Documentation for class contexts in data-constructor declarations

[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 are all enabled by options; by default GHC
understands only plain Haskell 98.
</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>These flags control what variation of the language are
    permitted.  Leaving out all of them gives you standard Haskell
    98.</para>

    <para>NB. 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.  So, together with each option below, we
    list the special syntax which is enabled by this option.  We use
    notation and nonterminal names from the Haskell 98 lexical syntax
    (see the Haskell 98 Report).  There are two classes of special
    syntax:</para>

    <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>

    <para>We are only listing 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>

    <variablelist>

      <varlistentry>
        <term>
          <option>-fglasgow-exts</option>:
          <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
        </term>
        <listitem>
          <para>This simultaneously enables all of the extensions to
          Haskell 98 described in <xref
          linkend="ghc-language-features"/>, except where otherwise
          noted. </para>

          <para>New reserved words: <literal>forall</literal> (only in
          types), <literal>mdo</literal>.</para>

          <para>Other syntax stolen:
              <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>,    
              <literal>(&num;</literal>, <literal>&num;)</literal>,         
              <literal>|)</literal>, <literal>{|</literal>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-ffi</option> and <option>-fffi</option>:
          <indexterm><primary><option>-ffi</option></primary></indexterm>
          <indexterm><primary><option>-fffi</option></primary></indexterm>
        </term>
        <listitem>
          <para>This option enables the language extension defined in the
          Haskell 98 Foreign Function Interface Addendum.</para>

          <para>New reserved words: <literal>foreign</literal>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
        </term>
        <listitem>
          <para> These two flags control how generalisation is done.
            See <xref linkend="monomorphism"/>.
          </para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-fextended-default-rules</option>:
          <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
        </term>
        <listitem>
          <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
          Independent of the <option>-fglasgow-exts</option>
          flag. </para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-fallow-overlapping-instances</option>
          <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
        </term>
        <term>
          <option>-fallow-undecidable-instances</option>
          <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
        </term>
        <term>
          <option>-fallow-incoherent-instances</option>
          <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
        </term>
        <term>
          <option>-fcontext-stack=N</option>
          <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
        </term>
        <listitem>
          <para> See <xref linkend="instance-decls"/>.  Only relevant
          if you also use <option>-fglasgow-exts</option>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-finline-phase</option>
          <indexterm><primary><option>-finline-phase</option></primary></indexterm>
        </term>
        <listitem>
          <para>See <xref linkend="rewrite-rules"/>.  Only relevant if
          you also use <option>-fglasgow-exts</option>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-farrows</option>
          <indexterm><primary><option>-farrows</option></primary></indexterm>
        </term>
        <listitem>
          <para>See <xref linkend="arrow-notation"/>.  Independent of
          <option>-fglasgow-exts</option>.</para>

          <para>New reserved words/symbols: <literal>rec</literal>,
          <literal>proc</literal>, <literal>-&lt;</literal>,
          <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
          <literal>&gt;&gt;-</literal>.</para>

          <para>Other syntax stolen: <literal>(|</literal>,
          <literal>|)</literal>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term>
          <option>-fgenerics</option>
          <indexterm><primary><option>-fgenerics</option></primary></indexterm>
        </term>
        <listitem>
          <para>See <xref linkend="generic-classes"/>.  Independent of
          <option>-fglasgow-exts</option>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term><option>-fno-implicit-prelude</option></term>
        <listitem>
          <para><indexterm><primary>-fno-implicit-prelude
          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>-fno-implicit-prelude</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>Even though you have not imported the Prelude, most of
          the built-in syntax still refers to the built-in Haskell
          Prelude types and values, as specified by the Haskell
          Report.  For example, the type <literal>[Int]</literal>
          still means <literal>Prelude.[] Int</literal>; tuples
          continue to refer to the standard Prelude tuples; the
          translation for list comprehensions continues to use
          <literal>Prelude.map</literal> etc.</para>

          <para>However, <option>-fno-implicit-prelude</option> does
          change the handling of certain built-in syntax: see <xref
          linkend="rebindable-syntax"/>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term><option>-fimplicit-params</option></term>
        <listitem>
          <para>Enables implicit parameters (see <xref
          linkend="implicit-parameters"/>).  Currently also implied by 
          <option>-fglasgow-exts</option>.</para>

          <para>Syntax stolen:
          <literal>?<replaceable>varid</replaceable></literal>,
          <literal>%<replaceable>varid</replaceable></literal>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term><option>-fscoped-type-variables</option></term>
        <listitem>
          <para>Enables lexically-scoped type variables (see <xref
          linkend="scoped-type-variables"/>).  Implied by
          <option>-fglasgow-exts</option>.</para>
        </listitem>
      </varlistentry>

      <varlistentry>
        <term><option>-fth</option></term>
        <listitem>
          <para>Enables Template Haskell (see <xref
          linkend="template-haskell"/>).  This flag must
          be given explicitly; it is no longer implied by
          <option>-fglasgow-exts</option>.</para>

          <para>Syntax stolen: <literal>[|</literal>,
          <literal>[e|</literal>, <literal>[p|</literal>,
          <literal>[d|</literal>, <literal>[t|</literal>,
          <literal>$(</literal>,
          <literal>$<replaceable>varid</replaceable></literal>.</para>
        </listitem>
      </varlistentry>

    </variablelist>
  </sect1>

<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
<!--    included from primitives.sgml  -->
<!-- &primitives; -->
<sect1 id="primitives">
  <title>Unboxed types and primitive operations</title>

<para>GHC is built on a raft of primitive data types and operations.
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>We do not currently have good, up-to-date documentation about the
primitives, perhaps because they are mainly intended for internal use.
There used to be a long section about them here in the User Guide, but it
became out of date, and wrong information is worse than none.</para>

<para>The Real Truth about what primitive types there are, and what operations
work over those types, is held in the file
<filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
This file is used directly to generate GHC's primitive-operation definitions, so
it is always correct!  It is also intended for processing into text.</para>

<para> Indeed,
the result of such processing is part of the description of the 
 <ulink
      url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
         Core language</ulink>.
So that document is a good place to look for a type-set version.
We would be very happy if someone wanted to volunteer to produce an SGML
back end to the program that processes <filename>primops.txt</filename> so that
we could include the results here in the User Guide.</para>

<para>What follows here is a brief summary of some main points.</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 that primitive types, values, and
operations have a <literal>&num;</literal> suffix.
</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 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 any such variable causes the entire
pattern-match
to become strict.  For example:
<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>, the entire pattern
match
is strict, and the program behaves as if you had written
<programlisting>
  data Foo = Foo Int Int#

  f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
</programlisting>
</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're available by default with <option>-fglasgow-exts</option>.  An
unboxed tuple looks like this:
</para>

<para>

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

</para>

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

<para>
Unboxed tuples are used for functions that need to return multiple
values, but they avoid the heap allocation normally associated with
using fully-fledged tuples.  When an unboxed tuple is returned, the
components are put directly into registers or on the stack; the
unboxed tuple itself does not have a composite representation.  Many
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 pretty stringent 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>
No variable can have an unboxed tuple type, nor may a constructor or function
argument have an unboxed tuple type.  The following are all illegal:


<programlisting>
  data Foo = Foo (# Int, Int #)

  f :: (# Int, Int #) -&#62; (# Int, Int #)
  f x = x

  g :: (# Int, Int #) -&#62; Int
  g (# a,b #) = a

  h x = let y = (# x,x #) in ...
</programlisting>
</para>
</listitem>
</itemizedlist>
</para>
<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 o f{ (# p,q #) -> (p,q)
            p = fst t
            q = snd t
        in ..body..
</programlisting>
Indeed, the bindings can even be recursive.
</para>

</sect2>
</sect1>


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

<sect1 id="syntax-extns">
<title>Syntactic extensions</title>
 
    <!-- ====================== 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 library documentation.
      There is an ongoing project to create and maintain a stable set
      of <quote>core</quote> libraries used by several Haskell
      compilers, and the libraries that GHC comes with represent the
      current status of that project.  For more details, see <ulink
      url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
      Libraries</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 var1 = 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 var1
  | 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>

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

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

<para> The recursive do-notation (also known as mdo-notation) is implemented as described in
"A recursive do for Haskell",
Levent Erkok, John Launchbury",
Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania. 
</para>
<para>
The do-notation of Haskell 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. It turns out that several applications can benefit from recursive bindings in
the do-notation, and this extension provides the necessary syntactic support.
</para>
<para>
Here is a simple (yet contrived) example:
</para>
<programlisting>
import Control.Monad.Fix

justOnes = mdo xs &lt;- Just (1:xs)
               return xs
</programlisting>
<para>
As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
</para>

<para>
The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
</para>
<programlisting>
class Monad m => MonadFix m where
   mfix :: (a -> m a) -> m a
</programlisting>
<para>
The function <literal>mfix</literal>
dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
then that monad must be declared an instance of the <literal>MonadFix</literal> class.
For details, see the above mentioned reference.
</para>
<para>
The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO. 
Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class 
for Haskell's internal state monad (strict and lazy, respectively).
</para>
<para>
There are three important points in using the recursive-do notation:
<itemizedlist>
<listitem><para>
The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
than <literal>do</literal>).
</para></listitem>

<listitem><para>
You should <literal>import Control.Monad.Fix</literal>.
(Note: Strictly speaking, this import is required only when you need to refer to the name
<literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
are encouraged to always import this module when using the mdo-notation.)
</para></listitem>

<listitem><para>
As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
</para></listitem>
</itemizedlist>
</para>

<para>
The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
contains up to date information on recursive monadic bindings.
</para>

<para>
Historical note: The old implementation of the mdo-notation (and most
of the existing documents) used the name
<literal>MonadRec</literal> for the class and the corresponding library.
This name is not supported by GHC.
</para>

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

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

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

<programlisting>
   [ 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>

<sect2 id="rebindable-syntax">
<title>Rebindable syntax</title>


      <para>GHC allows most kinds of built-in syntax to be rebound by
      the user, to facilitate replacing the <literal>Prelude</literal>
      with a home-grown version, for example.</para>

            <para>You may want 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>-fno-implicit-prelude</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>"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="mdo-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>
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 emample, 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>
GHC allows 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>Since this extension goes beyond Haskell 98, it should really be enabled
by a flag; but in fact it is enabled all the time.  (No Haskell 98 programs
change their behaviour, of course.)
</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>

</sect1>


<!-- TYPE SYSTEM EXTENSIONS -->
<sect1 id="type-extensions">
<title>Type system extensions</title>


<sect2>
<title>Data types and type synonyms</title>

<sect3 id="nullary-types">
<title>Data types with no constructors</title>

<para>With the <option>-fglasgow-exts</option> flag, 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="sec-kinding"/>).</para>

<para>Such data types have only one value, namely bottom.
Nevertheless, they can be useful when defining "phantom types".</para>
</sect3>

<sect3 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>
  A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
  The lexical syntax is the same as that for variable operators, excluding "(.)",
  "(!)", and "(*)".  In a binding position, the operator must be
  parenthesised.  For example:
<programlisting>
   type T (+) = Int + Int
   f :: T Either
   f = Left 3
 
   liftA2 :: Arrow (~>)
          => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
   liftA2 = ...
</programlisting>
  </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>
</sect3>

<sect3 id="type-synonyms">
<title>Liberalised type synonyms</title>

<para>
Type synonyms are like macros at the type level, and
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>
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.
</para></listitem>
<listitem><para>
Unboxed tuple on left of an arrow.
</para></listitem>
<listitem><para>
Partially-applied type synonym.
</para></listitem>
</itemizedlist>
So, for example,
this will be rejected:
<programlisting>
  type Pr = (# Int, Int #)

  h :: Pr -> Int
  h x = ...
</programlisting>
because GHC does not allow  unboxed tuples on the left of a function arrow.
</para>
</sect3>


<sect3 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 heterogenous 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>

<sect4 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>

</sect4>

<sect4>
<title>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>

<para>
Notice the way that the syntax fits smoothly with that used for
universal quantification earlier.
</para>

</sect4>

<sect4 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>_output</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>

At the moment, record update syntax is only supported for Haskell 98 data types,
so the following function does <emphasis>not</emphasis> work:

<programlisting>
-- This is invalid; use explicit NewCounter instead for now
setTag :: Counter a -> a -> Counter a
setTag obj t = obj{ tag = t }
</programlisting>

</para>

</sect4>


<sect4>
<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>

</sect4>
</sect3>

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

<sect3 id="gadt-style">
<title>Declaring data types with explicit constructor signatures</title>

<para>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>This behaviour contrasts with Haskell 98's peculiar treament of 
contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
In Haskell 98 the defintion
<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>
For example, a possible application of GHC's behaviour 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>
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>
The type signature of
each constructor is independent, and is implicitly universally quantified as usual. 
Different constructors may have different universally-quantified type variables
and different type-class constraints.  
For example, this is fine:
<programlisting>
  data T a where
    T1 :: Eq b => b -> T b
    T2 :: (Show c, Ix c) => c -> [c] -> T c
</programlisting>
</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 Foo 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 Foo 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>
You can use record syntax on a GADT-style data type declaration:

<programlisting>
  data Person where
      Adult { name :: String, children :: [Person] } :: Person
      Child { name :: String } :: 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).
</para>
<para>
At the moment, record updates are not yet possible with GADT-style declarations, 
so support is limited to record construction, selection and pattern matching.
For exmaple
<programlisting>
  aPerson = Adult { name = "Fred", children = [] }

  shortName :: Person -> Bool
  hasChildren (Adult { children = kids }) = not (null kids)
  hasChildren (Child {})                  = False
</programlisting>
</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>
</itemizedlist></para>
</sect3>

<sect3 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/index.htm">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://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. 
<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> may not be a type variable (e.g. the <literal>Lit</literal>
constructor).
</para></listitem>

<listitem><para>
You cannot use a <literal>deriving</literal> clause for a GADT; only for
an ordianary 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>

</itemizedlist>
</para>

</sect3>

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


</sect2>



<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>
<para>
All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
</para>

<sect3>
<title>Multi-parameter type classes</title>
<para>
Multi-parameter type classes are permitted. For example:


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

</para>
</sect3>

<sect3>
<title>The superclasses of a class declaration</title>

<para>
There are no restrictions on the context in a class declaration
(which introduces superclasses), except 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>
</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.
</para>


</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://www.cse.ogi.edu/~mpj/pubs/fundeps.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="type-restrictions"/>)
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,
we cannot guarantee a well-defined semantics for any term with an ambiguous
type.
</para>
<para>
We can sidestep this specific problem by removing the empty member from the
class declaration. However, although the remaining members, insert and member,
do not have ambiguous types, we still run into problems when we try to use
them. For example, consider the following two functions: 
<programlisting>
   f x y = insert x . insert y
   g     = f True 'a'
</programlisting>
for which GHC infers the following types: 
<programlisting>
   f :: (Collects a c, Collects b c) => a -> b -> c -> c
   g :: (Collects Bool c, Collects Char c) => c -> c
</programlisting>
Notice that the type for f allows the two parameters x and y to be assigned
different types, even though it attempts to insert each of the two values, one
after the other, into the same collection. If we're trying to model collections
that contain only one type of value, then this is clearly an inaccurate
type. Worse still, the definition for g is accepted, without causing a type
error. As a result, the error in this code will not be flagged at the point
where it appears. Instead, it will show up only when we try to use g, which
might even be in a different module.
</para>

<sect4><title>An attempt to use constructor classes</title>

<para>
Faced with the problems described above, some Haskell programmers might be
tempted to use something like the following version of the class declaration: 
<programlisting>
   class Collects e c where
      empty  :: c e
      insert :: e -> c e -> c e
      member :: e -> c e -> Bool
</programlisting>
The key difference here is that we abstract over the type constructor c that is
used to form the collection type c e, and not over that collection type itself,
represented by ce in the original class declaration. This avoids the immediate
problems that we mentioned above: empty has type <literal>Collects e c => c
e</literal>, which is not ambiguous. 
</para>
<para>
The function f from the previous section has a more accurate type: 
<programlisting>
   f :: (Collects e c) => e -> e -> c e -> c e
</programlisting>
The function g from the previous section is now rejected with a type error as
we would hope because the type of f does not allow the two arguments to have
different types. 
This, then, is an example of a multiple parameter class that does actually work
quite well in practice, without ambiguity problems.
There is, however, a catch. This version of the Collects class is nowhere near
as general as the original class seemed to be: only one of the four instances
for <literal>Collects</literal>
given above can be used with this version of Collects because only one of
them---the instance for lists---has a collection type that can be written in
the form c e, for some type constructor c, and element type e.
</para>
</sect4>

<sect4><title>Adding functional dependencies</title>

<para>
To get a more useful version of the Collects class, Hugs provides a mechanism
that allows programmers to specify dependencies between the parameters of a
multiple parameter class (For readers with an interest in theoretical
foundations and previous work: The use of dependency information can be seen
both as a generalization of the proposal for `parametric type classes' that was
put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
later framework for "improvement" of qualified types. The
underlying ideas are also discussed in a more theoretical and abstract setting
in a manuscript [implparam], where they are identified as one point in a
general design space for systems of implicit parameterization.).

To start with an abstract example, consider a declaration such as: 
<programlisting>
   class C a b where ...
</programlisting>
which tells us simply that C can be thought of as a binary relation on types
(or type constructors, depending on the kinds of a and b). Extra clauses can be
included in the definition of classes to add information about dependencies
between parameters, as in the following examples: 
<programlisting>
   class D a b | a -> b where ...
   class E a b | a -> b, b -> a where ...
</programlisting>
The notation <literal>a -&gt; b</literal> used here between the | and where
symbols --- not to be
confused with a function type --- indicates that the a parameter uniquely
determines the b parameter, and might be read as "a determines b." Thus D is
not just a relation, but actually a (partial) function. Similarly, from the two
dependencies that are included in the definition of E, we can see that E
represents a (partial) one-one mapping between types.
</para>
<para>
More generally, dependencies take the form <literal>x1 ... xn -&gt; y1 ... ym</literal>,
where x1, ..., xn, and y1, ..., yn are type variables with n&gt;0 and
m&gt;=0, meaning that the y parameters are uniquely determined by the x
parameters. Spaces can be used as separators if more than one variable appears
on any single side of a dependency, as in <literal>t -&gt; a b</literal>. Note that a class may be
annotated with multiple dependencies using commas as separators, as in the
definition of E above. Some dependencies that we can write in this notation are
redundant, and will be rejected because they don't serve any useful
purpose, and may instead indicate an error in the program. Examples of
dependencies like this include  <literal>a -&gt; a </literal>,  
<literal>a -&gt; a a </literal>,  
<literal>a -&gt; </literal>, etc. There can also be
some redundancy if multiple dependencies are given, as in  
<literal>a-&gt;b</literal>, 
 <literal>b-&gt;c </literal>,  <literal>a-&gt;c </literal>, and
in which some subset implies the remaining dependencies. Examples like this are
not treated as errors. Note that dependencies appear only in class
declarations, and not in any other part of the language. In particular, the
syntax for instance declarations, class constraints, and types is completely
unchanged.
</para>
<para>
By including dependencies in a class declaration, we provide a mechanism for
the programmer to specify each multiple parameter class more precisely. The
compiler, on the other hand, is responsible for ensuring that the set of
instances that are in scope at any given point in the program is consistent
with any declared dependencies. For example, the following pair of instance
declarations cannot appear together in the same scope because they violate the
dependency for D, even though either one on its own would be acceptable: 
<programlisting>
   instance D Bool Int where ...
   instance D Bool Char where ...
</programlisting>
Note also that the following declaration is not allowed, even by itself: 
<programlisting>
   instance D [a] b where ...
</programlisting>
The problem here is that this instance would allow one particular choice of [a]
to be associated with more than one choice for b, which contradicts the
dependency specified in the definition of D. More generally, this means that,
in any instance of the form: 
<programlisting>
   instance D t s where ...
</programlisting>
for some particular types t and s, the only variables that can appear in s are
the ones that appear in t, and hence, if the type t is known, then s will be
uniquely determined.
</para>
<para>
The benefit of including dependency information is that it allows us to define
more general multiple parameter classes, without ambiguity problems, and with
the benefit of more accurate types. To illustrate this, we return to the
collection class example, and annotate the original definition of <literal>Collects</literal>
with a simple dependency: 
<programlisting>
   class Collects e ce | ce -> e where
      empty  :: ce
      insert :: e -> ce -> ce
      member :: e -> ce -> Bool
</programlisting>
The dependency <literal>ce -&gt; e</literal> here specifies that the type e of elements is uniquely
determined by the type of the collection ce. Note that both parameters of
Collects are of kind *; there are no constructor classes here. Note too that
all of the instances of Collects that we gave earlier can be used
together with this new definition.
</para>
<para>
What about the ambiguity problems that we encountered with the original
definition? The empty function still has type Collects e ce => ce, but it is no
longer necessary to regard that as an ambiguous type: Although the variable e
does not appear on the right of the => symbol, the dependency for class
Collects tells us that it is uniquely determined by ce, which does appear on
the right of the => symbol. Hence the context in which empty is used can still
give enough information to determine types for both ce and e, without
ambiguity. More generally, we need only regard a type as ambiguous if it
contains a variable on the left of the => that is not uniquely determined
(either directly or indirectly) by the variables on the right.
</para>
<para>
Dependencies also help to produce more accurate types for user defined
functions, and hence to provide earlier detection of errors, and less cluttered
types for programmers to work with. Recall the previous definition for a
function f: 
<programlisting>
   f x y = insert x y = insert x . insert y
</programlisting>
for which we originally obtained a type: 
<programlisting>
   f :: (Collects a c, Collects b c) => a -> b -> c -> c
</programlisting>
Given the dependency information that we have for Collects, however, we can
deduce that a and b must be equal because they both appear as the second
parameter in a Collects constraint with the same first parameter c. Hence we
can infer a shorter and more accurate type for f: 
<programlisting>
   f :: (Collects a c) => a -> a -> c -> c
</programlisting>
In a similar way, the earlier definition of g will now be flagged as a type error.
</para>
<para>
Although we have given only a few examples here, it should be clear that the
addition of dependency information can help to make multiple parameter classes
more useful in practice, avoiding ambiguity problems, and allowing more general
sets of instance declarations.
</para>
</sect4>
</sect3>
</sect2>

<sect2 id="instance-decls">
<title>Instance declarations</title>

<sect3 id="instance-rules">
<title>Relaxed rules for instance declarations</title>

<para>An instance declaration has the form
<screen>
  instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) =&gt; <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
</screen>
The part before the "<literal>=&gt;</literal>" is the
<emphasis>context</emphasis>, while the part after the
"<literal>=&gt;</literal>" is the <emphasis>head</emphasis> of the instance declaration.
</para>

<para>
In Haskell 98 the head of an instance declaration
must be of the form <literal>C (T a1 ... an)</literal>, where
<literal>C</literal> is the class, <literal>T</literal> is a type constructor,
and the <literal>a1 ... an</literal> are distinct type variables.
Furthermore, the assertions in the context of the instance declaration
must be of the form <literal>C a</literal> where <literal>a</literal>
is a type variable that occurs in the head.
</para>
<para>
The <option>-fglasgow-exts</option> flag loosens these restrictions
considerably.  Firstly, multi-parameter type classes are permitted.  Secondly,
the context and head of the instance declaration can each consist of arbitrary
(well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
following rules:
<orderedlist>
<listitem><para>
For each assertion in the context:
<orderedlist>
<listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
<listitem><para>The assertion has fewer constructors and variables (taken together
      and counting repetitions) than the head</para></listitem>
</orderedlist>
</para></listitem>

<listitem><para>The coverage condition.  For each functional dependency,
<replaceable>tvs</replaceable><subscript>left</subscript> <literal>-&gt;</literal>
<replaceable>tvs</replaceable><subscript>right</subscript>,  of the class,
every type variable in
S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in 
S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
substitution mapping each type variable in the class declaration to the
corresponding type in the instance declaration.
</para></listitem>
</orderedlist>
These restrictions ensure that context reduction terminates: each reduction
step makes the problem smaller by at least one
constructor.  For example, the following would make the type checker
loop if it wasn't excluded:
<programlisting>
  instance C a => C a where ...
</programlisting>
For example, these are OK:
<programlisting>
  instance C Int [a]          -- Multiple parameters
  instance Eq (S [a])         -- Structured type in head

      -- Repeated type variable in head
  instance C4 a a => C4 [a] [a] 
  instance Stateful (ST s) (MutVar s)

      -- Head can consist of type variables only
  instance C a
  instance (Eq a, Show b) => C2 a b

      -- Non-type variables in context
  instance Show (s a) => Show (Sized s a)
  instance C2 Int a => C3 Bool [a]
  instance C2 Int a => C3 [a] b
</programlisting>
But these are not:
<programlisting>
      -- Context assertion no smaller than head
  instance C a => C a where ...
      -- (C b b) has more more occurrences of b than the head
  instance C b b => Foo [b] where ...
</programlisting>
</para>

<para>
The same restrictions apply to instances generated by
<literal>deriving</literal> clauses.  Thus the following is accepted:
<programlisting>
  data MinHeap h a = H a (h a)
    deriving (Show)
</programlisting>
because the derived instance
<programlisting>
  instance (Show a, Show (h a)) => Show (MinHeap h a)
</programlisting>
conforms to the above rules.
</para>

<para>
A useful idiom permitted by the above rules is as follows.
If one allows overlapping instance declarations then it's quite
convenient to have a "default instance" declaration that applies if
something more specific does not:
<programlisting>
  instance C a where
    op = ... -- Default
</programlisting>
</para>
<para>You can find lots of background material about the reason for these
restrictions in the paper <ulink
url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
Understanding functional dependencies via Constraint Handling Rules</ulink>.
</para>
</sect3>

<sect3 id="undecidable-instances">
<title>Undecidable instances</title>

<para>
Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
For example, sometimes you might want to use the following to get the
effect of a "class synonym":
<programlisting>
  class (C1 a, C2 a, C3 a) => C a where { }

  instance (C1 a, C2 a, C3 a) => C a where { }
</programlisting>
This allows you to write shorter signatures:
<programlisting>
  f :: C a => ...
</programlisting>
instead of
<programlisting>
  f :: (C1 a, C2 a, C3 a) => ...
</programlisting>
The restrictions on functional dependencies (<xref
linkend="functional-dependencies"/>) are particularly troublesome.
It is tempting to introduce type variables in the context that do not appear in
the head, something that is excluded by the normal rules. For example:
<programlisting>
  class HasConverter a b | a -> b where
     convert :: a -> b
   
  data Foo a = MkFoo a

  instance (HasConverter a b,Show b) => Show (Foo a) where
     show (MkFoo value) = show (convert value)
</programlisting>
This is dangerous territory, however. Here, for example, is a program that would make the
typechecker loop:
<programlisting>
  class D a
  class F a b | a->b
  instance F [a] [[a]]
  instance (D c, F a c) => D [a]   -- 'c' is not mentioned in the head
</programlisting>  
Similarly, it can be tempting to lift the coverage condition:
<programlisting>
  class Mul a b c | a b -> c where
        (.*.) :: a -> b -> c

  instance Mul Int Int Int where (.*.) = (*)
  instance Mul Int Float Float where x .*. y = fromIntegral x * y
  instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
</programlisting>
The third instance declaration does not obey the coverage condition;
and indeed the (somewhat strange) definition:
<programlisting>
  f = \ b x y -> if b then x .*. [y] else y
</programlisting>
makes instance inference go into a loop, because it requires the constraint
<literal>(Mul a [b] b)</literal>.
</para>
<para>
Nevertheless, GHC allows you to experiment with more liberal rules.  If you use
the experimental flag <option>-fallow-undecidable-instances</option>
<indexterm><primary>-fallow-undecidable-instances
option</primary></indexterm>, you can use arbitrary
types in both an instance context and instance head.  Termination is ensured by having a
fixed-depth recursion stack.  If you exceed the stack depth you get a
sort of backtrace, and the opportunity to increase the stack depth
with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
</para>

</sect3>


<sect3 id="instance-overlap">
<title>Overlapping instances</title>
<para>
In general, <emphasis>GHC requires that that it be unambiguous which instance
declaration
should be used to resolve a type-class constraint</emphasis>. This behaviour
can be modified by two flags: <option>-fallow-overlapping-instances</option>
<indexterm><primary>-fallow-overlapping-instances
</primary></indexterm> 
and <option>-fallow-incoherent-instances</option>
<indexterm><primary>-fallow-incoherent-instances
</primary></indexterm>, as this section discusses.  Both these
flags are dynamic flags, and can be set on a per-module basis, using 
an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
<para>
When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
it tries to match every instance declaration against the
constraint,
by instantiating the head of the instance declaration.  For example, consider
these declarations:
<programlisting>
  instance context1 => C Int a     where ...  -- (A)
  instance context2 => C a   Bool  where ...  -- (B)
  instance context3 => C Int [a]   where ...  -- (C)
  instance context4 => C Int [Int] where ...  -- (D)
</programlisting>
The instances (A) and (B) match the constraint <literal>C Int Bool</literal>, 
but (C) and (D) do not.  When matching, GHC takes
no account of the context of the instance declaration
(<literal>context1</literal> etc).
GHC's default behaviour is that <emphasis>exactly one instance must match the
constraint it is trying to resolve</emphasis>.  
It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
including both declarations (A) and (B), say); an error is only reported if a 
particular constraint matches more than one.
</para>

<para>
The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
more than one instance to match, provided there is a most specific one.  For
example, the constraint <literal>C Int [Int]</literal> matches instances (A),
(C) and (D), but the last is more specific, and hence is chosen.  If there is no
most-specific match, the program is rejected.
</para>
<para>
However, GHC is conservative about committing to an overlapping instance.  For example:
<programlisting>
  f :: [b] -> [b]
  f x = ...
</programlisting>
Suppose that from the RHS of <literal>f</literal> we get the constraint
<literal>C Int [b]</literal>.  But
GHC does not commit to instance (C), because in a particular
call of <literal>f</literal>, <literal>b</literal> might be instantiate 
to <literal>Int</literal>, in which case instance (D) would be more specific still.
So GHC rejects the program.  If you add the flag <option>-fallow-incoherent-instances</option>,
GHC will instead pick (C), without complaining about 
the problem of subsequent instantiations.
</para>
<para>
The willingness to be overlapped or incoherent is a property of 
the <emphasis>instance declaration</emphasis> itself, controlled by the
presence or otherwise of the <option>-fallow-overlapping-instances</option> 
and <option>-fallow-incoherent-instances</option> flags when that mdodule is
being defined.  Neither flag is required in a module that imports and uses the
instance declaration.  Specifically, during the lookup process:
<itemizedlist>
<listitem><para>
An instance declaration is ignored during the lookup process if (a) a more specific
match is found, and (b) the instance declaration was compiled with 
<option>-fallow-overlapping-instances</option>.  The flag setting for the
more-specific instance does not matter.
</para></listitem>
<listitem><para>
Suppose an instance declaration does not matche the constraint being looked up, but
does unify with it, so that it might match when the constraint is further 
instantiated.  Usually GHC will regard this as a reason for not committing to
some other constraint.  But if the instance declaration was compiled with
<option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?" 
check for that declaration.
</para></listitem>
</itemizedlist>
These rules make it possible for a library author to design a library that relies on 
overlapping instances without the library client having to know.  
</para>
<para>
If an instance declaration is compiled without
<option>-fallow-overlapping-instances</option>,
then that instance can never be overlapped.  This could perhaps be
inconvenient.  Perhaps the rule should instead say that the
<emphasis>overlapping</emphasis> instance declaration should be compiled in
this way, rather than the <emphasis>overlapped</emphasis> one.  Perhaps overlap
at a usage site should be permitted regardless of how the instance declarations
are compiled, if the <option>-fallow-overlapping-instances</option> flag is
used at the usage site.  (Mind you, the exact usage site can occasionally be
hard to pin down.)  We are interested to receive feedback on these points.
</para>
<para>The <option>-fallow-incoherent-instances</option> flag implies the
<option>-fallow-overlapping-instances</option> flag, but not vice versa.
</para>
</sect3>

<sect3>
<title>Type synonyms in the instance head</title>

<para>
<emphasis>Unlike Haskell 98, instance heads may use type
synonyms</emphasis>.  (The instance "head" is the bit after the "=>" in an instance decl.)
As always, using a type synonym is just shorthand for
writing the RHS of the type synonym definition.  For example:


<programlisting>
  type Point = (Int,Int)
  instance C Point   where ...
  instance C [Point] where ...
</programlisting>


is legal.  However, if you added


<programlisting>
  instance C (Int,Int) where ...
</programlisting>


as well, then the compiler will complain about the overlapping
(actually, identical) instance declarations.  As always, type synonyms
must be fully applied.  You cannot, for example, write:


<programlisting>
  type P a = [[a]]
  instance Monad P where ...
</programlisting>


This design decision is independent of all the others, and easily
reversed, but it makes sense to me.

</para>
</sect3>


</sect2>

<sect2 id="type-restrictions">
<title>Type signatures</title>

<sect3><title>The context of a type signature</title>
<para>
Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
the form <emphasis>(class type-variable)</emphasis> or
<emphasis>(class (type-variable type-variable ...))</emphasis>.  Thus,
these type signatures are perfectly OK
<programlisting>
  g :: Eq [a] => ...
  g :: Ord (T a ()) => ...
</programlisting>
</para>
<para>
GHC imposes the following restrictions on the constraints in a type signature.
Consider the type:

<programlisting>
  forall tv1..tvn (c1, ...,cn) => type
</programlisting>

(Here, we write the "foralls" explicitly, although the Haskell source
language omits them; in Haskell 98, all the free type variables of an
explicit source-language type signature are universally quantified,
except for the class type variables in a class declaration.  However,
in GHC, you can give the foralls if you want.  See <xref linkend="universal-quantification"/>).
</para>

<para>

<orderedlist>
<listitem>

<para>
 <emphasis>Each universally quantified type variable
<literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.

A type variable <literal>a</literal> is "reachable" if it it appears
in the same constraint as either a type variable free in in
<literal>type</literal>, or another reachable type variable.  
A value with a type that does not obey 
this reachability restriction cannot be used without introducing
ambiguity; that is why the type is rejected.
Here, for example, is an illegal type:


<programlisting>
  forall a. Eq a => Int
</programlisting>


When a value with this type was used, the constraint <literal>Eq tv</literal>
would be introduced where <literal>tv</literal> is a fresh type variable, and
(in the dictionary-translation implementation) the value would be
applied to a dictionary for <literal>Eq tv</literal>.  The difficulty is that we
can never know which instance of <literal>Eq</literal> to use because we never
get any more information about <literal>tv</literal>.
</para>
<para>
Note
that the reachability condition is weaker than saying that <literal>a</literal> is
functionally dependent on a type variable free in
<literal>type</literal> (see <xref
linkend="functional-dependencies"/>).  The reason for this is there
might be a "hidden" dependency, in a superclass perhaps.  So
"reachable" is a conservative approximation to "functionally dependent".
For example, consider:
<programlisting>
  class C a b | a -> b where ...
  class C a b => D a b where ...
  f :: forall a b. D a b => a -> a
</programlisting>
This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
but that is not immediately apparent from <literal>f</literal>'s type.
</para>
</listitem>
<listitem>

<para>
 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
universally quantified type variables <literal>tvi</literal></emphasis>.

For example, this type is OK because <literal>C a b</literal> mentions the
universally quantified type variable <literal>b</literal>:


<programlisting>
  forall a. C a b => burble
</programlisting>


The next type is illegal because the constraint <literal>Eq b</literal> does not
mention <literal>a</literal>:


<programlisting>
  forall a. Eq b => burble
</programlisting>


The reason for this restriction is milder than the other one.  The
excluded types are never useful or necessary (because the offending
context doesn't need to be witnessed at this point; it can be floated
out).  Furthermore, floating them out increases sharing. Lastly,
excluding them is a conservative choice; it leaves a patch of
territory free in case we need it later.

</para>
</listitem>

</orderedlist>

</para>
</sect3>

<sect3 id="hoist">
<title>For-all hoisting</title>
<para>
It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
end of an arrow, thus:
<programlisting>
  type Discard a = forall b. a -> b -> a

  g :: Int -> Discard Int
  g x y z = x+y
</programlisting>
Simply expanding the type synonym would give
<programlisting>
  g :: Int -> (forall b. Int -> b -> Int)
</programlisting>
but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
<programlisting>
  g :: forall b. Int -> Int -> b -> Int
</programlisting>
In general, the rule is this: <emphasis>to determine the type specified by any explicit
user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
performs the transformation:</emphasis>
<programlisting>
  <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
==>
  forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
</programlisting>
(In fact, GHC tries to retain as much synonym information as possible for use in
error messages, but that is a usability issue.)  This rule applies, of course, whether
or not the <literal>forall</literal> comes from a synonym. For example, here is another
valid way to write <literal>g</literal>'s type signature:
<programlisting>
  g :: Int -> Int -> forall b. b -> Int
</programlisting>
</para>
<para>
When doing this hoisting operation, GHC eliminates duplicate constraints.  For
example:
<programlisting>
  type Foo a = (?x::Int) => Bool -> a
  g :: Foo (Foo Int)
</programlisting>
means
<programlisting>
  g :: (?x::Int) => Bool -> Bool -> Int
</programlisting>
</para>
</sect3>


</sect2>

<sect2 id="implicit-parameters">
<title>Implicit parameters</title>

<para> Implicit parameters are implemented as described in 
"Implicit parameters: dynamic scoping with static types", 
J Lewis, MB Shields, E Meijer, J Launchbury,
27th ACM Symposium on Principles of Programming Languages (POPL'00),
Boston, Jan 2000.
</para>

<para>(Most of the following, stil rather incomplete, documentation is
due to Jeff Lewis.)</para>

<para>Implicit parameter support is enabled with the option
<option>-fimplicit-params</option>.</para>

<para>
A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
context. In Haskell, all variables are statically bound. Dynamic
binding of variables is a notion that goes back to Lisp, but was later
discarded in more modern incarnations, such as Scheme. Dynamic binding
can be very confusing in an untyped language, and unfortunately, typed
languages, in particular Hindley-Milner typed languages like Haskell,
only support static scoping of variables.
</para>
<para>
However, by a simple extension to the type class system of Haskell, we
can support dynamic binding. Basically, we express the use of a
dynamically bound variable as a constraint on the type. These
constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
function uses a dynamically-bound variable <literal>?x</literal> 
of type <literal>t'</literal>". For
example, the following expresses the type of a sort function,
implicitly parameterized by a comparison function named <literal>cmp</literal>.
<programlisting>
  sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
</programlisting>
The dynamic binding constraints are just a new form of predicate in the type class system.
</para>
<para>
An implicit parameter occurs in an expression using the special form <literal>?x</literal>, 
where <literal>x</literal> is
any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression). 
Use of this construct also introduces a new
dynamic-binding constraint in the type of the expression. 
For example, the following definition
shows how we can define an implicitly parameterized sort function in
terms of an explicitly parameterized <literal>sortBy</literal> function:
<programlisting>
  sortBy :: (a -> a -> Bool) -> [a] -> [a]

  sort   :: (?cmp :: a -> a -> Bool) => [a] -> [a]
  sort    = sortBy ?cmp
</programlisting>
</para>

<sect3>
<title>Implicit-parameter type constraints</title>
<para>
Dynamic binding constraints behave just like other type class
constraints in that they are automatically propagated. Thus, when a
function is used, its implicit parameters are inherited by the
function that called it. For example, our <literal>sort</literal> function might be used
to pick out the least value in a list:
<programlisting>
  least   :: (?cmp :: a -> a -> Bool) => [a] -> a
  least xs = head (sort xs)
</programlisting>
Without lifting a finger, the <literal>?cmp</literal> parameter is
propagated to become a parameter of <literal>least</literal> as well. With explicit
parameters, the default is that parameters must always be explicit
propagated. With implicit parameters, the default is to always
propagate them.
</para>
<para>
An implicit-parameter type constraint differs from other type class constraints in the
following way: All uses of a particular implicit parameter must have
the same type. This means that the type of <literal>(?x, ?x)</literal> 
is <literal>(?x::a) => (a,a)</literal>, and not 
<literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
class constraints.
</para>

<para> You can't have an implicit parameter in the context of a class or instance
declaration.  For example, both these declarations are illegal:
<programlisting>
  class (?x::Int) => C a where ...
  instance (?x::a) => Foo [a] where ...
</programlisting>
Reason: exactly which implicit parameter you pick up depends on exactly where
you invoke a function. But the ``invocation'' of instance declarations is done
behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
Easiest thing is to outlaw the offending types.</para>
<para>
Implicit-parameter constraints do not cause ambiguity.  For example, consider:
<programlisting>
   f :: (?x :: [a]) => Int -> Int
   f n = n + length ?x

   g :: (Read a, Show a) => String -> String
   g s = show (read s)
</programlisting>
Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
is fine.  The binding for <literal>?x</literal> at <literal>f</literal>'s call site is 
quite unambiguous, and fixes the type <literal>a</literal>.
</para>
</sect3>

<sect3>
<title>Implicit-parameter bindings</title>

<para>
An implicit parameter is <emphasis>bound</emphasis> using the standard
<literal>let</literal> or <literal>where</literal> binding forms.
For example, we define the <literal>min</literal> function by binding
<literal>cmp</literal>.
<programlisting>
  min :: [a] -> a
  min  = let ?cmp = (&lt;=) in least
</programlisting>
</para>
<para>
A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
bindings can occur, except at top level.  That is, they can occur in a <literal>let</literal> 
(including in a list comprehension, or do-notation, or pattern guards), 
or a <literal>where</literal> clause.
Note the following points:
<itemizedlist>
<listitem><para>
An implicit-parameter binding group must be a
collection of simple bindings to implicit-style variables (no
function-style bindings, and no type signatures); these bindings are
neither polymorphic or recursive.  
</para></listitem>
<listitem><para>
You may not mix implicit-parameter bindings with ordinary bindings in a 
single <literal>let</literal>
expression; use two nested <literal>let</literal>s instead.
(In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
</para></listitem>

<listitem><para>
You may put multiple implicit-parameter bindings in a
single binding group; but they are <emphasis>not</emphasis> treated
as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
Instead they are treated as a non-recursive group, simultaneously binding all the implicit
parameter.  The bindings are not nested, and may be re-ordered without changing
the meaning of the program.
For example, consider:
<programlisting>
  f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
</programlisting>
The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
<programlisting>
  f :: (?x::Int) => Int -> Int
</programlisting>
</para></listitem>
</itemizedlist>
</para>

</sect3>

<sect3><title>Implicit parameters and polymorphic recursion</title>

<para>
Consider these two definitions:
<programlisting>
  len1 :: [a] -> Int
  len1 xs = let ?acc = 0 in len_acc1 xs

  len_acc1 [] = ?acc
  len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs

  ------------

  len2 :: [a] -> Int
  len2 xs = let ?acc = 0 in len_acc2 xs

  len_acc2 :: (?acc :: Int) => [a] -> Int
  len_acc2 [] = ?acc
  len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
</programlisting>
The only difference between the two groups is that in the second group
<literal>len_acc</literal> is given a type signature.
In the former case, <literal>len_acc1</literal> is monomorphic in its own
right-hand side, so the implicit parameter <literal>?acc</literal> is not
passed to the recursive call.  In the latter case, because <literal>len_acc2</literal>
has a type signature, the recursive call is made to the
<emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
as an implicit parameter.  So we get the following results in GHCi:
<programlisting>
  Prog> len1 "hello"
  0
  Prog> len2 "hello"
  5
</programlisting>
Adding a type signature dramatically changes the result!  This is a rather
counter-intuitive phenomenon, worth watching out for.
</para>
</sect3>

<sect3><title>Implicit parameters and monomorphism</title>

<para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
Haskell Report) to implicit parameters.  For example, consider:
<programlisting>
 f :: Int -> Int
  f v = let ?x = 0     in
        let y = ?x + v in
        let ?x = 5     in
        y
</programlisting>
Since the binding for <literal>y</literal> falls under the Monomorphism
Restriction it is not generalised, so the type of <literal>y</literal> is
simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
If you add a type signature for <literal>y</literal>, then <literal>y</literal>
will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
<literal>y</literal> in the body of the <literal>let</literal> will see the
inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
<literal>14</literal>.
</para>
</sect3>
</sect2>

    <!--   ======================= COMMENTED OUT ========================

    We intend to remove linear implicit parameters, so I'm at least removing
    them from the 6.6 user manual

<sect2 id="linear-implicit-parameters">
<title>Linear implicit parameters</title>
<para>
Linear implicit parameters are an idea developed by Koen Claessen,
Mark Shields, and Simon PJ.  They address the long-standing
problem that monads seem over-kill for certain sorts of problem, notably:
</para>
<itemizedlist>
<listitem> <para> distributing a supply of unique names </para> </listitem>
<listitem> <para> distributing a supply of random numbers </para> </listitem>
<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
</itemizedlist>

<para>
Linear implicit parameters are just like ordinary implicit parameters,
except that they are "linear"; that is, they cannot be copied, and
must be explicitly "split" instead.  Linear implicit parameters are
written '<literal>%x</literal>' instead of '<literal>?x</literal>'.  
(The '/' in the '%' suggests the split!)
</para>
<para>
For example:
<programlisting>
    import GHC.Exts( Splittable )

    data NameSupply = ...
    
    splitNS :: NameSupply -> (NameSupply, NameSupply)
    newName :: NameSupply -> Name

    instance Splittable NameSupply where
        split = splitNS


    f :: (%ns :: NameSupply) => Env -> Expr -> Expr
    f env (Lam x e) = Lam x' (f env e)
                    where
                      x'   = newName %ns
                      env' = extend env x x'
    ...more equations for f...
</programlisting>
Notice that the implicit parameter %ns is consumed 
<itemizedlist>
<listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
<listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
</itemizedlist>
</para>
<para>
So the translation done by the type checker makes
the parameter explicit:
<programlisting>
    f :: NameSupply -> Env -> Expr -> Expr
    f ns env (Lam x e) = Lam x' (f ns1 env e)
                       where
                         (ns1,ns2) = splitNS ns
                         x' = newName ns2
                         env = extend env x x'
</programlisting>
Notice the call to 'split' introduced by the type checker.
How did it know to use 'splitNS'?  Because what it really did
was to introduce a call to the overloaded function 'split',
defined by the class <literal>Splittable</literal>:
<programlisting>
        class Splittable a where
          split :: a -> (a,a)
</programlisting>
The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
split for name supplies.  But we can simply write
<programlisting>
        g x = (x, %ns, %ns)
</programlisting>
and GHC will infer
<programlisting>
        g :: (Splittable a, %ns :: a) => b -> (b,a,a)
</programlisting>
The <literal>Splittable</literal> class is built into GHC.  It's exported by module 
<literal>GHC.Exts</literal>.
</para>
<para>
Other points:
<itemizedlist>
<listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>' 
are entirely distinct implicit parameters: you 
  can use them together and they won't intefere with each other. </para>
</listitem>

<listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>

<listitem> <para>You cannot have implicit parameters (whether linear or not)
  in the context of a class or instance declaration. </para></listitem>
</itemizedlist>
</para>

<sect3><title>Warnings</title>

<para>
The monomorphism restriction is even more important than usual.
Consider the example above:
<programlisting>
    f :: (%ns :: NameSupply) => Env -> Expr -> Expr
    f env (Lam x e) = Lam x' (f env e)
                    where
                      x'   = newName %ns
                      env' = extend env x x'
</programlisting>
If we replaced the two occurrences of x' by (newName %ns), which is
usually a harmless thing to do, we get:
<programlisting>
    f :: (%ns :: NameSupply) => Env -> Expr -> Expr
    f env (Lam x e) = Lam (newName %ns) (f env e)
                    where
                      env' = extend env x (newName %ns)
</programlisting>
But now the name supply is consumed in <emphasis>three</emphasis> places
(the two calls to newName,and the recursive call to f), so
the result is utterly different.  Urk!  We don't even have 
the beta rule.
</para>
<para>
Well, this is an experimental change.  With implicit
parameters we have already lost beta reduction anyway, and
(as John Launchbury puts it) we can't sensibly reason about
Haskell programs without knowing their typing.
</para>

</sect3>

<sect3><title>Recursive functions</title>
<para>Linear implicit parameters can be particularly tricky when you have a recursive function
Consider
<programlisting>
        foo :: %x::T => Int -> [Int]
        foo 0 = []
        foo n = %x : foo (n-1)
</programlisting>
where T is some type in class Splittable.</para>
<para>
Do you get a list of all the same T's or all different T's
(assuming that split gives two distinct T's back)?
</para><para>
If you supply the type signature, taking advantage of polymorphic
recursion, you get what you'd probably expect.  Here's the
translated term, where the implicit param is made explicit:
<programlisting>
        foo x 0 = []
        foo x n = let (x1,x2) = split x
                  in x1 : foo x2 (n-1)
</programlisting>
But if you don't supply a type signature, GHC uses the Hindley
Milner trick of using a single monomorphic instance of the function
for the recursive calls. That is what makes Hindley Milner type inference
work.  So the translation becomes
<programlisting>
        foo x = let
                  foom 0 = []
                  foom n = x : foom (n-1)
                in
                foom
</programlisting>
Result: 'x' is not split, and you get a list of identical T's.  So the
semantics of the program depends on whether or not foo has a type signature.
Yikes!
</para><para>
You may say that this is a good reason to dislike linear implicit parameters
and you'd be right.  That is why they are an experimental feature. 
</para>
</sect3>

</sect2>

================ END OF Linear Implicit Parameters commented out -->

<sect2 id="sec-kinding">
<title>Explicitly-kinded quantification</title>

<para>
Haskell infers the kind of each type variable.  Sometimes it is nice to be able
to give the kind explicitly as (machine-checked) documentation, 
just as it is nice to give a type signature for a function.  On some occasions,
it is essential to do so.  For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
John Hughes had to define the data type:
<screen>
     data Set cxt a = Set [a]
                    | Unused (cxt a -> ())
</screen>
The only use for the <literal>Unused</literal> constructor was to force the correct
kind for the type variable <literal>cxt</literal>.
</para>
<para>
GHC now instead allows you to specify the kind of a type variable directly, wherever
a type variable is explicitly bound.  Namely:
<itemizedlist>
<listitem><para><literal>data</literal> declarations:
<screen>
  data Set (cxt :: * -> *) a = Set [a]
</screen></para></listitem>
<listitem><para><literal>type</literal> declarations:
<screen>
  type T (f :: * -> *) = f Int
</screen></para></listitem>
<listitem><para><literal>class</literal> declarations:
<screen>
  class (Eq a) => C (f :: * -> *) a where ...
</screen></para></listitem>
<listitem><para><literal>forall</literal>'s in type signatures:
<screen>
  f :: forall (cxt :: * -> *). Set cxt Int
</screen></para></listitem>
</itemizedlist>
</para>

<para>
The parentheses are required.  Some of the spaces are required too, to
separate the lexemes.  If you write <literal>(f::*->*)</literal> you
will get a parse error, because "<literal>::*->*</literal>" is a
single lexeme in Haskell.
</para>

<para>
As part of the same extension, you can put kind annotations in types
as well.  Thus:
<screen>
   f :: (Int :: *) -> Int
   g :: forall a. a -> (a :: *)
</screen>
The syntax is
<screen>
   atype ::= '(' ctype '::' kind ')
</screen>
The parentheses are required.
</para>
</sect2>


<sect2 id="universal-quantification">
<title>Arbitrary-rank polymorphism
</title>

<para>
Haskell type signatures are implicitly quantified.  The new keyword <literal>forall</literal>
allows us to say exactly what this means.  For example:
</para>
<para>
<programlisting>
        g :: b -> b
</programlisting>
means this:
<programlisting>
        g :: forall b. (b -> b)
</programlisting>
The two are treated identically.
</para>

<para>
However, GHC's type system supports <emphasis>arbitrary-rank</emphasis> 
explicit universal quantification in
types. 
For example, all the following types are legal:
<programlisting>
    f1 :: forall a b. a -> b -> a
    g1 :: forall a b. (Ord a, Eq  b) => a -> b -> a

    f2 :: (forall a. a->a) -> Int -> Int
    g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int

    f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
</programlisting>
Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
The <literal>forall</literal> makes explicit the universal quantification that
is implicitly added by Haskell.
</para>
<para>
The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
the <literal>forall</literal> is on the left of a function arrow.  As <literal>g2</literal>
shows, the polymorphic type on the left of the function arrow can be overloaded.
</para>
<para>
The function <literal>f3</literal> has a rank-3 type;
it has rank-2 types on the left of a function arrow.
</para>
<para>
GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
arbitrarily deep in function arrows.   (GHC used to be restricted to rank 2, but
that restriction has now been lifted.)
In particular, a forall-type (also called a "type scheme"),
including an operational type class context, is legal:
<itemizedlist>
<listitem> <para> On the left of a function arrow </para> </listitem>
<listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
<listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
field type signatures.</para> </listitem>
<listitem> <para> As the type of an implicit parameter </para> </listitem>
<listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
</itemizedlist>
There is one place you cannot put a <literal>forall</literal>:
you cannot instantiate a type variable with a forall-type.  So you cannot 
make a forall-type the argument of a type constructor.  So these types are illegal:
<programlisting>
    x1 :: [forall a. a->a]
    x2 :: (forall a. a->a, Int)
    x3 :: Maybe (forall a. a->a)
</programlisting>
Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
a type variable any more!
</para>


<sect3 id="univ">
<title>Examples
</title>

<para>
In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
the types of the constructor arguments.  Here are several examples:
</para>

<para>

<programlisting>
data T a = T1 (forall b. b -> b -> b) a

data MonadT m = MkMonad { return :: forall a. a -> m a,
                          bind   :: forall a b. m a -> (a -> m b) -> m b
                        }

newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
</programlisting>

</para>

<para>
The constructors have rank-2 types:
</para>

<para>

<programlisting>
T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
MkMonad :: forall m. (forall a. a -> m a)
                  -> (forall a b. m a -> (a -> m b) -> m b)
                  -> MonadT m
MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
</programlisting>

</para>

<para>
Notice that you don't need to use a <literal>forall</literal> if there's an
explicit context.  For example in the first argument of the
constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
prefixed to the argument type.  The implicit <literal>forall</literal>
quantifies all type variables that are not already in scope, and are
mentioned in the type quantified over.
</para>

<para>
As for type signatures, implicit quantification happens for non-overloaded
types too.  So if you write this:

<programlisting>
  data T a = MkT (Either a b) (b -> b)
</programlisting>

it's just as if you had written this:

<programlisting>
  data T a = MkT (forall b. Either a b) (forall b. b -> b)
</programlisting>

That is, since the type variable <literal>b</literal> isn't in scope, it's
implicitly universally quantified.  (Arguably, it would be better
to <emphasis>require</emphasis> explicit quantification on constructor arguments
where that is what is wanted.  Feedback welcomed.)
</para>

<para>
You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
the constructor to suitable values, just as usual.  For example,
</para>

<para>

<programlisting>
    a1 :: T Int
    a1 = T1 (\xy->x) 3
    
    a2, a3 :: Swizzle
    a2 = MkSwizzle sort
    a3 = MkSwizzle reverse
    
    a4 :: MonadT Maybe
    a4 = let r x = Just x
             b m k = case m of
                       Just y -> k y
                       Nothing -> Nothing
         in
         MkMonad r b

    mkTs :: (forall b. b -> b -> b) -> a -> [T a]
    mkTs f x y = [T1 f x, T1 f y]
</programlisting>

</para>

<para>
The type of the argument can, as usual, be more general than the type
required, as <literal>(MkSwizzle reverse)</literal> shows.  (<function>reverse</function>
does not need the <literal>Ord</literal> constraint.)
</para>

<para>
When you use pattern matching, the bound variables may now have
polymorphic types.  For example:
</para>

<para>

<programlisting>
    f :: T a -> a -> (a, Char)
    f (T1 w k) x = (w k x, w 'c' 'd')

    g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
    g (MkSwizzle s) xs f = s (map f (s xs))

    h :: MonadT m -> [m a] -> m [a]
    h m [] = return m []
    h m (x:xs) = bind m x          $ \y ->
                 bind m (h m xs)   $ \ys ->
                 return m (y:ys)
</programlisting>

</para>

<para>
In the function <function>h</function> we use the record selectors <literal>return</literal>
and <literal>bind</literal> to extract the polymorphic bind and return functions
from the <literal>MonadT</literal> data structure, rather than using pattern
matching.
</para>
</sect3>

<sect3>
<title>Type inference</title>

<para>
In general, type inference for arbitrary-rank types is undecidable.
GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
to get a decidable algorithm by requiring some help from the programmer.
We do not yet have a formal specification of "some help" but the rule is this:
</para>
<para>
<emphasis>For a lambda-bound or case-bound variable, x, either the programmer
provides an explicit polymorphic type for x, or GHC's type inference will assume
that x's type has no foralls in it</emphasis>.
</para>
<para>
What does it mean to "provide" an explicit type for x?  You can do that by 
giving a type signature for x directly, using a pattern type signature
(<xref linkend="scoped-type-variables"/>), thus:
<programlisting>
     \ f :: (forall a. a->a) -> (f True, f 'c')
</programlisting>
Alternatively, you can give a type signature to the enclosing
context, which GHC can "push down" to find the type for the variable:
<programlisting>
     (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
</programlisting>
Here the type signature on the expression can be pushed inwards
to give a type signature for f.  Similarly, and more commonly,
one can give a type signature for the function itself:
<programlisting>
     h :: (forall a. a->a) -> (Bool,Char)
     h f = (f True, f 'c')
</programlisting>
You don't need to give a type signature if the lambda bound variable
is a constructor argument.  Here is an example we saw earlier:
<programlisting>
    f :: T a -> a -> (a, Char)
    f (T1 w k) x = (w k x, w 'c' 'd')
</programlisting>
Here we do not need to give a type signature to <literal>w</literal>, because
it is an argument of constructor <literal>T1</literal> and that tells GHC all
it needs to know.
</para>

</sect3>


<sect3 id="implicit-quant">
<title>Implicit quantification</title>

<para>
GHC performs implicit quantification as follows.  <emphasis>At the top level (only) of 
user-written types, if and only if there is no explicit <literal>forall</literal>,
GHC finds all the type variables mentioned in the type that are not already
in scope, and universally quantifies them.</emphasis>  For example, the following pairs are 
equivalent:
<programlisting>
  f :: a -> a
  f :: forall a. a -> a

  g (x::a) = let
                h :: a -> b -> b
                h x y = y
             in ...
  g (x::a) = let
                h :: forall b. a -> b -> b
                h x y = y
             in ...
</programlisting>
</para>
<para>
Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
point.  For example:
<programlisting>
  f :: (a -> a) -> Int
           -- MEANS
  f :: forall a. (a -> a) -> Int
           -- NOT
  f :: (forall a. a -> a) -> Int


  g :: (Ord a => a -> a) -> Int
           -- MEANS the illegal type
  g :: forall a. (Ord a => a -> a) -> Int
           -- NOT
  g :: (forall a. Ord a => a -> a) -> Int
</programlisting>
The latter produces an illegal type, which you might think is silly,
but at least the rule is simple.  If you want the latter type, you
can write your for-alls explicitly.  Indeed, doing so is strongly advised
for rank-2 types.
</para>
</sect3>
</sect2>


<sect2 id="impredicative-polymorphism">
<title>Impredicative polymorphism
</title>
<para>GHC supports <emphasis>impredicative polymorphism</emphasis>.  This means
that you can call a polymorphic function at a polymorphic type, and
parameterise data structures over polymorphic types.  For example:
<programlisting>
  f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
  f (Just g) = Just (g [3], g "hello")
  f Nothing  = Nothing
</programlisting>
Notice here that the <literal>Maybe</literal> type is parameterised by the
<emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
[a])</literal>.
</para>
<para>The technical details of this extension are described in the paper
<ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
type inference for higher-rank types and impredicativity</ulink>,
which appeared at ICFP 2006.  
</para>
</sect2>

<sect2 id="scoped-type-variables">
<title>Lexically scoped type variables
</title>

<para>
GHC supports <emphasis>lexically scoped type variables</emphasis>, without
which some type signatures are simply impossible to write. For example:
<programlisting>
f :: forall a. [a] -> [a]
f xs = ys ++ ys
     where
       ys :: [a]
       ys = reverse xs
</programlisting>
The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
the entire definition of <literal>f</literal>.
In particular, it is in scope at the type signature for <varname>ys</varname>. 
In Haskell 98 it is not possible to declare
a type for <varname>ys</varname>; a major benefit of scoped type variables is that
it becomes possible to do so.
</para>
<para>Lexically-scoped type variables are enabled by
<option>-fglasgow-exts</option>.
</para>
<para>Note: GHC 6.6 contains substantial changes to the way that scoped type
variables work, compared to earlier releases.  Read this section
carefully!</para>

<sect3>
<title>Overview</title>

<para>The design follows the following principles
<itemizedlist>
<listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
a <emphasis>type</emphasis>. (This is a change from GHC's earlier
design.)</para></listitem>
<listitem><para>Furthermore, distinct lexical type variables stand for distinct
type variables.  This means that every programmer-written type signature
(includin one that contains free scoped type variables) denotes a
<emphasis>rigid</emphasis> type; that is, the type is fully known to the type
checker, and no inference is involved.</para></listitem>
<listitem><para>Lexical type variables may be alpha-renamed freely, without
changing the program.</para></listitem>
</itemizedlist>
</para>
<para>
A <emphasis>lexically scoped type variable</emphasis> can be bound by:
<itemizedlist>
<listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
<listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
<listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
<listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
</itemizedlist>
</para>
<para>
In Haskell, a programmer-written type signature is implicitly quantifed over
its free type variables (<ulink
url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
4.1.2</ulink> 
of the Haskel Report).
Lexically scoped type variables affect this implicit quantification rules
as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
quantified. For example, if type variable <literal>a</literal> is in scope,
then
<programlisting>
  (e :: a -> a)     means     (e :: a -> a)
  (e :: b -> b)     means     (e :: forall b. b->b)
  (e :: a -> b)     means     (e :: forall b. a->b)
</programlisting>
</para>


</sect3>


<sect3 id="decl-type-sigs">
<title>Declaration type signatures</title>
<para>A declaration type signature that has <emphasis>explicit</emphasis>
quantification (using <literal>forall</literal>) brings into scope the
explicitly-quantified
type variables, in the definition of the named function(s).  For example:
<programlisting>
  f :: forall a. [a] -> [a]
  f (x:xs) = xs ++ [ x :: a ]
</programlisting>
The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
the definition of "<literal>f</literal>".
</para>
<para>This only happens if the quantification in <literal>f</literal>'s type
signature is explicit.  For example:
<programlisting>
  g :: [a] -> [a]
  g (x:xs) = xs ++ [ x :: a ]
</programlisting>
This program will be rejected, because "<literal>a</literal>" does not scope
over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
quantification rules.
</para>
</sect3>

<sect3 id="exp-type-sigs">
<title>Expression type signatures</title>

<para>An expression type signature that has <emphasis>explicit</emphasis>
quantification (using <literal>forall</literal>) brings into scope the
explicitly-quantified
type variables, in the annotated expression.  For example:
<programlisting>
  f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
</programlisting>
Here, the type signature <literal>forall a. ST s Bool</literal> brings the 
type variable <literal>s</literal> into scope, in the annotated expression 
<literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
</para>

</sect3>

<sect3 id="pattern-type-sigs">
<title>Pattern type signatures</title>
<para>
A type signature may occur in any pattern; this is a <emphasis>pattern type
signature</emphasis>.  
For example:
<programlisting>
  -- f and g assume that 'a' is already in scope
  f = \(x::Int, y::a) -> x
  g (x::a) = x
  h ((x,y) :: (Int,Bool)) = (y,x)
</programlisting>
In the case where all the type variables in the pattern type sigature are
already in scope (i.e. bound by the enclosing context), matters are simple: the
signature simply constrains the type of the pattern in the obvious way.
</para>
<para>
There is only one situation in which you can write a pattern type signature that
mentions a type variable that is not already in scope, namely in pattern match
of an existential data constructor.  For example:
<programlisting>
  data T = forall a. MkT [a]

  k :: T -> T
  k (MkT [t::a]) = MkT t3
                 where
                   t3::[a] = [t,t,t]
</programlisting>
Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
variable that is not already in scope.  Indeed, it cannot already be in scope,
because it is bound by the pattern match.  GHC's rule is that in this situation
(and only then), a pattern type signature can mention a type variable that is
not already in scope; the effect is to bring it into scope, standing for the
existentially-bound type variable.
</para>
<para>
If this seems a little odd, we think so too.  But we must have
<emphasis>some</emphasis> way to bring such type variables into scope, else we
could not name existentially-bound type variables in subequent type signatures.
</para>
<para>
This is (now) the <emphasis>only</emphasis> situation in which a pattern type 
signature is allowed to mention a lexical variable that is not already in
scope.
For example, both <literal>f</literal> and <literal>g</literal> would be
illegal if <literal>a</literal> was not already in scope.
</para>


</sect3>

<!-- ==================== Commented out part about result type signatures 

<sect3 id="result-type-sigs">
<title>Result type signatures</title>

<para>
The result type of a function, lambda, or case expression alternative can be given a signature, thus:

<programlisting>
  {- f assumes that 'a' is already in scope -}
  f x y :: [a] = [x,y,x]

  g = \ x :: [Int] -> [3,4]

  h :: forall a. [a] -> a
  h xs = case xs of
            (y:ys) :: a -> y
</programlisting>
The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of 
the result of the function.  Similarly, the body of the lambda in the RHS of
<literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
alternative in <literal>h</literal> is <literal>a</literal>.
</para>
<para> A result type signature never brings new type variables into scope.</para>
<para>
There are a couple of syntactic wrinkles.  First, notice that all three
examples would parse quite differently with parentheses:
<programlisting>
  {- f assumes that 'a' is already in scope -}
  f x (y :: [a]) = [x,y,x]

  g = \ (x :: [Int]) -> [3,4]

  h :: forall a. [a] -> a
  h xs = case xs of
            ((y:ys) :: a) -> y
</programlisting>
Now the signature is on the <emphasis>pattern</emphasis>; and
<literal>h</literal> would certainly be ill-typed (since the pattern
<literal>(y:ys)</literal> cannot have the type <literal>a</literal>.

Second, to avoid ambiguity, the type after the &ldquo;<literal>::</literal>&rdquo; in a result
pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
token or a parenthesised type of some sort).  To see why,
consider how one would parse this:
<programlisting>
  \ x :: a -> b -> x
</programlisting>
</para>
</sect3>

 -->

<sect3 id="cls-inst-scoped-tyvars">
<title>Class and instance declarations</title>
<para>

The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
scope over the methods defined in the <literal>where</literal> part.  For example:


<programlisting>
  class C a where
    op :: [a] -> a

    op xs = let ys::[a]
                ys = reverse xs
            in
            head ys
</programlisting>
</para>
</sect3>

</sect2>

<sect2 id="deriving-typeable">
<title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></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 two more classes that may be automatically derived 
(provided the <option>-fglasgow-exts</option> flag is specified):
<literal>Typeable</literal>, and <literal>Data</literal>.  These classes are defined in the library
modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
</para>
<para>An instance of <literal>Typeable</literal> can only be derived if the
data type has seven or fewer type parameters, all of kind <literal>*</literal>.
The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
described in
<ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
</ulink>.
(Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
are used, and only <literal>Typeable1</literal> up to
<literal>Typeable7</literal> are provided in the library.)
In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
class, whose kind suits that of the data type constructor, and
then writing the data type instance by hand.
</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> <title> Generalising the deriving clause </title>
<para>
GHC now permits such instances to be derived instead, 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>
</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>

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

<para>
GHC now allows stand-alone <literal>deriving</literal> declarations:
</para>

<programlisting>
  data Foo = Bar Int | Baz String

  deriving Eq for Foo
</programlisting>

<para>Deriving instances of multi-parameter type classes for newtypes is
also allowed:</para>

<programlisting>
  newtype Foo a = MkFoo (State Int a)

  deriving (MonadState Int) for Foo
</programlisting>

<para>
</para>

</sect2>

<sect2 id="typing-binds">
<title>Generalised typing of mutually recursive bindings</title>

<para>
The Haskell Report specifies that a group of bindings (at top level, or in a
<literal>let</literal> or <literal>where</literal>) should be sorted into
strongly-connected components, and then type-checked in dependency order
(<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
Report, Section 4.5.1</ulink>).  
As each group is type-checked, any binders of the group that
have
an explicit type signature are put in the type environment with the specified
polymorphic type,
and all others are monomorphic until the group is generalised 
(<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
</para>

<para>Following a suggestion of Mark Jones, in his paper
<ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
Haskell</ulink>,
GHC implements a more general scheme.  If <option>-fglasgow-exts</option> is
specified:
<emphasis>the dependency analysis ignores references to variables that have an explicit
type signature</emphasis>.
As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
typecheck.  For example, consider:
<programlisting>
  f :: Eq a =&gt; a -> Bool
  f x = (x == x) || g True || g "Yes"
  
  g y = (y &lt;= y) || f True
</programlisting>
This is rejected by Haskell 98, but under Jones's scheme the definition for
<literal>g</literal> is typechecked first, separately from that for
<literal>f</literal>,
because the reference to <literal>f</literal> in <literal>g</literal>'s right
hand side is ingored by the dependency analysis.  Then <literal>g</literal>'s
type is generalised, to get
<programlisting>
  g :: Ord a =&gt; a -> Bool
</programlisting>
Now, the defintion for <literal>f</literal> is typechecked, with this type for
<literal>g</literal> in the type environment.
</para>

<para>
The same refined dependency analysis also allows the type signatures of 
mutually-recursive functions to have different contexts, something that is illegal in
Haskell 98 (Section 4.5.2, last sentence).  With
<option>-fglasgow-exts</option>
GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
type signatures; in practice this means that only variables bound by the same
pattern binding must have the same context.  For example, this is fine:
<programlisting>
  f :: Eq a =&gt; a -> Bool
  f x = (x == x) || g True
  
  g :: Ord a =&gt; a -> Bool
  g y = (y &lt;= y) || f True
</programlisting>
</para>
</sect2>

</sect1>
<!-- ==================== End of type system extensions =================  -->
  
<!-- ====================== TEMPLATE HASKELL =======================  -->

<sect1 id="template-haskell">
<title>Template Haskell</title>

<para>Template Haskell allows you to do compile-time meta-programming in
Haskell.  
The background to
the main technical innovations is discussed in "<ulink
url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
</para>
<para>
There is a Wiki page about
Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
http://www.haskell.org/th/</ulink>, and that is the best place to look for
further details.
You may also 
consult the <ulink
url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
Haskell library reference material</ulink> 
(search for the type ExpQ).
[Temporary: many changes to the original design are described in 
      <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.