-patterns">
<title>n+k patterns</title>
<indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>

<para>
<literal>n+k</literal> pattern support is enabled by default. To disable
it, you can use the <option>-XNoNPlusKPatterns</option> flag.
</para>

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</sect2>

    <!-- ===================== Recursive do-notation ===================  -->

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<sect2 id="recursive-do-notation">
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<title>The recursive do-notation
</title>

<para>
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The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
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that is, the variables bound in a do-expression are visible only in the textually following
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code block. Compare this to a let-expression, where bound variables are visible in the entire binding
group. It turns out that several applications can benefit from recursive bindings in
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the do-notation.  The <option>-XDoRec</option> flag provides the necessary syntactic support.
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</para>
<para>
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Here is a simple (albeit contrived) example:
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<programlisting>
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{-# LANGUAGE DoRec #-}
justOnes = do { rec { xs &lt;- Just (1:xs) }
              ; return (map negate xs) }
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</programlisting>
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As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
</para>
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<para>
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The background and motivation for recursive do-notation is described in
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<ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
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by Levent Erkok, John Launchbury,
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Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
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The theory behind monadic value recursion is explained further in Erkok's thesis
<ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.
However, note that GHC uses a different syntax than the one described in these documents.
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</para>

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<sect3>
<title>Details of recursive do-notation</title>
<para>
The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
the LANGUAGE pragma <option>DoRec</option>.  It introduces the single new keyword "<literal>rec</literal>",
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which wraps a mutually-recursive group of monadic statements,
producing a single statement.
</para>
<para>Similar to a <literal>let</literal>
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statement, the variables bound in the <literal>rec</literal> are
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visible throughout the <literal>rec</literal> group, and below it.
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For example, compare
<programlisting>
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do { a &lt;- getChar              do { a &lt;- getChar
   ; let { r1 = f a r2	           ; rec { r1 &lt;- f a r2
         ; r2 = g r1 }	                 ; r2 &lt;- g r1 }
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   ; return (r1 ++ r2) }          ; return (r1 ++ r2) }
</programlisting>
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In both cases, <literal>r1</literal> and <literal>r2</literal> are
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available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
in the statements that follow it.  The difference is that <literal>let</literal> is non-monadic,
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while <literal>rec</literal> is monadic.  (In Haskell <literal>let</literal> is
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really <literal>letrec</literal>, of course.)
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</para>
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<para>
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The static and dynamic semantics of <literal>rec</literal> can be described as follows:
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<itemizedlist>
<listitem><para>
First,
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similar to let-bindings, the <literal>rec</literal> is broken into
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minimal recursive groups, a process known as <emphasis>segmentation</emphasis>.
For example:
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<programlisting>
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rec { a &lt;- getChar      ===>     a &lt;- getChar
    ; b &lt;- f a c                 rec { b &lt;- f a c
    ; c &lt;- f b a                     ; c &lt;- f b a }
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    ; putChar c }                putChar c
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</programlisting>
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The details of segmentation are described in Section 3.2 of
<ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>.
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Segmentation improves polymorphism, reduces the size of the recursive "knot", and, as the paper
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describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
</para></listitem>
<listitem><para>
Then each resulting <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal>.
For example, the <literal>rec</literal> group in the preceding example is desugared like this:
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<programlisting>
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rec { b &lt;- f a c     ===>    (b,c) &lt;- mfix (\~(b,c) -> do { b &lt;- f a c
    ; c &lt;- f b a }                                        ; c &lt;- f b a
                                                          ; return (b,c) })
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</programlisting>
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In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
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is desugared to the statement
<programlisting>
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<replaceable>vs</replaceable> &lt;- mfix (\~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
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</programlisting>
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where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
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</para><para>
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The original <literal>rec</literal> typechecks exactly
when the above desugared version would do so.  For example, this means that
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the variables <replaceable>vs</replaceable> are all monomorphic in the statements
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following the <literal>rec</literal>, because they are bound by a lambda.
</para>
<para>
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The <literal>mfix</literal> function is defined in the <literal>MonadFix</literal>
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class, in <literal>Control.Monad.Fix</literal>, thus:
<programlisting>
class Monad m => MonadFix m where
   mfix :: (a -> m a) -> m a
</programlisting>
</para>
</listitem>
</itemizedlist>
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</para>
<para>
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Here are some other important points in using the recursive-do notation:
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<itemizedlist>
<listitem><para>
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It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
<literal>-fglasgow-exts</literal>.
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</para></listitem>

<listitem><para>
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If recursive bindings are required for a monad,
then that monad must be declared an instance of the <literal>MonadFix</literal> class.
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</para></listitem>

<listitem><para>
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The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
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for Haskell's internal state monad (strict and lazy, respectively).
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</para></listitem>

<listitem><para>
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Like <literal>let</literal> and <literal>where</literal> bindings,
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name shadowing is not allowed within a <literal>rec</literal>;
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that is, all the names bound in a single <literal>rec</literal> must
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be distinct (Section 3.3 of the paper).
</para></listitem>
<listitem><para>
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It supports rebindable syntax (see <xref linkend="rebindable-syntax"/>).
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</para></listitem>
</itemizedlist>
</para>
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</sect3>

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<sect3 id="mdo-notation"> <title> Mdo-notation (deprecated) </title>
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<para> GHC used to support the flag <option>-XRecursiveDo</option>,
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which enabled the keyword <literal>mdo</literal>, precisely as described in
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<ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
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but this is now deprecated.  Instead of <literal>mdo { Q; e }</literal>, write
<literal>do { rec Q; e }</literal>.
</para>
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<para>
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Historical note: The old implementation of the mdo-notation (and most
of the existing documents) used the name
<literal>MonadRec</literal> for the class and the corresponding library.
This name is not supported by GHC.
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</para>
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</sect3>
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</sect2>


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   <!-- ===================== PARALLEL LIST COMPREHENSIONS ===================  -->

  <sect2 id="parallel-list-comprehensions">
    <title>Parallel List Comprehensions</title>
    <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
    </indexterm>
    <indexterm><primary>parallel list comprehensions</primary>
    </indexterm>

    <para>Parallel list comprehensions are a natural extension to list
    comprehensions.  List comprehensions can be thought of as a nice
    syntax for writing maps and filters.  Parallel comprehensions
    extend this to include the zipWith family.</para>

    <para>A parallel list comprehension has multiple independent
    branches of qualifier lists, each separated by a `|' symbol.  For
    example, the following zips together two lists:</para>

<programlisting>
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   [ (x, y) | x &lt;- xs | y &lt;- ys ]
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</programlisting>

    <para>The behavior of parallel list comprehensions follows that of
    zip, in that the resulting list will have the same length as the
    shortest branch.</para>

    <para>We can define parallel list comprehensions by translation to
    regular comprehensions.  Here's the basic idea:</para>

    <para>Given a parallel comprehension of the form: </para>

<programlisting>
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   [ e | p1 &lt;- e11, p2 &lt;- e12, ...
       | q1 &lt;- e21, q2 &lt;- e22, ...
       ...
   ]
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</programlisting>

    <para>This will be translated to: </para>

<programlisting>
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   [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
                                         [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
                                         ...
   ]
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</programlisting>

    <para>where `zipN' is the appropriate zip for the given number of
    branches.</para>

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  </sect2>
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  <!-- ===================== TRANSFORM LIST COMPREHENSIONS ===================  -->

  <sect2 id="generalised-list-comprehensions">
    <title>Generalised (SQL-Like) List Comprehensions</title>
    <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
    </indexterm>
    <indexterm><primary>extended list comprehensions</primary>
    </indexterm>
    <indexterm><primary>group</primary></indexterm>
    <indexterm><primary>sql</primary></indexterm>


    <para>Generalised list comprehensions are a further enhancement to the
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    list comprehension syntactic sugar to allow operations such as sorting
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    and grouping which are familiar from SQL.   They are fully described in the
	paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
	  Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
    except that the syntax we use differs slightly from the paper.</para>
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<para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
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<para>Here is an example:
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<programlisting>
employees = [ ("Simon", "MS", 80)
, ("Erik", "MS", 100)
, ("Phil", "Ed", 40)
, ("Gordon", "Ed", 45)
, ("Paul", "Yale", 60)]

output = [ (the dept, sum salary)
| (name, dept, salary) &lt;- employees
, then group by dept
, then sortWith by (sum salary)
, then take 5 ]
</programlisting>
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In this example, the list <literal>output</literal> would take on
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    the value:
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<programlisting>
[("Yale", 60), ("Ed", 85), ("MS", 180)]
</programlisting>
</para>
<para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
(The function <literal>sortWith</literal> is not a keyword; it is an ordinary
function that is exported by <literal>GHC.Exts</literal>.)</para>

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<para>There are five new forms of comprehension qualifier,
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all introduced by the (existing) keyword <literal>then</literal>:
    <itemizedlist>
    <listitem>
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<programlisting>
then f
</programlisting>

    This statement requires that <literal>f</literal> have the type <literal>
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    forall a. [a] -> [a]</literal>. You can see an example of its use in the
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    motivating example, as this form is used to apply <literal>take 5</literal>.
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    </listitem>
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    <listitem>
<para>
<programlisting>
then f by e
</programlisting>

    This form is similar to the previous one, but allows you to create a function
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    which will be passed as the first argument to f. As a consequence f must have
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    the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
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    from the type, this function lets f &quot;project out&quot; some information
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    from the elements of the list it is transforming.</para>

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    <para>An example is shown in the opening example, where <literal>sortWith</literal>
    is supplied with a function that lets it find out the <literal>sum salary</literal>
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    for any item in the list comprehension it transforms.</para>

    </listitem>


    <listitem>

<programlisting>
then group by e using f
</programlisting>

    <para>This is the most general of the grouping-type statements. In this form,
    f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
    As with the <literal>then f by e</literal> case above, the first argument
    is a function supplied to f by the compiler which lets it compute e on every
    element of the list being transformed. However, unlike the non-grouping case,
    f additionally partitions the list into a number of sublists: this means that
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    at every point after this statement, binders occurring before it in the comprehension
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    refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
    this, let's look at an example:</para>
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<programlisting>
-- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
groupRuns f = groupBy (\x y -> f x == f y)

output = [ (the x, y)
| x &lt;- ([1..3] ++ [1..2])
, y &lt;- [4..6]
, then group by x using groupRuns ]
</programlisting>

    <para>This results in the variable <literal>output</literal> taking on the value below:</para>

<programlisting>
[(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
</programlisting>

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    <para>Note that we have used the <literal>the</literal> function to change the type
    of x from a list to its original numeric type. The variable y, in contrast, is left
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    unchanged from the list form introduced by the grouping.</para>

    </listitem>

    <listitem>

<programlisting>
then group by e
</programlisting>

    <para>This form of grouping is essentially the same as the one described above. However,
    since no function to use for the grouping has been supplied it will fall back on the
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    <literal>groupWith</literal> function defined in
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    <ulink url="&libraryBaseLocation;/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
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    is the form of the group statement that we made use of in the opening example.</para>

    </listitem>
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    <listitem>

<programlisting>
then group using f
</programlisting>

    <para>With this form of the group statement, f is required to simply have the type
    <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
    comprehension so far directly. An example of this form is as follows:</para>
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<programlisting>
output = [ x
| y &lt;- [1..5]
, x &lt;- "hello"
, then group using inits]
</programlisting>

    <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>

<programlisting>
["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
</programlisting>

    </listitem>
</itemizedlist>
</para>
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  </sect2>

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   <!-- ===================== MONAD COMPREHENSIONS ===================== -->

<sect2 id="monad-comprehensions">
    <title>Monad comprehensions</title>
    <indexterm><primary>monad comprehensions</primary></indexterm>

    <para>
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        Monad comprehensions generalise the list comprehension notation,
        including parallel comprehensions
        (<xref linkend="parallel-list-comprehensions"/>) and
        transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
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        to work for any monad.
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    </para>

    <para>Monad comprehensions support:</para>

    <itemizedlist>
        <listitem>
            <para>
                Bindings:
            </para>

<programlisting>
[ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
</programlisting>

            <para>
                Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
                <literal>return</literal> functions to the usual do-notation:
            </para>

<programlisting>
do x &lt;- Just 1
   y &lt;- Just 2
   return (x+y)
</programlisting>

        </listitem>
        <listitem>
            <para>
                Guards:
            </para>

<programlisting>
[ x | x &lt;- [1..10], x &lt;= 5 ]
</programlisting>

            <para>
                Guards are translated with the <literal>guard</literal> function,
                which requires a <literal>MonadPlus</literal> instance:
            </para>

<programlisting>
do x &lt;- [1..10]
   guard (x &lt;= 5)
   return x
</programlisting>

        </listitem>
        <listitem>
            <para>
                Transform statements (as with <literal>-XTransformListComp</literal>):
            </para>

<programlisting>
[ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
</programlisting>

            <para>
                This translates to:
            </para>

<programlisting>
do (x,y) &lt;- take 2 (do x &lt;- [1..10]
                       y &lt;- [1..x]
                       return (x,y))
   return (x+y)
</programlisting>

        </listitem>
        <listitem>
            <para>
                Group statements (as with <literal>-XTransformListComp</literal>):
            </para>

<programlisting>
[ x | x &lt;- [1,1,2,2,3], then group by x ]
[ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
[ x | x &lt;- [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 &lt;- mgroupWith (do x &lt;- [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 &lt;- [1..10]
        | y &lt;- [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) &lt;- mzip (do x &lt;- [1..10]
                     return x)
                 (do y &lt;- [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>
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<para> More formally, the desugaring is as follows.  We write <literal>D[ e | Q]</literal>
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to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
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<programlisting>
Expressions: e
Declarations: d
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Lists of qualifiers: Q,R,S
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-- Basic forms
D[ e | ]               = return e
D[ e | p &lt;- e, Q ]     = e &gt;&gt;= \p -&gt; D[ e | Q ]
D[ e | e, Q ]          = guard e &gt;&gt; \p -&gt; 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 ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]

-- Transform comprehensions
D[ e | Q then f, R ]                  = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]

D[ e | Q then f by b, R ]             = f b D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]

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D[ e | Q then group using f, R ]      = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
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                                        case (fmap selQv1 ys, ..., fmap selQvn ys) of
                                 	     Qv -&gt; D[ e | R ]

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D[ e | Q then group by b using f, R ] = f b D[ Qv | Q ] &gt;&gt;= \ys -&gt;
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                                        case (fmap selQv1 ys, ..., fmap selQvn ys) of
                                           Qv -&gt; 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 -&gt; m t2
(&gt;&gt;=)        GHC.Base               m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
(&gt;&gt;)         GHC.Base               m1 t1 -&gt; m2 t2         -&gt; m3 t3
guard        Control.Monad          t1 -&gt; m t2
fmap         GHC.Base               forall a b. (a-&gt;b) -&gt; n a -&gt; n b
mgroupWith   Control.Monad.Group    forall a. (a -&gt; t) -&gt; m1 a -&gt; m2 (n a)
mzip         Control.Monad.Zip      forall a b. m a -&gt; m b -&gt; m (a,b)
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</programlisting>
The comprehension should typecheck when its desugaring would typecheck.
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</para>
<para>
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Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
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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>
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The rebindable operators must have the "Expected type" given in the
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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>
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</sect2>

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   <!-- ===================== REBINDABLE SYNTAX ===================  -->

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<sect2 id="rebindable-syntax">