Fix typo in User's Guide

[ghc.git] / docs / users_guide / glasgow_exts.xml

<?xml version="1.0" encoding="iso-8859-1"?>
<para>
<indexterm><primary>language, GHC</primary></indexterm>
<indexterm><primary>extensions, GHC</primary></indexterm>
As with all known Haskell systems, GHC implements some extensions to
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.
</para>

<para>
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!
</para>

<para>
Before you get too carried away working at the lowest level (e.g.,
sloshing <literal>MutableByteArray&num;</literal>s around your
program), you may wish to check if there are libraries that provide a
&ldquo;Haskellised veneer&rdquo; over the features you want.  The
separate <ulink url="../libraries/index.html">libraries
documentation</ulink> describes all the libraries that come with GHC.
</para>

<!-- LANGUAGE OPTIONS -->
  <sect1 id="options-language">
    <title>Language options</title>

    <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>

    <para>The language option flags control what variation of the language are
    permitted.</para>

    <para>Language options can be controlled in two ways:
    <itemizedlist>
      <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>";
        (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>

    <para>The flag <option>-fglasgow-exts</option>
          <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
          is equivalent to enabling the following extensions:
          &what_glasgow_exts_does;
            Enabling these options is the <emphasis>only</emphasis>
            effect of <option>-fglasgow-exts</option>.
          We are trying to move away from this portmanteau flag,
          and towards enabling features individually.</para>

  </sect1>

<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
<sect1 id="primitives">
  <title>Unboxed types and primitive operations</title>

<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.
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>

<para>All these primitive data types and operations are exported by the
library <literal>GHC.Prim</literal>, for which there is
<ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
(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>

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

<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
bottom.  We use the convention (but it is only a convention)
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>.
</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.
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.
</para>

<para>
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
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>
</listitem>
<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>
<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,
non-top-level) pattern binding, but you must make any such pattern-match
strict.  For example, rather than:
<programlisting>
  data Foo = Foo Int Int#

  f x = let (Foo a b, w) = ..rhs.. in ..body..
</programlisting>
you must write:
<programlisting>
  data Foo = Foo Int Int#

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

</sect2>

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

<para>
Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>;
they are a syntactic extension enabled by the language flag <option>-XUnboxedTuples</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>
Note that when unboxed tuples are enabled,
<literal>(#</literal> is a single lexeme, so for example when using
operators like <literal>#</literal> and <literal>#-</literal> you need
to write <literal>( # )</literal> and <literal>( #- )</literal> rather than
<literal>(#)</literal> and <literal>(#-)</literal>.
</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
of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
tuples.
In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
tuples to avoid unnecessary allocation during sequences of operations.
</para>

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

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

<listitem>
<para>
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,
the resulting binding is lazy like any other Haskell pattern binding.  The
above example desugars like this:
<programlisting>
  f x = let t = case h x of { (# p,q #) -> (p,q) }
            p = fst t
            q = snd t
        in ..body..
</programlisting>
Indeed, the bindings can even be recursive.
</para>
</listitem>
</itemizedlist>

</para>

</sect2>
</sect1>


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

<sect1 id="syntax-extns">
<title>Syntactic extensions</title>

    <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>

<!--
               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.
            -->

          <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>

          <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>

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

    <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>

      <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>),
        but there is no requirement to do so; they are just plain ordinary variables.
        Nor does the <option>-XMagicHash</option> extension bring anything into scope.
        For example, to bring <literal>Int&num;</literal> into scope you must
        import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
        the <option>-XMagicHash</option> extension
        then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
        that is now in scope. Note that with this option, the meaning of <literal>x&num;y = 0</literal>
        is changed: it defines a function <literal>x&num;</literal> taking a single argument <literal>y</literal>;
        to define the operator <literal>&num;</literal>, put a space: <literal>x &num; y = 0</literal>.

</para>
      <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
        <itemizedlist>
          <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,
          any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
            <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,
          any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
              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>

    <sect2 id="negative-literals">
      <title>Negative literals</title>
      <para>
          The literal <literal>-123</literal> is, according to
          Haskell98 and Haskell 2010, desugared as
          <literal>negate (fromInteger 123)</literal>.
         The language extension <option>-XNegativeLiterals</option>
         means that it is instead desugared as
         <literal>fromInteger (-123)</literal>.
      </para>

      <para>
      This can make a difference when the positive and negative range of 
      a numeric data type don't match up.  For example, 
      in 8-bit arithmetic -128 is representable, but +128 is not.
      So <literal>negate (fromInteger 128)</literal> will elicit an 
      unexpected integer-literal-overflow message.
      </para>
   </sect2>

    <sect2 id="num-decimals">
      <title>Fractional looking integer literals</title>
      <para>
          Haskell 2010 and Haskell 98 define floating literals with
          the syntax <literal>1.2e6</literal>. These literals have the
          type <literal>Fractional a => a</literal>.
      </para>

      <para>
         The language extension <option>-XNumDecimals</option> allows
         you to also use the floating literal syntax for instances of
         <literal>Integral</literal>, and have values like
         <literal>(1.2e6 :: Num a => a)</literal>
      </para>
   </sect2>


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


    <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>

      <para>For details on how GHC searches for source and interface
      files in the presence of hierarchical modules, see <xref
      linkend="search-path"/>.</para>

      <para>GHC comes with a large collection of libraries arranged
      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>
    </sect2>

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

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

<para>
<indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
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.)
</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,
where <varname>v</varname> is the value that the key maps to.  Now consider the following definition:
</para>

<programlisting>
clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
| 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>
The auxiliary functions are
</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>
What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
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
returned values to <varname>val1</varname> and <varname>val2</varname>
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>
clunky env var1 var2 = case lookup env var1 of
  Nothing -&gt; fail
  Just val1 -&gt; case lookup env var2 of
    Nothing -&gt; fail
    Just val2 -&gt; val1 + val2
where
  fail = var1 + var2
</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
the cases we want to consider, one at a time, independently of each other.
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
tends to become more and more indented.
</para>

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

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

<para>
The semantics should be clear enough.  The qualifiers are matched in order.
For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
right hand side is evaluated and matched against the pattern on the left.
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>
f x | [y] &lt;- x
    , y > 3
    , Just z &lt;- h y
    = ...
</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>
</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://ghc.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

data TypView = Unit
             | Arrow Typ Typ

view :: Typ -> TypView

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

The representation of Typ is held abstract, permitting implementations
to use a fancy representation (e.g., hash-consing to manage sharing).

Without view patterns, using this signature a little inconvenient:
<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
matching against the result:
<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>
More precisely, the scoping rules are:
<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
were collected into a tuple.
</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>

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

</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>
case v of { (e -> p) -> e1 ; _ -> e2 }
 =
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
<replaceable>pat</replaceable>.
</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>

</sect2>

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

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

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

</sect2>

    <!-- ===================== Traditional record syntax ===================  -->

<sect2 id="traditional-record-syntax">
<title>Traditional record syntax</title>
<indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>

<para>
Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
</para>

</sect2>

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

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

<para>
    The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
    that is, the variables bound in a do-expression are visible only in the textually following
    code block. Compare this to a let-expression, where bound variables are visible in the entire binding
    group.
</para>

<para>
    It turns out that such recursive bindings do indeed make sense for a variety of monads, but
    not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
    monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
<programlisting>
class Monad m => MonadFix m where
   mfix :: (a -> m a) -> m a
</programlisting>
    Haskell's
    <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
    <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
    side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
</para>

<para>
    For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
    an extended version of the do-notation that allows recursive bindings.
    The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
    provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
    <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
    bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
    are recursively defined, much like in an ordinary let-expression. Due to the new
    keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
</para>

<para>
    Here is a simple (albeit contrived) example:
<programlisting>
{-# LANGUAGE RecursiveDo #-}
justOnes = mdo { xs &lt;- Just (1:xs)
               ; return (map negate xs) }
</programlisting>
or equivalently
<programlisting>
{-# LANGUAGE RecursiveDo #-}
justOnes = do { rec { xs &lt;- Just (1:xs) }
              ; return (map negate xs) }
</programlisting>
As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
</para>

<para>
   GHC's implementation the mdo-notation closely follows the original translation as described in the paper
   <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
   in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
   in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
   with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
</para>

<sect3>
<title>Recursive binding groups</title>

<para>
    The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
    mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
    Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
    the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it.  For example, compare
<programlisting>
    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 }
       ; return (r1 ++ r2) }        ; return (r1 ++ r2) }
</programlisting>
    In both cases, <literal>r1</literal> and <literal>r2</literal> are 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, while <literal>rec</literal> is monadic.
    (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
</para>

<para>
    The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
    group, it will compute its set of bound variables, and will introduce an appropriate call
    to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
    <literal>MonadFix</literal> class. Here is an example:
<programlisting>
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) })
</programlisting>
   As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
   In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
<programlisting>
<replaceable>vs</replaceable> &lt;- mfix (\ ~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
</programlisting>
  where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
</para>

<para>
    Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
    to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
    for the <literal>mdo</literal> notation, which is described next.
</para>
</sect3>

<sect3>
<title>The <literal>mdo</literal> notation</title>

<para>
    A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
    the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
    around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
    in detail in Secton 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
    Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
    unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
    axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
    have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
    interference, changing the termination behavior of the resulting translation.
    (Details can be found in Sections 3.1 and 7.2.2 of
    <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
</para>

<para>
    The <literal>mdo</literal> notation removes the burden of placing
    explicit <literal>rec</literal> blocks in the code.  Unlike an
    ordinary <literal>do</literal> expression, in which variables bound by
    statements are only in scope for later statements, variables bound in
    an <literal>mdo</literal> expression are in scope for all statements
    of the expression.  The compiler then automatically identifies minimal
    mutually recursively dependent segments of statements, treating them as
    if the user had wrapped a <literal>rec</literal> qualifier around them.
</para>

<para>
   The definition is syntactic:
</para>
<itemizedlist>
   <listitem>
       <para>
         A generator <replaceable>g</replaceable>
         <emphasis>depends</emphasis> on a textually following generator
         <replaceable>g'</replaceable>, if
       </para>
       <itemizedlist>
         <listitem>
           <para>
             <replaceable>g'</replaceable> defines a variable that
             is used by <replaceable>g</replaceable>, or
           </para>
         </listitem>
         <listitem>
           <para>
           <replaceable>g'</replaceable> textually appears between
           <replaceable>g</replaceable> and
           <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
           depends on <replaceable>g''</replaceable>.
           </para>
         </listitem>
       </itemizedlist>
   </listitem>
   <listitem>
       <para>
         A <emphasis>segment</emphasis> of a given
         <literal>mdo</literal>-expression is a minimal sequence of generators
         such that no generator of the sequence depends on an outside
         generator. As a special case, although it is not a generator,
         the final expression in an <literal>mdo</literal>-expression is
         considered to form a segment by itself.
       </para>
   </listitem>
</itemizedlist>
<para>
   Segments in this sense are
   related to <emphasis>strongly-connected components</emphasis> analysis,
   with the exception that bindings in a segment cannot be reordered and
   must be contiguous.
</para>

<para>
    Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
<programlisting>
mdo { a &lt;- getChar      ===> do { a &lt;- getChar
    ; b &lt;- f a c                ; rec { b &lt;- f a c
    ; c &lt;- f b a                ;     ; c &lt;- f b a }
    ; z &lt;- h a b                ; z &lt;- h a b
    ; d &lt;- g d e                ; rec { d &lt;- g d e
    ; e &lt;- g a z                ;     ; e &lt;- g a z }
    ; putChar c }               ; putChar c }
</programlisting>
Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
would expect.
</para>

<para>
    In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
    <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
    <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
    in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
    version would do so.
</para>

<para>
Here are some other important points in using the recursive-do notation:

<itemizedlist>
    <listitem>
        <para>
            It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
            pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
            blocks inside <literal>do</literal> expressions.)
        </para>
    </listitem>
    <listitem>
        <para>
            <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
            treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
            <literal>rec</literal> blocks in a single expression.
        </para>
    </listitem>
    <listitem>
        <para>
            If recursive bindings are required for a monad, then that monad must be declared an instance of
            the <literal>MonadFix</literal> class.
        </para>
    </listitem>
    <listitem>
        <para>
            The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
            Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
            modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
            state monad (strict and lazy, respectively).
        </para>
    </listitem>
    <listitem>
        <para>
            Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
            an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
            a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
        </para>
    </listitem>
</itemizedlist>
</para>
</sect3>


</sect2>


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

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

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

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

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

  </sect2>

  <!-- ===================== 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
    list comprehension syntactic sugar to allow operations such as sorting
    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>
<para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
<para>Here is an example:
<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 using groupWith
, then sortWith by (sum salary)
, then take 5 ]
</programlisting>
In this example, the list <literal>output</literal> would take on
    the value:

<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 functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
functions that are exported by <literal>GHC.Exts</literal>.)</para>

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

<programlisting>
then f
</programlisting>

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

    </listitem>


    <listitem>
<para>
<programlisting>
then f by e
</programlisting>

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

    <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>
    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
    at every point after this statement, binders occurring before it in the comprehension
    refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
    this, let's look at an example:</para>

<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>

    <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
    unchanged from the list form introduced by the grouping.</para>

    </listitem>

    <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>

<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>
  </sect2>

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

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

    <para>
        Monad comprehensions generalise the list comprehension notation,
        including parallel comprehensions
        (<xref linkend="parallel-list-comprehensions"/>) and
        transform comprehensions (<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 &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 using GHC.Exts.groupWith ]
[ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
</programlisting>

        </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>
<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 &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 (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]

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

D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
                                        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
mzip         Control.Monad.Zip      forall a b. m a -&gt; m b -&gt; 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">
<title>Rebindable syntax and the implicit Prelude import</title>

 <para><indexterm><primary>-XNoImplicitPrelude
 option</primary></indexterm> GHC normally imports
 <filename>Prelude.hi</filename> files for you.  If you'd
 rather it didn't, then give it a
 <option>-XNoImplicitPrelude</option> option.  The idea is
 that you can then import a Prelude of your own.  (But don't
 call it <literal>Prelude</literal>; the Haskell module
 namespace is flat, and you must not conflict with any
 Prelude module.)</para>

            <para>Suppose you are importing a Prelude of your own
              in order to define your own numeric class
            hierarchy.  It completely defeats that purpose if the
            literal "1" means "<literal>Prelude.fromInteger
            1</literal>", which is what the Haskell Report specifies.
            So the <option>-XRebindableSyntax</option>
              flag causes
            the following pieces of built-in syntax to refer to
            <emphasis>whatever is in scope</emphasis>, not the Prelude
            versions:
            <itemizedlist>
              <listitem>
                <para>An integer literal <literal>368</literal> means
                "<literal>fromInteger (368::Integer)</literal>", rather than
                "<literal>Prelude.fromInteger (368::Integer)</literal>".
</para> </listitem>

      <listitem><para>Fractional literals are handed in just the same way,
          except that the translation is
              <literal>fromRational (3.68::Rational)</literal>.
</para> </listitem>

          <listitem><para>The equality test in an overloaded numeric pattern
              uses whatever <literal>(==)</literal> is in scope.
</para> </listitem>

          <listitem><para>The subtraction operation, and the
          greater-than-or-equal test, in <literal>n+k</literal> patterns
              use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
              </para></listitem>

              <listitem>
                <para>Negation (e.g. "<literal>- (f x)</literal>")
                means "<literal>negate (f x)</literal>", both in numeric
                patterns, and expressions.
              </para></listitem>

              <listitem>
                <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
                means "<literal>ifThenElse</literal> e1 e2 e3".  However <literal>case</literal> expressions are unaffected.
              </para></listitem>

              <listitem>
          <para>"Do" notation is translated using whatever
              functions <literal>(>>=)</literal>,
              <literal>(>>)</literal>, and <literal>fail</literal>,
              are in scope (not the Prelude
              versions).  List comprehensions, mdo (<xref linkend="recursive-do-notation"/>), and parallel array
              comprehensions, are unaffected.  </para></listitem>

              <listitem>
                <para>Arrow
                notation (see <xref linkend="arrow-notation"/>)
                uses whatever <literal>arr</literal>,
                <literal>(>>>)</literal>, <literal>first</literal>,
                <literal>app</literal>, <literal>(|||)</literal> and
                <literal>loop</literal> functions are in scope. But unlike the
                other constructs, the types of these functions must match the
                Prelude types very closely.  Details are in flux; if you want
                to use this, ask!
              </para></listitem>
            </itemizedlist>
<option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
</para>
<para>
In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
even if that is a little unexpected. For example, the
static semantics of the literal <literal>368</literal>
is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
<literal>fromInteger</literal> to have any of the types:
<programlisting>
fromInteger :: Integer -> Integer
fromInteger :: forall a. Foo a => Integer -> a
fromInteger :: Num a => a -> Integer
fromInteger :: Integer -> Bool -> Bool
</programlisting>
</para>

             <para>Be warned: this is an experimental facility, with
             fewer checks than usual.  Use <literal>-dcore-lint</literal>
             to typecheck the desugared program.  If Core Lint is happy
             you should be all right.</para>

</sect2>

<sect2 id="postfix-operators">
<title>Postfix operators</title>

<para>
  The <option>-XPostfixOperators</option> flag enables a small
extension to the syntax of left operator sections, which allows you to
define postfix operators.  The extension is this: the left section
<programlisting>
  (e !)
</programlisting>
is equivalent (from the point of view of both type checking and execution) to the expression
<programlisting>
  ((!) e)
</programlisting>
(for any expression <literal>e</literal> and operator <literal>(!)</literal>.
The strict Haskell 98 interpretation is that the section is equivalent to
<programlisting>
  (\y -> (!) e y)
</programlisting>
That is, the operator must be a function of two arguments.  GHC allows it to
take only one argument, and that in turn allows you to write the function
postfix.
</para>
<para>The extension does not extend to the left-hand side of function
definitions; you must define such a function in prefix form.</para>

</sect2>

<sect2 id="tuple-sections">
<title>Tuple sections</title>

<para>
  The <option>-XTupleSections</option> flag enables Python-style partially applied
  tuple constructors. For example, the following program
<programlisting>
  (, True)
</programlisting>
  is considered to be an alternative notation for the more unwieldy alternative
<programlisting>
  \x -> (x, True)
</programlisting>
You can omit any combination of arguments to the tuple, as in the following
<programlisting>
  (, "I", , , "Love", , 1337)
</programlisting>
which translates to
<programlisting>
  \a b c d -> (a, "I", b, c, "Love", d, 1337)
</programlisting>
</para>

<para>
  If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
  will also be available for them, like so
<programlisting>
  (# , True #)
</programlisting>
Because there is no unboxed unit tuple, the following expression
<programlisting>
  (# #)
</programlisting>
continues to stand for the unboxed singleton tuple data constructor.
</para>

</sect2>

<sect2 id="lambda-case">
<title>Lambda-case</title>
<para>
The <option>-XLambdaCase</option> flag enables expressions of the form
<programlisting>
  \case { p1 -> e1; ...; pN -> eN }
</programlisting>
which is equivalent to
<programlisting>
  \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
</programlisting>
Note that <literal>\case</literal> starts a layout, so you can write
<programlisting>
  \case
    p1 -> e1
    ...
    pN -> eN
</programlisting>
</para>
</sect2>

<sect2 id="empty-case">
<title>Empty case alternatives</title>
<para>
The <option>-XEmptyCase</option> flag enables
case expressions, or lambda-case expressions, that have no alternatives,
thus:
<programlisting>
    case e of { }   -- No alternatives
or
    \case { }       -- -XLambdaCase is also required
</programlisting>
This can be useful when you know that the expression being scrutinised
has no non-bottom values.  For example:
<programlisting>
  data Void
  f :: Void -> Int
  f x = case x of { }
</programlisting>
With dependently-typed features it is more useful
(see <ulink url="http://ghc.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
For example, consider these two candidate definitions of <literal>absurd</literal>:
<programlisting>
data a :==: b where
  Refl :: a :==: a

absurd :: True :~: False -> a
absurd x = error "absurd"    -- (A)
absurd x = case x of {}      -- (B)
</programlisting>
We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
is an empty type. So (B) has no partiality and GHC should be able to compile with
<option>-fwarn-incomplete-patterns</option>.  (Though the pattern match checking is not
yet clever enough to do that.)
On the other hand (A) looks dangerous, and GHC doesn't check to make
sure that, in fact, the function can never get called.
</para>
</sect2>

<sect2 id="multi-way-if">
<title>Multi-way if-expressions</title>
<para>
With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
with multiple branches:
<programlisting>
  if | guard1 -> expr1
     | ...
     | guardN -> exprN
</programlisting>
which is roughly equivalent to
<programlisting>
  case () of
    _ | guard1 -> expr1
    ...
    _ | guardN -> exprN
</programlisting>
</para>

<para>Multi-way if expressions introduce a new layout context.  So the
example above is equivalent to:
<programlisting>
  if { | guard1 -> expr1
     ; | ...
     ; | guardN -> exprN
     }
</programlisting>
The following behaves as expected:
<programlisting>
  if | guard1 -> if | guard2 -> expr2
                    | guard3 -> expr3
     | guard4 -> expr4
</programlisting>
because layout translates it as
<programlisting>
  if { | guard1 -> if { | guard2 -> expr2
                      ; | guard3 -> expr3
                      }
     ; | guard4 -> expr4
     }
</programlisting>
Layout with multi-way if works in the same way as other layout
contexts, except that the semi-colons between guards in a multi-way if
are optional.  So it is not necessary to line up all the guards at the
same column; this is consistent with the way guards work in function
definitions and case expressions.
</para>
</sect2>

<sect2 id="disambiguate-fields">
<title>Record field disambiguation</title>
<para>
In record construction and record pattern matching
it is entirely unambiguous which field is referred to, even if there are two different
data types in scope with a common field name.  For example:
<programlisting>
module M where
  data S = MkS { x :: Int, y :: Bool }

module Foo where
  import M

  data T = MkT { x :: Int }

  ok1 (MkS { x = n }) = n+1   -- Unambiguous
  ok2 n = MkT { x = n+1 }     -- Unambiguous

  bad1 k = k { x = 3 }  -- Ambiguous
  bad2 k = x k          -- Ambiguous
</programlisting>
Even though there are two <literal>x</literal>'s in scope,
it is clear that the <literal>x</literal> in the pattern in the
definition of <literal>ok1</literal> can only mean the field
<literal>x</literal> from type <literal>S</literal>. Similarly for
the function <literal>ok2</literal>.  However, in the record update
in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
it is not clear which of the two types is intended.
</para>
<para>
Haskell 98 regards all four as ambiguous, but with the
<option>-XDisambiguateRecordFields</option> flag, GHC will accept
the former two.  The rules are precisely the same as those for instance
declarations in Haskell 98, where the method names on the left-hand side
of the method bindings in an instance declaration refer unambiguously
to the method of that class (provided they are in scope at all), even
if there are other variables in scope with the same name.
This reduces the clutter of qualified names when you import two
records from different modules that use the same field name.
</para>
<para>
Some details:
<itemizedlist>
<listitem><para>
Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
<programlisting>
module Foo where
  import M
  x=True
  ok3 (MkS { x }) = x+1   -- Uses both disambiguation and punning
</programlisting>
</para></listitem>

<listitem><para>
With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
<programlisting>
module Foo where
  import qualified M    -- Note qualified

  ok4 (M.MkS { x = n }) = n+1   -- Unambiguous
</programlisting>
Since the constructor <literal>MkS</literal> is only in scope qualified, you must
name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
is not.  (In effect, it is qualified by the constructor.)
</para></listitem>
</itemizedlist>
</para>

</sect2>

    <!-- ===================== Record puns ===================  -->

<sect2 id="record-puns">
<title>Record puns
</title>

<para>
Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
</para>

<para>
When using records, it is common to write a pattern that binds a
variable with the same name as a record field, such as:

<programlisting>
data C = C {a :: Int}
f (C {a = a}) = a
</programlisting>
</para>

<para>
Record punning permits the variable name to be elided, so one can simply
write

<programlisting>
f (C {a}) = a
</programlisting>

to mean the same pattern as above.  That is, in a record pattern, the
pattern <literal>a</literal> expands into the pattern <literal>a =
a</literal> for the same name <literal>a</literal>.
</para>

<para>
Note that:
<itemizedlist>
<listitem><para>
Record punning can also be used in an expression, writing, for example,
<programlisting>
let a = 1 in C {a}
</programlisting>
instead of
<programlisting>
let a = 1 in C {a = a}
</programlisting>
The expansion is purely syntactic, so the expanded right-hand side
expression refers to the nearest enclosing variable that is spelled the
same as the field name.
</para></listitem>

<listitem><para>
Puns and other patterns can be mixed in the same record:
<programlisting>
data C = C {a :: Int, b :: Int}
f (C {a, b = 4}) = a
</programlisting>
</para></listitem>

<listitem><para>
Puns can be used wherever record patterns occur (e.g. in
<literal>let</literal> bindings or at the top-level).
</para></listitem>

<listitem><para>
A pun on a qualified field name is expanded by stripping off the module qualifier.
For example:
<programlisting>
f (C {M.a}) = a
</programlisting>
means
<programlisting>
f (M.C {M.a = a}) = a
</programlisting>
(This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
is only in scope in qualified form.)
</para></listitem>
</itemizedlist>
</para>


</sect2>

    <!-- ===================== Record wildcards ===================  -->

<sect2 id="record-wildcards">
<title>Record wildcards
</title>

<para>
Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
This flag implies <literal>-XDisambiguateRecordFields</literal>.
</para>

<para>
For records with many fields, it can be tiresome to write out each field
individually in a record pattern, as in
<programlisting>
data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
f (C {a = 1, b = b, c = c, d = d}) = b + c + d
</programlisting>
</para>

<para>
Record wildcard syntax permits a "<literal>..</literal>" in a record
pattern, where each elided field <literal>f</literal> is replaced by the
pattern <literal>f = f</literal>.  For example, the above pattern can be
written as
<programlisting>
f (C {a = 1, ..}) = b + c + d
</programlisting>
</para>

<para>
More details:
<itemizedlist>
<listitem><para>
Wildcards can be mixed with other patterns, including puns
(<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
= 1, b, ..})</literal>.  Additionally, record wildcards can be used
wherever record patterns occur, including in <literal>let</literal>
bindings and at the top-level.  For example, the top-level binding
<programlisting>
C {a = 1, ..} = e
</programlisting>
defines <literal>b</literal>, <literal>c</literal>, and
<literal>d</literal>.
</para></listitem>

<listitem><para>
Record wildcards can also be used in expressions, writing, for example,
<programlisting>
let {a = 1; b = 2; c = 3; d = 4} in C {..}
</programlisting>
in place of
<programlisting>
let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
</programlisting>
The expansion is purely syntactic, so the record wildcard
expression refers to the nearest enclosing variables that are spelled
the same as the omitted field names.
</para></listitem>

<listitem><para>
The "<literal>..</literal>" expands to the missing
<emphasis>in-scope</emphasis> record fields.
Specifically the expansion of "<literal>C {..}</literal>" includes
<literal>f</literal> if and only if:
<itemizedlist>
<listitem><para>
<literal>f</literal> is a record field of constructor <literal>C</literal>.
</para></listitem>
<listitem><para>
The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
</para></listitem>
<listitem><para>
In the case of expressions (but not patterns),
the variable <literal>f</literal> is in scope unqualified,
apart from the binding of the record selector itself.
</para></listitem>
</itemizedlist>
For example
<programlisting>
module M where
  data R = R { a,b,c :: Int }
module X where
  import M( R(a,c) )
  f b = R { .. }
</programlisting>
The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
omitting <literal>b</literal> since the record field is not in scope,
and omitting <literal>c</literal> since the variable <literal>c</literal>
is not in scope (apart from the binding of the
record selector <literal>c</literal>, of course).
</para></listitem>
</itemizedlist>
</para>

</sect2>

    <!-- ===================== Local fixity declarations ===================  -->

<sect2 id="local-fixity-declarations">
<title>Local Fixity Declarations
</title>

<para>A careful reading of the Haskell 98 Report reveals that fixity
declarations (<literal>infix</literal>, <literal>infixl</literal>, and
<literal>infixr</literal>) are permitted to appear inside local bindings
such those introduced by <literal>let</literal> and
<literal>where</literal>.  However, the Haskell Report does not specify
the semantics of such bindings very precisely.
</para>

<para>In GHC, a fixity declaration may accompany a local binding:
<programlisting>
let f = ...
    infixr 3 `f`
in
    ...
</programlisting>
and the fixity declaration applies wherever the binding is in scope.
For example, in a <literal>let</literal>, it applies in the right-hand
sides of other <literal>let</literal>-bindings and the body of the
<literal>let</literal>C. Or, in recursive <literal>do</literal>
expressions (<xref linkend="recursive-do-notation"/>), the local fixity
declarations of a <literal>let</literal> statement scope over other
statements in the group, just as the bound name does.
</para>

<para>
Moreover, a local fixity declaration *must* accompany a local binding of
that name: it is not possible to revise the fixity of name bound
elsewhere, as in
<programlisting>
let infixr 9 $ in ...
</programlisting>

Because local fixity declarations are technically Haskell 98, no flag is
necessary to enable them.
</para>
</sect2>

<sect2 id="package-imports">
  <title>Package-qualified imports</title>

  <para>With the <option>-XPackageImports</option> flag, GHC allows
  import declarations to be qualified by the package name that the
    module is intended to be imported from.  For example:</para>

<programlisting>
import "network" Network.Socket
</programlisting>

  <para>would import the module <literal>Network.Socket</literal> from
    the package <literal>network</literal> (any version).  This may
    be used to disambiguate an import when the same module is
    available from multiple packages, or is present in both the
    current package being built and an external package.</para>

  <para>The special package name <literal>this</literal> can be used to
    refer to the current package being built.</para>

  <para>Note: you probably don't need to use this feature, it was
    added mainly so that we can build backwards-compatible versions of
    packages when APIs change.  It can lead to fragile dependencies in
    the common case: modules occasionally move from one package to
    another, rendering any package-qualified imports broken.</para>
</sect2>

<sect2 id="safe-imports-ext">
  <title>Safe imports</title>

  <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
    and <option>-XUnsafe</option> language flags, GHC extends
    the import declaration syntax to take an optional <literal>safe</literal>
    keyword after the <literal>import</literal> keyword. This feature
    is part of the Safe Haskell GHC extension. For example:</para>

<programlisting>
import safe qualified Network.Socket as NS
</programlisting>

  <para>would import the module <literal>Network.Socket</literal>
    with compilation only succeeding if Network.Socket can be
    safely imported. For a description of when a import is
    considered safe see <xref linkend="safe-haskell"/></para>

</sect2>

<sect2 id="explicit-namespaces">
<title>Explicit namespaces in import/export</title>

<para> In an import or export list, such as 
<programlisting>
  module M( f, (++) ) where ...
    import N( f, (++) ) 
    ...
</programlisting>
the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
However, with type operators (<xref linkend="type-operators"/>) it becomes possible
to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>.  In that
case, how would you export or import it?
</para>
<para>
The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of 
a type constructor in an import or export list with "<literal>type</literal>" to 
disambiguate this case, thus:
<programlisting>
  module M( f, type (++) ) where ...
    import N( f, type (++) ) 
    ...
  module N( f, type (++) ) where
    data family a ++ b = L a | R b
</programlisting>
The extension <option>-XExplicitNamespaces</option>
is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
</para>
</sect2>

<sect2 id="syntax-stolen">
<title>Summary of stolen syntax</title>

    <para>Turning on an option that enables special syntax
    <emphasis>might</emphasis> cause working Haskell 98 code to fail
    to compile, perhaps because it uses a variable name which has
    become a reserved word.  This section lists the syntax that is
    "stolen" by language extensions.
     We use
    notation and nonterminal names from the Haskell 98 lexical syntax
    (see the Haskell 98 Report).
    We only list syntax changes here that might affect
    existing working programs (i.e. "stolen" syntax).  Many of these
    extensions will also enable new context-free syntax, but in all
    cases programs written to use the new syntax would not be
    compilable without the option enabled.</para>

<para>There are two classes of special
    syntax:

    <itemizedlist>
      <listitem>
        <para>New reserved words and symbols: character sequences
        which are no longer available for use as identifiers in the
        program.</para>
      </listitem>
      <listitem>
        <para>Other special syntax: sequences of characters that have
        a different meaning when this particular option is turned
        on.</para>
      </listitem>
    </itemizedlist>

The following syntax is stolen:

    <variablelist>
      <varlistentry>
        <term>
          <literal>forall</literal>
          <indexterm><primary><literal>forall</literal></primary></indexterm>
        </term>
        <listitem><para>
        Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
            <option>-XScopedTypeVariables</option>,
            <option>-XLiberalTypeSynonyms</option>,
            <option>-XRankNTypes</option>,
            <option>-XExistentialQuantification</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>mdo</literal>
          <indexterm><primary><literal>mdo</literal></primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XRecursiveDo</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>foreign</literal>
          <indexterm><primary><literal>foreign</literal></primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XForeignFunctionInterface</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>rec</literal>,
          <literal>proc</literal>, <literal>-&lt;</literal>,
          <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
          <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
          <literal>|)</literal> brackets
          <indexterm><primary><literal>proc</literal></primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XArrows</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>?<replaceable>varid</replaceable></literal>,
          <literal>%<replaceable>varid</replaceable></literal>
          <indexterm><primary>implicit parameters</primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XImplicitParams</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>[|</literal>,
          <literal>[e|</literal>, <literal>[p|</literal>,
          <literal>[d|</literal>, <literal>[t|</literal>,
          <literal>$(</literal>,
          <literal>$<replaceable>varid</replaceable></literal>
          <indexterm><primary>Template Haskell</primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XTemplateHaskell</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <literal>[:<replaceable>varid</replaceable>|</literal>
          <indexterm><primary>quasi-quotation</primary></indexterm>
        </term>
        <listitem><para>
        Stolen by: <option>-XQuasiQuotes</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
              <replaceable>varid</replaceable>{<literal>&num;</literal>},
              <replaceable>char</replaceable><literal>&num;</literal>,
              <replaceable>string</replaceable><literal>&num;</literal>,
              <replaceable>integer</replaceable><literal>&num;</literal>,
              <replaceable>float</replaceable><literal>&num;</literal>,
              <replaceable>float</replaceable><literal>&num;&num;</literal>
        </term>
        <listitem><para>
        Stolen by: <option>-XMagicHash</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
              <literal>(&num;</literal>, <literal>&num;)</literal>
        </term>
        <listitem><para>
        Stolen by: <option>-XUnboxedTuples</option>
          </para></listitem>
      </varlistentry>

      <varlistentry>
        <term>
              <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
        </term>
        <listitem><para>
        Stolen by: <option>-XBangPatterns</option>
          </para></listitem>
      </varlistentry>
    </variablelist>
</para>
</sect2>
</sect1>


<!-- TYPE SYSTEM EXTENSIONS -->
<sect1 id="data-type-extensions">
<title>Extensions to data types and type synonyms</title>

<sect2 id="nullary-types">
<title>Data types with no constructors</title>

<para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
GHC lets you declare a data type with no constructors.  For example:</para>

<programlisting>
  data S      -- S :: *
  data T a    -- T :: * -> *
</programlisting>

<para>Syntactically, the declaration lacks the "= constrs" part.  The
type can be parameterised over types of any kind, but if the kind is
not <literal>*</literal> then an explicit kind annotation must be used
(see <xref linkend="kinding"/>).</para>

<para>Such data types have only one value, namely bottom.
Nevertheless, they can be useful when defining "phantom types".</para>
</sect2>

<sect2 id="datatype-contexts">
<title>Data type contexts</title>

<para>Haskell allows datatypes to be given contexts, e.g.</para>

<programlisting>
data Eq a => Set a = NilSet | ConsSet a (Set a)
</programlisting>

<para>give constructors with types:</para>

<programlisting>
NilSet :: Set a
ConsSet :: Eq a => a -> Set a -> Set a
</programlisting>

<para>This is widely considered a misfeature, and is going to be removed from
the language.  In GHC, it is controlled by the deprecated extension
<literal>DatatypeContexts</literal>.</para>
</sect2>

<sect2 id="infix-tycons">
<title>Infix type constructors, classes, and type variables</title>

<para>
GHC allows type constructors, classes, and type variables to be operators, and
to be written infix, very much like expressions.  More specifically:
<itemizedlist>
<listitem><para>
  A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
  The lexical syntax is the same as that for data constructors.
  </para></listitem>
<listitem><para>
  Data type and type-synonym declarations can be written infix, parenthesised
  if you want further arguments.  E.g.
<screen>
  data a :*: b = Foo a b
  type a :+: b = Either a b
  class a :=: b where ...

  data (a :**: b) x = Baz a b x
  type (a :++: b) y = Either (a,b) y
</screen>
  </para></listitem>
<listitem><para>
  Types, and class constraints, can be written infix.  For example
<screen>
  x :: Int :*: Bool
  f :: (a :=: b) => a -> b
</screen>
  </para></listitem>
<listitem><para>
  Back-quotes work
  as for expressions, both for type constructors and type variables;  e.g. <literal>Int `Either` Bool</literal>, or
  <literal>Int `a` Bool</literal>.  Similarly, parentheses work the same; e.g.  <literal>(:*:) Int Bool</literal>.
  </para></listitem>
<listitem><para>
  Fixities may be declared for type constructors, or classes, just as for data constructors.  However,
  one cannot distinguish between the two in a fixity declaration; a fixity declaration
  sets the fixity for a data constructor and the corresponding type constructor.  For example:
<screen>
  infixl 7 T, :*:
</screen>
  sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
  and similarly for <literal>:*:</literal>.
  <literal>Int `a` Bool</literal>.
  </para></listitem>
<listitem><para>
  Function arrow is <literal>infixr</literal> with fixity 0.  (This might change; I'm not sure what it should be.)
  </para></listitem>

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

<sect2 id="type-operators">
<title>Type operators</title>
<para>
In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
<emphasis>variable</emphasis>, just like <literal>a</literal>.  Thus in Haskell 98 you can say
<programlisting>
type T (+) = ((+), (+))
-- Just like: type T a = (a,a)

f :: T Int -> Int
f (x,y)= x
</programlisting>
As you can see, using operators in this way is not very useful, and Haskell 98 does not even
allow you to write them infix.
</para>
<para>
The language <option>-XTypeOperators</option> changes this behaviour:
<itemizedlist>
<listitem><para>
Operator symbols become type <emphasis>constructors</emphasis> rather than 
type <emphasis>variables</emphasis>.
</para></listitem>
<listitem><para>
Operator symbols in types can be written infix, both in definitions and uses. 
for example:
<programlisting>
data a + b = Plus a b
type Foo = Int + Bool
</programlisting>
</para></listitem>
<listitem><para>
There is now some potential ambiguity in import and export lists; for example
if you write <literal>import M( (+) )</literal> do you mean the 
<emphasis>function</emphasis> <literal>(+)</literal> or the 
<emphasis>type constructor</emphasis> <literal>(+)</literal>?
The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
by <option>-XExplicitTypeOperators</option>) GHC allows you to specify the latter
by preceding it with the keyword <literal>type</literal>, thus:
<programlisting>
import M( type (+) )
</programlisting>
See <xref linkend="explicit-namespaces"/>.
</para></listitem>
<listitem><para>
The fixity of a type operator may be set using the usual fixity declarations
but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
a single fixity.
</para></listitem>
</itemizedlist>
</para>
</sect2>

<sect2 id="type-synonyms">
<title>Liberalised type synonyms</title>

<para>
Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
on individual synonym declarations.
With the <option>-XLiberalTypeSynonyms</option> extension,
GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
That means that GHC can be very much more liberal about type synonyms than Haskell 98.

<itemizedlist>
<listitem> <para>You can write a <literal>forall</literal> (including overloading)
in a type synonym, thus:
<programlisting>
  type Discard a = forall b. Show b => a -> b -> (a, String)

  f :: Discard a
  f x y = (x, show y)

  g :: Discard Int -> (Int,String)    -- A rank-2 type
  g f = f 3 True
</programlisting>
</para>
</listitem>

<listitem><para>
If you also use <option>-XUnboxedTuples</option>,
you can write an unboxed tuple in a type synonym:
<programlisting>
  type Pr = (# Int, Int #)

  h :: Int -> Pr
  h x = (# x, x #)
</programlisting>
</para></listitem>

<listitem><para>
You can apply a type synonym to a forall type:
<programlisting>
  type Foo a = a -> a -> Bool

  f :: Foo (forall b. b->b)
</programlisting>
After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
<programlisting>
  f :: (forall b. b->b) -> (forall b. b->b) -> Bool
</programlisting>
</para></listitem>

<listitem><para>
You can apply a type synonym to a partially applied type synonym:
<programlisting>
  type Generic i o = forall x. i x -> o x
  type Id x = x

  foo :: Generic Id []
</programlisting>
After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
<programlisting>
  foo :: forall x. x -> [x]
</programlisting>
</para></listitem>

</itemizedlist>
</para>

<para>
GHC currently does kind checking before expanding synonyms (though even that
could be changed.)
</para>
<para>
After expanding type synonyms, GHC does validity checking on types, looking for
the following mal-formedness which isn't detected simply by kind checking:
<itemizedlist>
<listitem><para>
Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
is off)
</para></listitem>
<listitem><para>
Partially-applied type synonym.
</para></listitem>
</itemizedlist>
So, for example, this will be rejected:
<programlisting>
  type Pr = forall a. a

  h :: [Pr]
  h = ...
</programlisting>
because GHC does not allow type constructors applied to for-all types.
</para>
</sect2>


<sect2 id="existential-quantification">
<title>Existentially quantified data constructors
</title>

<para>
The idea of using existential quantification in data type declarations
was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
London, 1991). It was later formalised by Laufer and Odersky
(<emphasis>Polymorphic type inference and abstract data types</emphasis>,
TOPLAS, 16(5), pp1411-1430, 1994).
It's been in Lennart
Augustsson's <command>hbc</command> Haskell compiler for several years, and
proved very useful.  Here's the idea.  Consider the declaration:
</para>

<para>

<programlisting>
  data Foo = forall a. MkFoo a (a -> Bool)
           | Nil
</programlisting>

</para>

<para>
The data type <literal>Foo</literal> has two constructors with types:
</para>

<para>

<programlisting>
  MkFoo :: forall a. a -> (a -> Bool) -> Foo
  Nil   :: Foo
</programlisting>

</para>

<para>
Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
does not appear in the data type itself, which is plain <literal>Foo</literal>.
For example, the following expression is fine:
</para>

<para>

<programlisting>
  [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
</programlisting>

</para>

<para>
Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
<function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
isUpper</function> packages a character with a compatible function.  These
two things are each of type <literal>Foo</literal> and can be put in a list.
</para>

<para>
What can we do with a value of type <literal>Foo</literal>?.  In particular,
what happens when we pattern-match on <function>MkFoo</function>?
</para>

<para>

<programlisting>
  f (MkFoo val fn) = ???
</programlisting>

</para>

<para>
Since all we know about <literal>val</literal> and <function>fn</function> is that they
are compatible, the only (useful) thing we can do with them is to
apply <function>fn</function> to <literal>val</literal> to get a boolean.  For example:
</para>

<para>

<programlisting>
  f :: Foo -> Bool
  f (MkFoo val fn) = fn val
</programlisting>

</para>

<para>
What this allows us to do is to package heterogeneous values
together with a bunch of functions that manipulate them, and then treat
that collection of packages in a uniform manner.  You can express
quite a bit of object-oriented-like programming this way.
</para>

<sect3 id="existential">
<title>Why existential?
</title>

<para>
What has this to do with <emphasis>existential</emphasis> quantification?
Simply that <function>MkFoo</function> has the (nearly) isomorphic type
</para>

<para>

<programlisting>
  MkFoo :: (exists a . (a, a -> Bool)) -> Foo
</programlisting>

</para>

<para>
But Haskell programmers can safely think of the ordinary
<emphasis>universally</emphasis> quantified type given above, thereby avoiding
adding a new existential quantification construct.
</para>

</sect3>

<sect3 id="existential-with-context">
<title>Existentials and type classes</title>

<para>
An easy extension is to allow
arbitrary contexts before the constructor.  For example:
</para>

<para>

<programlisting>
data Baz = forall a. Eq a => Baz1 a a
         | forall b. Show b => Baz2 b (b -> b)
</programlisting>

</para>

<para>
The two constructors have the types you'd expect:
</para>

<para>

<programlisting>
Baz1 :: forall a. Eq a => a -> a -> Baz
Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
</programlisting>

</para>

<para>
But when pattern matching on <function>Baz1</function> the matched values can be compared
for equality, and when pattern matching on <function>Baz2</function> the first matched
value can be converted to a string (as well as applying the function to it).
So this program is legal:
</para>

<para>

<programlisting>
  f :: Baz -> String
  f (Baz1 p q) | p == q    = "Yes"
               | otherwise = "No"
  f (Baz2 v fn)            = show (fn v)
</programlisting>

</para>

<para>
Operationally, in a dictionary-passing implementation, the
constructors <function>Baz1</function> and <function>Baz2</function> must store the
dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
extract it on pattern matching.
</para>

</sect3>

<sect3 id="existential-records">
<title>Record Constructors</title>

<para>
GHC allows existentials to be used with records syntax as well.  For example:

<programlisting>
data Counter a = forall self. NewCounter
    { _this    :: self
    , _inc     :: self -> self
    , _display :: self -> IO ()
    , tag      :: a
    }
</programlisting>
Here <literal>tag</literal> is a public field, with a well-typed selector
function <literal>tag :: Counter a -> a</literal>.  The <literal>self</literal>
type is hidden from the outside; any attempt to apply <literal>_this</literal>,
<literal>_inc</literal> or <literal>_display</literal> as functions will raise a
compile-time error.  In other words, <emphasis>GHC defines a record selector function
only for fields whose type does not mention the existentially-quantified variables</emphasis>.
(This example used an underscore in the fields for which record selectors
will not be defined, but that is only programming style; GHC ignores them.)
</para>

<para>
To make use of these hidden fields, we need to create some helper functions:

<programlisting>
inc :: Counter a -> Counter a
inc (NewCounter x i d t) = NewCounter
    { _this = i x, _inc = i, _display = d, tag = t }

display :: Counter a -> IO ()
display NewCounter{ _this = x, _display = d } = d x
</programlisting>

Now we can define counters with different underlying implementations:

<programlisting>
counterA :: Counter String
counterA = NewCounter
    { _this = 0, _inc = (1+), _display = print, tag = "A" }

counterB :: Counter String
counterB = NewCounter
    { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }

main = do
    display (inc counterA)         -- prints "1"
    display (inc (inc counterB))   -- prints "##"
</programlisting>

Record update syntax is supported for existentials (and GADTs):
<programlisting>
setTag :: Counter a -> a -> Counter a
setTag obj t = obj{ tag = t }
</programlisting>
The rule for record update is this: <emphasis>
the types of the updated fields may
mention only the universally-quantified type variables
of the data constructor.  For GADTs, the field may mention only types
that appear as a simple type-variable argument in the constructor's result
type</emphasis>.  For example:
<programlisting>
data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
upd1 t x = t { f1=x }   -- OK:   upd1 :: T a b -> a' -> T a' b
upd2 t x = t { f3=x }   -- BAD   (f3's type mentions c, which is
                        --        existentially quantified)

data G a b where { G1 { g1::a, g2::c } :: G a [c] }
upd3 g x = g { g1=x }   -- OK:   upd3 :: G a b -> c -> G c b
upd4 g x = g { g2=x }   -- BAD (f2's type mentions c, which is not a simple
                        --      type-variable argument in G1's result type)
</programlisting>
</para>

</sect3>


<sect3>
<title>Restrictions</title>

<para>
There are several restrictions on the ways in which existentially-quantified
constructors can be use.
</para>

<para>

<itemizedlist>
<listitem>

<para>
 When pattern matching, each pattern match introduces a new,
distinct, type for each existential type variable.  These types cannot
be unified with any other type, nor can they escape from the scope of
the pattern match.  For example, these fragments are incorrect:


<programlisting>
f1 (MkFoo a f) = a
</programlisting>


Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
is the result of <function>f1</function>.  One way to see why this is wrong is to
ask what type <function>f1</function> has:


<programlisting>
  f1 :: Foo -> a             -- Weird!
</programlisting>


What is this "<literal>a</literal>" in the result type? Clearly we don't mean
this:


<programlisting>
  f1 :: forall a. Foo -> a   -- Wrong!
</programlisting>


The original program is just plain wrong.  Here's another sort of error


<programlisting>
  f2 (Baz1 a b) (Baz1 p q) = a==q
</programlisting>


It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
<literal>a==q</literal> is wrong because it equates the two distinct types arising
from the two <function>Baz1</function> constructors.


</para>
</listitem>
<listitem>

<para>
You can't pattern-match on an existentially quantified
constructor in a <literal>let</literal> or <literal>where</literal> group of
bindings. So this is illegal:


<programlisting>
  f3 x = a==b where { Baz1 a b = x }
</programlisting>

Instead, use a <literal>case</literal> expression:

<programlisting>
  f3 x = case x of Baz1 a b -> a==b
</programlisting>

In general, you can only pattern-match
on an existentially-quantified constructor in a <literal>case</literal> expression or
in the patterns of a function definition.

The reason for this restriction is really an implementation one.
Type-checking binding groups is already a nightmare without
existentials complicating the picture.  Also an existential pattern
binding at the top level of a module doesn't make sense, because it's
not clear how to prevent the existentially-quantified type "escaping".
So for now, there's a simple-to-state restriction.  We'll see how
annoying it is.

</para>
</listitem>
<listitem>

<para>
You can't use existential quantification for <literal>newtype</literal>
declarations.  So this is illegal:


<programlisting>
  newtype T = forall a. Ord a => MkT a
</programlisting>


Reason: a value of type <literal>T</literal> must be represented as a
pair of a dictionary for <literal>Ord t</literal> and a value of type
<literal>t</literal>.  That contradicts the idea that
<literal>newtype</literal> should have no concrete representation.
You can get just the same efficiency and effect by using
<literal>data</literal> instead of <literal>newtype</literal>.  If
there is no overloading involved, then there is more of a case for
allowing an existentially-quantified <literal>newtype</literal>,
because the <literal>data</literal> version does carry an
implementation cost, but single-field existentially quantified
constructors aren't much use.  So the simple restriction (no
existential stuff on <literal>newtype</literal>) stands, unless there
are convincing reasons to change it.


</para>
</listitem>
<listitem>

<para>
 You can't use <literal>deriving</literal> to define instances of a
data type with existentially quantified data constructors.

Reason: in most cases it would not make sense. For example:;

<programlisting>
data T = forall a. MkT [a] deriving( Eq )
</programlisting>

To derive <literal>Eq</literal> in the standard way we would need to have equality
between the single component of two <function>MkT</function> constructors:

<programlisting>
instance Eq T where
  (MkT a) == (MkT b) = ???
</programlisting>

But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
It's just about possible to imagine examples in which the derived instance
would make sense, but it seems altogether simpler simply to prohibit such
declarations.  Define your own instances!
</para>
</listitem>

</itemizedlist>

</para>

</sect3>
</sect2>

<!-- ====================== Generalised algebraic data types =======================  -->

<sect2 id="gadt-style">
<title>Declaring data types with explicit constructor signatures</title>

<para>When the <literal>GADTSyntax</literal> extension is enabled,
GHC allows you to declare an algebraic data type by
giving the type signatures of constructors explicitly.  For example:
<programlisting>
  data Maybe a where
      Nothing :: Maybe a
      Just    :: a -> Maybe a
</programlisting>
The form is called a "GADT-style declaration"
because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
can only be declared using this form.</para>
<para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
For example, these two declarations are equivalent:
<programlisting>
  data Foo = forall a. MkFoo a (a -> Bool)
  data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
</programlisting>
</para>
<para>Any data type that can be declared in standard Haskell-98 syntax
can also be declared using GADT-style syntax.
The choice is largely stylistic, but GADT-style declarations differ in one important respect:
they treat class constraints on the data constructors differently.
Specifically, if the constructor is given a type-class context, that
context is made available by pattern matching.  For example:
<programlisting>
  data Set a where
    MkSet :: Eq a => [a] -> Set a

  makeSet :: Eq a => [a] -> Set a
  makeSet xs = MkSet (nub xs)

  insert :: a -> Set a -> Set a
  insert a (MkSet as) | a `elem` as = MkSet as
                      | otherwise   = MkSet (a:as)
</programlisting>
A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
gives rise to a <literal>(Eq a)</literal>
constraint, as you would expect.  The new feature is that pattern-matching on <literal>MkSet</literal>
(as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
context.  In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
when pattern-matching that dictionary becomes available for the right-hand side of the match.
In the example, the equality dictionary is used to satisfy the equality constraint
generated by the call to <literal>elem</literal>, so that the type of
<literal>insert</literal> itself has no <literal>Eq</literal> constraint.
</para>
<para>
For example, one possible application is to reify dictionaries:
<programlisting>
   data NumInst a where
     MkNumInst :: Num a => NumInst a

   intInst :: NumInst Int
   intInst = MkNumInst

   plus :: NumInst a -> a -> a -> a
   plus MkNumInst p q = p + q
</programlisting>
Here, a value of type <literal>NumInst a</literal> is equivalent
to an explicit <literal>(Num a)</literal> dictionary.
</para>
<para>
All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
For example, the <literal>NumInst</literal> data type above could equivalently be declared
like this:
<programlisting>
   data NumInst a
      = Num a => MkNumInst (NumInst a)
</programlisting>
Notice that, unlike the situation when declaring an existential, there is
no <literal>forall</literal>, because the <literal>Num</literal> constrains the
data type's universally quantified type variable <literal>a</literal>.
A constructor may have both universal and existential type variables: for example,
the following two declarations are equivalent:
<programlisting>
   data T1 a
        = forall b. (Num a, Eq b) => MkT1 a b
   data T2 a where
        MkT2 :: (Num a, Eq b) => a -> b -> T2 a
</programlisting>
</para>
<para>All this behaviour contrasts with Haskell 98's peculiar treatment of
contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
In Haskell 98 the definition
<programlisting>
  data Eq a => Set' a = MkSet' [a]
</programlisting>
gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above.  But instead of
<emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
GHC faithfully implements this behaviour, odd though it is.  But for GADT-style declarations,
GHC's behaviour is much more useful, as well as much more intuitive.
</para>

<para>
The rest of this section gives further details about GADT-style data
type declarations.

<itemizedlist>
<listitem><para>
The result type of each data constructor must begin with the type constructor being defined.
If the result type of all constructors
has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
</para></listitem>

<listitem><para>
As with other type signatures, you can give a single signature for several data constructors.
In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
<programlisting>
  data T a where
    T1,T2 :: a -> T a
    T3 :: T a
</programlisting>
</para></listitem>

<listitem><para>
The type signature of
each constructor is independent, and is implicitly universally quantified as usual.
In particular, the type variable(s) in the "<literal>data T a where</literal>" header
have no scope, and different constructors may have different universally-quantified type variables:
<programlisting>
  data T a where        -- The 'a' has no scope
    T1,T2 :: b -> T b   -- Means forall b. b -> T b
    T3 :: T a           -- Means forall a. T a
</programlisting>
</para></listitem>

<listitem><para>
A constructor signature may mention type class constraints, which can differ for
different constructors.  For example, this is fine:
<programlisting>
  data T a where
    T1 :: Eq b => b -> b -> T b
    T2 :: (Show c, Ix c) => c -> [c] -> T c
</programlisting>
When pattern matching, these constraints are made available to discharge constraints
in the body of the match. For example:
<programlisting>
  f :: T a -> String
  f (T1 x y) | x==y      = "yes"
             | otherwise = "no"
  f (T2 a b)             = show a
</programlisting>
Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
</para></listitem>

<listitem><para>
Unlike a Haskell-98-style
data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
have no scope.  Indeed, one can write a kind signature instead:
<programlisting>
  data Set :: * -> * where ...
</programlisting>
or even a mixture of the two:
<programlisting>
  data Bar a :: (* -> *) -> * where ...
</programlisting>
The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
like this:
<programlisting>
  data Bar a (b :: * -> *) where ...
</programlisting>
</para></listitem>


<listitem><para>
You can use strictness annotations, in the obvious places
in the constructor type:
<programlisting>
  data Term a where
      Lit    :: !Int -> Term Int
      If     :: Term Bool -> !(Term a) -> !(Term a) -> Term a
      Pair   :: Term a -> Term b -> Term (a,b)
</programlisting>
</para></listitem>

<listitem><para>
You can use a <literal>deriving</literal> clause on a GADT-style data type
declaration.   For example, these two declarations are equivalent
<programlisting>
  data Maybe1 a where {
      Nothing1 :: Maybe1 a ;
      Just1    :: a -> Maybe1 a
    } deriving( Eq, Ord )

  data Maybe2 a = Nothing2 | Just2 a
       deriving( Eq, Ord )
</programlisting>
</para></listitem>

<listitem><para>
The type signature may have quantified type variables that do not appear
in the result type:
<programlisting>
  data Foo where
     MkFoo :: a -> (a->Bool) -> Foo
     Nil   :: Foo
</programlisting>
Here the type variable <literal>a</literal> does not appear in the result type
of either constructor.
Although it is universally quantified in the type of the constructor, such
a type variable is often called "existential".
Indeed, the above declaration declares precisely the same type as
the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
</para><para>
The type may contain a class context too, of course:
<programlisting>
  data Showable where
    MkShowable :: Show a => a -> Showable
</programlisting>
</para></listitem>

<listitem><para>
You can use record syntax on a GADT-style data type declaration:

<programlisting>
  data Person where
      Adult :: { name :: String, children :: [Person] } -> Person
      Child :: Show a => { name :: !String, funny :: a } -> Person
</programlisting>
As usual, for every constructor that has a field <literal>f</literal>, the type of
field <literal>f</literal> must be the same (modulo alpha conversion).
The <literal>Child</literal> constructor above shows that the signature
may have a context, existentially-quantified variables, and strictness annotations,
just as in the non-record case.  (NB: the "type" that follows the double-colon
is not really a type, because of the record syntax and strictness annotations.
A "type" of this form can appear only in a constructor signature.)
</para></listitem>

<listitem><para>
Record updates are allowed with GADT-style declarations,
only fields that have the following property: the type of the field
mentions no existential type variables.
</para></listitem>

<listitem><para>
As in the case of existentials declared using the Haskell-98-like record syntax
(<xref linkend="existential-records"/>),
record-selector functions are generated only for those fields that have well-typed
selectors.
Here is the example of that section, in GADT-style syntax:
<programlisting>
data Counter a where
    NewCounter :: { _this    :: self
                  , _inc     :: self -> self
                  , _display :: self -> IO ()
                  , tag      :: a
                  } -> Counter a
</programlisting>
As before, only one selector function is generated here, that for <literal>tag</literal>.
Nevertheless, you can still use all the field names in pattern matching and record construction.
</para></listitem>

<listitem><para>
In a GADT-style data type declaration there is no obvious way to specify that a data constructor
should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
(Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
So GHC implements the following design: a data constructor declared in a GADT-style data type
declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
(b) it has two arguments, (c) it has a programmer-supplied fixity declaration.  For example
<programlisting>
   infix 6 (:--:)
   data T a where
     (:--:) :: Int -> Bool -> T Int
</programlisting>
</para></listitem>
</itemizedlist></para>
</sect2>

<sect2 id="gadt">
<title>Generalised Algebraic Data Types (GADTs)</title>

<para>Generalised Algebraic Data Types generalise ordinary algebraic data types
by allowing constructors to have richer return types.  Here is an example:
<programlisting>
  data Term a where
      Lit    :: Int -> Term Int
      Succ   :: Term Int -> Term Int
      IsZero :: Term Int -> Term Bool
      If     :: Term Bool -> Term a -> Term a -> Term a
      Pair   :: Term a -> Term b -> Term (a,b)
</programlisting>
Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
case with ordinary data types.  This generality allows us to
write a well-typed <literal>eval</literal> function
for these <literal>Terms</literal>:
<programlisting>
  eval :: Term a -> a
  eval (Lit i)      = i
  eval (Succ t)     = 1 + eval t
  eval (IsZero t)   = eval t == 0
  eval (If b e1 e2) = if eval b then eval e1 else eval e2
  eval (Pair e1 e2) = (eval e1, eval e2)
</programlisting>
The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
For example, in the right hand side of the equation
<programlisting>
  eval :: Term a -> a
  eval (Lit i) =  ...
</programlisting>
the type <literal>a</literal> is refined to <literal>Int</literal>.  That's the whole point!
A precise specification of the type rules is beyond what this user manual aspires to,
but the design closely follows that described in
the paper <ulink
url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
unification-based type inference for GADTs</ulink>,
(ICFP 2006).
The general principle is this: <emphasis>type refinement is only carried out
based on user-supplied type annotations</emphasis>.
So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
and lots of obscure error messages will
occur.  However, the refinement is quite general.  For example, if we had:
<programlisting>
  eval :: Term a -> a -> a
  eval (Lit i) j =  i+j
</programlisting>
the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
the result type of the <literal>case</literal> expression.  Hence the addition <literal>i+j</literal> is legal.
</para>
<para>
These and many other examples are given in papers by Hongwei Xi, and
Tim Sheard. There is a longer introduction
<ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
and Ralf Hinze's
<ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
may use different notation to that implemented in GHC.
</para>
<para>
The rest of this section outlines the extensions to GHC that support GADTs.   The extension is enabled with
<option>-XGADTs</option>.  The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
<itemizedlist>
<listitem><para>
A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
the old Haskell-98 syntax for data declarations always declares an ordinary data type.
The result type of each constructor must begin with the type constructor being defined,
but for a GADT the arguments to the type constructor can be arbitrary monotypes.
For example, in the <literal>Term</literal> data
type above, the type of each constructor must end with <literal>Term ty</literal>, but
the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
constructor).
</para></listitem>

<listitem><para>
It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
whose result type is not just <literal>T a b</literal>.
</para></listitem>

<listitem><para>
You cannot use a <literal>deriving</literal> clause for a GADT; only for
an ordinary data type.
</para></listitem>

<listitem><para>
As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
For example:
<programlisting>
  data Term a where
      Lit    :: { val  :: Int }      -> Term Int
      Succ   :: { num  :: Term Int } -> Term Int
      Pred   :: { num  :: Term Int } -> Term Int
      IsZero :: { arg  :: Term Int } -> Term Bool
      Pair   :: { arg1 :: Term a
                , arg2 :: Term b
                }                    -> Term (a,b)
      If     :: { cnd  :: Term Bool
                , tru  :: Term a
                , fls  :: Term a
                }                    -> Term a
</programlisting>
However, for GADTs there is the following additional constraint:
every constructor that has a field <literal>f</literal> must have
the same result type (modulo alpha conversion)
Hence, in the above example, we cannot merge the <literal>num</literal>
and <literal>arg</literal> fields above into a
single name.  Although their field types are both <literal>Term Int</literal>,
their selector functions actually have different types:

<programlisting>
  num :: Term Int -> Term Int
  arg :: Term Bool -> Term Int
</programlisting>
</para></listitem>

<listitem><para>
When pattern-matching against data constructors drawn from a GADT,
for example in a <literal>case</literal> expression, the following rules apply:
<itemizedlist>
<listitem><para>The type of the scrutinee must be rigid.</para></listitem>
<listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
<listitem><para>The type of any free variable mentioned in any of
the <literal>case</literal> alternatives must be rigid.</para></listitem>
</itemizedlist>
A type is "rigid" if it is completely known to the compiler at its binding site.  The easiest
way to ensure that a variable a rigid type is to give it a type signature.
For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
Simple unification-based type inference for GADTs
</ulink>. The criteria implemented by GHC are given in the Appendix.

</para></listitem>

</itemizedlist>
</para>

</sect2>
</sect1>

<!-- ====================== End of Generalised algebraic data types =======================  -->

<sect1 id="deriving">
<title>Extensions to the "deriving" mechanism</title>

<sect2 id="deriving-inferred">
<title>Inferred context for deriving clauses</title>

<para>
The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
legal.  For example:
<programlisting>
  data T0 f a = MkT0 a         deriving( Eq )
  data T1 f a = MkT1 (f a)     deriving( Eq )
  data T2 f a = MkT2 (f (f a)) deriving( Eq )
</programlisting>
The natural generated <literal>Eq</literal> code would result in these instance declarations:
<programlisting>
  instance Eq a         => Eq (T0 f a) where ...
  instance Eq (f a)     => Eq (T1 f a) where ...
  instance Eq (f (f a)) => Eq (T2 f a) where ...
</programlisting>
The first of these is obviously fine. The second is still fine, although less obviously.
The third is not Haskell 98, and risks losing termination of instances.
</para>
<para>
GHC takes a conservative position: it accepts the first two, but not the third.  The  rule is this:
each constraint in the inferred instance context must consist only of type variables,
with no repetitions.
</para>
<para>
This rule is applied regardless of flags.  If you want a more exotic context, you can write
it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
</para>
</sect2>

<sect2 id="stand-alone-deriving">
<title>Stand-alone deriving declarations</title>

<para>
GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
<programlisting>
  data Foo a = Bar a | Baz String

  deriving instance Eq a => Eq (Foo a)
</programlisting>
The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
<literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
Note the following points:
<itemizedlist>
<listitem><para>
You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
exactly as you would in an ordinary instance declaration.
(In contrast, in a <literal>deriving</literal> clause
attached to a data type declaration, the context is inferred.)
</para></listitem>

<listitem><para>
A <literal>deriving instance</literal> declaration
must obey the same rules concerning form and termination as ordinary instance declarations,
controlled by the same flags; see <xref linkend="instance-decls"/>.
</para></listitem>

<listitem><para>
Unlike a <literal>deriving</literal>
declaration attached to a <literal>data</literal> declaration, the instance can be more specific
than the data type (assuming you also use
<literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>).  Consider
for example
<programlisting>
  data Foo a = Bar a | Baz String

  deriving instance Eq a => Eq (Foo [a])
  deriving instance Eq a => Eq (Foo (Maybe a))
</programlisting>
This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
</para></listitem>

<listitem><para>
Unlike a <literal>deriving</literal>
declaration attached to a <literal>data</literal> declaration,
GHC does not restrict the form of the data type.  Instead, GHC simply generates the appropriate
boilerplate code for the specified class, and typechecks it. If there is a type error, it is
your problem. (GHC will show you the offending code if it has a type error.)
The merit of this is that you can derive instances for GADTs and other exotic
data types, providing only that the boilerplate code does indeed typecheck.  For example:
<programlisting>
  data T a where
     T1 :: T Int
     T2 :: T Bool

  deriving instance Show (T a)
</programlisting>
In this example, you cannot say <literal>... deriving( Show )</literal> on the
data type declaration for <literal>T</literal>,
because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
the instance declaration using stand-alone deriving.
</para>
</listitem>

<listitem>
<para>The stand-alone syntax is generalised for newtypes in exactly the same
way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
For example:
<programlisting>
  newtype Foo a = MkFoo (State Int a)

  deriving instance MonadState Int Foo
</programlisting>
GHC always treats the <emphasis>last</emphasis> parameter of the instance
(<literal>Foo</literal> in this example) as the type whose instance is being derived.
</para></listitem>
</itemizedlist></para>

</sect2>


<sect2 id="deriving-typeable">
<title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>

<para>
Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
classes <literal>Eq</literal>, <literal>Ord</literal>,
<literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
</para>
<para>
GHC extends this list with several more classes that may be automatically derived:
<itemizedlist>
<listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
<literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
modules <literal>Data.Typeable</literal> and <literal>Data.Data</literal> respectively.
</para>
<para>Since GHC 7.8.1, <literal>Typeable</literal> is kind-polymorphic (see
<xref linkend="kind-polymorphism"/>) and can be derived for any datatype and
type class. Instances for datatypes can be derived by attaching a
<literal>deriving Typeable</literal> clause to the datatype declaration, or by
using standalone deriving (see <xref linkend="stand-alone-deriving"/>).
Instances for type classes can only be derived using standalone deriving.
For data families, <literal>Typeable</literal> should only be derived for the
uninstantiated family type; each instance will then automatically have a
<literal>Typeable</literal> instance too.
See also <xref linkend="auto-derive-typeable"/>.
</para>
<para>
Also since GHC 7.8.1, handwritten (ie. not derived) instances of
<literal>Typeable</literal> are forbidden, and will result in an error.
</para>
</listitem>

<listitem><para> With <option>-XDeriveGeneric</option>, you can derive
instances of the classes <literal>Generic</literal> and
<literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
You can use these to define generic functions,
as described in <xref linkend="generic-programming"/>.
</para></listitem>

<listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
the class <literal>Functor</literal>,
defined in <literal>GHC.Base</literal>.
</para></listitem>

<listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
the class <literal>Foldable</literal>,
defined in <literal>Data.Foldable</literal>.
</para></listitem>

<listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
the class <literal>Traversable</literal>,
defined in <literal>Data.Traversable</literal>.
</para></listitem>
</itemizedlist>
In each case the appropriate class must be in scope before it
can be mentioned in the <literal>deriving</literal> clause.
</para>
</sect2>

<sect2 id="auto-derive-typeable">
<title>Automatically deriving <literal>Typeable</literal> instances</title>

<para>
The flag <option>-XAutoDeriveTypeable</option> triggers the generation
of derived <literal>Typeable</literal> instances for every datatype and type
class declaration in the module it is used. It will also generate
<literal>Typeable</literal> instances for any promoted data constructors
(<xref linkend="promotion"/>). This flag implies
<option>-XDeriveDataTypeable</option> (<xref linkend="deriving-typeable"/>).
</para>

</sect2>

<sect2 id="newtype-deriving">
<title>Generalised derived instances for newtypes</title>

<para>
When you define an abstract type using <literal>newtype</literal>, you may want
the new type to inherit some instances from its representation. In
Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
<literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
other classes you have to write an explicit instance declaration. For
example, if you define

<programlisting>
  newtype Dollars = Dollars Int
</programlisting>

and you want to use arithmetic on <literal>Dollars</literal>, you have to
explicitly define an instance of <literal>Num</literal>:

<programlisting>
  instance Num Dollars where
    Dollars a + Dollars b = Dollars (a+b)
    ...
</programlisting>
All the instance does is apply and remove the <literal>newtype</literal>
constructor. It is particularly galling that, since the constructor
doesn't appear at run-time, this instance declaration defines a
dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
dictionary, only slower!
</para>


<sect3 id="generalized-newtype-deriving"> <title> Generalising the deriving clause </title>
<para>
GHC now permits such instances to be derived instead,
using the flag <option>-XGeneralizedNewtypeDeriving</option>,
so one can write
<programlisting>
  newtype Dollars = Dollars Int deriving (Eq,Show,Num)
</programlisting>

and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
derives an instance declaration of the form

<programlisting>
  instance Num Int => Num Dollars
</programlisting>

which just adds or removes the <literal>newtype</literal> constructor according to the type.
</para>
<para>

We can also derive instances of constructor classes in a similar
way. For example, suppose we have implemented state and failure monad
transformers, such that

<programlisting>
  instance Monad m => Monad (State s m)
  instance Monad m => Monad (Failure m)
</programlisting>
In Haskell 98, we can define a parsing monad by
<programlisting>
  type Parser tok m a = State [tok] (Failure m) a
</programlisting>

which is automatically a monad thanks to the instance declarations
above. With the extension, we can make the parser type abstract,
without needing to write an instance of class <literal>Monad</literal>, via

<programlisting>
  newtype Parser tok m a = Parser (State [tok] (Failure m) a)
                         deriving Monad
</programlisting>
In this case the derived instance declaration is of the form
<programlisting>
  instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
</programlisting>

Notice that, since <literal>Monad</literal> is a constructor class, the
instance is a <emphasis>partial application</emphasis> of the new type, not the
entire left hand side. We can imagine that the type declaration is
"eta-converted" to generate the context of the instance
declaration.
</para>
<para>

We can even derive instances of multi-parameter classes, provided the
newtype is the last class parameter. In this case, a ``partial
application'' of the class appears in the <literal>deriving</literal>
clause. For example, given the class

<programlisting>
  class StateMonad s m | m -> s where ...
  instance Monad m => StateMonad s (State s m) where ...
</programlisting>
then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
<programlisting>
  newtype Parser tok m a = Parser (State [tok] (Failure m) a)
                         deriving (Monad, StateMonad [tok])
</programlisting>

The derived instance is obtained by completing the application of the
class to the new type:

<programlisting>
  instance StateMonad [tok] (State [tok] (Failure m)) =>
           StateMonad [tok] (Parser tok m)
</programlisting>
</para>
<para>

As a result of this extension, all derived instances in newtype
 declarations are treated uniformly (and implemented just by reusing
the dictionary for the representation type), <emphasis>except</emphasis>
<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
the newtype and its representation.
</para>
</sect3>

<sect3> <title> A more precise specification </title>
<para>
Derived instance declarations are constructed as follows. Consider the
declaration (after expansion of any type synonyms)

<programlisting>
  newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
</programlisting>

where
 <itemizedlist>
<listitem><para>
  The <literal>ci</literal> are partial applications of
  classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
  is exactly <literal>j+1</literal>.  That is, <literal>C</literal> lacks exactly one type argument.
</para></listitem>
<listitem><para>
  The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
</para></listitem>
<listitem><para>
  The type <literal>t</literal> is an arbitrary type.
</para></listitem>
<listitem><para>
  The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
  nor in the <literal>ci</literal>, and
</para></listitem>
<listitem><para>
  None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
                <literal>Typeable</literal>, or <literal>Data</literal>.  These classes
                should not "look through" the type or its constructor.  You can still
                derive these classes for a newtype, but it happens in the usual way, not
                via this new mechanism.
</para></listitem>
<listitem><para>
  It is safe to coerce each of the methods of <literal>ci</literal>. That is,
  the missing last argument to each of the <literal>ci</literal> is not used
  at a nominal role in any of the <literal>ci</literal>'s methods.
  (See <xref linkend="roles"/>.)</para></listitem>
</itemizedlist>
Then, for each <literal>ci</literal>, the derived instance
declaration is:
<programlisting>
  instance ci t => ci (T v1...vk)
</programlisting>
As an example which does <emphasis>not</emphasis> work, consider
<programlisting>
  newtype NonMonad m s = NonMonad (State s m s) deriving Monad
</programlisting>
Here we cannot derive the instance
<programlisting>
  instance Monad (State s m) => Monad (NonMonad m)
</programlisting>

because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
and so cannot be "eta-converted" away. It is a good thing that this
<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
not, in fact, a monad --- for the same reason. Try defining
<literal>>>=</literal> with the correct type: you won't be able to.
</para>
<para>

Notice also that the <emphasis>order</emphasis> of class parameters becomes
important, since we can only derive instances for the last one. If the
<literal>StateMonad</literal> class above were instead defined as

<programlisting>
  class StateMonad m s | m -> s where ...
</programlisting>

then we would not have been able to derive an instance for the
<literal>Parser</literal> type above. We hypothesise that multi-parameter
classes usually have one "main" parameter for which deriving new
instances is most interesting.
</para>
<para>Lastly, all of this applies only for classes other than
<literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
and <literal>Data</literal>, for which the built-in derivation applies (section
4.3.3. of the Haskell Report).
(For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
<literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
the standard method is used or the one described here.)
</para>
</sect3>
</sect2>
</sect1>


<!-- TYPE SYSTEM EXTENSIONS -->
<sect1 id="type-class-extensions">
<title>Class and instances declarations</title>

<sect2 id="multi-param-type-classes">
<title>Class declarations</title>

<para>
This section, and the next one, documents GHC's type-class extensions.
There's lots of background in the paper <ulink
url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
Jones, Erik Meijer).
</para>

<sect3>
<title>Multi-parameter type classes</title>
<para>
Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
For example:


<programlisting>
  class Collection c a where
    union :: c a -> c a -> c a
    ...etc.
</programlisting>

</para>
</sect3>

<sect3 id="superclass-rules">
<title>The superclasses of a class declaration</title>

<para>
In Haskell 98 the context of a class declaration (which introduces superclasses)
must be simple; that is, each predicate must consist of a class applied to
type variables.  The flag <option>-XFlexibleContexts</option>
(<xref linkend="flexible-contexts"/>)
lifts this restriction,
so that the only restriction on the context in a class declaration is
that the class hierarchy must be acyclic.  So these class declarations are OK:


<programlisting>
  class Functor (m k) => FiniteMap m k where
    ...

  class (Monad m, Monad (t m)) => Transform t m where
    lift :: m a -> (t m) a
</programlisting>


</para>
<para>
As in Haskell 98, The class hierarchy must be acyclic.  However, the definition
of "acyclic" involves only the superclass relationships.  For example,
this is OK:


<programlisting>
  class C a where {
    op :: D b => a -> b -> b
  }

  class C a => D a where { ... }
</programlisting>


Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>.  (It
would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
</para>
<para>
With the extension that adds a <link linkend="constraint-kind">kind of constraints</link>,
you can write more exotic superclass definitions. The superclass cycle check is even more
liberal in these case. For example, this is OK:

<programlisting>
  class A cls c where
    meth :: cls c => c -> c

  class A B c => B c where
</programlisting>

A superclass context for a class <literal>C</literal> is allowed if, after expanding
type synonyms to their right-hand-sides, and uses of classes (other than <literal>C</literal>)
to their superclasses, <literal>C</literal> does not occur syntactically in the context.
</para>
</sect3>




<sect3 id="class-method-types">
<title>Class method types</title>

<para>
Haskell 98 prohibits class method types to mention constraints on the
class type variable, thus:
<programlisting>
  class Seq s a where
    fromList :: [a] -> s a
    elem     :: Eq a => a -> s a -> Bool
</programlisting>
The type of <literal>elem</literal> is illegal in Haskell 98, because it
contains the constraint <literal>Eq a</literal>, constrains only the
class type variable (in this case <literal>a</literal>).
GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
</para>


</sect3>


<sect3 id="class-default-signatures">
<title>Default method signatures</title>

<para>
Haskell 98 allows you to define a default implementation when declaring a class:
<programlisting>
  class Enum a where
    enum :: [a]
    enum = []
</programlisting>
The type of the <literal>enum</literal> method is <literal>[a]</literal>, and
this is also the type of the default method. You can lift this restriction
and give another type to the default method using the flag
<option>-XDefaultSignatures</option>. For instance, if you have written a
generic implementation of enumeration in a class <literal>GEnum</literal>
with method <literal>genum</literal> in terms of <literal>GHC.Generics</literal>,
you can specify a default method that uses that generic implementation:
<programlisting>
  class Enum a where
    enum :: [a]
    default enum :: (Generic a, GEnum (Rep a)) => [a]
    enum = map to genum
</programlisting>
We reuse the keyword <literal>default</literal> to signal that a signature
applies to the default method only; when defining instances of the
<literal>Enum</literal> class, the original type <literal>[a]</literal> of
<literal>enum</literal> still applies. When giving an empty instance, however,
the default implementation <literal>map to genum</literal> is filled-in,
and type-checked with the type
<literal>(Generic a, GEnum (Rep a)) => [a]</literal>.
</para>

<para>
We use default signatures to simplify generic programming in GHC
(<xref linkend="generic-programming"/>).
</para>


</sect3>

<sect3 id="nullary-type-classes">
<title>Nullary type classes</title>
Nullary (no parameter) type classes are enabled with <option>-XNullaryTypeClasses</option>.
Since there are no available parameters, there can be at most one instance
of a nullary class. A nullary type class might be used to document some assumption
in a type signature (such as reliance on the Riemann hypothesis) or add some
globally configurable settings in a program. For example,

<programlisting>
  class RiemannHypothesis where
    assumeRH :: a -> a

  -- Deterministic version of the Miller test
  -- correctness depends on the generalized Riemann hypothesis
  isPrime :: RiemannHypothesis => Integer -> Bool
  isPrime n = assumeRH (...)
</programlisting>

The type signature of <literal>isPrime</literal> informs users that its correctness
depends on an unproven conjecture. If the function is used, the user has
to acknowledge the dependence with:

<programlisting>
  instance RiemannHypothesis where
    assumeRH = id
</programlisting>

</sect3>
</sect2>

<sect2 id="functional-dependencies">
<title>Functional dependencies
</title>

<para> Functional dependencies are implemented as described by Mark Jones
in &ldquo;<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>&rdquo;, Mark P. Jones,
In Proceedings of the 9th European Symposium on Programming,
ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
.
</para>
<para>
Functional dependencies are introduced by a vertical bar in the syntax of a
class declaration;  e.g.
<programlisting>
  class (Monad m) => MonadState s m | m -> s where ...

  class Foo a b c | a b -> c where ...
</programlisting>
There should be more documentation, but there isn't (yet).  Yell if you need it.
</para>

<sect3><title>Rules for functional dependencies </title>
<para>
In a class declaration, all of the class type variables must be reachable (in the sense
mentioned in <xref linkend="flexible-contexts"/>)
from the free variables of each method type.
For example:

<programlisting>
  class Coll s a where
    empty  :: s
    insert :: s -> a -> s
</programlisting>

is not OK, because the type of <literal>empty</literal> doesn't mention
<literal>a</literal>.  Functional dependencies can make the type variable
reachable:
<programlisting>
  class Coll s a | s -> a where
    empty  :: s
    insert :: s -> a -> s
</programlisting>

Alternatively <literal>Coll</literal> might be rewritten

<programlisting>
  class Coll s a where
    empty  :: s a
    insert :: s a -> a -> s a
</programlisting>


which makes the connection between the type of a collection of
<literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
Occasionally this really doesn't work, in which case you can split the
class like this:


<programlisting>
  class CollE s where
    empty  :: s

  class CollE s => Coll s a where
    insert :: s -> a -> s
</programlisting>
</para>
</sect3>


<sect3>
<title>Background on functional dependencies</title>

<para>The following description of the motivation and use of functional dependencies is taken
from the Hugs user manual, reproduced here (with minor changes) by kind
permission of Mark Jones.
</para>
<para>
Consider the following class, intended as part of a
library for collection types:
<programlisting>
   class Collects e ce where
       empty  :: ce
       insert :: e -> ce -> ce
       member :: e -> ce -> Bool
</programlisting>
The type variable e used here represents the element type, while ce is the type
of the container itself. Within this framework, we might want to define
instances of this class for lists or characteristic functions (both of which
can be used to represent collections of any equality type), bit sets (which can
be used to represent collections of characters), or hash tables (which can be
used to represent any collection whose elements have a hash function). Omitting
standard implementation details, this would lead to the following declarations:
<programlisting>
   instance Eq e => Collects e [e] where ...
   instance Eq e => Collects e (e -> Bool) where ...
   instance Collects Char BitSet where ...
   instance (Hashable e, Collects a ce)
              => Collects e (Array Int ce) where ...
</programlisting>
All this looks quite promising; we have a class and a range of interesting
implementations. Unfortunately, there are some serious problems with the class
declaration. First, the empty function has an ambiguous type:
<programlisting>
   empty :: Collects e ce => ce
</programlisting>
By "ambiguous" we mean that there is a type variable e that appears on the left
of the <literal>=&gt;</literal> symbol, but not on the right. The problem with
this is that, according to the theoretical foundations of Haskell overloading,