</varlistentry>
<varlistentry>
+ <term><option>-fimplicit-params</option></term>
+ <listitem>
+ <para>Enables implicit parameters (see <xref
+ linkend="implicit-parameters"/>). Currently also implied by
+ <option>-fglasgow-exts</option>.</para>
+
+ <para>Syntax stolen:
+ <literal>?<replaceable>varid</replaceable></literal>,
+ <literal>%<replaceable>varid</replaceable></literal>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fscoped-type-variables</option></term>
+ <listitem>
+ <para>Enables lexically-scoped type variables (see <xref
+ linkend="scoped-type-variables"/>). Implied by
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
<term><option>-fth</option></term>
<listitem>
<para>Enables Template Haskell (see <xref
</listitem>
</varlistentry>
- <varlistentry>
- <term><option>-fimplicit-params</option></term>
- <listitem>
- <para>Enables implicit parameters (see <xref
- linkend="implicit-parameters"/>). Currently also implied by
- <option>-fglasgow-exts</option>.</para>
-
- <para>Syntax stolen:
- <literal>?<replaceable>varid</replaceable></literal>,
- <literal>%<replaceable>varid</replaceable></literal>.</para>
- </listitem>
- </varlistentry>
-
</variablelist>
</sect1>
<para>The Real Truth about what primitive types there are, and what operations
work over those types, is held in the file
-<filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
+<filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
This file is used directly to generate GHC's primitive-operation definitions, so
it is always correct! It is also intended for processing into text.</para>
represents a primitive value, then it really does point to that value:
no unevaluated thunks, no indirections…nothing can be at the
other end of the pointer than the primitive value.
+A numerically-intensive program using unboxed types can
+go a <emphasis>lot</emphasis> faster than its “standard”
+counterpart—we saw a threefold speedup on one example.
</para>
<para>
-There are some restrictions on the use of primitive types, the main
-one being that you can't pass a primitive value to a polymorphic
+There are some restrictions on the use of primitive types:
+<itemizedlist>
+<listitem><para>The main restriction
+is that you can't pass a primitive value to a polymorphic
function or store one in a polymorphic data type. This rules out
things like <literal>[Int#]</literal> (i.e. lists of primitive
integers). The reason for this restriction is that polymorphic
worse, the unboxed value might be larger than a pointer
(<literal>Double#</literal> for instance).
</para>
+</listitem>
+<listitem><para> You cannot bind a variable with an unboxed type
+in a <emphasis>top-level</emphasis> binding.
+</para></listitem>
+<listitem><para> You cannot bind a variable with an unboxed type
+in a <emphasis>recursive</emphasis> binding.
+</para></listitem>
+<listitem><para> You may bind unboxed variables in a (non-recursive,
+non-top-level) pattern binding, but any such variable causes the entire
+pattern-match
+to become strict. For example:
+<programlisting>
+ data Foo = Foo Int Int#
-<para>
-Nevertheless, A numerically-intensive program using unboxed types can
-go a <emphasis>lot</emphasis> faster than its “standard”
-counterpart—we saw a threefold speedup on one example.
+ f x = let (Foo a b, w) = ..rhs.. in ..body..
+</programlisting>
+Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
+match
+is strict, and the program behaves as if you had written
+<programlisting>
+ data Foo = Foo Int Int#
+
+ f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
+</programlisting>
+</para>
+</listitem>
+</itemizedlist>
</para>
</sect2>
using fully-fledged tuples. When an unboxed tuple is returned, the
components are put directly into registers or on the stack; the
unboxed tuple itself does not have a composite representation. Many
-of the primitive operations listed in this section return unboxed
+of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
tuples.
+In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
+tuples to avoid unnecessary allocation during sequences of operations.
</para>
<para>
There are some pretty stringent restrictions on the use of unboxed tuples:
-</para>
-
-<para>
-
<itemizedlist>
<listitem>
<para>
- Unboxed tuple types are subject to the same restrictions as
+Values of unboxed tuple types are subject to the same restrictions as
other unboxed types; i.e. they may not be stored in polymorphic data
structures or passed to polymorphic functions.
<listitem>
<para>
- Unboxed tuples may only be constructed as the direct result of
-a function, and may only be deconstructed with a <literal>case</literal> expression.
-eg. the following are valid:
-
-
-<programlisting>
-f x y = (# x+1, y-1 #)
-g x = case f x x of { (# a, b #) -> a + b }
-</programlisting>
-
-
-but the following are invalid:
+No variable can have an unboxed tuple type, nor may a constructor or function
+argument have an unboxed tuple type. The following are all illegal:
<programlisting>
-f x y = g (# x, y #)
-g (# x, y #) = x + y
-</programlisting>
-
-
-</para>
-</listitem>
-<listitem>
+ data Foo = Foo (# Int, Int #)
-<para>
- No variable can have an unboxed tuple type. This is illegal:
+ f :: (# Int, Int #) -> (# Int, Int #)
+ f x = x
+ g :: (# Int, Int #) -> Int
+ g (# a,b #) = a
-<programlisting>
-f :: (# Int, Int #) -> (# Int, Int #)
-f x = x
+ h x = let y = (# x,x #) in ...
</programlisting>
-
-
-because <literal>x</literal> has an unboxed tuple type.
-
</para>
</listitem>
-
</itemizedlist>
-
-</para>
-
-<para>
-Note: we may relax some of these restrictions in the future.
</para>
-
<para>
-The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
-tuples to avoid unnecessary allocation during sequences of operations.
+The typical use of unboxed tuples is simply to return multiple values,
+binding those multiple results with a <literal>case</literal> expression, thus:
+<programlisting>
+ f x y = (# x+1, y-1 #)
+ g x = case f x x of { (# a, b #) -> a + b }
+</programlisting>
+You can have an unboxed tuple in a pattern binding, thus
+<programlisting>
+ f x = let (# p,q #) = h x in ..body..
+</programlisting>
+If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
+the resulting binding is lazy like any other Haskell pattern binding. The
+above example desugars like this:
+<programlisting>
+ f x = let t = case h x o f{ (# p,q #) -> (p,q)
+ p = fst t
+ q = snd t
+ in ..body..
+</programlisting>
+Indeed, the bindings can even be recursive.
</para>
</sect2>
</programlisting>
<para>
-The semantics should be clear enough. The qualifers are matched in order.
+The semantics should be clear enough. The qualifiers are matched in order.
For a <literal><-</literal> qualifier, which I call a pattern guard, the
right hand side is evaluated and matched against the pattern on the left.
If the match fails then the whole guard fails and the next equation is
So the <option>-fno-implicit-prelude</option> flag causes
the following pieces of built-in syntax to refer to
<emphasis>whatever is in scope</emphasis>, not the Prelude
- versions:</para>
+ versions:
<itemizedlist>
<listitem>
- <para>Integer and fractional literals mean
- "<literal>fromInteger 1</literal>" and
- "<literal>fromRational 3.2</literal>", not the
- Prelude-qualified versions; both in expressions and in
- patterns. </para>
- <para>However, the standard Prelude <literal>Eq</literal> class
- is still used for the equality test necessary for literal patterns.</para>
- </listitem>
+ <para>An integer literal <literal>368</literal> means
+ "<literal>fromInteger (368::Integer)</literal>", rather than
+ "<literal>Prelude.fromInteger (368::Integer)</literal>".
+</para> </listitem>
- <listitem>
- <para>Negation (e.g. "<literal>- (f x)</literal>")
- means "<literal>negate (f x)</literal>" (not
- <literal>Prelude.negate</literal>).</para>
- </listitem>
+ <listitem><para>Fractional literals are handed in just the same way,
+ except that the translation is
+ <literal>fromRational (3.68::Rational)</literal>.
+</para> </listitem>
+
+ <listitem><para>The equality test in an overloaded numeric pattern
+ uses whatever <literal>(==)</literal> is in scope.
+</para> </listitem>
+
+ <listitem><para>The subtraction operation, and the
+ greater-than-or-equal test, in <literal>n+k</literal> patterns
+ use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
+ </para></listitem>
<listitem>
- <para>In an n+k pattern, the standard Prelude
- <literal>Ord</literal> class is still used for comparison,
- but the necessary subtraction uses whatever
- "<literal>(-)</literal>" is in scope (not
- "<literal>Prelude.(-)</literal>").</para>
- </listitem>
+ <para>Negation (e.g. "<literal>- (f x)</literal>")
+ means "<literal>negate (f x)</literal>", both in numeric
+ patterns, and expressions.
+ </para></listitem>
<listitem>
<para>"Do" notation is translated using whatever
functions <literal>(>>=)</literal>,
- <literal>(>>)</literal>, <literal>fail</literal>, and
- <literal>return</literal>, are in scope (not the Prelude
- versions). List comprehensions, and parallel array
+ <literal>(>>)</literal>, and <literal>fail</literal>,
+ are in scope (not the Prelude
+ versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
comprehensions, are unaffected. </para></listitem>
- </itemizedlist>
- <para>Be warned: this is an experimental facility, with fewer checks than
- usual. In particular, it is essential that the functions GHC finds in scope
- must have the appropriate types, namely:
- <screen>
- fromInteger :: forall a. (...) => Integer -> a
- fromRational :: forall a. (...) => Rational -> a
- negate :: forall a. (...) => a -> a
- (-) :: forall a. (...) => a -> a -> a
- (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
- (>>) :: forall m a. (...) => m a -> m b -> m b
- return :: forall m a. (...) => a -> m a
- fail :: forall m a. (...) => String -> m a
- </screen>
- (The (...) part can be any context including the empty context; that part
- is up to you.)
- If the functions don't have the right type, very peculiar things may
- happen. Use <literal>-dcore-lint</literal> to
- typecheck the desugared program. If Core Lint is happy you should be all right.</para>
+ <listitem>
+ <para>Arrow
+ notation (see <xref linkend="arrow-notation"/>)
+ uses whatever <literal>arr</literal>,
+ <literal>(>>>)</literal>, <literal>first</literal>,
+ <literal>app</literal>, <literal>(|||)</literal> and
+ <literal>loop</literal> functions are in scope. But unlike the
+ other constructs, the types of these functions must match the
+ Prelude types very closely. Details are in flux; if you want
+ to use this, ask!
+ </para></listitem>
+ </itemizedlist>
+In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
+even if that is a little unexpected. For emample, the
+static semantics of the literal <literal>368</literal>
+is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
+<literal>fromInteger</literal> to have any of the types:
+<programlisting>
+fromInteger :: Integer -> Integer
+fromInteger :: forall a. Foo a => Integer -> a
+fromInteger :: Num a => a -> Integer
+fromInteger :: Integer -> Bool -> Bool
+</programlisting>
+</para>
+
+ <para>Be warned: this is an experimental facility, with
+ fewer checks than usual. Use <literal>-dcore-lint</literal>
+ to typecheck the desugared program. If Core Lint is happy
+ you should be all right.</para>
</sect2>
</sect1>
</sect3>
<sect3 id="infix-tycons">
-<title>Infix type constructors</title>
+<title>Infix type constructors, classes, and type variables</title>
<para>
-GHC allows type constructors to be operators, and to be written infix, very much
-like expressions. More specifically:
+GHC allows type constructors, classes, and type variables to be operators, and
+to be written infix, very much like expressions. More specifically:
<itemizedlist>
<listitem><para>
- A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
+ A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
The lexical syntax is the same as that for data constructors.
</para></listitem>
<listitem><para>
- Types can be written infix. For example <literal>Int :*: Bool</literal>.
+ Data type and type-synonym declarations can be written infix, parenthesised
+ if you want further arguments. E.g.
+<screen>
+ data a :*: b = Foo a b
+ type a :+: b = Either a b
+ class a :=: b where ...
+
+ data (a :**: b) x = Baz a b x
+ type (a :++: b) y = Either (a,b) y
+</screen>
+ </para></listitem>
+<listitem><para>
+ Types, and class constraints, can be written infix. For example
+ <screen>
+ x :: Int :*: Bool
+ f :: (a :=: b) => a -> b
+ </screen>
+ </para></listitem>
+<listitem><para>
+ A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
+ The lexical syntax is the same as that for variable operators, excluding "(.)",
+ "(!)", and "(*)". In a binding position, the operator must be
+ parenthesised. For example:
+<programlisting>
+ type T (+) = Int + Int
+ f :: T Either
+ f = Left 3
+
+ liftA2 :: Arrow (~>)
+ => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
+ liftA2 = ...
+</programlisting>
</para></listitem>
<listitem><para>
Back-quotes work
<literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
</para></listitem>
<listitem><para>
- Fixities may be declared for type constructors just as for data constructors. However,
+ Fixities may be declared for type constructors, or classes, just as for data constructors. However,
one cannot distinguish between the two in a fixity declaration; a fixity declaration
sets the fixity for a data constructor and the corresponding type constructor. For example:
<screen>
<listitem><para>
Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
</para></listitem>
-<listitem><para>
- Data type and type-synonym declarations can be written infix. E.g.
-<screen>
- data a :*: b = Foo a b
- type a :+: b = Either a b
-</screen>
- </para></listitem>
-<listitem><para>
- The only thing that differs between operators in types and operators in expressions is that
- ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
- are not allowed in types. Reason: the uniform thing to do would be to make them type
- variables, but that's not very useful. A less uniform but more useful thing would be to
- allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
- lists. So for now we just exclude them.
- </para></listitem>
</itemizedlist>
</para>
<title>Liberalised type synonyms</title>
<para>
-Type synonmys are like macros at the type level, and
+Type synonyms are like macros at the type level, and
GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
That means that GHC can be very much more liberal about type synonyms than Haskell 98:
<itemizedlist>
foo :: Generic Id []
</programlisting>
-After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
+After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
<programlisting>
foo :: forall x. x -> [x]
</programlisting>
<para>
The idea of using existential quantification in data type declarations
-was suggested by Laufer (I believe, thought doubtless someone will
-correct me), and implemented in Hope+. It's been in Lennart
+was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
+of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
+London, 1991). It was later formalised by Laufer and Odersky
+(<emphasis>Polymorphic type inference and abstract data types</emphasis>,
+TOPLAS, 16(5), pp1411-1430, 1994).
+It's been in Lennart
Augustsson's <command>hbc</command> Haskell compiler for several years, and
proved very useful. Here's the idea. Consider the declaration:
</para>
<title>Type classes</title>
<para>
-An easy extension (implemented in <command>hbc</command>) is to allow
+An easy extension is to allow
arbitrary contexts before the constructor. For example:
</para>
</sect4>
<sect4>
+<title>Record Constructors</title>
+
+<para>
+GHC allows existentials to be used with records syntax as well. For example:
+
+<programlisting>
+data Counter a = forall self. NewCounter
+ { _this :: self
+ , _inc :: self -> self
+ , _display :: self -> IO ()
+ , tag :: a
+ }
+</programlisting>
+Here <literal>tag</literal> is a public field, with a well-typed selector
+function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
+type is hidden from the outside; any attempt to apply <literal>_this</literal>,
+<literal>_inc</literal> or <literal>_output</literal> as functions will raise a
+compile-time error. In other words, <emphasis>GHC defines a record selector function
+only for fields whose type does not mention the existentially-quantified variables</emphasis>.
+(This example used an underscore in the fields for which record selectors
+will not be defined, but that is only programming style; GHC ignores them.)
+</para>
+
+<para>
+To make use of these hidden fields, we need to create some helper functions:
+
+<programlisting>
+inc :: Counter a -> Counter a
+inc (NewCounter x i d t) = NewCounter
+ { _this = i x, _inc = i, _display = d, tag = t }
+
+display :: Counter a -> IO ()
+display NewCounter{ _this = x, _display = d } = d x
+</programlisting>
+
+Now we can define counters with different underlying implementations:
+
+<programlisting>
+counterA :: Counter String
+counterA = NewCounter
+ { _this = 0, _inc = (1+), _display = print, tag = "A" }
+
+counterB :: Counter String
+counterB = NewCounter
+ { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
+
+main = do
+ display (inc counterA) -- prints "1"
+ display (inc (inc counterB)) -- prints "##"
+</programlisting>
+
+In GADT declarations (see <xref linkend="gadt"/>), the explicit
+<literal>forall</literal> may be omitted. For example, we can express
+the same <literal>Counter a</literal> using GADT:
+
+<programlisting>
+data Counter a where
+ NewCounter { _this :: self
+ , _inc :: self -> self
+ , _display :: self -> IO ()
+ , tag :: a
+ }
+ :: Counter a
+</programlisting>
+
+At the moment, record update syntax is only supported for Haskell 98 data types,
+so the following function does <emphasis>not</emphasis> work:
+
+<programlisting>
+-- This is invalid; use explicit NewCounter instead for now
+setTag :: Counter a -> a -> Counter a
+setTag obj t = obj{ tag = t }
+</programlisting>
+
+</para>
+
+</sect4>
+
+
+<sect4>
<title>Restrictions</title>
<para>
<title>Class declarations</title>
<para>
-This section documents GHC's implementation of multi-parameter type
-classes. There's lots of background in the paper <ulink
-url="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
+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>
-There are the following constraints on class declarations:
-<orderedlist>
-<listitem>
+All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
+</para>
+<sect3>
+<title>Multi-parameter type classes</title>
<para>
- <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
+Multi-parameter type classes are permitted. For example:
<programlisting>
...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:
-</para>
-</listitem>
-<listitem>
+<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>
- <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
+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:
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>
-</listitem>
-<listitem>
+</sect3>
-<para>
- <emphasis>There are no restrictions on the context in a class declaration
-(which introduces superclasses), except that the class hierarchy must
-be acyclic</emphasis>. 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
+<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>
-</listitem>
+<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 ...
-<listitem>
+ 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>
- <emphasis>All of the class type variables must be reachable (in the sense
+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 varibles of each method type
-</emphasis>. For example:
-
+from the free variables of each method type.
+For example:
<programlisting>
class Coll s a where
insert :: s -> a -> s
</programlisting>
-
is not OK, because the type of <literal>empty</literal> doesn't mention
-<literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
-types, and has the same motivation.
-
-Sometimes, offending class declarations exhibit misunderstandings. For
-example, <literal>Coll</literal> might be rewritten
+<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
class CollE s => Coll s a where
insert :: s -> a -> s
</programlisting>
+</para>
+</sect3>
-</para>
-</listitem>
+<sect3>
+<title>Background on functional dependencies</title>
-</orderedlist>
+<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>
-
-<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>
+Consider the following class, intended as part of a
+library for collection types:
<programlisting>
- class Seq s a where
- fromList :: [a] -> s a
- elem :: Eq a => a -> s a -> Bool
+ class Collects e ce where
+ empty :: ce
+ insert :: e -> ce -> ce
+ member :: e -> ce -> 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>).
+The type variable e used here represents the element type, while ce is the type
+of the container itself. Within this framework, we might want to define
+instances of this class for lists or characteristic functions (both of which
+can be used to represent collections of any equality type), bit sets (which can
+be used to represent collections of characters), or hash tables (which can be
+used to represent any collection whose elements have a hash function). Omitting
+standard implementation details, this would lead to the following declarations:
+<programlisting>
+ instance Eq e => Collects e [e] where ...
+ instance Eq e => Collects e (e -> Bool) where ...
+ instance Collects Char BitSet where ...
+ instance (Hashable e, Collects a ce)
+ => Collects e (Array Int ce) where ...
+</programlisting>
+All this looks quite promising; we have a class and a range of interesting
+implementations. Unfortunately, there are some serious problems with the class
+declaration. First, the empty function has an ambiguous type:
+<programlisting>
+ empty :: Collects e ce => ce
+</programlisting>
+By "ambiguous" we mean that there is a type variable e that appears on the left
+of the <literal>=></literal> symbol, but not on the right. The problem with
+this is that, according to the theoretical foundations of Haskell overloading,
+we cannot guarantee a well-defined semantics for any term with an ambiguous
+type.
</para>
<para>
-With the <option>-fglasgow-exts</option> GHC lifts this restriction.
+We can sidestep this specific problem by removing the empty member from the
+class declaration. However, although the remaining members, insert and member,
+do not have ambiguous types, we still run into problems when we try to use
+them. For example, consider the following two functions:
+<programlisting>
+ f x y = insert x . insert y
+ g = f True 'a'
+</programlisting>
+for which GHC infers the following types:
+<programlisting>
+ f :: (Collects a c, Collects b c) => a -> b -> c -> c
+ g :: (Collects Bool c, Collects Char c) => c -> c
+</programlisting>
+Notice that the type for f allows the two parameters x and y to be assigned
+different types, even though it attempts to insert each of the two values, one
+after the other, into the same collection. If we're trying to model collections
+that contain only one type of value, then this is clearly an inaccurate
+type. Worse still, the definition for g is accepted, without causing a type
+error. As a result, the error in this code will not be flagged at the point
+where it appears. Instead, it will show up only when we try to use g, which
+might even be in a different module.
</para>
-</sect3>
-
-</sect2>
+<sect4><title>An attempt to use constructor classes</title>
-<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
+Faced with the problems described above, some Haskell programmers might be
+tempted to use something like the following version of the class declaration:
<programlisting>
- g :: Eq [a] => ...
- g :: Ord (T a ()) => ...
+ class Collects e c where
+ empty :: c e
+ insert :: e -> c e -> c e
+ member :: e -> c e -> Bool
</programlisting>
+The key difference here is that we abstract over the type constructor c that is
+used to form the collection type c e, and not over that collection type itself,
+represented by ce in the original class declaration. This avoids the immediate
+problems that we mentioned above: empty has type <literal>Collects e c => c
+e</literal>, which is not ambiguous.
</para>
<para>
-GHC imposes the following restrictions on the constraints in a type signature.
-Consider the type:
-
+The function f from the previous section has a more accurate type:
<programlisting>
- forall tv1..tvn (c1, ...,cn) => type
+ f :: (Collects e c) => e -> e -> c e -> c e
</programlisting>
-
-(Here, we write the "foralls" explicitly, although the Haskell source
-language omits them; in Haskell 98, all the free type variables of an
-explicit source-language type signature are universally quantified,
-except for the class type variables in a class declaration. However,
-in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
+The function g from the previous section is now rejected with a type error as
+we would hope because the type of f does not allow the two arguments to have
+different types.
+This, then, is an example of a multiple parameter class that does actually work
+quite well in practice, without ambiguity problems.
+There is, however, a catch. This version of the Collects class is nowhere near
+as general as the original class seemed to be: only one of the four instances
+for <literal>Collects</literal>
+given above can be used with this version of Collects because only one of
+them---the instance for lists---has a collection type that can be written in
+the form c e, for some type constructor c, and element type e.
</para>
+</sect4>
+<sect4><title>Adding functional dependencies</title>
+
+<para>
+To get a more useful version of the Collects class, Hugs provides a mechanism
+that allows programmers to specify dependencies between the parameters of a
+multiple parameter class (For readers with an interest in theoretical
+foundations and previous work: The use of dependency information can be seen
+both as a generalization of the proposal for `parametric type classes' that was
+put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
+later framework for "improvement" of qualified types. The
+underlying ideas are also discussed in a more theoretical and abstract setting
+in a manuscript [implparam], where they are identified as one point in a
+general design space for systems of implicit parameterization.).
+
+To start with an abstract example, consider a declaration such as:
+<programlisting>
+ class C a b where ...
+</programlisting>
+which tells us simply that C can be thought of as a binary relation on types
+(or type constructors, depending on the kinds of a and b). Extra clauses can be
+included in the definition of classes to add information about dependencies
+between parameters, as in the following examples:
+<programlisting>
+ class D a b | a -> b where ...
+ class E a b | a -> b, b -> a where ...
+</programlisting>
+The notation <literal>a -> b</literal> used here between the | and where
+symbols --- not to be
+confused with a function type --- indicates that the a parameter uniquely
+determines the b parameter, and might be read as "a determines b." Thus D is
+not just a relation, but actually a (partial) function. Similarly, from the two
+dependencies that are included in the definition of E, we can see that E
+represents a (partial) one-one mapping between types.
+</para>
<para>
-
-<orderedlist>
-<listitem>
-
+More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
+where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
+m>=0, meaning that the y parameters are uniquely determined by the x
+parameters. Spaces can be used as separators if more than one variable appears
+on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
+annotated with multiple dependencies using commas as separators, as in the
+definition of E above. Some dependencies that we can write in this notation are
+redundant, and will be rejected because they don't serve any useful
+purpose, and may instead indicate an error in the program. Examples of
+dependencies like this include <literal>a -> a </literal>,
+<literal>a -> a a </literal>,
+<literal>a -> </literal>, etc. There can also be
+some redundancy if multiple dependencies are given, as in
+<literal>a->b</literal>,
+ <literal>b->c </literal>, <literal>a->c </literal>, and
+in which some subset implies the remaining dependencies. Examples like this are
+not treated as errors. Note that dependencies appear only in class
+declarations, and not in any other part of the language. In particular, the
+syntax for instance declarations, class constraints, and types is completely
+unchanged.
+</para>
<para>
- <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:
-
-
+By including dependencies in a class declaration, we provide a mechanism for
+the programmer to specify each multiple parameter class more precisely. The
+compiler, on the other hand, is responsible for ensuring that the set of
+instances that are in scope at any given point in the program is consistent
+with any declared dependencies. For example, the following pair of instance
+declarations cannot appear together in the same scope because they violate the
+dependency for D, even though either one on its own would be acceptable:
<programlisting>
- forall a. Eq a => Int
+ instance D Bool Int where ...
+ instance D Bool Char where ...
</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>.
+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>
-Note
-that the reachability condition is weaker than saying that <literal>a</literal> is
-functionally dependendent 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:
+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 C a b | a -> b where ...
- class C a b => D a b where ...
- f :: forall a b. D a b => a -> a
+ class Collects e ce | ce -> e where
+ empty :: ce
+ insert :: e -> ce -> ce
+ member :: e -> ce -> Bool
</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.
+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>
-</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>:
-
-
+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>
- forall a. C a b => burble
-</programlisting>
-
-
-The next type is illegal because the constraint <literal>Eq b</literal> does not
-mention <literal>a</literal>:
-
-
+ 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>
- forall a. Eq b => burble
+ 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>
-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.
+<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>
-</listitem>
-
-</orderedlist>
+<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>
-</sect3>
-
-<sect3 id="hoist">
-<title>For-all hoisting</title>
<para>
-It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
-end of an arrow, thus:
-<programlisting>
- type Discard a = forall b. a -> b -> a
+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>
- g :: Int -> Discard Int
- g x y z = x+y
+<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>
-Simply expanding the type synonym would give
+For example, these are OK:
<programlisting>
- g :: Int -> (forall b. Int -> b -> Int)
+ 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 GHC "hoists" the <literal>forall</literal> to give the isomorphic type
+But these are not:
<programlisting>
- g :: forall b. Int -> Int -> b -> Int
+ -- 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>
-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>
+</para>
+
+<para>
+The same restrictions apply to instances generated by
+<literal>deriving</literal> clauses. Thus the following is accepted:
<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>
+ data MinHeap h a = H a (h a)
+ deriving (Show)
</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:
+because the derived instance
<programlisting>
- g :: Int -> Int -> forall b. b -> Int
+ instance (Show a, Show (h a)) => Show (MinHeap h a)
</programlisting>
+conforms to the above rules.
</para>
+
<para>
-When doing this hoisting operation, GHC eliminates duplicate constraints. For
-example:
-<programlisting>
- type Foo a = (?x::Int) => Bool -> a
- g :: Foo (Foo Int)
-</programlisting>
-means
+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>
- g :: (?x::Int) => Bool -> Bool -> Int
+ instance C a where
+ op = ... -- Default
</programlisting>
</para>
</sect3>
+<sect3 id="undecidable-instances">
+<title>Undecidable instances</title>
-</sect2>
-
-<sect2 id="instance-decls">
-<title>Instance declarations</title>
-
-<sect3>
-<title>Overlapping instances</title>
<para>
-In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
-declarations
-
+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>
- instance context1 => C type1 where ...
- instance context2 => C type2 where ...
+ 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
-"overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
-</para>
-<para>
-However, if you give the command line option
-<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
-option</primary></indexterm> then overlapping instance declarations are permitted.
-However, GHC arranges never to commit to using an instance declaration
-if another instance declaration also applies, either now or later.
-
-<itemizedlist>
-<listitem>
+ 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
-<para>
- EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
+ instance Mul Int Int Int where (.*.) = (*)
+ instance Mul Int Float Float where x .*. y = fromIntegral x * y
+ instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
+</programlisting>
+The third instance declaration does not obey the coverage condition;
+and indeed the (somewhat strange) definition:
+<programlisting>
+ f = \ b x y -> if b then x .*. [y] else y
+</programlisting>
+makes instance inference go into a loop, because it requires the constraint
+<literal>(Mul a [b] b)</literal>.
</para>
-</listitem>
-<listitem>
-
<para>
- OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
-(but not identical to <literal>type1</literal>), or vice versa.
+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>
-</listitem>
-</itemizedlist>
-Notice that these rules
-<itemizedlist>
-<listitem>
-<para>
- make it clear which instance decl to use
-(pick the most specific one that matches)
-
-</para>
-</listitem>
-<listitem>
+</sect3>
-<para>
- do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
-Reason: you can pick which instance decl
-"matches" based on the type.
-</para>
-</listitem>
-</itemizedlist>
-However the rules are over-conservative. Two instance declarations can overlap,
-but it can still be clear in particular situations which to use. For example:
-<programlisting>
- instance C (Int,a) where ...
- instance C (a,Bool) where ...
-</programlisting>
-These are rejected by GHC's rules, but it is clear what to do when trying
-to solve the constraint <literal>C (Int,Int)</literal> because the second instance
-cannot apply. Yell if this restriction bites you.
-</para>
+<sect3 id="instance-overlap">
+<title>Overlapping instances</title>
<para>
-GHC is also conservative about committing to an overlapping instance. For example:
-<programlisting>
- class C a where { op :: a -> a }
- instance C [Int] where ...
- instance C a => C [a] where ...
-
- f :: C b => [b] -> [b]
- f x = op x
-</programlisting>
-From the RHS of f we get the constraint <literal>C [b]</literal>. But
-GHC does not commit to the second instance declaration, because in a paricular
-call of f, b might be instantiate to Int, so the first instance declaration
-would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
-GHC will instead silently pick the second instance, without complaining about
+In general, <emphasis>GHC requires that that it be unambiguous which instance
+declaration
+should be used to resolve a type-class constraint</emphasis>. This behaviour
+can be modified by two flags: <option>-fallow-overlapping-instances</option>
+<indexterm><primary>-fallow-overlapping-instances
+</primary></indexterm>
+and <option>-fallow-incoherent-instances</option>
+<indexterm><primary>-fallow-incoherent-instances
+</primary></indexterm>, as this section discusses.</para>
+<para>
+When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
+it tries to match every instance declaration against the
+constraint,
+by instantiating the head of the instance declaration. For example, consider
+these declarations:
+<programlisting>
+ instance context1 => C Int a where ... -- (A)
+ instance context2 => C a Bool where ... -- (B)
+ instance context3 => C Int [a] where ... -- (C)
+ instance context4 => C Int [Int] where ... -- (D)
+</programlisting>
+The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
+but (C) and (D) do not. When matching, GHC takes
+no account of the context of the instance declaration
+(<literal>context1</literal> etc).
+GHC's default behaviour is that <emphasis>exactly one instance must match the
+constraint it is trying to resolve</emphasis>.
+It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
+including both declarations (A) and (B), say); an error is only reported if a
+particular constraint matches more than one.
+</para>
+
+<para>
+The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
+more than one instance to match, provided there is a most specific one. For
+example, the constraint <literal>C Int [Int]</literal> matches instances (A),
+(C) and (D), but the last is more specific, and hence is chosen. If there is no
+most-specific match, the program is rejected.
+</para>
+<para>
+However, GHC is conservative about committing to an overlapping instance. For example:
+<programlisting>
+ f :: [b] -> [b]
+ f x = ...
+</programlisting>
+Suppose that from the RHS of <literal>f</literal> we get the constraint
+<literal>C Int [b]</literal>. But
+GHC does not commit to instance (C), because in a particular
+call of <literal>f</literal>, <literal>b</literal> might be instantiate
+to <literal>Int</literal>, in which case instance (D) would be more specific still.
+So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
+GHC will instead pick (C), without complaining about
the problem of subsequent instantiations.
</para>
<para>
-Regrettably, GHC doesn't guarantee to detect overlapping instance
-declarations if they appear in different modules. GHC can "see" the
-instance declarations in the transitive closure of all the modules
-imported by the one being compiled, so it can "see" all instance decls
-when it is compiling <literal>Main</literal>. However, it currently chooses not
-to look at ones that can't possibly be of use in the module currently
-being compiled, in the interests of efficiency. (Perhaps we should
-change that decision, at least for <literal>Main</literal>.)
+The willingness to be overlapped or incoherent is a property of
+the <emphasis>instance declaration</emphasis> itself, controlled by the
+presence or otherwise of the <option>-fallow-overlapping-instances</option>
+and <option>-fallow-incoherent-instances</option> flags when that mdodule is
+being defined. Neither flag is required in a module that imports and uses the
+instance declaration. Specifically, during the lookup process:
+<itemizedlist>
+<listitem><para>
+An instance declaration is ignored during the lookup process if (a) a more specific
+match is found, and (b) the instance declaration was compiled with
+<option>-fallow-overlapping-instances</option>. The flag setting for the
+more-specific instance does not matter.
+</para></listitem>
+<listitem><para>
+Suppose an instance declaration does not matche the constraint being looked up, but
+does unify with it, so that it might match when the constraint is further
+instantiated. Usually GHC will regard this as a reason for not committing to
+some other constraint. But if the instance declaration was compiled with
+<option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
+check for that declaration.
+</para></listitem>
+</itemizedlist>
+All this makes it possible for a library author to design a library that relies on
+overlapping instances without the library client having to know.
+</para>
+<para>The <option>-fallow-incoherent-instances</option> flag implies the
+<option>-fallow-overlapping-instances</option> flag, but not vice versa.
</para>
</sect3>
</para>
</sect3>
-<sect3 id="undecidable-instances">
-<title>Undecidable instances</title>
-<para>An instance declaration must normally obey the following rules:
-<orderedlist>
-<listitem><para>At least one of the types in the <emphasis>head</emphasis> of
-an instance declaration <emphasis>must not</emphasis> be a type variable.
-For example, these are OK:
-
-<programlisting>
- instance C Int a where ...
+</sect2>
- instance D (Int, Int) where ...
+<sect2 id="type-restrictions">
+<title>Type signatures</title>
- instance E [[a]] where ...
-</programlisting>
-but this is not:
+<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>
- instance F a where ...
+ g :: Eq [a] => ...
+ g :: Ord (T a ()) => ...
</programlisting>
-Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
-For example, this is OK:
+</para>
+<para>
+GHC imposes the following restrictions on the constraints in a type signature.
+Consider the type:
+
<programlisting>
- instance Stateful (ST s) (MutVar s) where ...
+ forall tv1..tvn (c1, ...,cn) => type
</programlisting>
+
+(Here, we write the "foralls" explicitly, although the Haskell source
+language omits them; in Haskell 98, all the free type variables of an
+explicit source-language type signature are universally quantified,
+except for the class type variables in a class declaration. However,
+in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
</para>
-</listitem>
+<para>
+<orderedlist>
<listitem>
-<para>All of the types in the <emphasis>context</emphasis> of
-an instance declaration <emphasis>must</emphasis> be type variables.
-Thus
+
+<para>
+ <emphasis>Each universally quantified type variable
+<literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
+
+A type variable <literal>a</literal> is "reachable" if it it appears
+in the same constraint as either a type variable free in in
+<literal>type</literal>, or another reachable type variable.
+A value with a type that does not obey
+this reachability restriction cannot be used without introducing
+ambiguity; that is why the type is rejected.
+Here, for example, is an illegal type:
+
+
<programlisting>
-instance C a b => Eq (a,b) where ...
+ forall a. Eq a => Int
</programlisting>
-is OK, but
+
+
+When a value with this type was used, the constraint <literal>Eq tv</literal>
+would be introduced where <literal>tv</literal> is a fresh type variable, and
+(in the dictionary-translation implementation) the value would be
+applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
+can never know which instance of <literal>Eq</literal> to use because we never
+get any more information about <literal>tv</literal>.
+</para>
+<para>
+Note
+that the reachability condition is weaker than saying that <literal>a</literal> is
+functionally dependent on a type variable free in
+<literal>type</literal> (see <xref
+linkend="functional-dependencies"/>). The reason for this is there
+might be a "hidden" dependency, in a superclass perhaps. So
+"reachable" is a conservative approximation to "functionally dependent".
+For example, consider:
<programlisting>
-instance C Int b => Foo b where ...
+ 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>
-is not OK.
+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>
-</orderedlist>
-These restrictions ensure that
-context reduction terminates: each reduction step removes one type
-constructor. For example, the following would make the type checker
-loop if it wasn't excluded:
-<programlisting>
- instance C a => C a where ...
-</programlisting>
-There are two situations in which the rule is a bit of a pain. First,
-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:
+<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>
- instance C a where
- op = ... -- Default
+ forall a. C a b => burble
</programlisting>
-Second, sometimes you might want to use the following to get the
-effect of a "class synonym":
+The next type is illegal because the constraint <literal>Eq b</literal> does not
+mention <literal>a</literal>:
<programlisting>
- class (C1 a, C2 a, C3 a) => C a where { }
-
- instance (C1 a, C2 a, C3 a) => C a where { }
+ forall a. Eq b => burble
</programlisting>
-This allows you to write shorter signatures:
-
+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.
-<programlisting>
- f :: C a => ...
-</programlisting>
+</para>
+</listitem>
+</orderedlist>
-instead of
+</para>
+</sect3>
+<sect3 id="hoist">
+<title>For-all hoisting</title>
+<para>
+It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
+end of an arrow, thus:
+<programlisting>
+ type Discard a = forall b. a -> b -> a
+ g :: Int -> Discard Int
+ g x y z = x+y
+</programlisting>
+Simply expanding the type synonym would give
<programlisting>
- f :: (C1 a, C2 a, C3 a) => ...
+ g :: Int -> (forall b. Int -> b -> Int)
+</programlisting>
+but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
+<programlisting>
+ g :: forall b. Int -> Int -> b -> Int
+</programlisting>
+In general, the rule is this: <emphasis>to determine the type specified by any explicit
+user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
+performs the transformation:</emphasis>
+<programlisting>
+ <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
+==>
+ forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
+</programlisting>
+(In fact, GHC tries to retain as much synonym information as possible for use in
+error messages, but that is a usability issue.) This rule applies, of course, whether
+or not the <literal>forall</literal> comes from a synonym. For example, here is another
+valid way to write <literal>g</literal>'s type signature:
+<programlisting>
+ g :: Int -> Int -> forall b. b -> Int
</programlisting>
-
-
-Voluminous correspondence on the Haskell mailing list has convinced me
-that it's worth experimenting 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>
<para>
-I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
-allowing these idioms interesting idioms.
+When doing this hoisting operation, GHC eliminates duplicate constraints. For
+example:
+<programlisting>
+ type Foo a = (?x::Int) => Bool -> a
+ g :: Foo (Foo Int)
+</programlisting>
+means
+<programlisting>
+ g :: (?x::Int) => Bool -> Bool -> Int
+</programlisting>
</para>
</sect3>
<sect2 id="implicit-parameters">
<title>Implicit parameters</title>
-<para> Implicit paramters are implemented as described in
+<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),
</para>
</sect3>
+
+<sect3><title>Implicit parameters and polymorphic recursion</title>
+
+<para>
+Consider these two definitions:
+<programlisting>
+ len1 :: [a] -> Int
+ len1 xs = let ?acc = 0 in len_acc1 xs
+
+ len_acc1 [] = ?acc
+ len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
+
+ ------------
+
+ len2 :: [a] -> Int
+ len2 xs = let ?acc = 0 in len_acc2 xs
+
+ len_acc2 :: (?acc :: Int) => [a] -> Int
+ len_acc2 [] = ?acc
+ len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
+</programlisting>
+The only difference between the two groups is that in the second group
+<literal>len_acc</literal> is given a type signature.
+In the former case, <literal>len_acc1</literal> is monomorphic in its own
+right-hand side, so the implicit parameter <literal>?acc</literal> is not
+passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
+has a type signature, the recursive call is made to the
+<emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
+as an implicit parameter. So we get the following results in GHCi:
+<programlisting>
+ Prog> len1 "hello"
+ 0
+ Prog> len2 "hello"
+ 5
+</programlisting>
+Adding a type signature dramatically changes the result! This is a rather
+counter-intuitive phenomenon, worth watching out for.
+</para>
+</sect3>
+
+<sect3><title>Implicit parameters and monomorphism</title>
+
+<para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
+Haskell Report) to implicit parameters. For example, consider:
+<programlisting>
+ f :: Int -> Int
+ f v = let ?x = 0 in
+ let y = ?x + v in
+ let ?x = 5 in
+ y
+</programlisting>
+Since the binding for <literal>y</literal> falls under the Monomorphism
+Restriction it is not generalised, so the type of <literal>y</literal> is
+simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
+Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
+If you add a type signature for <literal>y</literal>, then <literal>y</literal>
+will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
+<literal>y</literal> in the body of the <literal>let</literal> will see the
+inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
+<literal>14</literal>.
+</para>
+</sect3>
</sect2>
<sect2 id="linear-implicit-parameters">
</para>
<itemizedlist>
<listitem> <para> distributing a supply of unique names </para> </listitem>
-<listitem> <para> distributing a suppply of random numbers </para> </listitem>
+<listitem> <para> distributing a supply of random numbers </para> </listitem>
<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
</itemizedlist>
</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>
-</sect2>
-
-
-
<sect2 id="sec-kinding">
<title>Explicitly-kinded quantification</title>
</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 arrrow. As <literal>g2</literal>
+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>
<title>Type inference</title>
<para>
-In general, type inference for arbitrary-rank types is undecideable.
+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:
</title>
<para>
-A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
-variable</emphasis>. For example
-</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>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
+<listitem><para>A result type signature (<xref linkend="result-type-sigs"/>)</para></listitem>
+</itemizedlist>
+For example:
<programlisting>
f (xs::[a]) = ys ++ ys
where
ys :: [a]
ys = reverse xs
</programlisting>
-
-</para>
-
-<para>
The pattern <literal>(xs::[a])</literal> includes a type signature for <varname>xs</varname>.
This brings the type variable <literal>a</literal> into scope; it scopes over
all the patterns and right hand sides for this equation for <function>f</function>.
</para>
<para>
- Pattern type signatures are completely orthogonal to ordinary, separate
-type signatures. The two can be used independently or together.
At ordinary type signatures, such as that for <varname>ys</varname>, any type variables
mentioned in the type signature <emphasis>that are not in scope</emphasis> are
implicitly universally quantified. (If there are no type variables in
</para>
<sect3>
-<title>What a pattern type signature means</title>
+<title>What a scoped type variable means</title>
<para>
-A type variable brought into scope by a pattern type signature is simply
-the name for a type. The restriction they express is that all occurrences
+A lexically-scoped type variable is simply
+the name for a type. The restriction it expresses is that all occurrences
of the same name mean the same type. For example:
<programlisting>
f :: [Int] -> Int -> Int
</sect3>
-<sect3>
+<sect3 id="decl-type-sigs">
+<title>Declaration type signatures</title>
+<para>A declaration type signature that has <emphasis>explicit</emphasis>
+quantification (using <literal>forall</literal>) brings into scope the
+explicitly-quantified
+type variables, in the definition of the named function(s). For example:
+<programlisting>
+ f :: forall a. [a] -> [a]
+ f (x:xs) = xs ++ [ x :: a ]
+</programlisting>
+The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
+the definition of "<literal>f</literal>".
+</para>
+<para>This only happens if the quantification in <literal>f</literal>'s type
+signature is explicit. For example:
+<programlisting>
+ g :: [a] -> [a]
+ g (x:xs) = xs ++ [ x :: a ]
+</programlisting>
+This program will be rejected, because "<literal>a</literal>" does not scope
+over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
+means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
+quantification rules.
+</para>
+</sect3>
+
+<sect3 id="pattern-type-sigs">
<title>Where a pattern type signature can occur</title>
<para>
<listitem>
<para>
A pattern type signature can be on an arbitrary sub-pattern, not
-ust on a variable:
+just on a variable:
<programlisting>
</listitem>
</itemizedlist>
</para>
+<para>Pattern type signatures are completely orthogonal to ordinary, separate
+type signatures. The two can be used independently or together.</para>
</sect3>
-<sect3>
+<sect3 id="result-type-sigs">
<title>Result type signatures</title>
<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.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
+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">
<para>
As a result of this extension, all derived instances in newtype
-declarations are treated uniformly (and implemented just by reusing
+ 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.
classes usually have one "main" parameter for which deriving new
instances is most interesting.
</para>
+<para>Lastly, all of this applies only for classes other than
+<literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
+and <literal>Data</literal>, for which the built-in derivation applies (section
+4.3.3. of the Haskell Report).
+(For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
+the standard method is used or the one described here.)
+</para>
</sect3>
</sect2>
+<sect2 id="typing-binds">
+<title>Generalised typing of mutually recursive bindings</title>
+
+<para>
+The Haskell Report specifies that a group of bindings (at top level, or in a
+<literal>let</literal> or <literal>where</literal>) should be sorted into
+strongly-connected components, and then type-checked in dependency order
+(<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
+Report, Section 4.5.1</ulink>).
+As each group is type-checked, any binders of the group that
+have
+an explicit type signature are put in the type environment with the specified
+polymorphic type,
+and all others are monomorphic until the group is generalised
+(<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
+</para>
+
+<para>Following a suggestion of Mark Jones, in his paper
+<ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
+Haskell</ulink>,
+GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
+specified:
+<emphasis>the dependency analysis ignores references to variables that have an explicit
+type signature</emphasis>.
+As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
+typecheck. For example, consider:
+<programlisting>
+ f :: Eq a => a -> Bool
+ f x = (x == x) || g True || g "Yes"
+
+ g y = (y <= y) || f True
+</programlisting>
+This is rejected by Haskell 98, but under Jones's scheme the definition for
+<literal>g</literal> is typechecked first, separately from that for
+<literal>f</literal>,
+because the reference to <literal>f</literal> in <literal>g</literal>'s right
+hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
+type is generalised, to get
+<programlisting>
+ g :: Ord a => a -> Bool
+</programlisting>
+Now, the defintion for <literal>f</literal> is typechecked, with this type for
+<literal>g</literal> in the type environment.
+</para>
+
+<para>
+The same refined dependency analysis also allows the type signatures of
+mutually-recursive functions to have different contexts, something that is illegal in
+Haskell 98 (Section 4.5.2, last sentence). With
+<option>-fglasgow-exts</option>
+GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
+type signatures; in practice this means that only variables bound by the same
+pattern binding must have the same context. For example, this is fine:
+<programlisting>
+ f :: Eq a => a -> Bool
+ f x = (x == x) || g True
+
+ g :: Ord a => a -> Bool
+ g y = (y <= y) || f True
+</programlisting>
+</para>
+</sect2>
</sect1>
<!-- ==================== End of type system extensions ================= -->
+<!-- ====================== Generalised algebraic data types ======================= -->
+
+<sect1 id="gadt">
+<title>Generalised Algebraic Data Types</title>
+
+<para>Generalised Algebraic Data Types (GADTs) generalise ordinary algebraic data types by allowing you
+to give the type signatures of constructors explicitly. For example:
+<programlisting>
+ data Term a where
+ Lit :: Int -> Term Int
+ Succ :: Term Int -> Term Int
+ IsZero :: Term Int -> Term Bool
+ If :: Term Bool -> Term a -> Term a -> Term a
+ Pair :: Term a -> Term b -> Term (a,b)
+</programlisting>
+Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
+case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
+for these <literal>Terms</literal>:
+<programlisting>
+ eval :: Term a -> a
+ eval (Lit i) = i
+ eval (Succ t) = 1 + eval t
+ eval (IsZero t) = eval t == 0
+ eval (If b e1 e2) = if eval b then eval e1 else eval e2
+ eval (Pair e1 e2) = (eval e1, eval e2)
+</programlisting>
+These and many other examples are given in papers by Hongwei Xi, and Tim Sheard.
+</para>
+<para> The extensions to GHC are these:
+<itemizedlist>
+<listitem><para>
+ Data type declarations have a 'where' form, as exemplified above. The type signature of
+each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
+Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
+have no scope. Indeed, one can write a kind signature instead:
+<programlisting>
+ data Term :: * -> * where ...
+</programlisting>
+or even a mixture of the two:
+<programlisting>
+ data Foo a :: (* -> *) -> * where ...
+</programlisting>
+The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
+like this:
+<programlisting>
+ data Foo a (b :: * -> *) where ...
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+There are no restrictions on the type of the data constructor, except that the result
+type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
+type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
+</para></listitem>
+
+<listitem><para>
+You can use record syntax on a GADT-style data type declaration:
+
+<programlisting>
+ data Term a where
+ Lit { val :: Int } :: Term Int
+ Succ { num :: Term Int } :: Term Int
+ Pred { num :: Term Int } :: Term Int
+ IsZero { arg :: Term Int } :: Term Bool
+ Pair { arg1 :: Term a
+ , arg2 :: Term b
+ } :: Term (a,b)
+ If { cnd :: Term Bool
+ , tru :: Term a
+ , fls :: Term a
+ } :: Term a
+</programlisting>
+For every constructor that has a field <literal>f</literal>, (a) the type of
+field <literal>f</literal> must be the same; and (b) the
+result type of the constructor must be the same; both modulo alpha conversion.
+Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
+fields above into a
+single name. Although their field types are both <literal>Term Int</literal>,
+their selector functions actually have different types:
+
+<programlisting>
+ num :: Term Int -> Term Int
+ arg :: Term Bool -> Term Int
+</programlisting>
+
+At the moment, record updates are not yet possible with GADT, so support is
+limited to record construction, selection and pattern matching:
+
+<programlisting>
+ someTerm :: Term Bool
+ someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
+
+ eval :: Term a -> a
+ eval Lit { val = i } = i
+ eval Succ { num = t } = eval t + 1
+ eval Pred { num = t } = eval t - 1
+ eval IsZero { arg = t } = eval t == 0
+ eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
+ eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
+</programlisting>
+
+</para></listitem>
+
+<listitem><para>
+You can use strictness annotations, in the obvious places
+in the constructor type:
+<programlisting>
+ data Term a where
+ Lit :: !Int -> Term Int
+ If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
+ Pair :: Term a -> Term b -> Term (a,b)
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+You can use a <literal>deriving</literal> clause on a GADT-style data type
+declaration, but only if the data type could also have been declared in
+Haskell-98 syntax. For example, these two declarations are equivalent
+<programlisting>
+ data Maybe1 a where {
+ Nothing1 :: Maybe a ;
+ Just1 :: a -> Maybe a
+ } deriving( Eq, Ord )
+
+ data Maybe2 a = Nothing2 | Just2 a
+ deriving( Eq, Ord )
+</programlisting>
+This simply allows you to declare a vanilla Haskell-98 data type using the
+<literal>where</literal> form without losing the <literal>deriving</literal> clause.
+</para></listitem>
+
+<listitem><para>
+Pattern matching causes type refinement. For example, in the right hand side of the equation
+<programlisting>
+ eval :: Term a -> a
+ eval (Lit i) = ...
+</programlisting>
+the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
+A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
+about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
+
+<para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
+So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
+occur. However, the refinement is quite general. For example, if we had:
+<programlisting>
+ eval :: Term a -> a -> a
+ eval (Lit i) j = i+j
+</programlisting>
+the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
+of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
+the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
+</para>
+</listitem>
+</itemizedlist>
+</para>
+
+<para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
+<programlisting>
+ data T a = forall b. MkT b (b->a)
+ data T' a where { MKT :: b -> (b->a) -> T' a }
+</programlisting>
+</para>
+</sect1>
+
+<!-- ====================== End of Generalised algebraic data types ======================= -->
+
<!-- ====================== TEMPLATE HASKELL ======================= -->
<sect1 id="template-haskell">
</para>
<para> A splice can occur in place of
<itemizedlist>
- <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
+ <listitem><para> an expression; the spliced expression must
+ have type <literal>Q Exp</literal></para></listitem>
<listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
- <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
+ <listitem><para> [Planned, but not implemented yet.] a
+ type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
</itemizedlist>
(Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
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> <literal>[t| ... |]</literal>, where the "..." is a type;
+ <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
the quotation has type <literal>Type</literal>.</para></listitem>
</itemizedlist></para></listitem>
-- you intend to use it.
-- Import some Template Haskell syntax
-import Language.Haskell.TH.Syntax
+import Language.Haskell.TH
-- Describe a format string
data Format = D | S | L String
it won't make much sense unless you've read Hughes's paper.
This notation is translated to ordinary Haskell,
using combinators from the
-<ulink url="../libraries/base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module.
</para>
</screen>
which is equivalent to
<screen>
-arr (\ x -> (f, x+1)) >>> app
+arr (\ x -> (f x, x+1)) >>> app
</screen>
so in this case the arrow must belong to the <literal>ArrowApply</literal>
class.
the arrow <literal>f</literal>, and matches its output against
<literal>y</literal>.
In the next line, the output is discarded.
-The arrow <literal>returnA</literal> is defined in the
-<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+The arrow <function>returnA</function> is defined in the
+<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module as <literal>arr id</literal>.
The above example is treated as an abbreviation for
<screen>
Note that variables not used later in the composition are projected out.
After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
defined in the
-<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
module, this reduces to
<screen>
arr (\ x -> (x+1, x)) >>>
<para>
It's also possible to have mutually recursive bindings,
using the new <literal>rec</literal> keyword, as in the following example:
-<screen>
+<programlisting>
counter :: ArrowCircuit a => a Bool Int
counter = proc reset -> do
rec output <- returnA -< if reset then 0 else next
next <- delay 0 -< output+1
returnA -< output
-</screen>
-The translation of such forms uses the <literal>loop</literal> combinator,
+</programlisting>
+The translation of such forms uses the <function>loop</function> combinator,
so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
</para>
arr (\ (x,y) -> if f x y then Left x else Right y) >>>
(arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
</screen>
-Since the translation uses <literal>|||</literal>,
+Since the translation uses <function>|||</function>,
the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
</para>
arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
</screen>
at least for strict <literal>k</literal>.
-(This should be automatic if you're not using <literal>seq</literal>.)
+(This should be automatic if you're not using <function>seq</function>.)
This ensures that environments seen by the subcommands are environments
of the whole command,
and also allows the translation to safely trim these environments.
The input to the arrow represented by a command consists of values for
the free local variables in the command, plus a stack of anonymous values.
In all the prior examples, this stack was empty.
-In the second argument to <literal>handleA</literal>,
+In the second argument to <function>handleA</function>,
this stack consists of one value, the value of the exception.
The command form of lambda merely gives this value a name.
</para>
<para>
More concretely,
the values on the stack are paired to the right of the environment.
-So when designing operators like <literal>handleA</literal> that pass
-extra inputs to their subcommands,
+So operators like <function>handleA</function> that pass
+extra inputs to their subcommands can be designed for use with the notation
+by pairing the values with the environment in this way.
More precisely, the type of each argument of the operator (and its result)
should have the form
<screen>
(|runReader (do { ... })|) s
</screen>
which adds <literal>s</literal> to the stack of inputs to the command
-built using <literal>runReader</literal>.
+built using <function>runReader</function>.
</para>
<para>
bind_ :: Arrow a => a e b -> a e c -> a e c
u `bind_` f = u `bind` (arr fst >>> f)
</programlisting>
-We could simulate <literal>do</literal> by defining
+We could simulate <literal>if</literal> by defining
<programlisting>
cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
<listitem>
<para>
The module must import
-<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
+<ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
</para>
</listitem>
</para>
<para>
-To have the compiler ignore uses of assert, use the compiler option
-<option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
-option</primary></indexterm> That is, expressions of the form
+GHC ignores assertions when optimisation is turned on with the
+ <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
<literal>assert pred e</literal> will be rewritten to
-<literal>e</literal>.
-</para>
+<literal>e</literal>. You can also disable assertions using the
+ <option>-fignore-asserts</option>
+ option<indexterm><primary><option>-fignore-asserts</option></primary>
+ </indexterm>.</para>
<para>
Assertion failures can be caught, see the documentation for the
</listitem>
<listitem>
- <para>You can deprecate a function, class, or type, with the
+ <para>You can deprecate a function, class, type, or data constructor, with the
following top-level declaration:</para>
<programlisting>
{-# DEPRECATED f, C, T "Don't use these" #-}
</programlisting>
<para>When you compile any module that imports and uses any
- of the specifed entities, GHC will print the specified
+ of the specified entities, GHC will print the specified
message.</para>
+ <para> You can only depecate entities declared at top level in the module
+ being compiled, and you can only use unqualified names in the list of
+ entities being deprecated. A capitalised name, such as <literal>T</literal>
+ refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
+ <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
+ both are in scope. If both are in scope, there is currently no way to deprecate
+ one without the other (c.f. fixities <xref linkend="infix-tycons"/>).</para>
</listitem>
</itemizedlist>
Any use of the deprecated item, or of anything from a deprecated
<option>-fno-warn-deprecations</option>.</para>
</sect2>
+ <sect2 id="include-pragma">
+ <title>INCLUDE pragma</title>
+
+ <para>The <literal>INCLUDE</literal> pragma is for specifying the names
+ of C header files that should be <literal>#include</literal>'d into
+ the C source code generated by the compiler for the current module (if
+ compiling via C). For example:</para>
+
+<programlisting>
+{-# INCLUDE "foo.h" #-}
+{-# INCLUDE <stdio.h> #-}</programlisting>
+
+ <para>The <literal>INCLUDE</literal> pragma(s) must appear at the top of
+ your source file with any <literal>OPTIONS_GHC</literal>
+ pragma(s).</para>
+
+ <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
+ to the <option>-#include</option> option (<xref
+ linkend="options-C-compiler" />), because the
+ <literal>INCLUDE</literal> pragma is understood by other
+ compilers. Yet another alternative is to add the include file to each
+ <literal>foreign import</literal> declaration in your code, but we
+ don't recommend using this approach with GHC.</para>
+ </sect2>
+
<sect2 id="inline-noinline-pragma">
<title>INLINE and NOINLINE pragmas</title>
The normal unfolding machinery will then be very keen to
inline it.</para>
- <para>Syntactially, an <literal>INLINE</literal> pragma for a
+ <para>Syntactically, an <literal>INLINE</literal> pragma for a
function can be put anywhere its type signature could be
put.</para>
you're very cautious about code size.</para>
<para><literal>NOTINLINE</literal> is a synonym for
- <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
+ <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
specified by Haskell 98 as the standard way to disable
inlining, so it should be used if you want your code to be
portable).</para>
number</emphasis>; the phase number decreases towards zero.
If you use <option>-dverbose-core2core</option> you'll see the
sequence of phase numbers for successive runs of the
- simpifier. In an INLINE pragma you can optionally specify a
+ simplifier. In an INLINE pragma you can optionally specify a
phase number, thus:</para>
<itemizedlist>
</sect3>
</sect2>
+ <sect2 id="language-pragma">
+ <title>LANGUAGE pragma</title>
+
+ <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
+ <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
+
+ <para>This allows language extensions to be enabled in a portable way.
+ It is the intention that all Haskell compilers support the
+ <literal>LANGUAGE</literal> pragma with the same syntax, although not
+ all extensions are supported by all compilers, of
+ course. The <literal>LANGUAGE</literal> pragma should be used instead
+ of <literal>OPTIONS_GHC</literal>, if possible.</para>
+
+ <para>For example, to enable the FFI and preprocessing with CPP:</para>
+
+<programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
+
+ <para>Any extension from the <literal>Extension</literal> type defined in
+ <ulink
+ url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink> may be used. GHC will report an error if any of the requested extensions are not supported.</para>
+ </sect2>
+
+
<sect2 id="line-pragma">
<title>LINE pragma</title>
code. It lets you specify the line number and filename of the
original code; for example</para>
-<programlisting>
-{-# LINE 42 "Foo.vhs" #-}
-</programlisting>
+<programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
<para>if you'd generated the current file from something called
<filename>Foo.vhs</filename> and this line corresponds to line
</sect2>
<sect2 id="options-pragma">
- <title>OPTIONS pragma</title>
- <indexterm><primary>OPTIONS</primary>
+ <title>OPTIONS_GHC pragma</title>
+ <indexterm><primary>OPTIONS_GHC</primary>
</indexterm>
- <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
+ <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
</indexterm>
- <para>The <literal>OPTIONS</literal> pragma is used to specify
+ <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
additional options that are given to the compiler when compiling
this source file. See <xref linkend="source-file-options"/> for
details.</para>
+
+ <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
+ than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
</sect2>
<sect2 id="rules">
overloaded function:</para>
<programlisting>
-hammeredLookup :: Ord key => [(key, value)] -> key -> value
+ hammeredLookup :: Ord key => [(key, value)] -> key -> value
</programlisting>
<para>If it is heavily used on lists with
follows:</para>
<programlisting>
-{-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
+ {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
</programlisting>
<para>A <literal>SPECIALIZE</literal> pragma for a function can
(see <xref linkend="rewrite-rules"/>) that rewrites a call to the
un-specialised function into a call to the specialised one.</para>
- <para>In earlier versions of GHC, it was possible to provide your own
+ <para>The type in a SPECIALIZE pragma can be any type that is less
+ polymorphic than the type of the original function. In concrete terms,
+ if the original function is <literal>f</literal> then the pragma
+<programlisting>
+ {-# SPECIALIZE f :: <type> #-}
+</programlisting>
+ is valid if and only if the defintion
+<programlisting>
+ f_spec :: <type>
+ f_spec = f
+</programlisting>
+ is valid. Here are some examples (where we only give the type signature
+ for the original function, not its code):
+<programlisting>
+ f :: Eq a => a -> b -> b
+ {-# SPECIALISE f :: Int -> b -> b #-}
+
+ g :: (Eq a, Ix b) => a -> b -> b
+ {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
+
+ h :: Eq a => a -> a -> a
+ {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
+</programlisting>
+The last of these examples will generate a
+RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
+well. If you use this kind of specialisation, let us know how well it works.
+</para>
+
+<para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
+<literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
+followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
+The <literal>INLINE</literal> pragma affects the specialised verison of the
+function (only), and applies even if the function is recursive. The motivating
+example is this:
+<programlisting>
+-- A GADT for arrays with type-indexed representation
+data Arr e where
+ ArrInt :: !Int -> ByteArray# -> Arr Int
+ ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
+
+(!:) :: Arr e -> Int -> e
+{-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
+{-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
+(ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
+(ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
+</programlisting>
+Here, <literal>(!:)</literal> is a recursive function that indexes arrays
+of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
+at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
+the specialised function will be inlined. It has two calls to
+<literal>(!:)</literal>,
+both at type <literal>Int</literal>. Both these calls fire the first
+specialisation, whose body is also inlined. The result is a type-based
+unrolling of the indexing function.</para>
+<para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
+on an ordinarily-recursive function.</para>
+
+ <para>Note: In earlier versions of GHC, it was possible to provide your own
specialised function for a given type:
<programlisting>
<sect1 id="rewrite-rules">
<title>Rewrite rules
-<indexterm><primary>RULES pagma</primary></indexterm>
+<indexterm><primary>RULES pragma</primary></indexterm>
<indexterm><primary>pragma, RULES</primary></indexterm>
<indexterm><primary>rewrite rules</primary></indexterm></title>
<para>
GHC makes absolutely no attempt to verify that the LHS and RHS
-of a rule have the same meaning. That is undecideable in general, and
+of a rule have the same meaning. That is undecidable in general, and
infeasible in most interesting cases. The responsibility is entirely the programmer's!
</para>
for matching a rule LHS with an expression. It seeks a substitution
which makes the LHS and expression syntactically equal modulo alpha
conversion. The pattern (rule), but not the expression, is eta-expanded if
-necessary. (Eta-expanding the epression can lead to laziness bugs.)
+necessary. (Eta-expanding the expression can lead to laziness bugs.)
But not beta conversion (that's called higher-order matching).
</para>
<listitem>
<para>
- The defintion of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
+ The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks llike this:
<programlisting>
build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
</programlisting>
- Sematically, this is equivalent to:
+ Semantically, this is equivalent to:
<programlisting>
g x = show x