<indexterm><primary>extensions</primary><secondary>options controlling</secondary>
</indexterm>
- <para>These flags control what variation of the language are
+ <para>The language option flag 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
+ <para>Generally speaking, all the language options are introduced by "<option>-X</option>" or "<option>-X=</option>";
+ e.g. <option>-X=TemplateHaskell</option>. Before anything else is done, the string following
+ "<option>-X</option>" is normalised by removing hyphens and converting
+ to lower case. So <option>-X=TemplateHaskell</option>, <option>-XTemplateHaskell</option>, and
+ <option>-Xtemplate-haskell</option> are all equivalent.
+ </para>
+
+ <para> All the language options can be turned off by using the prefix "<option>No</option>";
+ e.g. "<option>-X=NoTemplateHaskell</option>".</para>
+
+ <para> Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
+ thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>>). </para>
+
+ <para> All the language options can be introduced with "<option>-f</option>" as well as "<option>-X</option>",
+ but this is a deprecated feature for backward compatibility. Use the "<option>-X</option>"
+ or LANGUAGE-pragma form.</para>
+
+ <para>Turning on an option that enables special syntax
<emphasis>might</emphasis> cause working Haskell 98 code to fail
to compile, perhaps because it uses a variable name which has
become a reserved word. So, together with each option below, we
<para>This simultaneously enables all of the extensions to
Haskell 98 described in <xref
linkend="ghc-language-features"/>, except where otherwise
- noted. </para>
+ noted. We are trying to move away from this portmanteau flag,
+ and towards enabling features individaully.</para>
<para>New reserved words: <literal>forall</literal> (only in
types), <literal>mdo</literal>.</para>
<replaceable>float</replaceable><literal>##</literal>,
<literal>(#</literal>, <literal>#)</literal>,
<literal>|)</literal>, <literal>{|</literal>.</para>
+
+ <para>Implies these specific language options:
+ <option>-X=ForeignFunctionInterface</option>,
+ <option>-X=ImplicitParams</option>,
+ <option>-X=ScopedTypeVariables</option>,
+ <option>-X=GADTs</option>,
+ <option>-X=TypeFamilies</option>. </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>
+ <option>-X=ffi</option> and <option>-X=ForeignFunctionInterface</option>:
+ <indexterm><primary><option>-X=FFI</option></primary></indexterm>
</term>
<listitem>
<para>This option enables the language extension defined in the
<varlistentry>
<term>
- <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
+ <option>-X=MonomorphismRestriction</option>,<option>-X=MonoPatBinds</option>:
</term>
<listitem>
<para> These two flags control how generalisation is done.
<varlistentry>
<term>
- <option>-fextended-default-rules</option>:
- <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
+ <option>-X=ExtendedDefaultRules</option>:
+ <indexterm><primary><option>-X=ExtendedDefaultRules</option></primary></indexterm>
</term>
<listitem>
<para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
<varlistentry>
<term>
- <option>-fallow-overlapping-instances</option>
- <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
+ <option>-X=AllowOverlappingInstances</option>
+ <indexterm><primary><option>-X=AllowOverlappingInstances</option></primary></indexterm>
</term>
<term>
- <option>-fallow-undecidable-instances</option>
- <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
+ <option>-X=AllowUndecidableInstances</option>
+ <indexterm><primary><option>-X=AllowUndecidableInstances</option></primary></indexterm>
</term>
<term>
- <option>-fallow-incoherent-instances</option>
- <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
+ <option>-X=AllowIncoherentInstances</option>
+ <indexterm><primary><option>-X=AllowIncoherentInstances</option></primary></indexterm>
</term>
<term>
<option>-fcontext-stack=N</option>
<varlistentry>
<term>
- <option>-farrows</option>
- <indexterm><primary><option>-farrows</option></primary></indexterm>
+ <option>-X=Arrows</option>
+ <indexterm><primary><option>-X=Arrows</option></primary></indexterm>
</term>
<listitem>
<para>See <xref linkend="arrow-notation"/>. Independent of
<varlistentry>
<term>
- <option>-fgenerics</option>
- <indexterm><primary><option>-fgenerics</option></primary></indexterm>
+ <option>-X=Generics</option>
+ <indexterm><primary><option>-X=Generics</option></primary></indexterm>
</term>
<listitem>
<para>See <xref linkend="generic-classes"/>. Independent of
</varlistentry>
<varlistentry>
- <term><option>-fno-implicit-prelude</option></term>
+ <term><option>-X=NoImplicitIrelude</option></term>
<listitem>
- <para><indexterm><primary>-fno-implicit-prelude
+ <para><indexterm><primary>-XnoImplicitPrelude
option</primary></indexterm> GHC normally imports
<filename>Prelude.hi</filename> files for you. If you'd
rather it didn't, then give it a
- <option>-fno-implicit-prelude</option> option. The idea is
+ <option>-XnoImplicitPrelude</option> option. The idea is
that you can then import a Prelude of your own. (But don't
call it <literal>Prelude</literal>; the Haskell module
namespace is flat, and you must not conflict with any
translation for list comprehensions continues to use
<literal>Prelude.map</literal> etc.</para>
- <para>However, <option>-fno-implicit-prelude</option> does
+ <para>However, <option>-X=NoImplicitPrelude</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>
+ <term><option>-X=ImplicitParams</option></term>
<listitem>
<para>Enables implicit parameters (see <xref
linkend="implicit-parameters"/>). Currently also implied by
</varlistentry>
<varlistentry>
- <term><option>-fscoped-type-variables</option></term>
+ <term><option>-X=OverloadedStrings</option></term>
+ <listitem>
+ <para>Enables overloaded string literals (see <xref
+ linkend="overloaded-strings"/>).</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-X=ScopedTypeVariables</option></term>
<listitem>
<para>Enables lexically-scoped type variables (see <xref
linkend="scoped-type-variables"/>). Implied by
</varlistentry>
<varlistentry>
- <term><option>-fth</option></term>
+ <term><option>-X=TH</option>, <option>-X=TemplateHaskell</option></term>
<listitem>
<para>Enables Template Haskell (see <xref
linkend="template-haskell"/>). This flag must
</sect1>
<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
-<!-- included from primitives.sgml -->
-<!-- &primitives; -->
<sect1 id="primitives">
<title>Unboxed types and primitive operations</title>
(<literal>Double#</literal> for instance).
</para>
</listitem>
+<listitem><para> You cannot define a newtype whose representation type
+(the argument type of the data constructor) is an unboxed type. Thus,
+this is illegal:
+<programlisting>
+ newtype A = MkA Int#
+</programlisting>
+</para></listitem>
<listitem><para> You cannot bind a variable with an unboxed type
in a <emphasis>top-level</emphasis> binding.
</para></listitem>
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>
-
+ hierarchically; see the accompanying <ulink
+ url="../libraries/index.html">library
+ documentation</ulink>. More libraries to install are available
+ from <ulink
+ url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
</sect2>
<!-- ====================== PATTERN GUARDS ======================= -->
</para>
<programlisting>
-clunky env var1 var1 = case lookup env var1 of
+clunky env var1 var2 = case lookup env var1 of
Nothing -> fail
Just val1 -> case lookup env var2 of
Nothing -> fail
</para>
<programlisting>
-clunky env var1 var1
+clunky env var1 var2
| Just val1 <- lookup env var1
, Just val2 <- lookup env var2
= val1 + val2
</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>
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
+ So the <option>-X=NoImplicitPrelude</option> flag causes
the following pieces of built-in syntax to refer to
<emphasis>whatever is in scope</emphasis>, not the Prelude
versions:
</sect2>
-</sect1>
+<sect2 id="disambiguate-fields">
+<title>Record field disambiguation</title>
+<para>
+In record construction and record pattern matching
+it is entirely unambiguous which field is referred to, even if there are two different
+data types in scope with a common field name. For example:
+<programlisting>
+module M where
+ data S = MkS { x :: Int, y :: Bool }
+module Foo where
+ import M
-<!-- TYPE SYSTEM EXTENSIONS -->
-<sect1 id="type-extensions">
-<title>Type system extensions</title>
+ data T = MkT { x :: Int }
+
+ ok1 (MkS { x = n }) = n+1 -- Unambiguous
+ ok2 n = MkT { x = n+1 } -- Unambiguous
-<sect2>
-<title>Data types and type synonyms</title>
+ bad1 k = k { x = 3 } -- Ambiguous
+ bad2 k = x k -- Ambiguous
+</programlisting>
+Even though there are two <literal>x</literal>'s in scope,
+it is clear that the <literal>x</literal> in the pattern in the
+definition of <literal>ok1</literal> can only mean the field
+<literal>x</literal> from type <literal>S</literal>. Similarly for
+the function <literal>ok2</literal>. However, in the record update
+in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
+it is not clear which of the two types is intended.
+</para>
+<para>
+Haskell 98 regards all four as ambiguous, but with the
+<option>-fdisambiguate-record-fields</option> flag, GHC will accept
+the former two. The rules are precisely the same as those for instance
+declarations in Haskell 98, where the method names on the left-hand side
+of the method bindings in an instance declaration refer unambiguously
+to the method of that class (provided they are in scope at all), even
+if there are other variables in scope with the same name.
+This reduces the clutter of qualified names when you import two
+records from different modules that use the same field name.
+</para>
+</sect2>
+</sect1>
+
+
+<!-- TYPE SYSTEM EXTENSIONS -->
+<sect1 id="data-type-extensions">
+<title>Extensions to data types and type synonyms</title>
-<sect3 id="nullary-types">
+<sect2 id="nullary-types">
<title>Data types with no constructors</title>
<para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
<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>
+(see <xref linkend="kinding"/>).</para>
<para>Such data types have only one value, namely bottom.
Nevertheless, they can be useful when defining "phantom types".</para>
-</sect3>
+</sect2>
-<sect3 id="infix-tycons">
+<sect2 id="infix-tycons">
<title>Infix type constructors, classes, and type variables</title>
<para>
</itemizedlist>
</para>
-</sect3>
+</sect2>
-<sect3 id="type-synonyms">
+<sect2 id="type-synonyms">
<title>Liberalised type synonyms</title>
<para>
</programlisting>
because GHC does not allow unboxed tuples on the left of a function arrow.
</para>
-</sect3>
+</sect2>
-<sect3 id="existential-quantification">
+<sect2 id="existential-quantification">
<title>Existentially quantified data constructors
</title>
quite a bit of object-oriented-like programming this way.
</para>
-<sect4 id="existential">
+<sect3 id="existential">
<title>Why existential?
</title>
adding a new existential quantification construct.
</para>
-</sect4>
+</sect3>
-<sect4>
+<sect3>
<title>Type classes</title>
<para>
universal quantification earlier.
</para>
-</sect4>
+</sect3>
-<sect4>
+<sect3 id="existential-records">
<title>Record Constructors</title>
<para>
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
+<literal>_inc</literal> or <literal>_display</literal> as functions will raise a
compile-time error. In other words, <emphasis>GHC defines a record selector function
only for fields whose type does not mention the existentially-quantified variables</emphasis>.
(This example used an underscore in the fields for which record selectors
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:
</para>
-</sect4>
+</sect3>
-<sect4>
+<sect3>
<title>Restrictions</title>
<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:#
+Reason: in most cases it would not make sense. For example:;
<programlisting>
data T = forall a. MkT [a] deriving( Eq )
</para>
-</sect4>
</sect3>
-
</sect2>
+<!-- ====================== Generalised algebraic data types ======================= -->
+<sect2 id="gadt-style">
+<title>Declaring data types with explicit constructor signatures</title>
-<sect2 id="multi-param-type-classes">
-<title>Class declarations</title>
-
-<para>
-This section, and the next one, documents GHC's type-class extensions.
-There's lots of background in the paper <ulink
-url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
-classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
-Jones, Erik Meijer).
-</para>
-<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:
-
-
+<para>GHC allows you to declare an algebraic data type by
+giving the type signatures of constructors explicitly. For example:
<programlisting>
- class Collection c a where
- union :: c a -> c a -> c a
- ...etc.
+ data Maybe a where
+ Nothing :: Maybe a
+ Just :: a -> Maybe a
</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:
-
-
+The form is called a "GADT-style declaration"
+because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
+can only be declared using this form.</para>
+<para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
+For example, these two declarations are equivalent:
<programlisting>
- class Functor (m k) => FiniteMap m k where
- ...
-
- class (Monad m, Monad (t m)) => Transform t m where
- lift :: m a -> (t m) a
+ data Foo = forall a. MkFoo a (a -> Bool)
+ data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
</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:
-
-
+<para>Any data type that can be declared in standard Haskell-98 syntax
+can also be declared using GADT-style syntax.
+The choice is largely stylistic, but GADT-style declarations differ in one important respect:
+they treat class constraints on the data constructors differently.
+Specifically, if the constructor is given a type-class context, that
+context is made available by pattern matching. For example:
<programlisting>
- class C a where {
- op :: D b => a -> b -> b
- }
-
- class C a => D a where { ... }
-</programlisting>
+ data Set a where
+ MkSet :: Eq a => [a] -> Set a
+ makeSet :: Eq a => [a] -> Set a
+ makeSet xs = MkSet (nub xs)
-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>.)
+ insert :: a -> Set a -> Set a
+ insert a (MkSet as) | a `elem` as = MkSet as
+ | otherwise = MkSet (a:as)
+</programlisting>
+A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
+gives rise to a <literal>(Eq a)</literal>
+constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
+(as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
+context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
+the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
+when pattern-matching that dictionary becomes available for the right-hand side of the match.
+In the example, the equality dictionary is used to satisfy the equality constraint
+generated by the call to <literal>elem</literal>, so that the type of
+<literal>insert</literal> itself has no <literal>Eq</literal> constraint.
</para>
-</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:
+<para>This behaviour contrasts with Haskell 98's peculiar treament of
+contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
+In Haskell 98 the defintion
<programlisting>
- class Seq s a where
- fromList :: [a] -> s a
- elem :: Eq a => a -> s a -> Bool
+ data Eq a => Set' a = MkSet' [a]
</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 “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.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,
-.
-</para>
+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>
-Functional dependencies are introduced by a vertical bar in the syntax of a
-class declaration; e.g.
+For example, a possible application of GHC's behaviour is to reify dictionaries:
<programlisting>
- class (Monad m) => MonadState s m | m -> s where ...
+ data NumInst a where
+ MkNumInst :: Num a => NumInst a
- class Foo a b c | a b -> c where ...
+ intInst :: NumInst Int
+ intInst = MkNumInst
+
+ plus :: NumInst a -> a -> a -> a
+ plus MkNumInst p q = p + q
</programlisting>
-There should be more documentation, but there isn't (yet). Yell if you need it.
+Here, a value of type <literal>NumInst a</literal> is equivalent
+to an explicit <literal>(Num a)</literal> dictionary.
</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:
+The rest of this section gives further details about GADT-style data
+type declarations.
+
+<itemizedlist>
+<listitem><para>
+The result type of each data constructor must begin with the type constructor being defined.
+If the result type of all constructors
+has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
+are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
+otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
+</para></listitem>
+<listitem><para>
+The type signature of
+each constructor is independent, and is implicitly universally quantified as usual.
+Different constructors may have different universally-quantified type variables
+and different type-class constraints.
+For example, this is fine:
<programlisting>
- class Coll s a where
- empty :: s
- insert :: s -> a -> s
+ data T a where
+ T1 :: Eq b => b -> T b
+ T2 :: (Show c, Ix c) => c -> [c] -> T c
</programlisting>
+</para></listitem>
-is not OK, because the type of <literal>empty</literal> doesn't mention
-<literal>a</literal>. Functional dependencies can make the type variable
-reachable:
+<listitem><para>
+Unlike a Haskell-98-style
+data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
+have no scope. Indeed, one can write a kind signature instead:
<programlisting>
- class Coll s a | s -> a where
- empty :: s
- insert :: s -> a -> s
+ data Set :: * -> * where ...
+</programlisting>
+or even a mixture of the two:
+<programlisting>
+ data Foo a :: (* -> *) -> * where ...
+</programlisting>
+The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
+like this:
+<programlisting>
+ data Foo a (b :: * -> *) where ...
</programlisting>
+</para></listitem>
-Alternatively <literal>Coll</literal> might be rewritten
+<listitem><para>
+You can use strictness annotations, in the obvious places
+in the constructor type:
<programlisting>
- class Coll s a where
- empty :: s a
- insert :: s a -> a -> s a
+ data Term a where
+ Lit :: !Int -> Term Int
+ If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
+ Pair :: Term a -> Term b -> Term (a,b)
</programlisting>
+</para></listitem>
+<listitem><para>
+You can use a <literal>deriving</literal> clause on a GADT-style data type
+declaration. For example, these two declarations are equivalent
+<programlisting>
+ data Maybe1 a where {
+ Nothing1 :: Maybe1 a ;
+ Just1 :: a -> Maybe1 a
+ } deriving( Eq, Ord )
-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:
+ data Maybe2 a = Nothing2 | Just2 a
+ deriving( Eq, Ord )
+</programlisting>
+</para></listitem>
+<listitem><para>
+You can use record syntax on a GADT-style data type declaration:
<programlisting>
- class CollE s where
- empty :: s
-
- class CollE s => Coll s a where
- insert :: s -> a -> s
+ data Person where
+ Adult { name :: String, children :: [Person] } :: Person
+ Child { name :: String } :: Person
</programlisting>
+As usual, for every constructor that has a field <literal>f</literal>, the type of
+field <literal>f</literal> must be the same (modulo alpha conversion).
</para>
-</sect3>
-
+<para>
+At the moment, record updates are not yet possible with GADT-style declarations,
+so support is limited to record construction, selection and pattern matching.
+For exmaple
+<programlisting>
+ aPerson = Adult { name = "Fred", children = [] }
-<sect3>
-<title>Background on functional dependencies</title>
+ shortName :: Person -> Bool
+ hasChildren (Adult { children = kids }) = not (null kids)
+ hasChildren (Child {}) = False
+</programlisting>
+</para></listitem>
-<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:
+<listitem><para>
+As in the case of existentials declared using the Haskell-98-like record syntax
+(<xref linkend="existential-records"/>),
+record-selector functions are generated only for those fields that have well-typed
+selectors.
+Here is the example of that section, in GADT-style syntax:
<programlisting>
- class Collects e ce where
- empty :: ce
- insert :: e -> ce -> ce
- member :: e -> ce -> Bool
+data Counter a where
+ NewCounter { _this :: self
+ , _inc :: self -> self
+ , _display :: self -> IO ()
+ , tag :: a
+ }
+ :: Counter a
</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
+As before, only one selector function is generated here, that for <literal>tag</literal>.
+Nevertheless, you can still use all the field names in pattern matching and record construction.
+</para></listitem>
+</itemizedlist></para>
+</sect2>
+
+<sect2 id="gadt">
+<title>Generalised Algebraic Data Types (GADTs)</title>
+
+<para>Generalised Algebraic Data Types generalise ordinary algebraic data types
+by allowing constructors to have richer return types. Here is an example:
+<programlisting>
+ data Term a where
+ Lit :: Int -> Term Int
+ Succ :: Term Int -> Term Int
+ IsZero :: Term Int -> Term Bool
+ If :: Term Bool -> Term a -> Term a -> Term a
+ Pair :: Term a -> Term b -> Term (a,b)
+</programlisting>
+Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
+case with ordinary data types. This generality allows us to
+write a well-typed <literal>eval</literal> function
+for these <literal>Terms</literal>:
+<programlisting>
+ eval :: Term a -> a
+ eval (Lit i) = i
+ eval (Succ t) = 1 + eval t
+ eval (IsZero t) = eval t == 0
+ eval (If b e1 e2) = if eval b then eval e1 else eval e2
+ eval (Pair e1 e2) = (eval e1, eval e2)
+</programlisting>
+The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
+For example, in the right hand side of the equation
+<programlisting>
+ eval :: Term a -> a
+ eval (Lit i) = ...
+</programlisting>
+the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
+A precise specification of the type rules is beyond what this user manual aspires to,
+but the design closely follows that described in
+the paper <ulink
+url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
+unification-based type inference for GADTs</ulink>,
+(ICFP 2006).
+The general principle is this: <emphasis>type refinement is only carried out
+based on user-supplied type annotations</emphasis>.
+So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
+and lots of obscure error messages will
+occur. However, the refinement is quite general. For example, if we had:
+<programlisting>
+ eval :: Term a -> a -> a
+ eval (Lit i) j = i+j
+</programlisting>
+the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
+of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
+the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
+</para>
+<para>
+These and many other examples are given in papers by Hongwei Xi, and
+Tim Sheard. There is a longer introduction
+<ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
+and Ralf Hinze's
+<ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
+may use different notation to that implemented in GHC.
+</para>
+<para>
+The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
+<option>-X=GADTs</option>.
+<itemizedlist>
+<listitem><para>
+A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
+the old Haskell-98 syntax for data declarations always declares an ordinary data type.
+The result type of each constructor must begin with the type constructor being defined,
+but for a GADT the arguments to the type constructor can be arbitrary monotypes.
+For example, in the <literal>Term</literal> data
+type above, the type of each constructor must end with <literal>Term ty</literal>, but
+the <literal>ty</literal> may not be a type variable (e.g. the <literal>Lit</literal>
+constructor).
+</para></listitem>
+
+<listitem><para>
+You cannot use a <literal>deriving</literal> clause for a GADT; only for
+an ordianary data type.
+</para></listitem>
+
+<listitem><para>
+As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
+For example:
+<programlisting>
+ data Term a where
+ Lit { val :: Int } :: Term Int
+ Succ { num :: Term Int } :: Term Int
+ Pred { num :: Term Int } :: Term Int
+ IsZero { arg :: Term Int } :: Term Bool
+ Pair { arg1 :: Term a
+ , arg2 :: Term b
+ } :: Term (a,b)
+ If { cnd :: Term Bool
+ , tru :: Term a
+ , fls :: Term a
+ } :: Term a
+</programlisting>
+However, for GADTs there is the following additional constraint:
+every constructor that has a field <literal>f</literal> must have
+the same result type (modulo alpha conversion)
+Hence, in the above example, we cannot merge the <literal>num</literal>
+and <literal>arg</literal> fields above into a
+single name. Although their field types are both <literal>Term Int</literal>,
+their selector functions actually have different types:
+
+<programlisting>
+ num :: Term Int -> Term Int
+ arg :: Term Bool -> Term Int
+</programlisting>
+</para></listitem>
+
+</itemizedlist>
+</para>
+
+</sect2>
+
+<!-- ====================== End of Generalised algebraic data types ======================= -->
+
+
+<sect2 id="deriving-typeable">
+<title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
+
+<para>
+Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
+declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
+In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
+classes <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
+</para>
+<para>
+GHC extends this list with two more classes that may be automatically derived
+(provided the <option>-fglasgow-exts</option> flag is specified):
+<literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
+modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
+appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
+</para>
+<para>An instance of <literal>Typeable</literal> can only be derived if the
+data type has seven or fewer type parameters, all of kind <literal>*</literal>.
+The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
+described in
+<ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
+Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
+</ulink>.
+(Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
+are used, and only <literal>Typeable1</literal> up to
+<literal>Typeable7</literal> are provided in the library.)
+In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
+class, whose kind suits that of the data type constructor, and
+then writing the data type instance by hand.
+</para>
+</sect2>
+
+<sect2 id="newtype-deriving">
+<title>Generalised derived instances for newtypes</title>
+
+<para>
+When you define an abstract type using <literal>newtype</literal>, you may want
+the new type to inherit some instances from its representation. In
+Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
+other classes you have to write an explicit instance declaration. For
+example, if you define
+
+<programlisting>
+ newtype Dollars = Dollars Int
+</programlisting>
+
+and you want to use arithmetic on <literal>Dollars</literal>, you have to
+explicitly define an instance of <literal>Num</literal>:
+
+<programlisting>
+ instance Num Dollars where
+ Dollars a + Dollars b = Dollars (a+b)
+ ...
+</programlisting>
+All the instance does is apply and remove the <literal>newtype</literal>
+constructor. It is particularly galling that, since the constructor
+doesn't appear at run-time, this instance declaration defines a
+dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
+dictionary, only slower!
+</para>
+
+
+<sect3> <title> Generalising the deriving clause </title>
+<para>
+GHC now permits such instances to be derived instead, so one can write
+<programlisting>
+ newtype Dollars = Dollars Int deriving (Eq,Show,Num)
+</programlisting>
+
+and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
+for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
+derives an instance declaration of the form
+
+<programlisting>
+ instance Num Int => Num Dollars
+</programlisting>
+
+which just adds or removes the <literal>newtype</literal> constructor according to the type.
+</para>
+<para>
+
+We can also derive instances of constructor classes in a similar
+way. For example, suppose we have implemented state and failure monad
+transformers, such that
+
+<programlisting>
+ instance Monad m => Monad (State s m)
+ instance Monad m => Monad (Failure m)
+</programlisting>
+In Haskell 98, we can define a parsing monad by
+<programlisting>
+ type Parser tok m a = State [tok] (Failure m) a
+</programlisting>
+
+which is automatically a monad thanks to the instance declarations
+above. With the extension, we can make the parser type abstract,
+without needing to write an instance of class <literal>Monad</literal>, via
+
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving Monad
+</programlisting>
+In this case the derived instance declaration is of the form
+<programlisting>
+ instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
+</programlisting>
+
+Notice that, since <literal>Monad</literal> is a constructor class, the
+instance is a <emphasis>partial application</emphasis> of the new type, not the
+entire left hand side. We can imagine that the type declaration is
+``eta-converted'' to generate the context of the instance
+declaration.
+</para>
+<para>
+
+We can even derive instances of multi-parameter classes, provided the
+newtype is the last class parameter. In this case, a ``partial
+application'' of the class appears in the <literal>deriving</literal>
+clause. For example, given the class
+
+<programlisting>
+ class StateMonad s m | m -> s where ...
+ instance Monad m => StateMonad s (State s m) where ...
+</programlisting>
+then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving (Monad, StateMonad [tok])
+</programlisting>
+
+The derived instance is obtained by completing the application of the
+class to the new type:
+
+<programlisting>
+ instance StateMonad [tok] (State [tok] (Failure m)) =>
+ StateMonad [tok] (Parser tok m)
+</programlisting>
+</para>
+<para>
+
+As a result of this extension, all derived instances in newtype
+ declarations are treated uniformly (and implemented just by reusing
+the dictionary for the representation type), <emphasis>except</emphasis>
+<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
+the newtype and its representation.
+</para>
+</sect3>
+
+<sect3> <title> A more precise specification </title>
+<para>
+Derived instance declarations are constructed as follows. Consider the
+declaration (after expansion of any type synonyms)
+
+<programlisting>
+ newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
+</programlisting>
+
+where
+ <itemizedlist>
+<listitem><para>
+ The <literal>ci</literal> are partial applications of
+ classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
+ is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
+</para></listitem>
+<listitem><para>
+ The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
+</para></listitem>
+<listitem><para>
+ The type <literal>t</literal> is an arbitrary type.
+</para></listitem>
+<listitem><para>
+ The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
+ nor in the <literal>ci</literal>, and
+</para></listitem>
+<listitem><para>
+ None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
+ <literal>Typeable</literal>, or <literal>Data</literal>. These classes
+ should not "look through" the type or its constructor. You can still
+ derive these classes for a newtype, but it happens in the usual way, not
+ via this new mechanism.
+</para></listitem>
+</itemizedlist>
+Then, for each <literal>ci</literal>, the derived instance
+declaration is:
+<programlisting>
+ instance ci t => ci (T v1...vk)
+</programlisting>
+As an example which does <emphasis>not</emphasis> work, consider
+<programlisting>
+ newtype NonMonad m s = NonMonad (State s m s) deriving Monad
+</programlisting>
+Here we cannot derive the instance
+<programlisting>
+ instance Monad (State s m) => Monad (NonMonad m)
+</programlisting>
+
+because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
+and so cannot be "eta-converted" away. It is a good thing that this
+<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
+not, in fact, a monad --- for the same reason. Try defining
+<literal>>>=</literal> with the correct type: you won't be able to.
+</para>
+<para>
+
+Notice also that the <emphasis>order</emphasis> of class parameters becomes
+important, since we can only derive instances for the last one. If the
+<literal>StateMonad</literal> class above were instead defined as
+
+<programlisting>
+ class StateMonad m s | m -> s where ...
+</programlisting>
+
+then we would not have been able to derive an instance for the
+<literal>Parser</literal> type above. We hypothesise that multi-parameter
+classes usually have one "main" parameter for which deriving new
+instances is most interesting.
+</para>
+<para>Lastly, all of this applies only for classes other than
+<literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
+and <literal>Data</literal>, for which the built-in derivation applies (section
+4.3.3. of the Haskell Report).
+(For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
+the standard method is used or the one described here.)
+</para>
+</sect3>
+
+</sect2>
+
+<sect2 id="stand-alone-deriving">
+<title>Stand-alone deriving declarations</title>
+
+<para>
+GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-fglasgow-exts</literal>:
+<programlisting>
+ data Foo a = Bar a | Baz String
+
+ derive instance Eq (Foo a)
+</programlisting>
+The token "<literal>derive</literal>" is a keyword only when followed by "<literal>instance</literal>";
+you can use it as a variable name elsewhere.</para>
+<para>The stand-alone syntax is generalised for newtypes in exactly the same
+way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
+For example:
+<programlisting>
+ newtype Foo a = MkFoo (State Int a)
+
+ derive instance MonadState Int Foo
+</programlisting>
+GHC always treats the <emphasis>last</emphasis> parameter of the instance
+(<literal>Foo</literal> in this exmample) as the type whose instance is being derived.
+</para>
+
+</sect2>
+
+</sect1>
+
+
+<!-- TYPE SYSTEM EXTENSIONS -->
+<sect1 id="other-type-extensions">
+<title>Other type system extensions</title>
+
+<sect2 id="multi-param-type-classes">
+<title>Class declarations</title>
+
+<para>
+This section, and the next one, documents GHC's type-class extensions.
+There's lots of background in the paper <ulink
+url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
+classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
+Jones, Erik Meijer).
+</para>
+<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 “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.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,
+.
+</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:
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 -> 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>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
-</screen>
-The part before the "<literal>=></literal>" is the
-<emphasis>context</emphasis>, while the part after the
-"<literal>=></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>-></literal>
-<replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
-every type variable in
-S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
-S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
-substitution mapping each type variable in the class declaration to the
-corresponding type in the instance declaration.
-</para></listitem>
-</orderedlist>
-These restrictions ensure that context reduction terminates: each reduction
-step makes the problem smaller by at least one
-constructor. For example, the following would make the type checker
-loop if it wasn't excluded:
-<programlisting>
- instance C a => C a where ...
-</programlisting>
-For example, these are OK:
-<programlisting>
- instance C Int [a] -- Multiple parameters
- instance Eq (S [a]) -- Structured type in head
-
- -- Repeated type variable in head
- instance C4 a a => C4 [a] [a]
- instance Stateful (ST s) (MutVar s)
-
- -- Head can consist of type variables only
- instance C a
- instance (Eq a, Show b) => C2 a b
-
- -- Non-type variables in context
- instance Show (s a) => Show (Sized s a)
- instance C2 Int a => C3 Bool [a]
- instance C2 Int a => C3 [a] b
-</programlisting>
-But these are not:
-<programlisting>
- -- Context assertion no smaller than head
- instance C a => C a where ...
- -- (C b b) has more more occurrences of b than the head
- instance C b b => Foo [b] where ...
-</programlisting>
-</para>
-
-<para>
-The same restrictions apply to instances generated by
-<literal>deriving</literal> clauses. Thus the following is accepted:
-<programlisting>
- data MinHeap h a = H a (h a)
- deriving (Show)
-</programlisting>
-because the derived instance
-<programlisting>
- instance (Show a, Show (h a)) => Show (MinHeap h a)
-</programlisting>
-conforms to the above rules.
-</para>
-
-<para>
-A useful idiom permitted by the above rules is as follows.
-If one allows overlapping instance declarations then it's quite
-convenient to have a "default instance" declaration that applies if
-something more specific does not:
-<programlisting>
- instance C a where
- op = ... -- Default
-</programlisting>
-</para>
-<para>You can find lots of background material about the reason for these
-restrictions in the paper <ulink
-url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
-Understanding functional dependencies via Constraint Handling Rules</ulink>.
-</para>
-</sect3>
-
-<sect3 id="undecidable-instances">
-<title>Undecidable instances</title>
-
-<para>
-Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
-For example, sometimes you might want to use the following to get the
-effect of a "class synonym":
-<programlisting>
- class (C1 a, C2 a, C3 a) => C a where { }
-
- instance (C1 a, C2 a, C3 a) => C a where { }
-</programlisting>
-This allows you to write shorter signatures:
-<programlisting>
- f :: C a => ...
-</programlisting>
-instead of
-<programlisting>
- f :: (C1 a, C2 a, C3 a) => ...
-</programlisting>
-The restrictions on functional dependencies (<xref
-linkend="functional-dependencies"/>) are particularly troublesome.
-It is tempting to introduce type variables in the context that do not appear in
-the head, something that is excluded by the normal rules. For example:
-<programlisting>
- class HasConverter a b | a -> b where
- convert :: a -> b
-
- data Foo a = MkFoo a
-
- instance (HasConverter a b,Show b) => Show (Foo a) where
- show (MkFoo value) = show (convert value)
-</programlisting>
-This is dangerous territory, however. Here, for example, is a program that would make the
-typechecker loop:
-<programlisting>
- class D a
- class F a b | a->b
- instance F [a] [[a]]
- instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
-</programlisting>
-Similarly, it can be tempting to lift the coverage condition:
-<programlisting>
- class Mul a b c | a b -> c where
- (.*.) :: a -> b -> c
-
- instance Mul Int Int Int where (.*.) = (*)
- instance Mul Int Float Float where x .*. y = fromIntegral x * y
- instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
+ instance D Bool Char where ...
</programlisting>
-The third instance declaration does not obey the coverage condition;
-and indeed the (somewhat strange) definition:
+Note also that the following declaration is not allowed, even by itself:
<programlisting>
- f = \ b x y -> if b then x .*. [y] else y
+ instance D [a] b where ...
</programlisting>
-makes instance inference go into a loop, because it requires the constraint
-<literal>(Mul a [b] b)</literal>.
-</para>
-<para>
-Nevertheless, GHC allows you to experiment with more liberal rules. If you use
-the experimental flag <option>-fallow-undecidable-instances</option>
-<indexterm><primary>-fallow-undecidable-instances
-option</primary></indexterm>, you can use arbitrary
-types in both an instance context and instance head. Termination is ensured by having a
-fixed-depth recursion stack. If you exceed the stack depth you get a
-sort of backtrace, and the opportunity to increase the stack depth
-with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
-</para>
-
-</sect3>
-
-
-<sect3 id="instance-overlap">
-<title>Overlapping instances</title>
-<para>
-In general, <emphasis>GHC requires that that it be unambiguous which instance
-declaration
-should be used to resolve a type-class constraint</emphasis>. This behaviour
-can be modified by two flags: <option>-fallow-overlapping-instances</option>
-<indexterm><primary>-fallow-overlapping-instances
-</primary></indexterm>
-and <option>-fallow-incoherent-instances</option>
-<indexterm><primary>-fallow-incoherent-instances
-</primary></indexterm>, as this section discusses. Both these
-flags are dynamic flags, and can be set on a per-module basis, using
-an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
-<para>
-When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
-it tries to match every instance declaration against the
-constraint,
-by instantiating the head of the instance declaration. For example, consider
-these declarations:
+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 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)
+ instance D t s where ...
</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.
+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>
-However, GHC is conservative about committing to an overlapping instance. For example:
+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>
- f :: [b] -> [b]
- f x = ...
+ class Collects e ce | ce -> e where
+ empty :: ce
+ insert :: e -> ce -> ce
+ member :: e -> ce -> Bool
</programlisting>
-Suppose that from the RHS of <literal>f</literal> we get the constraint
-<literal>C Int [b]</literal>. But
-GHC does not commit to instance (C), because in a particular
-call of <literal>f</literal>, <literal>b</literal> might be instantiate
-to <literal>Int</literal>, in which case instance (D) would be more specific still.
-So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
-GHC will instead pick (C), without complaining about
-the problem of subsequent instantiations.
-</para>
-<para>
-The willingness to be overlapped or incoherent is a property of
-the <emphasis>instance declaration</emphasis> itself, controlled by the
-presence or otherwise of the <option>-fallow-overlapping-instances</option>
-and <option>-fallow-incoherent-instances</option> flags when that mdodule is
-being defined. Neither flag is required in a module that imports and uses the
-instance declaration. Specifically, during the lookup process:
-<itemizedlist>
-<listitem><para>
-An instance declaration is ignored during the lookup process if (a) a more specific
-match is found, and (b) the instance declaration was compiled with
-<option>-fallow-overlapping-instances</option>. The flag setting for the
-more-specific instance does not matter.
-</para></listitem>
-<listitem><para>
-Suppose an instance declaration does not matche the constraint being looked up, but
-does unify with it, so that it might match when the constraint is further
-instantiated. Usually GHC will regard this as a reason for not committing to
-some other constraint. But if the instance declaration was compiled with
-<option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
-check for that declaration.
-</para></listitem>
-</itemizedlist>
-These rules make it possible for a library author to design a library that relies on
-overlapping instances without the library client having to know.
+The dependency <literal>ce -> 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>
-If an instance declaration is compiled without
-<option>-fallow-overlapping-instances</option>,
-then that instance can never be overlapped. This could perhaps be
-inconvenient. Perhaps the rule should instead say that the
-<emphasis>overlapping</emphasis> instance declaration should be compiled in
-this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
-at a usage site should be permitted regardless of how the instance declarations
-are compiled, if the <option>-fallow-overlapping-instances</option> flag is
-used at the usage site. (Mind you, the exact usage site can occasionally be
-hard to pin down.) We are interested to receive feedback on these points.
-</para>
-<para>The <option>-fallow-incoherent-instances</option> flag implies the
-<option>-fallow-overlapping-instances</option> flag, but not vice versa.
+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>
-</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:
-
-
+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>
- type Point = (Int,Int)
- instance C Point where ...
- instance C [Point] where ...
+ f x y = insert x y = insert x . insert y
</programlisting>
-
-
-is legal. However, if you added
-
-
+for which we originally obtained a type:
<programlisting>
- instance C (Int,Int) where ...
+ f :: (Collects a c, Collects b c) => a -> b -> c -> c
</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:
-
-
+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>
- type P a = [[a]]
- instance Monad P where ...
+ f :: (Collects a c) => a -> a -> c -> c
</programlisting>
-
-
-This design decision is independent of all the others, and easily
-reversed, but it makes sense to me.
-
+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="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:
+<sect2 id="instance-decls">
+<title>Instance declarations</title>
-<programlisting>
- forall tv1..tvn (c1, ...,cn) => type
-</programlisting>
+<sect3 id="instance-rules">
+<title>Relaxed rules for instance declarations</title>
-(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>An instance declaration has the form
+<screen>
+ instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
+</screen>
+The part before the "<literal>=></literal>" is the
+<emphasis>context</emphasis>, while the part after the
+"<literal>=></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>
+<listitem><para>
+The Paterson Conditions: 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>-></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. Both the Paterson Conditions and the Coverage Condition are lifted
+if you give the <option>-fallow-undecidable-instances</option>
+flag (<xref linkend="undecidable-instances"/>).
+You can find lots of background material about the reason for these
+restrictions in the paper <ulink
+url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
+Understanding functional dependencies via Constraint Handling Rules</ulink>.
+</para>
<para>
- <emphasis>Each universally quantified type variable
-<literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
+For example, these are OK:
+<programlisting>
+ instance C Int [a] -- Multiple parameters
+ instance Eq (S [a]) -- Structured type in head
-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:
+ -- 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
-<programlisting>
- forall a. Eq a => Int
+ -- 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>
-
-
-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:
+But these are not:
<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
+ -- 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>
-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>:
-
-
+The same restrictions apply to instances generated by
+<literal>deriving</literal> clauses. Thus the following is accepted:
<programlisting>
- forall a. C a b => burble
+ data MinHeap h a = H a (h a)
+ deriving (Show)
</programlisting>
-
-
-The next type is illegal because the constraint <literal>Eq b</literal> does not
-mention <literal>a</literal>:
-
-
+because the derived instance
<programlisting>
- forall a. Eq b => burble
+ instance (Show a, Show (h a)) => Show (MinHeap h a)
</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.
-
+conforms to the above rules.
</para>
-</listitem>
-
-</orderedlist>
+<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="hoist">
-<title>For-all hoisting</title>
+<sect3 id="undecidable-instances">
+<title>Undecidable instances</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:
+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>
- type Discard a = forall b. a -> b -> a
+ class (C1 a, C2 a, C3 a) => C a where { }
- g :: Int -> Discard Int
- g x y z = x+y
+ instance (C1 a, C2 a, C3 a) => C a where { }
</programlisting>
-Simply expanding the type synonym would give
+This allows you to write shorter signatures:
<programlisting>
- g :: Int -> (forall b. Int -> b -> Int)
+ f :: C a => ...
</programlisting>
-but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
+instead of
<programlisting>
- g :: forall b. Int -> Int -> b -> Int
+ f :: (C1 a, C2 a, C3 a) => ...
</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>
+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>
- <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
-==>
- forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
+ 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>
-(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:
+This is dangerous territory, however. Here, for example, is a program that would make the
+typechecker loop:
<programlisting>
- g :: Int -> Int -> forall b. b -> Int
-</programlisting>
-</para>
-<para>
-When doing this hoisting operation, GHC eliminates duplicate constraints. For
-example:
+ 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>
- type Foo a = (?x::Int) => Bool -> a
- g :: Foo (Foo Int)
+ 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>
-means
+The third instance declaration does not obey the coverage condition;
+and indeed the (somewhat strange) definition:
<programlisting>
- g :: (?x::Int) => Bool -> Bool -> Int
+ 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>
-</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>
+Nevertheless, GHC allows you to experiment with more liberal rules. If you use
+the experimental flag <option>-X=AllowUndecidableInstances</option>
+<indexterm><primary>-X=AllowUndecidableInstances</primary></indexterm>,
+both the Paterson Conditions and the Coverage Condition
+(described in <xref linkend="instance-rules"/>) are lifted. 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>
-<para>(Most of the following, stil rather incomplete, documentation is
-due to Jeff Lewis.)</para>
+</sect3>
-<para>Implicit parameter support is enabled with the option
-<option>-fimplicit-params</option>.</para>
+<sect3 id="instance-overlap">
+<title>Overlapping instances</title>
<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>
+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>-X=AllowOverlappingInstances</option>
+<indexterm><primary>-X=AllowOverlappingInstances
+</primary></indexterm>
+and <option>-X=AllowIncoherentInstances</option>
+<indexterm><primary>-X=AllowIncoherentInstances
+</primary></indexterm>, as this section discusses. Both these
+flags are dynamic flags, and can be set on a per-module basis, using
+an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
<para>
-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:
+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>
- least :: (?cmp :: a -> a -> Bool) => [a] -> a
- least xs = head (sort xs)
+ 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>
-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.
+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> 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>.
+The <option>-X=AllowOverlappingInstances</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>
-</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>.
+However, GHC is conservative about committing to an overlapping instance. For example:
<programlisting>
- min :: [a] -> a
- min = let ?cmp = (<=) in least
+ 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>-X=AllowIncoherentInstances</option>,
+GHC will instead pick (C), without complaining about
+the problem of subsequent instantiations.
</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:
+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>-X=AllowOverlappingInstances</option>
+and <option>-X=AllowIncoherentInstances</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 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.)
+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>-X=AllowOverlappingInstances</option>. The flag setting for the
+more-specific instance does not matter.
</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>
+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>-X=AllowIncoherentInstances</option>, GHC will skip the "does-it-unify?"
+check for that declaration.
</para></listitem>
</itemizedlist>
+These rules make it possible for a library author to design a library that relies on
+overlapping instances without the library client having to know.
+</para>
+<para>
+If an instance declaration is compiled without
+<option>-X=AllowOverlappingInstances</option>,
+then that instance can never be overlapped. This could perhaps be
+inconvenient. Perhaps the rule should instead say that the
+<emphasis>overlapping</emphasis> instance declaration should be compiled in
+this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
+at a usage site should be permitted regardless of how the instance declarations
+are compiled, if the <option>-X=AllowOverlappingInstances</option> flag is
+used at the usage site. (Mind you, the exact usage site can occasionally be
+hard to pin down.) We are interested to receive feedback on these points.
+</para>
+<para>The <option>-X=AllowIncoherentInstances</option> flag implies the
+<option>-X=AllowOverlappingInstances</option> flag, but not vice versa.
</para>
-
</sect3>
-<sect3><title>Implicit parameters and polymorphic recursion</title>
+<sect3>
+<title>Type synonyms in the instance head</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>
+<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:
-<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
+ type Point = (Int,Int)
+ instance C Point where ...
+ instance C [Point] where ...
</programlisting>
-Since the binding for <literal>y</literal> falls under the Monomorphism
-Restriction it is not generalised, so the type of <literal>y</literal> is
-simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
-Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
-If you add a type signature for <literal>y</literal>, then <literal>y</literal>
-will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
-<literal>y</literal> in the body of the <literal>let</literal> will see the
-inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
-<literal>14</literal>.
-</para>
-</sect3>
-</sect2>
- <!-- ======================= COMMENTED OUT ========================
- We intend to remove linear implicit parameters, so I'm at least removing
- them from the 6.6 user manual
+is legal. However, if you added
-<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 )
+ instance C (Int,Int) where ...
+</programlisting>
- data NameSupply = ...
-
- splitNS :: NameSupply -> (NameSupply, NameSupply)
- newName :: NameSupply -> Name
- instance Splittable NameSupply where
- split = splitNS
+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:
- 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)
+ type P a = [[a]]
+ instance Monad P where ...
</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>
+This design decision is independent of all the others, and easily
+reversed, but it makes sense to me.
+
</para>
+</sect3>
-<sect3><title>Warnings</title>
+</sect2>
+
+<sect2 id="type-restrictions">
+<title>Type signatures</title>
+
+<sect3><title>The context of a type signature</title>
<para>
-The monomorphism restriction is even more important than usual.
-Consider the example above:
+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>
- 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'
+ g :: Eq [a] => ...
+ g :: Ord (T a ()) => ...
</programlisting>
-If we replaced the two occurrences of x' by (newName %ns), which is
-usually a harmless thing to do, we get:
+</para>
+<para>
+GHC imposes the following restrictions on the constraints in a type signature.
+Consider the type:
+
<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)
+ forall tv1..tvn (c1, ...,cn) => type
</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.
+
+(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>
-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>
+<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:
+
-<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)
+ forall a. Eq a => Int
</programlisting>
-where T is some type in class Splittable.</para>
+
+
+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>
-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:
+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>
- foo x 0 = []
- foo x n = let (x1,x2) = split x
- in x1 : foo x2 (n-1)
+ 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>
-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
+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>
- foo x = let
- foom 0 = []
- foom n = x : foom (n-1)
- in
- foom
+ forall a. C a b => burble
</programlisting>
-Result: 'x' is not split, and you get a list of identical T's. So the
-semantics of the program depends on whether or not foo has a type signature.
-Yikes!
-</para><para>
-You may say that this is a good reason to dislike linear implicit parameters
-and you'd be right. That is why they are an experimental feature.
-</para>
-</sect3>
-</sect2>
-================ END OF Linear Implicit Parameters commented out -->
+The next type is illegal because the constraint <literal>Eq b</literal> does not
+mention <literal>a</literal>:
-<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>
+<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>
-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>
+</listitem>
+
+</orderedlist>
-<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>
+</sect3>
+
+
+
</sect2>
+<sect2 id="implicit-parameters">
+<title>Implicit parameters</title>
-<sect2 id="universal-quantification">
-<title>Arbitrary-rank polymorphism
-</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>-X=ImplicitParams</option>.</para>
<para>
-Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
-allows us to say exactly what this means. For example:
+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>
- g :: b -> b
-</programlisting>
-means this:
-<programlisting>
- g :: forall b. (b -> b)
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
</programlisting>
-The two are treated identically.
+The dynamic binding constraints are just a new form of predicate in the type class system.
</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:
+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>
- 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
+ sortBy :: (a -> a -> Bool) -> [a] -> [a]
- f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+ sort = sortBy ?cmp
</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>
+
+<sect3>
+<title>Implicit-parameter type constraints</title>
<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:
+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>
- x1 :: [forall a. a->a]
- x2 :: (forall a. a->a, Int)
- x3 :: Maybe (forall a. a->a)
+ least :: (?cmp :: a -> a -> Bool) => [a] -> a
+ least xs = head (sort xs)
</programlisting>
-Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
-a type variable any more!
+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>
-
-
-<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:
+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>
-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
- }
+ f :: (?x :: [a]) => Int -> Int
+ f n = n + length ?x
-newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
+ 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>
-The constructors have rank-2 types:
+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 = (<=) 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>
-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
+ 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>
-<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>
+</sect3>
-<para>
-As for type signatures, implicit quantification happens for non-overloaded
-types too. So if you write this:
+<sect3><title>Implicit parameters and polymorphic recursion</title>
+<para>
+Consider these two definitions:
<programlisting>
- data T a = MkT (Either a b) (b -> b)
-</programlisting>
+ len1 :: [a] -> Int
+ len1 xs = let ?acc = 0 in len_acc1 xs
-it's just as if you had written this:
+ len_acc1 [] = ?acc
+ len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
-<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>
+ len2 :: [a] -> Int
+ len2 xs = let ?acc = 0 in len_acc2 xs
-<para>
-You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
-the constructor to suitable values, just as usual. For example,
+ 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>
-<para>
+<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>
- 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]
+ f :: Int -> Int
+ f v = let ?x = 0 in
+ let y = ?x + v in
+ let ?x = 5 in
+ y
</programlisting>
+Since the binding for <literal>y</literal> falls under the Monomorphism
+Restriction it is not generalised, so the type of <literal>y</literal> is
+simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
+Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
+If you add a type signature for <literal>y</literal>, then <literal>y</literal>
+will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
+<literal>y</literal> in the body of the <literal>let</literal> will see the
+inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
+<literal>14</literal>.
+</para>
+</sect3>
+</sect2>
+
+ <!-- ======================= COMMENTED OUT ========================
-</para>
+ We intend to remove linear implicit parameters, so I'm at least removing
+ them from the 6.6 user manual
+<sect2 id="linear-implicit-parameters">
+<title>Linear implicit parameters</title>
<para>
-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.)
+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>
-When you use pattern matching, the bound variables may now have
-polymorphic types. For example:
+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>
- 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>
+ import GHC.Exts( Splittable )
-</para>
+ data NameSupply = ...
+
+ splitNS :: NameSupply -> (NameSupply, NameSupply)
+ newName :: NameSupply -> Name
-<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>
+ instance Splittable NameSupply where
+ split = splitNS
-<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>.
+ 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>
-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:
+So the translation done by the type checker makes
+the parameter explicit:
<programlisting>
- \ f :: (forall a. a->a) -> (f True, f 'c')
+ 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>
-Alternatively, you can give a type signature to the enclosing
-context, which GHC can "push down" to find the type for the variable:
+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>
- (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
+ class Splittable a where
+ split :: a -> (a,a)
</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:
+The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
+split for name supplies. But we can simply write
<programlisting>
- h :: (forall a. a->a) -> (Bool,Char)
- h f = (f True, f 'c')
+ g x = (x, %ns, %ns)
</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:
+and GHC will infer
<programlisting>
- f :: T a -> a -> (a, Char)
- f (T1 w k) x = (w k x, w 'c' 'd')
+ g :: (Splittable a, %ns :: a) => b -> (b,a,a)
</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.
+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>
-</sect3>
+<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 id="implicit-quant">
-<title>Implicit quantification</title>
+<sect3><title>Warnings</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:
+The monomorphism restriction is even more important than usual.
+Consider the example above:
<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 ...
+ 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>
-</para>
-<para>
-Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
-point. For example:
+If we replaced the two occurrences of x' by (newName %ns), which is
+usually a harmless thing to do, we get:
<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
+ 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>
-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.
+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>
-</sect2>
+</sect3>
-<sect2 id="impredicative-polymorphism">
-<title>Impredicative polymorphism
-</title>
-<para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
-that you can call a polymorphic function at a polymorphic type, and
-parameterise data structures over polymorphic types. For example:
+<sect3><title>Recursive functions</title>
+<para>Linear implicit parameters can be particularly tricky when you have a recursive function
+Consider
<programlisting>
- f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
- f (Just g) = Just (g [3], g "hello")
- f Nothing = Nothing
+ foo :: %x::T => Int -> [Int]
+ foo 0 = []
+ foo n = %x : foo (n-1)
</programlisting>
-Notice here that the <literal>Maybe</literal> type is parameterised by the
-<emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
-[a])</literal>.
-</para>
-<para>The technical details of this extension are described in the paper
-<ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
-type inference for higher-rank types and impredicativity</ulink>,
-which appeared at ICFP 2006.
-</para>
-</sect2>
-
-<sect2 id="scoped-type-variables">
-<title>Lexically scoped type variables
-</title>
-
+where T is some type in class Splittable.</para>
<para>
-GHC supports <emphasis>lexically scoped type variables</emphasis>, without
-which some type signatures are simply impossible to write. For example:
+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>
-f :: forall a. [a] -> [a]
-f xs = ys ++ ys
- where
- ys :: [a]
- ys = reverse xs
+ foo x 0 = []
+ foo x n = let (x1,x2) = split x
+ in x1 : foo x2 (n-1)
</programlisting>
-The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
-the entire definition of <literal>f</literal>.
-In particular, it is in scope at the type signature for <varname>ys</varname>.
-In Haskell 98 it is not possible to declare
-a type for <varname>ys</varname>; a major benefit of scoped type variables is that
-it becomes possible to do so.
-</para>
-<para>Lexically-scoped type variables are enabled by
-<option>-fglasgow-exts</option>.
+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>
-<para>Note: GHC 6.6 contains substantial changes to the way that scoped type
-variables work, compared to earlier releases. Read this section
-carefully!</para>
+</sect3>
-<sect3>
-<title>Overview</title>
+</sect2>
-<para>The design follows the following principles
-<itemizedlist>
-<listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
-a <emphasis>type</emphasis>. (This is a change from GHC's earlier
-design.)</para></listitem>
-<listitem><para>Furthermore, distinct lexical type variables stand for distinct
-type variables. This means that every programmer-written type signature
-(includin one that contains free scoped type variables) denotes a
-<emphasis>rigid</emphasis> type; that is, the type is fully known to the type
-checker, and no inference is involved.</para></listitem>
-<listitem><para>Lexical type variables may be alpha-renamed freely, without
-changing the program.</para></listitem>
-</itemizedlist>
+================ END OF Linear Implicit Parameters commented out -->
+
+<sect2 id="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>
-A <emphasis>lexically scoped type variable</emphasis> can be bound by:
+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>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
-<listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
-<listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
-<listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
+<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>
-In Haskell, a programmer-written type signature is implicitly quantifed over
-its free type variables (<ulink
-url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
-4.1.2</ulink>
-of the Haskel Report).
-Lexically scoped type variables affect this implicit quantification rules
-as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
-quantified. For example, if type variable <literal>a</literal> is in scope,
-then
-<programlisting>
- (e :: a -> a) means (e :: a -> a)
- (e :: b -> b) means (e :: forall b. b->b)
- (e :: a -> b) means (e :: forall b. a->b)
-</programlisting>
+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>
-</sect3>
+<sect2 id="universal-quantification">
+<title>Arbitrary-rank polymorphism
+</title>
-<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:
+<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>
- f :: forall a. [a] -> [a]
- f (x:xs) = xs ++ [ x :: a ]
+ g :: b -> b
</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:
+means this:
<programlisting>
- g :: [a] -> [a]
- g (x:xs) = xs ++ [ x :: a ]
+ g :: forall b. (b -> b)
</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.
+The two are treated identically.
</para>
-</sect3>
-
-<sect3 id="exp-type-sigs">
-<title>Expression type signatures</title>
-<para>An expression type signature that has <emphasis>explicit</emphasis>
-quantification (using <literal>forall</literal>) brings into scope the
-explicitly-quantified
-type variables, in the annotated expression. For example:
+<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>
- f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
+ 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
+
+ f4 :: Int -> (forall a. a -> a)
</programlisting>
-Here, the type signature <literal>forall a. ST s Bool</literal> brings the
-type variable <literal>s</literal> into scope, in the annotated expression
-<literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
+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 or right (see <literal>f4</literal>, for example)
+of a function arrow </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>
+Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
+a type variable any more!
</para>
-</sect3>
-<sect3 id="pattern-type-sigs">
-<title>Pattern type signatures</title>
+<sect3 id="univ">
+<title>Examples
+</title>
+
<para>
-A type signature may occur in any pattern; this is a <emphasis>pattern type
-signature</emphasis>.
-For example:
-<programlisting>
- -- f and g assume that 'a' is already in scope
- f = \(x::Int, y::a) -> x
- g (x::a) = x
- h ((x,y) :: (Int,Bool)) = (y,x)
-</programlisting>
-In the case where all the type variables in the pattern type sigature are
-already in scope (i.e. bound by the enclosing context), matters are simple: the
-signature simply constrains the type of the pattern in the obvious way.
+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>
-There is only one situation in which you can write a pattern type signature that
-mentions a type variable that is not already in scope, namely in pattern match
-of an existential data constructor. For example:
+
<programlisting>
- data T = forall a. MkT [a]
+data T a = T1 (forall b. b -> b -> b) a
- k :: T -> T
- k (MkT [t::a]) = MkT t3
- where
- t3::[a] = [t,t,t]
+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>
-Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
-variable that is not already in scope. Indeed, it cannot already be in scope,
-because it is bound by the pattern match. GHC's rule is that in this situation
-(and only then), a pattern type signature can mention a type variable that is
-not already in scope; the effect is to bring it into scope, standing for the
-existentially-bound type variable.
-</para>
-<para>
-If this seems a little odd, we think so too. But we must have
-<emphasis>some</emphasis> way to bring such type variables into scope, else we
-could not name existentially-bound type variables in subequent type signatures.
+
</para>
+
<para>
-This is (now) the <emphasis>only</emphasis> situation in which a pattern type
-signature is allowed to mention a lexical variable that is not already in
-scope.
-For example, both <literal>f</literal> and <literal>g</literal> would be
-illegal if <literal>a</literal> was not already in scope.
+The constructors have rank-2 types:
</para>
+<para>
-</sect3>
+<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>
-<!-- ==================== Commented out part about result type signatures
+</para>
-<sect3 id="result-type-sigs">
-<title>Result type signatures</title>
+<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>
-The result type of a function, lambda, or case expression alternative can be given a signature, thus:
+As for type signatures, implicit quantification happens for non-overloaded
+types too. So if you write this:
<programlisting>
- {- f assumes that 'a' is already in scope -}
- f x y :: [a] = [x,y,x]
+ data T a = MkT (Either a b) (b -> b)
+</programlisting>
- g = \ x :: [Int] -> [3,4]
+it's just as if you had written this:
- h :: forall a. [a] -> a
- h xs = case xs of
- (y:ys) :: a -> y
+<programlisting>
+ data T a = MkT (forall b. Either a b) (forall b. b -> b)
</programlisting>
-The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
-the result of the function. Similarly, the body of the lambda in the RHS of
-<literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
-alternative in <literal>h</literal> is <literal>a</literal>.
+
+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> A result type signature never brings new type variables into scope.</para>
-<para>
-There are a couple of syntactic wrinkles. First, notice that all three
-examples would parse quite differently with parentheses:
-<programlisting>
- {- f assumes that 'a' is already in scope -}
- f x (y :: [a]) = [x,y,x]
- g = \ (x :: [Int]) -> [3,4]
+<para>
+You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
+the constructor to suitable values, just as usual. For example,
+</para>
- h :: forall a. [a] -> a
- h xs = case xs of
- ((y:ys) :: a) -> y
-</programlisting>
-Now the signature is on the <emphasis>pattern</emphasis>; and
-<literal>h</literal> would certainly be ill-typed (since the pattern
-<literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
+<para>
-Second, to avoid ambiguity, the type after the “<literal>::</literal>” 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
+ 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>
-</sect3>
- -->
+</para>
-<sect3 id="cls-inst-scoped-tyvars">
-<title>Class and instance declarations</title>
<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>
-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:
+<para>
+When you use pattern matching, the bound variables may now have
+polymorphic types. For example:
+</para>
+<para>
<programlisting>
- class C a where
- op :: [a] -> a
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
- op xs = let ys::[a]
- ys = reverse xs
- in
- head ys
+ 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>
-</sect3>
-</sect2>
+<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>
-<sect2 id="deriving-typeable">
-<title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
+<sect3>
+<title>Type inference</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>.
+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>
-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.
+<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>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>
+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>
-</sect2>
-<sect2 id="newtype-deriving">
-<title>Generalised derived instances for newtypes</title>
+</sect3>
+
+
+<sect3 id="implicit-quant">
+<title>Implicit quantification</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
+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
-<programlisting>
- newtype Dollars = Dollars Int
-</programlisting>
+ 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
-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)
- ...
+ g :: (Ord a => a -> a) -> Int
+ -- MEANS the illegal type
+ g :: forall a. (Ord a => a -> a) -> Int
+ -- NOT
+ g :: (forall a. Ord a => a -> a) -> Int
+</programlisting>
+The latter produces an illegal type, which you might think is silly,
+but at least the rule is simple. If you want the latter type, you
+can write your for-alls explicitly. Indeed, doing so is strongly advised
+for rank-2 types.
+</para>
+</sect3>
+</sect2>
+
+
+<sect2 id="impredicative-polymorphism">
+<title>Impredicative polymorphism
+</title>
+<para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
+that you can call a polymorphic function at a polymorphic type, and
+parameterise data structures over polymorphic types. For example:
+<programlisting>
+ f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
+ f (Just g) = Just (g [3], g "hello")
+ f Nothing = Nothing
</programlisting>
-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!
+Notice here that the <literal>Maybe</literal> type is parameterised by the
+<emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
+[a])</literal>.
+</para>
+<para>The technical details of this extension are described in the paper
+<ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
+type inference for higher-rank types and impredicativity</ulink>,
+which appeared at ICFP 2006.
</para>
+</sect2>
+<sect2 id="scoped-type-variables">
+<title>Lexically scoped type variables
+</title>
-<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
+GHC supports <emphasis>lexically scoped type variables</emphasis>, without
+which some type signatures are simply impossible to write. For example:
+<programlisting>
+f :: forall a. [a] -> [a]
+f xs = ys ++ ys
+ where
+ ys :: [a]
+ ys = reverse xs
+</programlisting>
+The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
+the entire definition of <literal>f</literal>.
+In particular, it is in scope at the type signature for <varname>ys</varname>.
+In Haskell 98 it is not possible to declare
+a type for <varname>ys</varname>; a major benefit of scoped type variables is that
+it becomes possible to do so.
+</para>
+<para>Lexically-scoped type variables are enabled by
+<option>-fglasgow-exts</option>.
+</para>
+<para>Note: GHC 6.6 contains substantial changes to the way that scoped type
+variables work, compared to earlier releases. Read this section
+carefully!</para>
-<programlisting>
- instance Num Int => Num Dollars
-</programlisting>
+<sect3>
+<title>Overview</title>
-which just adds or removes the <literal>newtype</literal> constructor according to the type.
+<para>The design follows the following principles
+<itemizedlist>
+<listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
+a <emphasis>type</emphasis>. (This is a change from GHC's earlier
+design.)</para></listitem>
+<listitem><para>Furthermore, distinct lexical type variables stand for distinct
+type variables. This means that every programmer-written type signature
+(includin one that contains free scoped type variables) denotes a
+<emphasis>rigid</emphasis> type; that is, the type is fully known to the type
+checker, and no inference is involved.</para></listitem>
+<listitem><para>Lexical type variables may be alpha-renamed freely, without
+changing the program.</para></listitem>
+</itemizedlist>
+</para>
+<para>
+A <emphasis>lexically scoped type variable</emphasis> can be bound by:
+<itemizedlist>
+<listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
+<listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
+<listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
+<listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
+</itemizedlist>
</para>
<para>
+In Haskell, a programmer-written type signature is implicitly quantifed over
+its free type variables (<ulink
+url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
+4.1.2</ulink>
+of the Haskel Report).
+Lexically scoped type variables affect this implicit quantification rules
+as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
+quantified. For example, if type variable <literal>a</literal> is in scope,
+then
+<programlisting>
+ (e :: a -> a) means (e :: a -> a)
+ (e :: b -> b) means (e :: forall b. b->b)
+ (e :: a -> b) means (e :: forall b. a->b)
+</programlisting>
+</para>
-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>
+</sect3>
-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
+<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>
-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.
+The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
+the definition of "<literal>f</literal>".
</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])
+<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>
-The derived instance is obtained by completing the application of the
-class to the new type:
+<sect3 id="exp-type-sigs">
+<title>Expression type signatures</title>
-<programlisting>
- instance StateMonad [tok] (State [tok] (Failure m)) =>
- StateMonad [tok] (Parser tok m)
+<para>An expression type signature that has <emphasis>explicit</emphasis>
+quantification (using <literal>forall</literal>) brings into scope the
+explicitly-quantified
+type variables, in the annotated expression. For example:
+<programlisting>
+ f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
</programlisting>
+Here, the type signature <literal>forall a. ST s Bool</literal> brings the
+type variable <literal>s</literal> into scope, in the annotated expression
+<literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
</para>
-<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>
+<sect3 id="pattern-type-sigs">
+<title>Pattern type signatures</title>
<para>
-Derived instance declarations are constructed as follows. Consider the
-declaration (after expansion of any type synonyms)
-
-<programlisting>
- newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
-</programlisting>
-
-where
- <itemizedlist>
-<listitem><para>
- The <literal>ci</literal> are partial applications of
- classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
- is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
-</para></listitem>
-<listitem><para>
- The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
-</para></listitem>
-<listitem><para>
- The type <literal>t</literal> is an arbitrary type.
-</para></listitem>
-<listitem><para>
- The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
- nor in the <literal>ci</literal>, and
-</para></listitem>
-<listitem><para>
- None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
- <literal>Typeable</literal>, or <literal>Data</literal>. These classes
- should not "look through" the type or its constructor. You can still
- derive these classes for a newtype, but it happens in the usual way, not
- via this new mechanism.
-</para></listitem>
-</itemizedlist>
-Then, for each <literal>ci</literal>, the derived instance
-declaration is:
-<programlisting>
- instance ci t => ci (T v1...vk)
+A type signature may occur in any pattern; this is a <emphasis>pattern type
+signature</emphasis>.
+For example:
+<programlisting>
+ -- f and g assume that 'a' is already in scope
+ f = \(x::Int, y::a) -> x
+ g (x::a) = x
+ h ((x,y) :: (Int,Bool)) = (y,x)
</programlisting>
-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>
+In the case where all the type variables in the pattern type sigature are
+already in scope (i.e. bound by the enclosing context), matters are simple: the
+signature simply constrains the type of the pattern in the obvious way.
+</para>
+<para>
+There is only one situation in which you can write a pattern type signature that
+mentions a type variable that is not already in scope, namely in pattern match
+of an existential data constructor. For example:
+<programlisting>
+ data T = forall a. MkT [a]
-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.
+ k :: T -> T
+ k (MkT [t::a]) = MkT t3
+ where
+ t3::[a] = [t,t,t]
+</programlisting>
+Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
+variable that is not already in scope. Indeed, it cannot already be in scope,
+because it is bound by the pattern match. GHC's rule is that in this situation
+(and only then), a pattern type signature can mention a type variable that is
+not already in scope; the effect is to bring it into scope, standing for the
+existentially-bound type variable.
</para>
<para>
-
-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.
+If this seems a little odd, we think so too. But we must have
+<emphasis>some</emphasis> way to bring such type variables into scope, else we
+could not name existentially-bound type variables in subequent type signatures.
</para>
-<para>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>
+This is (now) the <emphasis>only</emphasis> situation in which a pattern type
+signature is allowed to mention a lexical variable that is not already in
+scope.
+For example, both <literal>f</literal> and <literal>g</literal> would be
+illegal if <literal>a</literal> was not already in scope.
</para>
+
+
</sect3>
-</sect2>
+<!-- ==================== Commented out part about result type signatures
-<sect2 id="stand-alone-deriving">
-<title>Stand-alone deriving declarations</title>
+<sect3 id="result-type-sigs">
+<title>Result type signatures</title>
<para>
-GHC now allows stand-alone <literal>deriving</literal> declarations:
-</para>
+The result type of a function, lambda, or case expression alternative can be given a signature, thus:
<programlisting>
- data Foo = Bar Int | Baz String
+ {- f assumes that 'a' is already in scope -}
+ f x y :: [a] = [x,y,x]
+
+ g = \ x :: [Int] -> [3,4]
- deriving Eq for Foo
+ h :: forall a. [a] -> a
+ h xs = case xs of
+ (y:ys) :: a -> y
</programlisting>
+The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
+the result of the function. Similarly, the body of the lambda in the RHS of
+<literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
+alternative in <literal>h</literal> is <literal>a</literal>.
+</para>
+<para> A result type signature never brings new type variables into scope.</para>
+<para>
+There are a couple of syntactic wrinkles. First, notice that all three
+examples would parse quite differently with parentheses:
+<programlisting>
+ {- f assumes that 'a' is already in scope -}
+ f x (y :: [a]) = [x,y,x]
+
+ g = \ (x :: [Int]) -> [3,4]
-<para>Deriving instances of multi-parameter type classes for newtypes is
-also allowed:</para>
+ h :: forall a. [a] -> a
+ h xs = case xs of
+ ((y:ys) :: a) -> y
+</programlisting>
+Now the signature is on the <emphasis>pattern</emphasis>; and
+<literal>h</literal> would certainly be ill-typed (since the pattern
+<literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
+Second, to avoid ambiguity, the type after the “<literal>::</literal>” 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>
- newtype Foo a = MkFoo (State Int a)
-
- deriving (MonadState Int) for Foo
+ \ x :: a -> b -> x
</programlisting>
+</para>
+</sect3>
+
+ -->
+<sect3 id="cls-inst-scoped-tyvars">
+<title>Class and instance declarations</title>
<para>
+
+The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
+scope over the methods defined in the <literal>where</literal> part. For example:
+
+
+<programlisting>
+ class C a where
+ op :: [a] -> a
+
+ op xs = let ys::[a]
+ ys = reverse xs
+ in
+ head ys
+</programlisting>
</para>
+</sect3>
</sect2>
+
<sect2 id="typing-binds">
<title>Generalised typing of mutually recursive bindings</title>
<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
+GHC implements a more general scheme. If <option>-X=RelaxedPolyRec</option> is
specified:
<emphasis>the dependency analysis ignores references to variables that have an explicit
type signature</emphasis>.
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>
+<option>-X=RelaxedPolyRec</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:
</para>
</sect2>
-</sect1>
-<!-- ==================== End of type system extensions ================= -->
-
-<!-- ====================== Generalised algebraic data types ======================= -->
-
-<sect1 id="gadt">
-<title>Generalised Algebraic Data Types (GADTs)</title>
+<sect2 id="overloaded-strings">
+<title>Overloaded string literals
+</title>
-<para>Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing you
-to give the type signatures of constructors explicitly. For example:
+<para>
+GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
+string literal has type <literal>String</literal>, but with overloaded string
+literals enabled (with <literal>-X=OverloadedStrings</literal>)
+ a string literal has type <literal>(IsString a) => a</literal>.
+</para>
+<para>
+This means that the usual string syntax can be used, e.g., for packed strings
+and other variations of string like types. String literals behave very much
+like integer literals, i.e., they can be used in both expressions and patterns.
+If used in a pattern the literal with be replaced by an equality test, in the same
+way as an integer literal is.
+</para>
+<para>
+The class <literal>IsString</literal> is defined as:
<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)
+class IsString a where
+ fromString :: String -> a
</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>:
+The only predefined instance is the obvious one to make strings work as usual:
<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)
+instance IsString [Char] where
+ fromString cs = cs
</programlisting>
-These and many other examples are given in papers by Hongwei Xi, and
-Tim Sheard. There is a longer introduction
-<ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
-and Ralf Hinze's
-<ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
-may use different notation to that implemented in GHC.
+The class <literal>IsString</literal> is not in scope by default. If you want to mention
+it explicitly (for exmaple, to give an instance declaration for it), you can import it
+from module <literal>GHC.Exts</literal>.
</para>
<para>
-The rest of this section outlines the extensions to GHC that support GADTs.
-It is far from comprehensive, but the design closely follows that described in
-the paper <ulink
-url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
-unification-based type inference for GADTs</ulink>,
-which appeared in ICFP 2006.
+Haskell's defaulting mechanism is extended to cover string literals, when <option>-X-OverloadedStrings</option> is specified.
+Specifically:
<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>
+Each type in a default declaration must be an
+instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
</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>.
+The standard defaulting rule (<ulink url="http://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>.
</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:
-
+</itemizedlist>
+</para>
+<para>
+A small example:
<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>
+module Main where
-</para></listitem>
+import GHC.Exts( IsString(..) )
-<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>
+newtype MyString = MyString String deriving (Eq, Show)
+instance IsString MyString where
+ fromString = MyString
-<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 :: Maybe1 a ;
- Just1 :: a -> Maybe1 a
- } deriving( Eq, Ord )
+greet :: MyString -> MyString
+greet "hello" = "world"
+greet other = other
- data Maybe2 a = Nothing2 | Just2 a
- deriving( Eq, Ord )
+main = do
+ print $ greet "hello"
+ print $ greet "fool"
</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>
+</para>
+<para>
+Note that deriving <literal>Eq</literal> is necessary for the pattern matching
+to work since it gets translated into an equality comparison.
+</para>
+</sect2>
-<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>
+<sect2 id="type-families">
+<title>Type families
+</title>
-<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>
+GHC supports the definition of type families indexed by types. They may be
+seen as an extension of Haskell 98's class-based overloading of values to
+types. When type families are declared in classes, they are also known as
+associated types.
</para>
-</listitem>
-</itemizedlist>
+<para>
+There are two forms of type families: data families and type synonym families.
+Currently, only the former are fully implemented, while we are still working
+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
+wiki page on type families</ulink>. The material will be moved to this user's
+guide when it has stabilised.
</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>
+Type families are enabled by the flag <option>-X=TypeFamilies</option>.
</para>
-</sect1>
-<!-- ====================== End of Generalised algebraic data types ======================= -->
+</sect2>
+
+</sect1>
+<!-- ==================== End of type system extensions ================= -->
+
<!-- ====================== TEMPLATE HASKELL ======================= -->
<sect1 id="template-haskell">
<para> Template Haskell has the following new syntactic
constructions. You need to use the flag
- <option>-fth</option><indexterm><primary><option>-fth</option></primary>
+ <option>-X=TemplateHaskell</option> or <option>-X=TH</option>
+ <indexterm><primary><option>-X=TemplateHaskell</option></primary>
</indexterm>to switch these syntactic extensions on
- (<option>-fth</option> is no longer implied by
+ (<option>-X=TemplateHaskell</option> is no longer implied by
<option>-fglasgow-exts</option>).</para>
<itemizedlist>
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;
+ <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
the quotation has type <literal>Type</literal>.</para></listitem>
</itemizedlist></para></listitem>
(It would make sense to do so, but it's hard to implement.)
</para></listitem>
+ <listitem><para>
+ Furthermore, you can only run a function at compile time if it is imported
+ from another module <emphasis>that is not part of a mutually-recursive group of modules
+ that includes the module currently being compiled</emphasis>. For example, when compiling module A,
+ you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
+ The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
+ </para></listitem>
+
<listitem><para>
The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
</para></listitem>
<para>Now run the compiler (here we are a Cygwin prompt on Windows):
</para>
<programlisting>
-$ ghc --make -fth main.hs -o main.exe
+$ ghc --make -X=TemplateHaskell main.hs -o main.exe
</programlisting>
<para>Run "main.exe" and here is your output:</para>
</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
+With the <option>-X=Arrows</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.
<!-- ==================== BANG PATTERNS ================= -->
-<sect1 id="sec-bang-patterns">
+<sect1 id="bang-patterns">
<title>Bang patterns
<indexterm><primary>Bang patterns</primary></indexterm>
</title>
than the material below.
</para>
<para>
-Bang patterns are enabled by the flag <option>-fbang-patterns</option>.
+Bang patterns are enabled by the flag <option>-X=BangPatterns</option>.
</para>
-<sect2 id="sec-bang-patterns-informal">
+<sect2 id="bang-patterns-informal">
<title>Informal description of bang patterns
</title>
<para>
</sect2>
-<sect2 id="sec-bang-patterns-sem">
+<sect2 id="bang-patterns-sem">
<title>Syntax and semantics
</title>
<para>
</programlisting>
Is this a definition of the infix function "<literal>(!)</literal>",
or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
-ambiguity inf favour of the latter. If you want to define
+ambiguity in favour of the latter. If you want to define
<literal>(!)</literal> with bang-patterns enabled, you have to do so using
prefix notation:
<programlisting>
<!-- ==================== ASSERTIONS ================= -->
-<sect1 id="sec-assertions">
+<sect1 id="assertions">
<title>Assertions
<indexterm><primary>Assertions</primary></indexterm>
</title>
<listitem>
<para>
- <function>length</function>
-</para>
-</listitem>
-<listitem>
-
-<para>
<function>++</function> (on its first argument)
</para>
</listitem>
described in this section. All are exported by
<literal>GHC.Exts</literal>.</para>
+<sect2> <title>The <literal>seq</literal> function </title>
+<para>
+The function <literal>seq</literal> is as described in the Haskell98 Report.
+<programlisting>
+ seq :: a -> b -> b
+</programlisting>
+It evaluates its first argument to head normal form, and then returns its
+second argument as the result. The reason that it is documented here is
+that, despite <literal>seq</literal>'s polymorphism, its
+second argument can have an unboxed type, or
+can be an unboxed tuple; for example <literal>(seq x 4#)</literal>
+or <literal>(seq x (# p,q #))</literal>. This requires <literal>b</literal>
+to be instantiated to an unboxed type, which is not usually allowed.
+</para>
+</sect2>
+
<sect2> <title>The <literal>inline</literal> function </title>
<para>
The <literal>inline</literal> function is somewhat experimental.
look strict in <literal>y</literal> which would defeat the whole
purpose of <literal>par</literal>.
</para>
+<para>
+Like <literal>seq</literal>, the argument of <literal>lazy</literal> can have
+an unboxed type.
+</para>
+
</sect2>
<sect2> <title>The <literal>unsafeCoerce#</literal> function </title>
well-typed, but where Haskell's type system is not expressive enough to prove
that it is well typed.
</para>
+<para>
+The argument to <literal>unsafeCoerce#</literal> can have unboxed types,
+although extremely bad things will happen if you coerce a boxed type
+to an unboxed type.
+</para>
+
</sect2>
+
</sect1>
<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),
+ <option>-X=Generics</option> (to generate extra per-data-type code),
and <option>-package lang</option> (to make the <literal>Generics</literal> library
available. </para>
</listitem>
<sect2>
<title>Switching off the dreaded Monomorphism Restriction</title>
- <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
+ <indexterm><primary><option>-X=NoMonomorphismRestriction</option></primary></indexterm>
<para>Haskell's monomorphism restriction (see
<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.5">Section
4.5.5</ulink>
of the Haskell Report)
can be completely switched off by
-<option>-fno-monomorphism-restriction</option>.
+<option>-X=NoMonomorphismRestriction</option>.
</para>
</sect2>
<sect2>
<title>Monomorphic pattern bindings</title>
- <indexterm><primary><option>-fno-mono-pat-binds</option></primary></indexterm>
- <indexterm><primary><option>-fmono-pat-binds</option></primary></indexterm>
+ <indexterm><primary><option>-X=NoMonoPatBinds</option></primary></indexterm>
+ <indexterm><primary><option>-X=MonoPatBinds</option></primary></indexterm>
<para> As an experimental change, we are exploring the possibility of
making pattern bindings monomorphic; that is, not generalised at all.
[x] = e -- A pattern binding
</programlisting>
Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
-default</emphasis>. Use <option>-fno-mono-pat-binds</option> to recover the
+default</emphasis>. Use <option>-X=MonoPatBinds</option> to recover the
standard behaviour.
</para>
</sect2>
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