<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
+ url="http://www.haskell.org/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
</para>
<para>
-The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
+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>
</sect3>
-<sect3>
-<title>Type classes</title>
+<sect3 id="existential-with-context">
+<title>Existentials and type classes</title>
<para>
An easy extension is to allow
generated by the call to <literal>elem</literal>, so that the type of
<literal>insert</literal> itself has no <literal>Eq</literal> constraint.
</para>
-<para>This behaviour contrasts with Haskell 98's peculiar treatment of
-contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
-In Haskell 98 the definition
-<programlisting>
- data Eq a => Set' a = MkSet' [a]
-</programlisting>
-gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
-<emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
-on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
-GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
-GHC's behaviour is much more useful, as well as much more intuitive.</para>
<para>
-For example, a possible application of GHC's behaviour is to reify dictionaries:
+For example, one possible application is to reify dictionaries:
<programlisting>
data NumInst a where
MkNumInst :: Num a => NumInst a
Here, a value of type <literal>NumInst a</literal> is equivalent
to an explicit <literal>(Num a)</literal> dictionary.
</para>
+<para>
+All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
+For example, the <literal>NumInst</literal> data type above could equivalently be declared
+like this:
+<programlisting>
+ data NumInst a
+ = Num a => MkNumInst (NumInst a)
+</programlisting>
+Notice that, unlike the situation when declaring an existental, there is
+no <literal>forall</literal>, because the <literal>Num</literal> constrains the
+data type's univerally quantified type variable <literal>a</literal>.
+A constructor may have both universal and existential type variables: for example,
+the following two declarations are equivalent:
+<programlisting>
+ data T1 a
+ = forall b. (Num a, Eq b) => MkT1 a b
+ data T2 a where
+ MkT2 :: (Num a, Eq b) => a -> b -> T2 a
+</programlisting>
+</para>
+<para>All this behaviour contrasts with Haskell 98's peculiar treatment of
+contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
+In Haskell 98 the definition
+<programlisting>
+ data Eq a => Set' a = MkSet' [a]
+</programlisting>
+gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
+<emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
+on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
+GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
+GHC's behaviour is much more useful, as well as much more intuitive.
+</para>
<para>
The rest of this section gives further details about GADT-style data
A precise specification of the type rules is beyond what this user manual aspires to,
but the design closely follows that described in
the paper <ulink
-url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
+url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
unification-based type inference for GADTs</ulink>,
(ICFP 2006).
The general principle is this: <emphasis>type refinement is only carried out
<para>
These and many other examples are given in papers by Hongwei Xi, and
Tim Sheard. There is a longer introduction
-<ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
+<ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
and Ralf Hinze's
<ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
may use different notation to that implemented in GHC.
<para>
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
+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>
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.
+GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
</para>
</title>
<para> Functional dependencies are implemented as described by Mark Jones
-in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
+in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
In Proceedings of the 9th European Symposium on Programming,
ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
.
is a type variable that occurs in the head.
</para>
<para>
-The <option>-fglasgow-exts</option> flag loosens these restrictions
+The <option>-XFlexibleInstances</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
</para></listitem>
<listitem><para>
-The standard defaulting rule (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
+The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
is extended thus: defaulting applies when all the unresolved constraints involve standard classes
<emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
<emphasis>or</emphasis> <literal>IsString</literal>.
<sect2 id="type-restrictions">
<title>Type signatures</title>
-<sect3><title>The context of a type signature</title>
+<sect3 id="flexible-contexts"><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
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.)
+GHC has three flags to control higher-rank types:
+<itemizedlist>
+<listitem><para>
+ <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argment types.
+</para></listitem>
+<listitem><para>
+ <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
+</para></listitem>
+<listitem><para>
+ <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
+That is, you can nest <literal>forall</literal>s
+arbitrarily deep in function arrows.
In particular, a forall-type (also called a "type scheme"),
including an operational type class context, is legal:
<itemizedlist>
<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>
+</para></listitem>
+</itemizedlist>
Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
a type variable any more!
</para>
[a])</literal>.
</para>
<para>The technical details of this extension are described in the paper
-<ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
+<ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
type inference for higher-rank types and impredicativity</ulink>,
which appeared at ICFP 2006.
</para>
<para>
In Haskell, a programmer-written type signature is implicitly quantified over
its free type variables (<ulink
-url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
+url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
4.1.2</ulink>
of the Haskel Report).
Lexically scoped type variables affect this implicit quantification rules
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
+(<ulink url="http://www.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>).
+(<ulink url="http://www.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
+<ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
Haskell</ulink>,
GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
specified:
on the latter. As a result, the specification of the language extension is
also still to some degree in flux. Hence, a more detailed description of
the language extension and its use is currently available
-from <ulink url="http://haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
+from <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the Haskell
wiki page on type families</ulink>. The material will be moved to this user's
guide when it has stabilised.
</para>
Haskell.
The background to
the main technical innovations is discussed in "<ulink
-url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
+url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
</para>
<para>
There is a Wiki page about
-Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
+Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
further details.
You may also
(!) f x = 3
</programlisting>
The semantics of Haskell pattern matching is described in <ulink
-url="http://haskell.org/onlinereport/exps.html#sect3.17.2">
+url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
Section 3.17.2</ulink> of the Haskell Report. To this description add
one extra item 10, saying:
<itemizedlist><listitem><para>Matching
<literal>v</literal></para></listitem>
</itemizedlist>
</para></listitem></itemizedlist>
-Similarly, in Figure 4 of <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.3">
+Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
Section 3.17.3</ulink>, add a new case (t):
<programlisting>
case v of { !pat -> e; _ -> e' }
</programlisting>
</para><para>
That leaves let expressions, whose translation is given in
-<ulink url="http://haskell.org/onlinereport/exps.html#sect3.12">Section
+<ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
3.12</ulink>
of the Haskell Report.
In the translation box, first apply
<indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
<para>Haskell's monomorphism restriction (see
-<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
+<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
4.5.5</ulink>
of the Haskell Report)
can be completely switched off by
[x] = e -- A pattern binding
</programlisting>
Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
-default</emphasis>. Use <option>-XMonoPatBinds</option> to recover the
+default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
standard behaviour.
</para>
</sect2>
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