path: root/ghc/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 plus deprecated
	  syntax of previous versions of the FFI for backwards
	  compatibility.</para> 

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

      <varlistentry>
	<term>
          <option>-fno-monomorphism-restriction</option>:
          <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
        </term>
	<listitem>
	  <para> Switch off the Haskell 98 monomorphism restriction.
          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</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"/>).  Currently also 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 = val1 + val2
</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>
</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,Bool)    -- A rank-2 type
  g f = f Int 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>
<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>

In GADT declarations (see <xref linkend="gadt"/>), the explicit
<literal>forall</literal> may be omitted.  For example, we can express
the same <literal>Counter a</literal> using GADT:

<programlisting>
data Counter a where
    NewCounter { _this    :: self
               , _inc     :: self -> self
               , _display :: self -> IO ()
               , tag      :: a
               }
        :: Counter a
</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:&num;

<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>

</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>
</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.</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>
All this makes it possible for a library author to design a library that relies on 
overlapping instances without the library client having to know.
</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 = fst (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>

<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>

<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="scoped-type-variables">
<title>Scoped type variables
</title>

<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>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
<listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
</itemizedlist>
For example:
<programlisting>
f (xs::[a]) = ys ++ ys
           where
              ys :: [a]
              ys = reverse xs
</programlisting>
The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
This brings the type variable <literal>a</literal> into scope; it scopes over
all the patterns and right hand sides for this equation for <function>f</function>.
In particular, it is in scope at the type signature for <varname>y</varname>.
</para>

<para>
At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
mentioned in the type signature <emphasis>that are not in scope</emphasis> are
implicitly universally quantified.  (If there are no type variables in
scope, all type variables mentioned in the signature are universally
quantified, which is just as in Haskell 98.)  In this case, since <varname>a</varname>
is in scope, it is not universally quantified, so the type of <varname>ys</varname> is
the same as that of <varname>xs</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>
Scoped type variables are implemented in both GHC and Hugs.  Where the
implementations differ from the specification below, those differences
are noted.
</para>

<para>
So much for the basic idea.  Here are the details.
</para>

<sect3>
<title>What a scoped type variable means</title>
<para>
A lexically-scoped type variable is simply
the name for a type.   The restriction it expresses is that all occurrences
of the same name mean the same type.  For example:
<programlisting>
  f :: [Int] -> Int -> Int
  f (xs::[a]) (y::a) = (head xs + y) :: a
</programlisting>
The pattern type signatures on the left hand side of
<literal>f</literal> express the fact that <literal>xs</literal>
must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
must have this same type.  The type signature on the expression <literal>(head xs)</literal>
specifies that this expression must have the same type <literal>a</literal>.
<emphasis>There is no requirement that the type named by "<literal>a</literal>" is
in fact a type variable</emphasis>.  Indeed, in this case, the type named by "<literal>a</literal>" is
<literal>Int</literal>.  (This is a slight liberalisation from the original rather complex
rules, which specified that a pattern-bound type variable should be universally quantified.)
For example, all of these are legal:</para>

<programlisting>
  t (x::a) (y::a) = x+y*2

  f (x::a) (y::b) = [x,y]       -- a unifies with b

  g (x::a) = x + 1::Int         -- a unifies with Int

  h x = let k (y::a) = [x,y]    -- a is free in the
        in k x                  -- environment

  k (x::a) True    = ...        -- a unifies with Int
  k (x::Int) False = ...

  w :: [b] -> [b]
  w (x::a) = x                  -- a unifies with [b]
</programlisting>

</sect3>

<sect3>
<title>Scope and implicit quantification</title>

<para>

<itemizedlist>
<listitem>

<para>
All the type variables mentioned in a pattern,
that are not already in scope,
are brought into scope by the pattern.  We describe this set as
the <emphasis>type variables bound by the pattern</emphasis>.
For example:
<programlisting>
  f (x::a) = let g (y::(a,b)) = fst y
             in
             g (x,True)
</programlisting>
The pattern <literal>(x::a)</literal> brings the type variable
<literal>a</literal> into scope, as well as the term 
variable <literal>x</literal>.  The pattern <literal>(y::(a,b))</literal>
contains an occurrence of the already-in-scope type variable <literal>a</literal>,
and brings into scope the type variable <literal>b</literal>.
</para>
</listitem>

<listitem>
<para>
The type variable(s) bound by the pattern have the same scope
as the term variable(s) bound by the pattern.  For example:
<programlisting>
  let
    f (x::a) = &lt;...rhs of f...>
    (p::b, q::b) = (1,2)
  in &lt;...body of let...>
</programlisting>
Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
just like <literal>p</literal> and <literal>q</literal> do.
Indeed, the newly bound type variables also scope over any ordinary, separate
type signatures in the <literal>let</literal> group.
</para>
</listitem>


<listitem>
<para>
The type variables bound by the pattern may be 
mentioned in ordinary type signatures or pattern 
type signatures anywhere within their scope.

</para>
</listitem>

<listitem>
<para>
 In ordinary type signatures, any type variable mentioned in the
signature that is in scope is <emphasis>not</emphasis> universally quantified.

</para>
</listitem>

<listitem>

<para>
 Ordinary type signatures do not bring any new type variables
into scope (except in the type signature itself!). So this is illegal:

<programlisting>
  f :: a -> a
  f x = x::a
</programlisting>

It's illegal because <varname>a</varname> is not in scope in the body of <function>f</function>,
so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
and that is an incorrect typing.

</para>
</listitem>

<listitem>
<para>
The pattern type signature is a monotype:
</para>

<itemizedlist>
<listitem> <para> 
A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
</para> </listitem>

<listitem>  <para> 
The type variables bound by a pattern type signature can only be instantiated to monotypes,
not to type schemes.
</para> </listitem>

<listitem>  <para> 
There is no implicit universal quantification on pattern type signatures (in contrast to
ordinary type signatures).
</para> </listitem>

</itemizedlist>

</listitem>

<listitem>
<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>


(Not implemented in Hugs yet, Dec 98).
</para>
</listitem>

</itemizedlist>

</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="pattern-type-sigs">
<title>Where a pattern type signature can occur</title>

<para>
A pattern type signature can occur in any pattern.  For example:
<itemizedlist>

<listitem>
<para>
A pattern type signature can be on an arbitrary sub-pattern, not
just on a variable:


<programlisting>
  f ((x,y)::(a,b)) = (y,x) :: (b,a)
</programlisting>


</para>
</listitem>
<listitem>

<para>
 Pattern type signatures, including the result part, can be used
in lambda abstractions:

<programlisting>
  (\ (x::a, y) :: a -> x)
</programlisting>
</para>
</listitem>
<listitem>

<para>
 Pattern type signatures, including the result part, can be used
in <literal>case</literal> expressions:

<programlisting>
  case e of { ((x::a, y) :: (a,b)) -> x }
</programlisting>

Note that the <literal>-&gt;</literal> symbol in a case alternative
leads to difficulties when parsing a type signature in the pattern: in
the absence of the extra parentheses in the example above, the parser
would try to interpret the <literal>-&gt;</literal> as a function
arrow and give a parse error later.

</para>

</listitem>

<listitem>
<para>
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>
</listitem>

<listitem>

<para>
 Pattern type signatures can bind existential type variables.
For example:


<programlisting>
  data T = forall a. MkT [a]

  f :: T -> T
  f (MkT [t::a]) = MkT t3
                 where
                   t3::[a] = [t,t,t]
</programlisting>


</para>
</listitem>


<listitem>

<para>
Pattern type signatures 
can be used in pattern bindings:

<programlisting>
  f x = let (y, z::a) = x in ...
  f1 x                = let (y, z::Int) = x in ...
  f2 (x::(Int,a))     = let (y, z::a)   = x in ...
  f3 :: (b->b)        = \x -> x
</programlisting>

In all such cases, the binding is not generalised over the pattern-bound
type variables.  Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
has type <literal>b -&gt; b</literal> for some type <literal>b</literal>, 
and <emphasis>not</emphasis> <literal>forall b. b -&gt; b</literal>.
In contrast, the binding
<programlisting>
  f4 :: b->b
  f4 = \x -> x
</programlisting>
makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
in <literal>f4</literal>'s scope.

</para>
</listitem>
</itemizedlist>
</para>
<para>Pattern type signatures are completely orthogonal to ordinary, separate
type signatures.  The two can be used independently or together.</para>

</sect3>

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

<para>
The result type of a function can be given a signature, thus:


<programlisting>
  f (x::a) :: [a] = [x,x,x]
</programlisting>


The final <literal>:: [a]</literal> after all the patterns gives a signature to the
result type.  Sometimes this is the only way of naming the type variable
you want:


<programlisting>
  f :: Int -> [a] -> [a]
  f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
                        in \xs -> map g (reverse xs `zip` xs)
</programlisting>

</para>
<para>
The type variables bound in a result type signature scope over the right hand side
of the definition. However, consider this corner-case:
<programlisting>
  rev1 :: [a] -> [a] = \xs -> reverse xs

  foo ys = rev (ys::[a])
</programlisting>
The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).  
</para>
<para>
As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
For example, the following program would be rejected, because it claims that <literal>rev1</literal>
is polymorphic:
<programlisting>
  rev1 :: [b] -> [b]
  rev1 :: [a] -> [a] = \xs -> reverse xs
</programlisting>
</para>

<para>
Result type signatures are not yet implemented in Hugs.
</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' (S t1...tk vk+1...vn) deriving (c1...cm) 
</programlisting> 

where 
 <itemizedlist>
<listitem><para>
  <literal>S</literal> is a type constructor, 
</para></listitem>
<listitem><para>
  The <literal>t1...tk</literal> are types,
</para></listitem>
<listitem><para>
  The <literal>vk+1...vn</literal> are type variables which do not occur in any of
  the <literal>ti</literal>, and
</para></listitem>
<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>
  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 (S t1...tk vk+1...v) => ci (T v1...vp)
</programlisting>
where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the 
right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
</para>
<para>

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

<sect1 id="gadt">
<title>Generalised Algebraic Data Types</title>

<para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
to give the type signatures of constructors explicitly.  For 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 vanilla data types.  Now we can 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>
These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
</para>
<para> The extensions to GHC are these:
<itemizedlist>
<listitem><para>
  Data type declarations have a 'where' form, as exemplified above.  The type signature of
each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header 
have no scope.  Indeed, one can write a kind signature instead:
<programlisting>
  data Term :: * -> * 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>
There are no restrictions on the type of the data constructor, except that the result
type must begin with the type constructor being defined.  For example, in the <literal>Term</literal> data
type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
</para></listitem>

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

<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>
For every constructor that has a field <literal>f</literal>, (a) the type of
field <literal>f</literal> must be the same; and (b) the
result type of the constructor must be the same; both modulo alpha conversion.
Hence, in our 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>

At the moment, record updates are not yet possible with GADT, so support is 
limited to record construction, selection and pattern matching:

<programlisting>
  someTerm :: Term Bool
  someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }

  eval :: Term a -> a
  eval Lit    { val = i } = i
  eval Succ   { num = t } = eval t + 1
  eval Pred   { num = t } = eval t - 1
  eval IsZero { arg = t } = eval t == 0
  eval Pair   { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
  eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
</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, but only if the data type could also have been declared in
Haskell-98 syntax.   For example, these two declarations are equivalent
<programlisting>
  data Maybe1 a where {
      Nothing1 :: Maybe a ;
      Just1    :: a -> Maybe a
    } deriving( Eq, Ord )

  data Maybe2 a = Nothing2 | Just2 a 
       deriving( Eq, Ord )
</programlisting>
This simply allows you to declare a vanilla Haskell-98 data type using the
<literal>where</literal> form without losing the <literal>deriving</literal> clause.
</para></listitem>

<listitem><para>
Pattern matching causes type refinement.  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 there is a paper
about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>

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

<para>Notice that GADTs generalise existential types.  For example, these two declarations are equivalent:
<programlisting>
  data T a = forall b. MkT b (b->a)
  data T' a where { MKT :: b -> (b->a) -> T' a }
</programlisting>
</para>
</sect1>

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

<!-- ====================== TEMPLATE HASKELL =======================  -->

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

<para>Template Haskell allows you to do compile-time meta-programming in Haskell.  There is a "home page" for
Template Haskell at <ulink url="http://www.haskell.org/th/">
http://www.haskell.org/th/</ulink>, while
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).
The details of the Template Haskell design are still in flux.  Make sure you
consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online 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>.
Not all of these changes are in GHC 6.2.]
</para>

<para> The first example from that paper is set out below as a worked example to help get you started. 
</para>

<para>
The documentation here describes the realisation in GHC.  (It's rather sketchy just now;
Tim Sheard is going to expand it.)
</para>

    <sect2>
      <title>Syntax</title>

      <para> Template Haskell has the following new syntactic
      constructions.  You need to use the flag
      <option>-fth</option><indexterm><primary><option>-fth</option></primary>
      </indexterm>to switch these syntactic extensions on
      (<option>-fth</option> is currently implied by
      <option>-fglasgow-exts</option>, but you are encouraged to
      specify it explicitly).</para>

	<itemizedlist>
	      <listitem><para>
		  A splice is written <literal>$x</literal>, where <literal>x</literal> is an
		  identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
		  There must be no space between the "$" and the identifier or parenthesis.  This use
		  of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
		  of "." as an infix operator.  If you want the infix operator, put spaces around it.
		  </para>
	      <para> A splice can occur in place of 
		  <itemizedlist>
		    <listitem><para> an expression; the spliced expression must
		    have type <literal>Q Exp</literal></para></listitem>
		    <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
		    <listitem><para> [Planned, but not implemented yet.] a
		    type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
		    </itemizedlist>
	   (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
	the paper. Also the type of the enclosed expression must be  <literal>Q [Dec]</literal>, not  <literal>[Q Dec]</literal>
	as in the paper.)
		</para></listitem>


	      <listitem><para>
		  A expression quotation is written in Oxford brackets, thus:
		  <itemizedlist>
		    <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression; 
                             the quotation has type <literal>Expr</literal>.</para></listitem>
		    <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
                             the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
		    <listitem><para>  [Planned, but not implemented yet.]  <literal>[t| ... |]</literal>, where the "..." is a type; 
                             the quotation has type <literal>Type</literal>.</para></listitem>
		  </itemizedlist></para></listitem>

	      <listitem><para>
		  Reification is written thus:
		  <itemizedlist>
		    <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
		      has type <literal>Dec</literal>. </para></listitem>
		    <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
		    <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
		    <listitem><para> Still to come: fixities </para></listitem>
		    
		  </itemizedlist></para>
		</listitem>

		  
	</itemizedlist>
</sect2>

<sect2>  <title> Using Template Haskell </title>
<para>
<itemizedlist>
    <listitem><para>
    The data types and monadic constructor functions for Template Haskell are in the library
    <literal>Language.Haskell.THSyntax</literal>.
    </para></listitem>

    <listitem><para>
    You can only run a function at compile time if it is imported from another module.  That is,
	    you can't define a function in a module, and call it from within a splice in the same module.
	    (It would make sense to do so, but it's hard to implement.)
   </para></listitem>

    <listitem><para>
	    The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
   </para></listitem>
    <listitem><para>
	    If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
	      run Template Haskell.  A stage-1 compiler will reject the TH constructs.  Reason: TH
	      compiles and runs a program, and then looks at the result.  So it's important that
	      the program it compiles produces results whose representations are identical to
	      those of the compiler itself.
   </para></listitem>
</itemizedlist>
</para>
<para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
	or file-at-a-time).  There used to be a restriction to the former two, but that restriction 
	has been lifted.
</para>
</sect2>
 
<sect2>  <title> A Template Haskell Worked Example </title>
<para>To help you get over the confidence barrier, try out this skeletal worked example.
  First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>

<programlisting>

{- Main.hs -}
module Main where

-- Import our template "pr"
import Printf ( pr )

-- The splice operator $ takes the Haskell source code
-- generated at compile time by "pr" and splices it into
-- the argument of "putStrLn".
main = putStrLn ( $(pr "Hello") )


{- Printf.hs -}
module Printf where

-- Skeletal printf from the paper.
-- It needs to be in a separate module to the one where
-- you intend to use it.

-- Import some Template Haskell syntax
import Language.Haskell.TH

-- Describe a format string
data Format = D | S | L String

-- Parse a format string.  This is left largely to you
-- as we are here interested in building our first ever
-- Template Haskell program and not in building printf.
parse :: String -> [Format]
parse s   = [ L s ]

-- Generate Haskell source code from a parsed representation
-- of the format string.  This code will be spliced into
-- the module which calls "pr", at compile time.
gen :: [Format] -> ExpQ
gen [D]   = [| \n -> show n |]
gen [S]   = [| \s -> s |]
gen [L s] = stringE s

-- Here we generate the Haskell code for the splice
-- from an input format string.
pr :: String -> ExpQ
pr s      = gen (parse s)
</programlisting>

<para>Now run the compiler (here we are a Cygwin prompt on Windows):
</para>
<programlisting>
$ ghc --make -fth main.hs -o main.exe
</programlisting>

<para>Run "main.exe" and here is your output:</para>

<programlisting>
$ ./main
Hello
</programlisting>

</sect2>
 
</sect1>

<!-- ===================== Arrow notation ===================  -->

<sect1 id="arrow-notation">
<title>Arrow notation
</title>

<para>Arrows are a generalization of monads introduced by John Hughes.
For more details, see
<itemizedlist>

<listitem>
<para>
&ldquo;Generalising Monads to Arrows&rdquo;,
John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
pp67&ndash;111, May 2000.
</para>
</listitem>

<listitem>
<para>
&ldquo;<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>&rdquo;,
Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
</para>
</listitem>

<listitem>
<para>
&ldquo;<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>&rdquo;,
Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
Palgrave, 2003.
</para>
</listitem>

</itemizedlist>
and the arrows web page at
<ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
With the <option>-farrows</option> flag, GHC supports the arrow
notation described in the second of these papers.
What follows is a brief introduction to the notation;
it won't make much sense unless you've read Hughes's paper.
This notation is translated to ordinary Haskell,
using combinators from the
<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module.
</para>

<para>The extension adds a new kind of expression for defining arrows:
<screen>
<replaceable>exp</replaceable><superscript>10</superscript> ::= ...
       |  proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
</screen>
where <literal>proc</literal> is a new keyword.
The variables of the pattern are bound in the body of the 
<literal>proc</literal>-expression,
which is a new sort of thing called a <firstterm>command</firstterm>.
The syntax of commands is as follows:
<screen>
<replaceable>cmd</replaceable>   ::= <replaceable>exp</replaceable><superscript>10</superscript> -&lt;  <replaceable>exp</replaceable>
       |  <replaceable>exp</replaceable><superscript>10</superscript> -&lt;&lt; <replaceable>exp</replaceable>
       |  <replaceable>cmd</replaceable><superscript>0</superscript>
</screen>
with <replaceable>cmd</replaceable><superscript>0</superscript> up to
<replaceable>cmd</replaceable><superscript>9</superscript> defined using
infix operators as for expressions, and
<screen>
<replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
       |  let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
       |  if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
       |  case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
       |  do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
       |  <replaceable>fcmd</replaceable>

<replaceable>fcmd</replaceable>  ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
       |  ( <replaceable>cmd</replaceable> )
       |  (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)

<replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
       |  <replaceable>pat</replaceable> &lt;- <replaceable>cmd</replaceable>
       |  rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
       |  <replaceable>cmd</replaceable>
</screen>
where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
except that the bodies are commands instead of expressions.
</para>

<para>
Commands produce values, but (like monadic computations)
may yield more than one value,
or none, and may do other things as well.
For the most part, familiarity with monadic notation is a good guide to
using commands.
However the values of expressions, even monadic ones,
are determined by the values of the variables they contain;
this is not necessarily the case for commands.
</para>

<para>
A simple example of the new notation is the expression
<screen>
proc x -> f -&lt; x+1
</screen>
We call this a <firstterm>procedure</firstterm> or
<firstterm>arrow abstraction</firstterm>.
As with a lambda expression, the variable <literal>x</literal>
is a new variable bound within the <literal>proc</literal>-expression.
It refers to the input to the arrow.
In the above example, <literal>-&lt;</literal> is not an identifier but an
new reserved symbol used for building commands from an expression of arrow
type and an expression to be fed as input to that arrow.
(The weird look will make more sense later.)
It may be read as analogue of application for arrows.
The above example is equivalent to the Haskell expression
<screen>
arr (\ x -> x+1) >>> f
</screen>
That would make no sense if the expression to the left of
<literal>-&lt;</literal> involves the bound variable <literal>x</literal>.
More generally, the expression to the left of <literal>-&lt;</literal>
may not involve any <firstterm>local variable</firstterm>,
i.e. a variable bound in the current arrow abstraction.
For such a situation there is a variant <literal>-&lt;&lt;</literal>, as in
<screen>
proc x -> f x -&lt;&lt; x+1
</screen>
which is equivalent to
<screen>
arr (\ x -> (f x, x+1)) >>> app
</screen>
so in this case the arrow must belong to the <literal>ArrowApply</literal>
class.
Such an arrow is equivalent to a monad, so if you're using this form
you may find a monadic formulation more convenient.
</para>

<sect2>
<title>do-notation for commands</title>

<para>
Another form of command is a form of <literal>do</literal>-notation.
For example, you can write
<screen>
proc x -> do
        y &lt;- f -&lt; x+1
        g -&lt; 2*y
        let z = x+y
        t &lt;- h -&lt; x*z
        returnA -&lt; t+z
</screen>
You can read this much like ordinary <literal>do</literal>-notation,
but with commands in place of monadic expressions.
The first line sends the value of <literal>x+1</literal> as an input to
the arrow <literal>f</literal>, and matches its output against
<literal>y</literal>.
In the next line, the output is discarded.
The arrow <function>returnA</function> is defined in the
<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module as <literal>arr id</literal>.
The above example is treated as an abbreviation for
<screen>
arr (\ x -> (x, x)) >>>
        first (arr (\ x -> x+1) >>> f) >>>
        arr (\ (y, x) -> (y, (x, y))) >>>
        first (arr (\ y -> 2*y) >>> g) >>>
        arr snd >>>
        arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
        first (arr (\ (x, z) -> x*z) >>> h) >>>
        arr (\ (t, z) -> t+z) >>>
        returnA
</screen>
Note that variables not used later in the composition are projected out.
After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
defined in the
<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module, this reduces to
<screen>
arr (\ x -> (x+1, x)) >>>
        first f >>>
        arr (\ (y, x) -> (2*y, (x, y))) >>>
        first g >>>
        arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
        first h >>>
        arr (\ (t, z) -> t+z)
</screen>
which is what you might have written by hand.
With arrow notation, GHC keeps track of all those tuples of variables for you.
</para>

<para>
Note that although the above translation suggests that
<literal>let</literal>-bound variables like <literal>z</literal> must be
monomorphic, the actual translation produces Core,
so polymorphic variables are allowed.
</para>

<para>
It's also possible to have mutually recursive bindings,
using the new <literal>rec</literal> keyword, as in the following example:
<programlisting>
counter :: ArrowCircuit a => a Bool Int
counter = proc reset -> do
        rec     output &lt;- returnA -&lt; if reset then 0 else next
                next &lt;- delay 0 -&lt; output+1
        returnA -&lt; output
</programlisting>
The translation of such forms uses the <function>loop</function> combinator,
so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
</para>

</sect2>

<sect2>
<title>Conditional commands</title>

<para>
In the previous example, we used a conditional expression to construct the
input for an arrow.
Sometimes we want to conditionally execute different commands, as in
<screen>
proc (x,y) ->
        if f x y
        then g -&lt; x+1
        else h -&lt; y+2
</screen>
which is translated to
<screen>
arr (\ (x,y) -> if f x y then Left x else Right y) >>>
        (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
</screen>
Since the translation uses <function>|||</function>,
the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
</para>

<para>
There are also <literal>case</literal> commands, like
<screen>
case input of
    [] -> f -&lt; ()
    [x] -> g -&lt; x+1
    x1:x2:xs -> do
        y &lt;- h -&lt; (x1, x2)
        ys &lt;- k -&lt; xs
        returnA -&lt; y:ys
</screen>
The syntax is the same as for <literal>case</literal> expressions,
except that the bodies of the alternatives are commands rather than expressions.
The translation is similar to that of <literal>if</literal> commands.
</para>

</sect2>

<sect2>
<title>Defining your own control structures</title>

<para>
As we're seen, arrow notation provides constructs,
modelled on those for expressions,
for sequencing, value recursion and conditionals.
But suitable combinators,
which you can define in ordinary Haskell,
may also be used to build new commands out of existing ones.
The basic idea is that a command defines an arrow from environments to values.
These environments assign values to the free local variables of the command.
Thus combinators that produce arrows from arrows
may also be used to build commands from commands.
For example, the <literal>ArrowChoice</literal> class includes a combinator
<programlisting>
ArrowChoice a => (&lt;+>) :: a e c -> a e c -> a e c
</programlisting>
so we can use it to build commands:
<programlisting>
expr' = proc x -> do
                returnA -&lt; x
        &lt;+> do
                symbol Plus -&lt; ()
                y &lt;- term -&lt; ()
                expr' -&lt; x + y
        &lt;+> do
                symbol Minus -&lt; ()
                y &lt;- term -&lt; ()
                expr' -&lt; x - y
</programlisting>
(The <literal>do</literal> on the first line is needed to prevent the first
<literal>&lt;+> ...</literal> from being interpreted as part of the
expression on the previous line.)
This is equivalent to
<programlisting>
expr' = (proc x -> returnA -&lt; x)
        &lt;+> (proc x -> do
                symbol Plus -&lt; ()
                y &lt;- term -&lt; ()
                expr' -&lt; x + y)
        &lt;+> (proc x -> do
                symbol Minus -&lt; ()
                y &lt;- term -&lt; ()
                expr' -&lt; x - y)
</programlisting>
It is essential that this operator be polymorphic in <literal>e</literal>
(representing the environment input to the command
and thence to its subcommands)
and satisfy the corresponding naturality property
<screen>
arr k >>> (f &lt;+> g) = (arr k >>> f) &lt;+> (arr k >>> g)
</screen>
at least for strict <literal>k</literal>.
(This should be automatic if you're not using <function>seq</function>.)
This ensures that environments seen by the subcommands are environments
of the whole command,
and also allows the translation to safely trim these environments.
The operator must also not use any variable defined within the current
arrow abstraction.
</para>

<para>
We could define our own operator
<programlisting>
untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
untilA body cond = proc x ->
        if cond x then returnA -&lt; ()
        else do
                body -&lt; x
                untilA body cond -&lt; x
</programlisting>
and use it in the same way.
Of course this infix syntax only makes sense for binary operators;
there is also a more general syntax involving special brackets:
<screen>
proc x -> do
        y &lt;- f -&lt; x+1
        (|untilA (increment -&lt; x+y) (within 0.5 -&lt; x)|)
</screen>
</para>

</sect2>

<sect2>
<title>Primitive constructs</title>

<para>
Some operators will need to pass additional inputs to their subcommands.
For example, in an arrow type supporting exceptions,
the operator that attaches an exception handler will wish to pass the
exception that occurred to the handler.
Such an operator might have a type
<screen>
handleA :: ... => a e c -> a (e,Ex) c -> a e c
</screen>
where <literal>Ex</literal> is the type of exceptions handled.
You could then use this with arrow notation by writing a command
<screen>
body `handleA` \ ex -> handler
</screen>
so that if an exception is raised in the command <literal>body</literal>,
the variable <literal>ex</literal> is bound to the value of the exception
and the command <literal>handler</literal>,
which typically refers to <literal>ex</literal>, is entered.
Though the syntax here looks like a functional lambda,
we are talking about commands, and something different is going on.
The input to the arrow represented by a command consists of values for
the free local variables in the command, plus a stack of anonymous values.
In all the prior examples, this stack was empty.
In the second argument to <function>handleA</function>,
this stack consists of one value, the value of the exception.
The command form of lambda merely gives this value a name.
</para>

<para>
More concretely,
the values on the stack are paired to the right of the environment.
So operators like <function>handleA</function> that pass
extra inputs to their subcommands can be designed for use with the notation
by pairing the values with the environment in this way.
More precisely, the type of each argument of the operator (and its result)
should have the form
<screen>
a (...(e,t1), ... tn) t
</screen>
where <replaceable>e</replaceable> is a polymorphic variable
(representing the environment)
and <replaceable>ti</replaceable> are the types of the values on the stack,
with <replaceable>t1</replaceable> being the <quote>top</quote>.
The polymorphic variable <replaceable>e</replaceable> must not occur in
<replaceable>a</replaceable>, <replaceable>ti</replaceable> or
<replaceable>t</replaceable>.
However the arrows involved need not be the same.
Here are some more examples of suitable operators:
<screen>
bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
runReader :: ... => a e c -> a' (e,State) c
runState :: ... => a e c -> a' (e,State) (c,State)
</screen>
We can supply the extra input required by commands built with the last two
by applying them to ordinary expressions, as in
<screen>
proc x -> do
        s &lt;- ...
        (|runReader (do { ... })|) s
</screen>
which adds <literal>s</literal> to the stack of inputs to the command
built using <function>runReader</function>.
</para>

<para>
The command versions of lambda abstraction and application are analogous to
the expression versions.
In particular, the beta and eta rules describe equivalences of commands.
These three features (operators, lambda abstraction and application)
are the core of the notation; everything else can be built using them,
though the results would be somewhat clumsy.
For example, we could simulate <literal>do</literal>-notation by defining
<programlisting>
bind :: Arrow a => a e b -> a (e,b) c -> a e c
u `bind` f = returnA &amp;&amp;&amp; u >>> f

bind_ :: Arrow a => a e b -> a e c -> a e c
u `bind_` f = u `bind` (arr fst >>> f)
</programlisting>
We could simulate <literal>if</literal> by defining
<programlisting>
cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
</programlisting>
</para>

</sect2>

<sect2>
<title>Differences with the paper</title>

<itemizedlist>

<listitem>
<para>Instead of a single form of arrow application (arrow tail) with two
translations, the implementation provides two forms
<quote><literal>-&lt;</literal></quote> (first-order)
and <quote><literal>-&lt;&lt;</literal></quote> (higher-order).
</para>
</listitem>

<listitem>
<para>User-defined operators are flagged with banana brackets instead of
a new <literal>form</literal> keyword.
</para>
</listitem>

</itemizedlist>

</sect2>

<sect2>
<title>Portability</title>

<para>
Although only GHC implements arrow notation directly,
there is also a preprocessor
(available from the 
<ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
that translates arrow notation into Haskell 98
for use with other Haskell systems.
You would still want to check arrow programs with GHC;
tracing type errors in the preprocessor output is not easy.
Modules intended for both GHC and the preprocessor must observe some
additional restrictions:
<itemizedlist>

<listitem>
<para>
The module must import
<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
</para>
</listitem>

<listitem>
<para>
The preprocessor cannot cope with other Haskell extensions.
These would have to go in separate modules.
</para>
</listitem>

<listitem>
<para>
Because the preprocessor targets Haskell (rather than Core),
<literal>let</literal>-bound variables are monomorphic.
</para>
</listitem>

</itemizedlist>
</para>

</sect2>

</sect1>

<!-- ==================== ASSERTIONS =================  -->

<sect1 id="sec-assertions">
<title>Assertions
<indexterm><primary>Assertions</primary></indexterm>
</title>

<para>
If you want to make use of assertions in your standard Haskell code, you
could define a function like the following:
</para>

<para>

<programlisting>
assert :: Bool -> a -> a
assert False x = error "assertion failed!"
assert _     x = x
</programlisting>

</para>

<para>
which works, but gives you back a less than useful error message --
an assertion failed, but which and where?
</para>

<para>
One way out is to define an extended <function>assert</function> function which also
takes a descriptive string to include in the error message and
perhaps combine this with the use of a pre-processor which inserts
the source location where <function>assert</function> was used.
</para>

<para>
Ghc offers a helping hand here, doing all of this for you. For every
use of <function>assert</function> in the user's source:
</para>

<para>

<programlisting>
kelvinToC :: Double -> Double
kelvinToC k = assert (k &gt;= 0.0) (k+273.15)
</programlisting>

</para>

<para>
Ghc will rewrite this to also include the source location where the
assertion was made,
</para>

<para>

<programlisting>
assert pred val ==> assertError "Main.hs|15" pred val
</programlisting>

</para>

<para>
The rewrite is only performed by the compiler when it spots
applications of <function>Control.Exception.assert</function>, so you
can still define and use your own versions of
<function>assert</function>, should you so wish. If not, import
<literal>Control.Exception</literal> to make use
<function>assert</function> in your code.
</para>

<para>
GHC ignores assertions when optimisation is turned on with the
      <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag.  That is, expressions of the form
<literal>assert pred e</literal> will be rewritten to
<literal>e</literal>.  You can also disable assertions using the
      <option>-fignore-asserts</option>
      option<indexterm><primary><option>-fignore-asserts</option></primary>
      </indexterm>.</para>

<para>
Assertion failures can be caught, see the documentation for the
<literal>Control.Exception</literal> library for the details.
</para>

</sect1>


<!-- =============================== PRAGMAS ===========================  -->

  <sect1 id="pragmas">
    <title>Pragmas</title>

    <indexterm><primary>pragma</primary></indexterm>

    <para>GHC supports several pragmas, or instructions to the
    compiler placed in the source code.  Pragmas don't normally affect
    the meaning of the program, but they might affect the efficiency
    of the generated code.</para>

    <para>Pragmas all take the form

<literal>{-# <replaceable>word</replaceable> ... #-}</literal>  

    where <replaceable>word</replaceable> indicates the type of
    pragma, and is followed optionally by information specific to that
    type of pragma.  Case is ignored in
    <replaceable>word</replaceable>.  The various values for
    <replaceable>word</replaceable> that GHC understands are described
    in the following sections; any pragma encountered with an
    unrecognised <replaceable>word</replaceable> is (silently)
    ignored.</para>

    <sect2 id="deprecated-pragma">
      <title>DEPRECATED pragma</title>
      <indexterm><primary>DEPRECATED</primary>
      </indexterm>

      <para>The DEPRECATED pragma lets you specify that a particular
      function, class, or type, is deprecated.  There are two
      forms.

      <itemizedlist>
	<listitem>
	  <para>You can deprecate an entire module thus:</para>
<programlisting>
   module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
     ...
</programlisting>
	  <para>When you compile any module that import
          <literal>Wibble</literal>, GHC will print the specified
          message.</para>
	</listitem>

	<listitem>
	  <para>You can deprecate a function, class, type, or data constructor, with the
	  following top-level declaration:</para>
<programlisting>
   {-# DEPRECATED f, C, T "Don't use these" #-}
</programlisting>
	  <para>When you compile any module that imports and uses any
          of the specified entities, GHC will print the specified
          message.</para>
	  <para> You can only depecate entities declared at top level in the module
	  being compiled, and you can only use unqualified names in the list of
	  entities being deprecated.  A capitalised name, such as <literal>T</literal>
	  refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
	  <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
	  both are in scope.  If both are in scope, there is currently no way to deprecate 
	  one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
	</listitem>
      </itemizedlist>
      Any use of the deprecated item, or of anything from a deprecated
      module, will be flagged with an appropriate message.  However,
      deprecations are not reported for
      (a) uses of a deprecated function within its defining module, and
      (b) uses of a deprecated function in an export list.
      The latter reduces spurious complaints within a library
      in which one module gathers together and re-exports 
      the exports of several others.
      </para>
      <para>You can suppress the warnings with the flag
      <option>-fno-warn-deprecations</option>.</para>
    </sect2>

    <sect2 id="include-pragma">
      <title>INCLUDE pragma</title>

      <para>The <literal>INCLUDE</literal> pragma is for specifying the names
	of C header files that should be <literal>#include</literal>'d into
	the C source code generated by the compiler for the current module (if
	compiling via C).  For example:</para>

<programlisting>
{-# INCLUDE "foo.h" #-}
{-# INCLUDE &lt;stdio.h&gt; #-}</programlisting>

      <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
	your source file with any <literal>OPTIONS_GHC</literal>
	pragma(s).</para>

      <para>An <literal>INCLUDE</literal> pragma is  the preferred alternative
	to the <option>-#include</option> option (<xref
	  linkend="options-C-compiler" />), because the
	<literal>INCLUDE</literal> pragma is understood by other
	compilers.  Yet another alternative is to add the include file to each
	<literal>foreign import</literal> declaration in your code, but we
	don't recommend using this approach with GHC.</para>
    </sect2>

    <sect2 id="inline-noinline-pragma">
      <title>INLINE and NOINLINE pragmas</title>

      <para>These pragmas control the inlining of function
      definitions.</para>

      <sect3 id="inline-pragma">
	<title>INLINE pragma</title>
	<indexterm><primary>INLINE</primary></indexterm>

	<para>GHC (with <option>-O</option>, as always) tries to
        inline (or &ldquo;unfold&rdquo;) functions/values that are
        &ldquo;small enough,&rdquo; thus avoiding the call overhead
        and possibly exposing other more-wonderful optimisations.
        Normally, if GHC decides a function is &ldquo;too
        expensive&rdquo; to inline, it will not do so, nor will it
        export that unfolding for other modules to use.</para>

        <para>The sledgehammer you can bring to bear is the
        <literal>INLINE</literal><indexterm><primary>INLINE
        pragma</primary></indexterm> pragma, used thusly:</para>

<programlisting>
key_function :: Int -> String -> (Bool, Double)

#ifdef __GLASGOW_HASKELL__
{-# INLINE key_function #-}
#endif
</programlisting>

	<para>(You don't need to do the C pre-processor carry-on
        unless you're going to stick the code through HBC&mdash;it
        doesn't like <literal>INLINE</literal> pragmas.)</para>

        <para>The major effect of an <literal>INLINE</literal> pragma
        is to declare a function's &ldquo;cost&rdquo; to be very low.
        The normal unfolding machinery will then be very keen to
        inline it.</para>

	<para>Syntactically, an <literal>INLINE</literal> pragma for a
        function can be put anywhere its type signature could be
        put.</para>

	<para><literal>INLINE</literal> pragmas are a particularly
        good idea for the
        <literal>then</literal>/<literal>return</literal> (or
        <literal>bind</literal>/<literal>unit</literal>) functions in
        a monad.  For example, in GHC's own
        <literal>UniqueSupply</literal> monad code, we have:</para>

<programlisting>
#ifdef __GLASGOW_HASKELL__
{-# INLINE thenUs #-}
{-# INLINE returnUs #-}
#endif
</programlisting>

	<para>See also the <literal>NOINLINE</literal> pragma (<xref
        linkend="noinline-pragma"/>).</para>
      </sect3>

      <sect3 id="noinline-pragma">
	<title>NOINLINE pragma</title>
	
	<indexterm><primary>NOINLINE</primary></indexterm>
	<indexterm><primary>NOTINLINE</primary></indexterm>

	<para>The <literal>NOINLINE</literal> pragma does exactly what
        you'd expect: it stops the named function from being inlined
        by the compiler.  You shouldn't ever need to do this, unless
        you're very cautious about code size.</para>

	<para><literal>NOTINLINE</literal> is a synonym for
        <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
        specified by Haskell 98 as the standard way to disable
        inlining, so it should be used if you want your code to be
        portable).</para>
      </sect3>

      <sect3 id="phase-control">
	<title>Phase control</title>

	<para> Sometimes you want to control exactly when in GHC's
        pipeline the INLINE pragma is switched on.  Inlining happens
        only during runs of the <emphasis>simplifier</emphasis>.  Each
        run of the simplifier has a different <emphasis>phase
        number</emphasis>; the phase number decreases towards zero.
        If you use <option>-dverbose-core2core</option> you'll see the
        sequence of phase numbers for successive runs of the
        simplifier.  In an INLINE pragma you can optionally specify a
        phase number, thus:</para>

	<itemizedlist>
	  <listitem>
	    <para>You can say "inline <literal>f</literal> in Phase 2
            and all subsequent phases":
<programlisting>
  {-# INLINE [2] f #-}
</programlisting>
            </para>
	  </listitem>

	  <listitem>
	    <para>You can say "inline <literal>g</literal> in all
            phases up to, but not including, Phase 3":
<programlisting>
  {-# INLINE [~3] g #-}
</programlisting>
            </para>
	  </listitem>

	  <listitem>
	    <para>If you omit the phase indicator, you mean "inline in
            all phases".</para>
	  </listitem>
	</itemizedlist>

	<para>You can use a phase number on a NOINLINE pragma too:</para>

	<itemizedlist>
	  <listitem>
	    <para>You can say "do not inline <literal>f</literal>
            until Phase 2; in Phase 2 and subsequently behave as if
            there was no pragma at all":
<programlisting>
  {-# NOINLINE [2] f #-}
</programlisting>
            </para>
	  </listitem>

	  <listitem>
	    <para>You can say "do not inline <literal>g</literal> in
            Phase 3 or any subsequent phase; before that, behave as if
            there was no pragma":
<programlisting>
  {-# NOINLINE [~3] g #-}
</programlisting>
            </para>
	  </listitem>

	  <listitem>
	    <para>If you omit the phase indicator, you mean "never
            inline this function".</para>
	  </listitem>
	</itemizedlist>

	<para>The same phase-numbering control is available for RULES
	(<xref linkend="rewrite-rules"/>).</para>
      </sect3>
    </sect2>

    <sect2 id="language-pragma">
      <title>LANGUAGE pragma</title>

      <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
      <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>

      <para>This allows language extensions to be enabled in a portable way.
	It is the intention that all Haskell compilers support the
	<literal>LANGUAGE</literal> pragma with the same syntax, although not
	all extensions are supported by all compilers, of
	course.  The <literal>LANGUAGE</literal> pragma should be used instead
	of <literal>OPTIONS_GHC</literal>, if possible.</para>

      <para>For example, to enable the FFI and preprocessing with CPP:</para>

<programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>

      <para>Any extension from the <literal>Extension</literal> type defined in
	<ulink
	  url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used.  GHC will report an error if any of the requested extensions are not supported.</para>
    </sect2>


    <sect2 id="line-pragma">
      <title>LINE pragma</title>

      <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
      <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
      <para>This pragma is similar to C's <literal>&num;line</literal>
      pragma, and is mainly for use in automatically generated Haskell
      code.  It lets you specify the line number and filename of the
      original code; for example</para>

<programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>

      <para>if you'd generated the current file from something called
      <filename>Foo.vhs</filename> and this line corresponds to line
      42 in the original.  GHC will adjust its error messages to refer
      to the line/file named in the <literal>LINE</literal>
      pragma.</para>
    </sect2>

    <sect2 id="options-pragma">
      <title>OPTIONS_GHC pragma</title>
      <indexterm><primary>OPTIONS_GHC</primary>
      </indexterm>
      <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
      </indexterm>

      <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
      additional options that are given to the compiler when compiling
      this source file.  See <xref linkend="source-file-options"/> for
      details.</para>

      <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
	than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
    </sect2>

    <sect2 id="rules">
      <title>RULES pragma</title>

      <para>The RULES pragma lets you specify rewrite rules.  It is
      described in <xref linkend="rewrite-rules"/>.</para>
    </sect2>

    <sect2 id="specialize-pragma">
      <title>SPECIALIZE pragma</title>

      <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
      <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
      <indexterm><primary>overloading, death to</primary></indexterm>

      <para>(UK spelling also accepted.)  For key overloaded
      functions, you can create extra versions (NB: more code space)
      specialised to particular types.  Thus, if you have an
      overloaded function:</para>

<programlisting>
  hammeredLookup :: Ord key => [(key, value)] -> key -> value
</programlisting>

      <para>If it is heavily used on lists with
      <literal>Widget</literal> keys, you could specialise it as
      follows:</para>

<programlisting>
  {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
</programlisting>

      <para>A <literal>SPECIALIZE</literal> pragma for a function can
      be put anywhere its type signature could be put.</para>

      <para>A <literal>SPECIALIZE</literal> has the effect of generating
      (a) a specialised version of the function and (b) a rewrite rule
      (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
      un-specialised function into a call to the specialised one.</para>

      <para>The type in a SPECIALIZE pragma can be any type that is less
	polymorphic than the type of the original function.  In concrete terms,
	if the original function is <literal>f</literal> then the pragma
<programlisting>
  {-# SPECIALIZE f :: &lt;type&gt; #-}
</programlisting>
      is valid if and only if the defintion
<programlisting>
  f_spec :: &lt;type&gt;
  f_spec = f
</programlisting>
      is valid.  Here are some examples (where we only give the type signature
      for the original function, not its code):
<programlisting>
  f :: Eq a => a -> b -> b
  {-# SPECIALISE f :: Int -> b -> b #-}

  g :: (Eq a, Ix b) => a -> b -> b
  {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}

  h :: Eq a => a -> a -> a
  {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
</programlisting>  
The last of these examples will generate a 
RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
well.  If you use this kind of specialisation, let us know how well it works.
</para>

<para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
<literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally 
followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
The <literal>INLINE</literal> pragma affects the specialised verison of the
function (only), and applies even if the function is recursive.  The motivating
example is this:
<programlisting>
-- A GADT for arrays with type-indexed representation
data Arr e where
  ArrInt :: !Int -> ByteArray# -> Arr Int
  ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)

(!:) :: Arr e -> Int -> e
{-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
{-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
(ArrInt _ ba)     !: (I# i) = I# (indexIntArray# ba i)
(ArrPair _ a1 a2) !: i      = (a1 !: i, a2 !: i)
</programlisting>
Here, <literal>(!:)</literal> is a recursive function that indexes arrays
of type <literal>Arr e</literal>.  Consider a call to  <literal>(!:)</literal>
at type <literal>(Int,Int)</literal>.  The second specialisation will fire, and
the specialised function will be inlined.  It has two calls to
<literal>(!:)</literal>,
both at type <literal>Int</literal>.  Both these calls fire the first
specialisation, whose body is also inlined.  The result is a type-based
unrolling of the indexing function.</para>
<para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
on an ordinarily-recursive function.</para>

      <para>Note: In earlier versions of GHC, it was possible to provide your own
      specialised function for a given type:

<programlisting>
{-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
</programlisting>

      This feature has been removed, as it is now subsumed by the
      <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>

    </sect2>

<sect2 id="specialize-instance-pragma">
<title>SPECIALIZE instance pragma
</title>

<para>
<indexterm><primary>SPECIALIZE pragma</primary></indexterm>
<indexterm><primary>overloading, death to</primary></indexterm>
Same idea, except for instance declarations.  For example:

<programlisting>
instance (Eq a) => Eq (Foo a) where { 
   {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
   ... usual stuff ...
 }
</programlisting>
The pragma must occur inside the <literal>where</literal> part
of the instance declaration.
</para>
<para>
Compatible with HBC, by the way, except perhaps in the placement
of the pragma.
</para>

</sect2>

    <sect2 id="unpack-pragma">
      <title>UNPACK pragma</title>

      <indexterm><primary>UNPACK</primary></indexterm>
      
      <para>The <literal>UNPACK</literal> indicates to the compiler
      that it should unpack the contents of a constructor field into
      the constructor itself, removing a level of indirection.  For
      example:</para>

<programlisting>
data T = T {-# UNPACK #-} !Float
           {-# UNPACK #-} !Float
</programlisting>

      <para>will create a constructor <literal>T</literal> containing
      two unboxed floats.  This may not always be an optimisation: if
      the <function>T</function> constructor is scrutinised and the
      floats passed to a non-strict function for example, they will
      have to be reboxed (this is done automatically by the
      compiler).</para>

      <para>Unpacking constructor fields should only be used in
      conjunction with <option>-O</option>, in order to expose
      unfoldings to the compiler so the reboxing can be removed as
      often as possible.  For example:</para>

<programlisting>
f :: T -&#62; Float
f (T f1 f2) = f1 + f2
</programlisting>

      <para>The compiler will avoid reboxing <function>f1</function>
      and <function>f2</function> by inlining <function>+</function>
      on floats, but only when <option>-O</option> is on.</para>

      <para>Any single-constructor data is eligible for unpacking; for
      example</para>

<programlisting>
data T = T {-# UNPACK #-} !(Int,Int)
</programlisting>

      <para>will store the two <literal>Int</literal>s directly in the
      <function>T</function> constructor, by flattening the pair.
      Multi-level unpacking is also supported:</para>

<programlisting>
data T = T {-# UNPACK #-} !S
data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
</programlisting>

      <para>will store two unboxed <literal>Int&num;</literal>s
      directly in the <function>T</function> constructor.  The
      unpacker can see through newtypes, too.</para>

      <para>If a field cannot be unpacked, you will not get a warning,
      so it might be an idea to check the generated code with
      <option>-ddump-simpl</option>.</para>

      <para>See also the <option>-funbox-strict-fields</option> flag,
      which essentially has the effect of adding
      <literal>{-#&nbsp;UNPACK&nbsp;#-}</literal> to every strict
      constructor field.</para>
    </sect2>

</sect1>

<!--  ======================= REWRITE RULES ======================== -->

<sect1 id="rewrite-rules">
<title>Rewrite rules

<indexterm><primary>RULES pragma</primary></indexterm>
<indexterm><primary>pragma, RULES</primary></indexterm>
<indexterm><primary>rewrite rules</primary></indexterm></title>

<para>
The programmer can specify rewrite rules as part of the source program
(in a pragma).  GHC applies these rewrite rules wherever it can, provided (a) 
the <option>-O</option> flag (<xref linkend="options-optimise"/>) is on, 
and (b) the <option>-frules-off</option> flag
(<xref linkend="options-f"/>) is not specified.
</para>

<para>
Here is an example:

<programlisting>
  {-# RULES
        "map/map"       forall f g xs. map f (map g xs) = map (f.g) xs
  #-}
</programlisting>

</para>

<sect2>
<title>Syntax</title>

<para>
From a syntactic point of view:

<itemizedlist>
<listitem>

<para>
 There may be zero or more rules in a <literal>RULES</literal> pragma.
</para>
</listitem>

<listitem>

<para>
 Each rule has a name, enclosed in double quotes.  The name itself has
no significance at all.  It is only used when reporting how many times the rule fired.
</para>
</listitem>

<listitem>
<para>
A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
immediately after the name of the rule.  Thus:
<programlisting>
  {-# RULES
        "map/map" [2]  forall f g xs. map f (map g xs) = map (f.g) xs
  #-}
</programlisting>
The "[2]" means that the rule is active in Phase 2 and subsequent phases.  The inverse
notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
Phase 2.
</para>
</listitem>


<listitem>

<para>
 Layout applies in a <literal>RULES</literal> pragma.  Currently no new indentation level
is set, so you must lay out your rules starting in the same column as the
enclosing definitions.
</para>
</listitem>

<listitem>

<para>
 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>).  The variables bound by
the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables.  They are separated
by spaces, just like in a type <literal>forall</literal>.
</para>
</listitem>
<listitem>

<para>
 A pattern variable may optionally have a type signature.
If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
For example, here is the <literal>foldr/build</literal> rule:

<programlisting>
"fold/build"  forall k z (g::forall b. (a->b->b) -> b -> b) .
              foldr k z (build g) = g k z
</programlisting>

Since <function>g</function> has a polymorphic type, it must have a type signature.

</para>
</listitem>
<listitem>

<para>
The left hand side of a rule must consist of a top-level variable applied
to arbitrary expressions.  For example, this is <emphasis>not</emphasis> OK:

<programlisting>
"wrong1"   forall e1 e2.  case True of { True -> e1; False -> e2 } = e1
"wrong2"   forall f.      f True = True
</programlisting>

In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
in the head.
</para>
</listitem>
<listitem>

<para>
 A rule does not need to be in the same module as (any of) the
variables it mentions, though of course they need to be in scope.
</para>
</listitem>
<listitem>

<para>
 Rules are automatically exported from a module, just as instance declarations are.
</para>
</listitem>

</itemizedlist>

</para>

</sect2>

<sect2>
<title>Semantics</title>

<para>
From a semantic point of view:

<itemizedlist>
<listitem>

<para>
Rules are only applied if you use the <option>-O</option> flag.
</para>
</listitem>

<listitem>
<para>
 Rules are regarded as left-to-right rewrite rules.
When GHC finds an expression that is a substitution instance of the LHS
of a rule, it replaces the expression by the (appropriately-substituted) RHS.
By "a substitution instance" we mean that the LHS can be made equal to the
expression by substituting for the pattern variables.

</para>
</listitem>
<listitem>

<para>
 The LHS and RHS of a rule are typechecked, and must have the
same type.

</para>
</listitem>
<listitem>

<para>
 GHC makes absolutely no attempt to verify that the LHS and RHS
of a rule have the same meaning.  That is undecidable in general, and
infeasible in most interesting cases.  The responsibility is entirely the programmer's!

</para>
</listitem>
<listitem>

<para>
 GHC makes no attempt to make sure that the rules are confluent or
terminating.  For example:

<programlisting>
  "loop"        forall x,y.  f x y = f y x
</programlisting>

This rule will cause the compiler to go into an infinite loop.

</para>
</listitem>
<listitem>

<para>
 If more than one rule matches a call, GHC will choose one arbitrarily to apply.

</para>
</listitem>
<listitem>
<para>
 GHC currently uses a very simple, syntactic, matching algorithm
for matching a rule LHS with an expression.  It seeks a substitution
which makes the LHS and expression syntactically equal modulo alpha
conversion.  The pattern (rule), but not the expression, is eta-expanded if
necessary.  (Eta-expanding the expression can lead to laziness bugs.)
But not beta conversion (that's called higher-order matching).
</para>

<para>
Matching is carried out on GHC's intermediate language, which includes
type abstractions and applications.  So a rule only matches if the
types match too.  See <xref linkend="rule-spec"/> below.
</para>
</listitem>
<listitem>

<para>
 GHC keeps trying to apply the rules as it optimises the program.
For example, consider:

<programlisting>
  let s = map f
      t = map g
  in
  s (t xs)
</programlisting>

The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
not be substituted, and the rule would not fire.

</para>
</listitem>
<listitem>

<para>
 In the earlier phases of compilation, GHC inlines <emphasis>nothing
that appears on the LHS of a rule</emphasis>, because once you have substituted
for something you can't match against it (given the simple minded
matching).  So if you write the rule

<programlisting>
        "map/map"       forall f,g.  map f . map g = map (f.g)
</programlisting>

this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
It will only match something written with explicit use of ".".
Well, not quite.  It <emphasis>will</emphasis> match the expression

<programlisting>
wibble f g xs
</programlisting>

where <function>wibble</function> is defined:

<programlisting>
wibble f g = map f . map g
</programlisting>

because <function>wibble</function> will be inlined (it's small).

Later on in compilation, GHC starts inlining even things on the
LHS of rules, but still leaves the rules enabled.  This inlining
policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.

</para>
</listitem>
<listitem>

<para>
 All rules are implicitly exported from the module, and are therefore
in force in any module that imports the module that defined the rule, directly
or indirectly.  (That is, if A imports B, which imports C, then C's rules are
in force when compiling A.)  The situation is very similar to that for instance
declarations.
</para>
</listitem>

</itemizedlist>

</para>

</sect2>

<sect2>
<title>List fusion</title>

<para>
The RULES mechanism is used to implement fusion (deforestation) of common list functions.
If a "good consumer" consumes an intermediate list constructed by a "good producer", the
intermediate list should be eliminated entirely.
</para>

<para>
The following are good producers:

<itemizedlist>
<listitem>

<para>
 List comprehensions
</para>
</listitem>
<listitem>

<para>
 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
</para>
</listitem>
<listitem>

<para>
 Explicit lists (e.g. <literal>[True, False]</literal>)
</para>
</listitem>
<listitem>

<para>
 The cons constructor (e.g <literal>3:4:[]</literal>)
</para>
</listitem>
<listitem>

<para>
 <function>++</function>
</para>
</listitem>

<listitem>
<para>
 <function>map</function>
</para>
</listitem>

<listitem>
<para>
 <function>filter</function>
</para>
</listitem>
<listitem>

<para>
 <function>iterate</function>, <function>repeat</function>
</para>
</listitem>
<listitem>

<para>
 <function>zip</function>, <function>zipWith</function>
</para>
</listitem>

</itemizedlist>

</para>

<para>
The following are good consumers:

<itemizedlist>
<listitem>

<para>
 List comprehensions
</para>
</listitem>
<listitem>

<para>
 <function>array</function> (on its second argument)
</para>
</listitem>
<listitem>

<para>
 <function>length</function>
</para>
</listitem>
<listitem>

<para>
 <function>++</function> (on its first argument)
</para>
</listitem>

<listitem>
<para>
 <function>foldr</function>
</para>
</listitem>

<listitem>
<para>
 <function>map</function>
</para>
</listitem>
<listitem>

<para>
 <function>filter</function>
</para>
</listitem>
<listitem>

<para>
 <function>concat</function>
</para>
</listitem>
<listitem>

<para>
 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
</para>
</listitem>
<listitem>

<para>
 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
will fuse with one but not the other)
</para>
</listitem>
<listitem>

<para>
 <function>partition</function>
</para>
</listitem>
<listitem>

<para>
 <function>head</function>
</para>
</listitem>
<listitem>

<para>
 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
</para>
</listitem>
<listitem>

<para>
 <function>sequence&lowbar;</function>
</para>
</listitem>
<listitem>

<para>
 <function>msum</function>
</para>
</listitem>
<listitem>

<para>
 <function>sortBy</function>
</para>
</listitem>

</itemizedlist>

</para>

 <para>
So, for example, the following should generate no intermediate lists:

<programlisting>
array (1,10) [(i,i*i) | i &#60;- map (+ 1) [0..9]]
</programlisting>

</para>

<para>
This list could readily be extended; if there are Prelude functions that you use
a lot which are not included, please tell us.
</para>

<para>
If you want to write your own good consumers or producers, look at the
Prelude definitions of the above functions to see how to do so.
</para>

</sect2>

<sect2 id="rule-spec">
<title>Specialisation
</title>

<para>
Rewrite rules can be used to get the same effect as a feature
present in earlier versions of GHC.
For example, suppose that:

<programlisting>
genericLookup :: Ord a => Table a b   -> a   -> b
intLookup     ::          Table Int b -> Int -> b
</programlisting>

where <function>intLookup</function> is an implementation of
<function>genericLookup</function> that works very fast for
keys of type <literal>Int</literal>.  You might wish
to tell GHC to use <function>intLookup</function> instead of
<function>genericLookup</function> whenever the latter was called with
type <literal>Table Int b -&gt; Int -&gt; b</literal>.
It used to be possible to write

<programlisting>
{-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
</programlisting>

This feature is no longer in GHC, but rewrite rules let you do the same thing:

<programlisting>
{-# RULES "genericLookup/Int" genericLookup = intLookup #-}
</programlisting>

This slightly odd-looking rule instructs GHC to replace
<function>genericLookup</function> by <function>intLookup</function>
<emphasis>whenever the types match</emphasis>.
What is more, this rule does not need to be in the same
file as <function>genericLookup</function>, unlike the
<literal>SPECIALIZE</literal> pragmas which currently do (so that they
have an original definition available to specialise).
</para>

<para>It is <emphasis>Your Responsibility</emphasis> to make sure that
<function>intLookup</function> really behaves as a specialised version
of <function>genericLookup</function>!!!</para>

<para>An example in which using <literal>RULES</literal> for
specialisation will Win Big:

<programlisting>
toDouble :: Real a => a -> Double
toDouble = fromRational . toRational

{-# RULES "toDouble/Int" toDouble = i2d #-}
i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
</programlisting>

The <function>i2d</function> function is virtually one machine
instruction; the default conversion&mdash;via an intermediate
<literal>Rational</literal>&mdash;is obscenely expensive by
comparison.
</para>

</sect2>

<sect2>
<title>Controlling what's going on</title>

<para>

<itemizedlist>
<listitem>

<para>
 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
</para>
</listitem>
<listitem>

<para>
 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
If you add <option>-dppr-debug</option> you get a more detailed listing.
</para>
</listitem>
<listitem>

<para>
 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:

<programlisting>
        build   :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
        {-# INLINE build #-}
        build g = g (:) []
</programlisting>

Notice the <literal>INLINE</literal>!  That prevents <literal>(:)</literal> from being inlined when compiling
<literal>PrelBase</literal>, so that an importing module will &ldquo;see&rdquo; the <literal>(:)</literal>, and can
match it on the LHS of a rule.  <literal>INLINE</literal> prevents any inlining happening
in the RHS of the <literal>INLINE</literal> thing.  I regret the delicacy of this.

</para>
</listitem>
<listitem>

<para>
 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
see how to write rules that will do fusion and yet give an efficient
program even if fusion doesn't happen.  More rules in <filename>GHC/List.lhs</filename>.
</para>
</listitem>

</itemizedlist>

</para>

</sect2>

<sect2 id="core-pragma">
  <title>CORE pragma</title>

  <indexterm><primary>CORE pragma</primary></indexterm>
  <indexterm><primary>pragma, CORE</primary></indexterm>
  <indexterm><primary>core, annotation</primary></indexterm>

<para>
  The external core format supports <quote>Note</quote> annotations;
  the <literal>CORE</literal> pragma gives a way to specify what these
  should be in your Haskell source code.  Syntactically, core
  annotations are attached to expressions and take a Haskell string
  literal as an argument.  The following function definition shows an
  example:

<programlisting>
f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
</programlisting>

  Semantically, this is equivalent to:

<programlisting>
g x = show x
</programlisting>
</para>

<para>
  However, when external for is generated (via
  <option>-fext-core</option>), there will be Notes attached to the
  expressions <function>show</function> and <varname>x</varname>.
  The core function declaration for <function>f</function> is:
</para>

<programlisting>
  f :: %forall a . GHCziShow.ZCTShow a ->
                   a -> GHCziBase.ZMZN GHCziBase.Char =
    \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
        (%note "foo"
         %case zddShow %of (tpl::GHCziShow.ZCTShow a)
           {GHCziShow.ZCDShow
            (tpl1::GHCziBase.Int ->
                   a ->
                   GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
r)
            (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
            (tpl3::GHCziBase.ZMZN a ->
                   GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
r) ->
              tpl2})
        (%note "foo"
         eta);
</programlisting>

<para>
  Here, we can see that the function <function>show</function> (which
  has been expanded out to a case expression over the Show dictionary)
  has a <literal>%note</literal> attached to it, as does the
  expression <varname>eta</varname> (which used to be called
  <varname>x</varname>).
</para>

</sect2>

</sect1>

<sect1 id="generic-classes">
<title>Generic classes</title>

    <para>(Note: support for generic classes is currently broken in
    GHC 5.02).</para>

<para>
The ideas behind this extension are described in detail in "Derivable type classes",
Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
An example will give the idea:
</para>

<programlisting>
  import Generics

  class Bin a where
    toBin   :: a -> [Int]
    fromBin :: [Int] -> (a, [Int])
  
    toBin {| Unit |}    Unit	  = []
    toBin {| a :+: b |} (Inl x)   = 0 : toBin x
    toBin {| a :+: b |} (Inr y)   = 1 : toBin y
    toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
  
    fromBin {| Unit |}    bs      = (Unit, bs)
    fromBin {| a :+: b |} (0:bs)  = (Inl x, bs')    where (x,bs') = fromBin bs
    fromBin {| a :+: b |} (1:bs)  = (Inr y, bs')    where (y,bs') = fromBin bs
    fromBin {| a :*: b |} bs	  = (x :*: y, bs'') where (x,bs' ) = fromBin bs
							  (y,bs'') = fromBin bs'
</programlisting>
<para>
This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
work for arbitrary data types.  They do so by giving cases for unit, product, and sum,
which are defined thus in the library module <literal>Generics</literal>:
</para>
<programlisting>
  data Unit    = Unit
  data a :+: b = Inl a | Inr b
  data a :*: b = a :*: b
</programlisting>
<para>
Now you can make a data type into an instance of Bin like this:
<programlisting>
  instance (Bin a, Bin b) => Bin (a,b)
  instance Bin a => Bin [a]
</programlisting>
That is, just leave off the "where" clause.  Of course, you can put in the
where clause and over-ride whichever methods you please.
</para>

    <sect2>
      <title> Using generics </title>
      <para>To use generics you need to</para>
      <itemizedlist>
	<listitem>
	  <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax), 
                <option>-fgenerics</option> (to generate extra per-data-type code),
                and <option>-package lang</option> (to make the <literal>Generics</literal> library
                available.  </para>
	</listitem>
	<listitem>
	  <para>Import the module <literal>Generics</literal> from the
          <literal>lang</literal> package.  This import brings into
          scope the data types <literal>Unit</literal>,
          <literal>:*:</literal>, and <literal>:+:</literal>.  (You
          don't need this import if you don't mention these types
          explicitly; for example, if you are simply giving instance
          declarations.)</para>
	</listitem>
      </itemizedlist>
    </sect2>

<sect2> <title> Changes wrt the paper </title>
<para>
Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal> 
can be written infix (indeed, you can now use
any operator starting in a colon as an infix type constructor).  Also note that
the type constructors are not exactly as in the paper (Unit instead of 1, etc).
Finally, note that the syntax of the type patterns in the class declaration
uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
alone would ambiguous when they appear on right hand sides (an extension we 
anticipate wanting).
</para>
</sect2>

<sect2> <title>Terminology and restrictions</title>
<para>
Terminology.  A "generic default method" in a class declaration
is one that is defined using type patterns as above.
A "polymorphic default method" is a default method defined as in Haskell 98.
A "generic class declaration" is a class declaration with at least one
generic default method.
</para>

<para>
Restrictions:
<itemizedlist>
<listitem>
<para>
Alas, we do not yet implement the stuff about constructor names and 
field labels.
</para>
</listitem>

<listitem>
<para>
A generic class can have only one parameter; you can't have a generic
multi-parameter class.
</para>
</listitem>

<listitem>
<para>
A default method must be defined entirely using type patterns, or entirely
without.  So this is illegal:
<programlisting>
  class Foo a where
    op :: a -> (a, Bool)
    op {| Unit |} Unit = (Unit, True)
    op x               = (x,    False)
</programlisting>
However it is perfectly OK for some methods of a generic class to have 
generic default methods and others to have polymorphic default methods.
</para>
</listitem>

<listitem>
<para>
The type variable(s) in the type pattern for a generic method declaration
scope over the right hand side.  So this is legal (note the use of the type variable ``p'' in a type signature on the right hand side:
<programlisting>
  class Foo a where
    op :: a -> Bool
    op {| p :*: q |} (x :*: y) = op (x :: p)
    ...
</programlisting>
</para>
</listitem>

<listitem>
<para>
The type patterns in a generic default method must take one of the forms:
<programlisting>
       a :+: b
       a :*: b
       Unit
</programlisting>
where "a" and "b" are type variables.  Furthermore, all the type patterns for
a single type constructor (<literal>:*:</literal>, say) must be identical; they
must use the same type variables.  So this is illegal:
<programlisting>
  class Foo a where
    op :: a -> Bool
    op {| a :+: b |} (Inl x) = True
    op {| p :+: q |} (Inr y) = False
</programlisting>
The type patterns must be identical, even in equations for different methods of the class.
So this too is illegal:
<programlisting>
  class Foo a where
    op1 :: a -> Bool
    op1 {| a :*: b |} (x :*: y) = True

    op2 :: a -> Bool
    op2 {| p :*: q |} (x :*: y) = False
</programlisting>
(The reason for this restriction is that we gather all the equations for a particular type consructor
into a single generic instance declaration.)
</para>
</listitem>

<listitem>
<para>
A generic method declaration must give a case for each of the three type constructors.
</para>
</listitem>

<listitem>
<para>
The type for a generic method can be built only from:
  <itemizedlist>
  <listitem> <para> Function arrows </para> </listitem>
  <listitem> <para> Type variables </para> </listitem>
  <listitem> <para> Tuples </para> </listitem>
  <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
  </itemizedlist>
Here are some example type signatures for generic methods:
<programlisting>
    op1 :: a -> Bool
    op2 :: Bool -> (a,Bool)
    op3 :: [Int] -> a -> a
    op4 :: [a] -> Bool
</programlisting>
Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
inside a list.  
</para>
<para>
This restriction is an implementation restriction: we just havn't got around to
implementing the necessary bidirectional maps over arbitrary type constructors.
It would be relatively easy to add specific type constructors, such as Maybe and list,
to the ones that are allowed.</para>
</listitem>

<listitem>
<para>
In an instance declaration for a generic class, the idea is that the compiler
will fill in the methods for you, based on the generic templates.  However it can only
do so if
  <itemizedlist>
  <listitem>
  <para>
  The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
  </para>
  </listitem>
  <listitem>
  <para>
  No constructor of the instance type has unboxed fields.
  </para>
  </listitem>
  </itemizedlist>
(Of course, these things can only arise if you are already using GHC extensions.)
However, you can still give an instance declarations for types which break these rules,
provided you give explicit code to override any generic default methods.
</para>
</listitem>

</itemizedlist>
</para>

<para>
The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of 
what the compiler does with generic declarations.
</para>

</sect2>

<sect2> <title> Another example </title>
<para>
Just to finish with, here's another example I rather like:
<programlisting>
  class Tag a where
    nCons :: a -> Int
    nCons {| Unit |}    _ = 1
    nCons {| a :*: b |} _ = 1
    nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
  
    tag :: a -> Int
    tag {| Unit |}    _       = 1
    tag {| a :*: b |} _       = 1   
    tag {| a :+: b |} (Inl x) = tag x
    tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
</programlisting>
</para>
</sect2>
</sect1>



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