</para>
<para>
-Executive summary of our extensions:
-</para>
-
- <variablelist>
-
- <varlistentry>
- <term>Unboxed types and primitive operations:</Term>
- <listitem>
- <para>You can get right down to the raw machine types and
- operations; included in this are “primitive
- arrays” (direct access to Big Wads of Bytes). Please
- see <XRef LinkEnd="glasgow-unboxed"> and following.</para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Type system extensions:</term>
- <listitem>
- <para> GHC supports a large number of extensions to Haskell's
- type system. Specifically:</para>
-
- <variablelist>
- <varlistentry>
- <term>Multi-parameter type classes:</term>
- <listitem>
- <para><xref LinkEnd="multi-param-type-classes"></para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Functional dependencies:</term>
- <listitem>
- <para><xref LinkEnd="functional-dependencies"></para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Implicit parameters:</term>
- <listitem>
- <para><xref LinkEnd="implicit-parameters"></para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Local universal quantification:</term>
- <listitem>
- <para><xref LinkEnd="universal-quantification"></para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Extistentially quantification in data types:</term>
- <listitem>
- <para><xref LinkEnd="existential-quantification"></para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Scoped type variables:</term>
- <listitem>
- <para>Scoped type variables enable the programmer to
- supply type signatures for some nested declarations,
- where this would not be legal in Haskell 98. Details in
- <xref LinkEnd="scoped-type-variables">.</para>
- </listitem>
- </varlistentry>
- </variablelist>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Pattern guards</term>
- <listitem>
- <para>Instead of being a boolean expression, a guard is a list
- of qualifiers, exactly as in a list comprehension. See <xref
- LinkEnd="pattern-guards">.</para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Foreign calling:</term>
- <listitem>
- <para>Just what it sounds like. We provide
- <emphasis>lots</emphasis> of rope that you can dangle around
- your neck. Please see <xref LinkEnd="ffi">.</para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Pragmas</term>
- <listitem>
- <para>Pragmas are special instructions to the compiler placed
- in the source file. The pragmas GHC supports are described in
- <xref LinkEnd="pragmas">.</para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Rewrite rules:</term>
- <listitem>
- <para>The programmer can specify rewrite rules as part of the
- source program (in a pragma). GHC applies these rewrite rules
- wherever it can. Details in <xref
- LinkEnd="rewrite-rules">.</para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
- <term>Generic classes:</term>
- <listitem>
- <para>Generic class declarations allow you to define a class
- whose methods say how to work over an arbitrary data type.
- Then it's really easy to make any new type into an instance of
- the class. This generalises the rather ad-hoc "deriving"
- feature of Haskell 98. Details in <xref
- LinkEnd="generic-classes">.</para>
- </listitem>
- </varlistentry>
- </variablelist>
-
-<para>
Before you get too carried away working at the lowest level (e.g.,
sloshing <literal>MutableByteArray#</literal>s around your
program), you may wish to check if there are libraries that provide a
-“Haskellised veneer” over the features you want. See
-<xref linkend="book-hslibs">.
+“Haskellised veneer” over the features you want. The
+separate libraries documentation describes all the libraries that come
+with GHC.
</para>
+<!-- LANGUAGE OPTIONS -->
<sect1 id="options-language">
<title>Language options</title>
</varlistentry>
<varlistentry>
+ <term><option>-ffi</option> and <option>-fffi</option>:</term>
+ <indexterm><primary><option>-ffi</option></primary></indexterm>
+ <indexterm><primary><option>-fffi</option></primary></indexterm>
+ <listitem>
+ <para>This option enables the language extension defined in the
+ Haskell 98 Foreign Function Interface Addendum plus deprecated
+ syntax of previous versions of the FFI for backwards
+ compatibility.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fwith</option>:</term>
+ <indexterm><primary><option>-fwith</option></primary></indexterm>
+ <listitem>
+ <para>This option enables the deprecated <literal>with</literal>
+ keyword for implicit parameters; it is merely provided for backwards
+ compatibility.
+ It is independent of the <option>-fglasgow-exts</option>
+ flag. </para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
<term><option>-fno-monomorphism-restriction</option>:</term>
<indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
<listitem>
<varlistentry>
<term><option>-fallow-overlapping-instances</option></term>
<term><option>-fallow-undecidable-instances</option></term>
+ <term><option>-fallow-incoherent-instances</option></term>
<term><option>-fcontext-stack</option></term>
<indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
<indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
module namespace is flat, and you must not conflict with
any Prelude module.)</para>
- <para>Even though you have not imported the Prelude, all
+ <para>Even though you have not imported the Prelude, most of
the built-in syntax still refers to the built-in Haskell
Prelude types and values, as specified by the Haskell
Report. For example, the type <literal>[Int]</literal>
translation for list comprehensions continues to use
<literal>Prelude.map</literal> etc.</para>
- <para> With one group of exceptions! You may want to
- define your own numeric class hierarchy. It completely
- defeats that purpose if the literal "1" means
- "<literal>Prelude.fromInteger 1</literal>", which is what
- the Haskell Report specifies. So the
- <option>-fno-implicit-prelude</option> flag causes the
- following pieces of built-in syntax to refer to whatever
- is in scope, not the Prelude versions:</para>
-
- <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>
- </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>In an n+k pattern, the standard Prelude
- <literal>Ord</literal> class is used for comparison,
- but the necessary subtraction uses whatever
- "<literal>(-)</literal>" is in scope (not
- "<literal>Prelude.(-)</literal>").</para>
- </listitem>
- </itemizedlist>
+ <para>However, <option>-fno-implicit-prelude</option> does
+ change the handling of certain built-in syntax: see
+ <xref LinkEnd="rebindable-syntax">.</para>
</listitem>
</varlistentry>
</variablelist>
</sect1>
-<sect1 id="primitives">
-<title>Unboxed types and primitive operations
-</title>
-<indexterm><primary>PrelGHC module</primary></indexterm>
+<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
+<!-- included from primitives.sgml -->
+&primitives;
-<para>
-This module defines all the types which are primitive in Glasgow
-Haskell, and the operations provided for them.
-</para>
-<sect2 id="glasgow-unboxed">
-<title>Unboxed types
-</title>
+<!-- TYPE SYSTEM EXTENSIONS -->
+<sect1 id="type-extensions">
+<title>Type system extensions</title>
+
+<sect2 id="nullary-types">
+<title>Data types with no constructors</title>
+
+<para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
+a data type with no constructors. For example:</para>
+
+<programlisting>
+ data S -- S :: *
+ data T a -- T :: * -> *
+</programlisting>
+
+<para>Syntactically, the declaration lacks the "= constrs" part. The
+type can be parameterised over types of any kind, but if the kind is
+not <literal>*</literal> then an explicit kind annotation must be used
+(see <xref linkend="sec-kinding">).</para>
+
+<para>Such data types have only one value, namely bottom.
+Nevertheless, they can be useful when defining "phantom types".</para>
+</sect2>
+
+<sect2 id="infix-tycons">
+<title>Infix type constructors</title>
<para>
-<indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
-</para>
+GHC allows type constructors 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>.
+ 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>.
+ </para></listitem>
+<listitem><para>
+ Back-quotes work
+ as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
+ <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
+ </para></listitem>
+<listitem><para>
+ Fixities may be declared for type constructors just as for data constructors. However,
+ one cannot distinguish between the two in a fixity declaration; a fixity declaration
+ sets the fixity for a data constructor and the corresponding type constructor. For example:
+<screen>
+ infixl 7 T, :*:
+</screen>
+ sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
+ and similarly for <literal>:*:</literal>.
+ <literal>Int `a` Bool</literal>.
+ </para></listitem>
+<listitem><para>
+ Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
+ </para></listitem>
+<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>
-<para>Most types in GHC are <firstterm>boxed</firstterm>, which means
-that values of that type are represented by a pointer to a heap
-object. The representation of a Haskell <literal>Int</literal>, for
-example, is a two-word heap object. An <firstterm>unboxed</firstterm>
-type, however, is represented by the value itself, no pointers or heap
-allocation are involved.
+</itemizedlist>
</para>
+</sect2>
+
+<sect2 id="sec-kinding">
+<title>Explicitly-kinded quantification</title>
<para>
-Unboxed types correspond to the “raw machine” types you
-would use in C: <literal>Int#</literal> (long int),
-<literal>Double#</literal> (double), <literal>Addr#</literal>
-(void *), etc. The <emphasis>primitive operations</emphasis>
-(PrimOps) on these types are what you might expect; e.g.,
-<literal>(+#)</literal> is addition on
-<literal>Int#</literal>s, and is the machine-addition that we all
-know and love—usually one instruction.
+Haskell infers the kind of each type variable. Sometimes it is nice to be able
+to give the kind explicitly as (machine-checked) documentation,
+just as it is nice to give a type signature for a function. On some occasions,
+it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
+John Hughes had to define the data type:
+<Screen>
+ data Set cxt a = Set [a]
+ | Unused (cxt a -> ())
+</Screen>
+The only use for the <literal>Unused</literal> constructor was to force the correct
+kind for the type variable <literal>cxt</literal>.
</para>
-
<para>
-Primitive (unboxed) types cannot be defined in Haskell, and are
-therefore built into the language and compiler. Primitive types are
-always unlifted; that is, a value of a primitive type cannot be
-bottom. We use the convention that primitive types, values, and
-operations have a <literal>#</literal> suffix.
+GHC now instead allows you to specify the kind of a type variable directly, wherever
+a type variable is explicitly bound. Namely:
+<itemizedlist>
+<listitem><para><literal>data</literal> declarations:
+<Screen>
+ data Set (cxt :: * -> *) a = Set [a]
+</Screen></para></listitem>
+<listitem><para><literal>type</literal> declarations:
+<Screen>
+ type T (f :: * -> *) = f Int
+</Screen></para></listitem>
+<listitem><para><literal>class</literal> declarations:
+<Screen>
+ class (Eq a) => C (f :: * -> *) a where ...
+</Screen></para></listitem>
+<listitem><para><literal>forall</literal>'s in type signatures:
+<Screen>
+ f :: forall (cxt :: * -> *). Set cxt Int
+</Screen></para></listitem>
+</itemizedlist>
</para>
<para>
-Primitive values are often represented by a simple bit-pattern, such
-as <literal>Int#</literal>, <literal>Float#</literal>,
-<literal>Double#</literal>. But this is not necessarily the case:
-a primitive value might be represented by a pointer to a
-heap-allocated object. Examples include
-<literal>Array#</literal>, the type of primitive arrays. A
-primitive array is heap-allocated because it is too big a value to fit
-in a register, and would be too expensive to copy around; in a sense,
-it is accidental that it is represented by a pointer. If a pointer
-represents a primitive value, then it really does point to that value:
-no unevaluated thunks, no indirections…nothing can be at the
-other end of the pointer than the primitive value.
+The parentheses are required. Some of the spaces are required too, to
+separate the lexemes. If you write <literal>(f::*->*)</literal> you
+will get a parse error, because "<literal>::*->*</literal>" is a
+single lexeme in Haskell.
</para>
<para>
-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
-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
-arguments and constructor fields are assumed to be pointers: if an
-unboxed integer is stored in one of these, the garbage collector would
-attempt to follow it, leading to unpredictable space leaks. Or a
-<function>seq</function> operation on the polymorphic component may
-attempt to dereference the pointer, with disastrous results. Even
-worse, the unboxed value might be larger than a pointer
-(<literal>Double#</literal> for instance).
+As part of the same extension, you can put kind annotations in types
+as well. Thus:
+<Screen>
+ f :: (Int :: *) -> Int
+ g :: forall a. a -> (a :: *)
+</Screen>
+The syntax is
+<Screen>
+ atype ::= '(' ctype '::' kind ')
+</Screen>
+The parentheses are required.
</para>
+</sect2>
+
+<sect2 id="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>).
+</para>
<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.
+With the <option>-fglasgow-exts</option> GHC lifts this restriction.
</para>
</sect2>
-<sect2 id="unboxed-tuples">
-<title>Unboxed Tuples
+<sect2 id="multi-param-type-classes">
+<title>Multi-parameter type classes
</title>
<para>
-Unboxed tuples aren't really exported by <literal>PrelGHC</literal>,
-they're available by default with <option>-fglasgow-exts</option>. An
-unboxed tuple looks like this:
+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
+classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
+Jones, Erik Meijer).
</para>
<para>
-
-<programlisting>
-(# e_1, ..., e_n #)
-</programlisting>
-
+I'd like to thank people who reported shorcomings in the GHC 3.02
+implementation. Our default decisions were all conservative ones, and
+the experience of these heroic pioneers has given useful concrete
+examples to support several generalisations. (These appear below as
+design choices not implemented in 3.02.)
</para>
<para>
-where <literal>e_1..e_n</literal> are expressions of any
-type (primitive or non-primitive). The type of an unboxed tuple looks
-the same.
+I've discussed these notes with Mark Jones, and I believe that Hugs
+will migrate towards the same design choices as I outline here.
+Thanks to him, and to many others who have offered very useful
+feedback.
</para>
-<para>
-Unboxed tuples are used for functions that need to return multiple
-values, but they avoid the heap allocation normally associated with
-using fully-fledged tuples. When an unboxed tuple is returned, the
-components are put directly into registers or on the stack; the
-unboxed tuple itself does not have a composite representation. Many
-of the primitive operations listed in this section return unboxed
-tuples.
-</para>
+<sect3>
+<title>Types</title>
<para>
-There are some pretty stringent restrictions on the use of unboxed tuples:
+There are the following restrictions on the form of a qualified
+type:
</para>
<para>
-<itemizedlist>
-<listitem>
-
-<para>
- 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.
+<programlisting>
+ forall tv1..tvn (c1, ...,cn) => type
+</programlisting>
</para>
-</listitem>
-<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:
+(Here, I write the "foralls" explicitly, although the Haskell source
+language omits them; in Haskell 1.4, all the free type variables of an
+explicit source-language type signature are universally quantified,
+except for the class type variables in a class declaration. However,
+in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
+</para>
+<para>
-<programlisting>
-f x y = (# x+1, y-1 #)
-g x = case f x x of { (# a, b #) -> a + b }
-</programlisting>
+<OrderedList>
+<listitem>
+<para>
+ <emphasis>Each universally quantified type variable
+<literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
-but the following are invalid:
+The reason for this is that a value with a type that does not obey
+this restriction could not be used without introducing
+ambiguity. Here, for example, is an illegal type:
<programlisting>
-f x y = g (# x, y #)
-g (# x, y #) = x + y
+ forall a. Eq a => Int
</programlisting>
+When a value with this type was used, the constraint <literal>Eq tv</literal>
+would be introduced where <literal>tv</literal> is a fresh type variable, and
+(in the dictionary-translation implementation) the value would be
+applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
+can never know which instance of <literal>Eq</literal> to use because we never
+get any more information about <literal>tv</literal>.
+
</para>
</listitem>
<listitem>
<para>
- No variable can have an unboxed tuple type. This is illegal:
+ <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>
-f :: (# Int, Int #) -> (# Int, Int #)
-f x = x
+ forall a. C a b => burble
</programlisting>
-because <literal>x</literal> has an unboxed tuple type.
+The next type is illegal because the constraint <literal>Eq b</literal> does not
+mention <literal>a</literal>:
-</para>
-</listitem>
-</itemizedlist>
+<programlisting>
+ forall a. Eq b => burble
+</programlisting>
-</para>
-<para>
-Note: we may relax some of these restrictions in the future.
-</para>
+The reason for this restriction is milder than the other one. The
+excluded types are never useful or necessary (because the offending
+context doesn't need to be witnessed at this point; it can be floated
+out). Furthermore, floating them out increases sharing. Lastly,
+excluding them is a conservative choice; it leaves a patch of
+territory free in case we need it later.
-<para>
-The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
-tuples to avoid unnecessary allocation during sequences of operations.
</para>
+</listitem>
-</sect2>
-
-<sect2>
-<title>Character and numeric types</title>
+</OrderedList>
-<indexterm><primary>character types, primitive</primary></indexterm>
-<indexterm><primary>numeric types, primitive</primary></indexterm>
-<indexterm><primary>integer types, primitive</primary></indexterm>
-<indexterm><primary>floating point types, primitive</primary></indexterm>
-<para>
-There are the following obvious primitive types:
</para>
-<programlisting>
-type Char#
-type Int#
-type Word#
-type Addr#
-type Float#
-type Double#
-type Int64#
-type Word64#
-</programlisting>
-
-<indexterm><primary><literal>Char#</literal></primary></indexterm>
-<indexterm><primary><literal>Int#</literal></primary></indexterm>
-<indexterm><primary><literal>Word#</literal></primary></indexterm>
-<indexterm><primary><literal>Addr#</literal></primary></indexterm>
-<indexterm><primary><literal>Float#</literal></primary></indexterm>
-<indexterm><primary><literal>Double#</literal></primary></indexterm>
-<indexterm><primary><literal>Int64#</literal></primary></indexterm>
-<indexterm><primary><literal>Word64#</literal></primary></indexterm>
-
<para>
-If you really want to know their exact equivalents in C, see
-<filename>ghc/includes/StgTypes.h</filename> in the GHC source tree.
+These restrictions apply to all types, whether declared in a type signature
+or inferred.
</para>
<para>
-Literals for these types may be written as follows:
+Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
+the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
+are perfectly OK
</para>
<para>
<programlisting>
-1# an Int#
-1.2# a Float#
-1.34## a Double#
-'a'# a Char#; for weird characters, use e.g. '\o<octal>'#
-"a"# an Addr# (a `char *'); only characters '\0'..'\255' allowed
+ f :: Eq (m a) => [m a] -> [m a]
+ g :: Eq [a] => ...
</programlisting>
-<indexterm><primary>literals, primitive</primary></indexterm>
-<indexterm><primary>constants, primitive</primary></indexterm>
-<indexterm><primary>numbers, primitive</primary></indexterm>
</para>
-</sect2>
-
-<sect2>
-<title>Comparison operations</title>
-
<para>
-<indexterm><primary>comparisons, primitive</primary></indexterm>
-<indexterm><primary>operators, comparison</primary></indexterm>
+This choice recovers principal types, a property that Haskell 1.4 does not have.
</para>
-<para>
-
-<programlisting>
-{>,>=,==,/=,<,<=}# :: Int# -> Int# -> Bool
-
-{gt,ge,eq,ne,lt,le}Char# :: Char# -> Char# -> Bool
- -- ditto for Word# and Addr#
-</programlisting>
+</sect3>
-<indexterm><primary><literal>>#</literal></primary></indexterm>
-<indexterm><primary><literal>>=#</literal></primary></indexterm>
-<indexterm><primary><literal>==#</literal></primary></indexterm>
-<indexterm><primary><literal>/=#</literal></primary></indexterm>
-<indexterm><primary><literal><#</literal></primary></indexterm>
-<indexterm><primary><literal><=#</literal></primary></indexterm>
-<indexterm><primary><literal>gt{Char,Word,Addr}#</literal></primary></indexterm>
-<indexterm><primary><literal>ge{Char,Word,Addr}#</literal></primary></indexterm>
-<indexterm><primary><literal>eq{Char,Word,Addr}#</literal></primary></indexterm>
-<indexterm><primary><literal>ne{Char,Word,Addr}#</literal></primary></indexterm>
-<indexterm><primary><literal>lt{Char,Word,Addr}#</literal></primary></indexterm>
-<indexterm><primary><literal>le{Char,Word,Addr}#</literal></primary></indexterm>
-</para>
+<sect3>
+<title>Class declarations</title>
-</sect2>
+<para>
-<sect2>
-<title>Primitive-character operations</title>
+<OrderedList>
+<listitem>
<para>
-<indexterm><primary>characters, primitive operations</primary></indexterm>
-<indexterm><primary>operators, primitive character</primary></indexterm>
-</para>
+ <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
-<para>
<programlisting>
-ord# :: Char# -> Int#
-chr# :: Int# -> Char#
+ class Collection c a where
+ union :: c a -> c a -> c a
+ ...etc.
</programlisting>
-<indexterm><primary><literal>ord#</literal></primary></indexterm>
-<indexterm><primary><literal>chr#</literal></primary></indexterm>
-</para>
-
-</sect2>
-<sect2>
-<title>Primitive-<literal>Int</literal> operations</title>
-<para>
-<indexterm><primary>integers, primitive operations</primary></indexterm>
-<indexterm><primary>operators, primitive integer</primary></indexterm>
</para>
+</listitem>
+<listitem>
<para>
+ <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
+of "acyclic" involves only the superclass relationships. For example,
+this is OK:
-<programlisting>
-{+,-,*,quotInt,remInt,gcdInt}# :: Int# -> Int# -> Int#
-negateInt# :: Int# -> Int#
-iShiftL#, iShiftRA#, iShiftRL# :: Int# -> Int# -> Int#
- -- shift left, right arithmetic, right logical
+<programlisting>
+ class C a where {
+ op :: D b => a -> b -> b
+ }
-addIntC#, subIntC#, mulIntC# :: Int# -> Int# -> (# Int#, Int# #)
- -- add, subtract, multiply with carry
+ class C a => D a where { ... }
</programlisting>
-<indexterm><primary><literal>+#</literal></primary></indexterm>
-<indexterm><primary><literal>-#</literal></primary></indexterm>
-<indexterm><primary><literal>*#</literal></primary></indexterm>
-<indexterm><primary><literal>quotInt#</literal></primary></indexterm>
-<indexterm><primary><literal>remInt#</literal></primary></indexterm>
-<indexterm><primary><literal>gcdInt#</literal></primary></indexterm>
-<indexterm><primary><literal>iShiftL#</literal></primary></indexterm>
-<indexterm><primary><literal>iShiftRA#</literal></primary></indexterm>
-<indexterm><primary><literal>iShiftRL#</literal></primary></indexterm>
-<indexterm><primary><literal>addIntC#</literal></primary></indexterm>
-<indexterm><primary><literal>subIntC#</literal></primary></indexterm>
-<indexterm><primary><literal>mulIntC#</literal></primary></indexterm>
-<indexterm><primary>shift operations, integer</primary></indexterm>
-</para>
-
-<para>
-<emphasis>Note:</emphasis> No error/overflow checking!
-</para>
-
-</sect2>
-<sect2>
-<title>Primitive-<literal>Double</literal> and <literal>Float</literal> operations</title>
+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>
-<indexterm><primary>floating point numbers, primitive</primary></indexterm>
-<indexterm><primary>operators, primitive floating point</primary></indexterm>
</para>
+</listitem>
+<listitem>
<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>
-{+,-,*,/}## :: Double# -> Double# -> Double#
-{<,<=,==,/=,>=,>}## :: Double# -> Double# -> Bool
-negateDouble# :: Double# -> Double#
-double2Int# :: Double# -> Int#
-int2Double# :: Int# -> Double#
+ class Functor (m k) => FiniteMap m k where
+ ...
-{plus,minux,times,divide}Float# :: Float# -> Float# -> Float#
-{gt,ge,eq,ne,lt,le}Float# :: Float# -> Float# -> Bool
-negateFloat# :: Float# -> Float#
-float2Int# :: Float# -> Int#
-int2Float# :: Int# -> Float#
+ class (Monad m, Monad (t m)) => Transform t m where
+ lift :: m a -> (t m) a
</programlisting>
-</para>
-<para>
-<indexterm><primary><literal>+##</literal></primary></indexterm>
-<indexterm><primary><literal>-##</literal></primary></indexterm>
-<indexterm><primary><literal>*##</literal></primary></indexterm>
-<indexterm><primary><literal>/##</literal></primary></indexterm>
-<indexterm><primary><literal><##</literal></primary></indexterm>
-<indexterm><primary><literal><=##</literal></primary></indexterm>
-<indexterm><primary><literal>==##</literal></primary></indexterm>
-<indexterm><primary><literal>=/##</literal></primary></indexterm>
-<indexterm><primary><literal>>=##</literal></primary></indexterm>
-<indexterm><primary><literal>>##</literal></primary></indexterm>
-<indexterm><primary><literal>negateDouble#</literal></primary></indexterm>
-<indexterm><primary><literal>double2Int#</literal></primary></indexterm>
-<indexterm><primary><literal>int2Double#</literal></primary></indexterm>
</para>
+</listitem>
+<listitem>
<para>
-<indexterm><primary><literal>plusFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>minusFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>timesFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>divideFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>gtFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>geFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>eqFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>neFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>ltFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>leFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>negateFloat#</literal></primary></indexterm>
-<indexterm><primary><literal>float2Int#</literal></primary></indexterm>
-<indexterm><primary><literal>int2Float#</literal></primary></indexterm>
-</para>
+ <emphasis>In the signature of a class operation, every constraint
+must mention at least one type variable that is not a class type
+variable</emphasis>.
-<para>
-And a full complement of trigonometric functions:
-</para>
+Thus:
-<para>
<programlisting>
-expDouble# :: Double# -> Double#
-logDouble# :: Double# -> Double#
-sqrtDouble# :: Double# -> Double#
-sinDouble# :: Double# -> Double#
-cosDouble# :: Double# -> Double#
-tanDouble# :: Double# -> Double#
-asinDouble# :: Double# -> Double#
-acosDouble# :: Double# -> Double#
-atanDouble# :: Double# -> Double#
-sinhDouble# :: Double# -> Double#
-coshDouble# :: Double# -> Double#
-tanhDouble# :: Double# -> Double#
-powerDouble# :: Double# -> Double# -> Double#
+ class Collection c a where
+ mapC :: Collection c b => (a->b) -> c a -> c b
</programlisting>
-<indexterm><primary>trigonometric functions, primitive</primary></indexterm>
-</para>
-
-<para>
-similarly for <literal>Float#</literal>.
-</para>
-<para>
-There are two coercion functions for <literal>Float#</literal>/<literal>Double#</literal>:
-</para>
+is OK because the constraint <literal>(Collection a b)</literal> mentions
+<literal>b</literal>, even though it also mentions the class variable
+<literal>a</literal>. On the other hand:
-<para>
<programlisting>
-float2Double# :: Float# -> Double#
-double2Float# :: Double# -> Float#
-</programlisting>
-
-<indexterm><primary><literal>float2Double#</literal></primary></indexterm>
-<indexterm><primary><literal>double2Float#</literal></primary></indexterm>
-</para>
-
-<para>
-The primitive version of <function>decodeDouble</function>
-(<function>encodeDouble</function> is implemented as an external C
-function):
-</para>
-
-<para>
-
-<programlisting>
-decodeDouble# :: Double# -> PrelNum.ReturnIntAndGMP
-</programlisting>
-
-<indexterm><primary><literal>encodeDouble#</literal></primary></indexterm>
-<indexterm><primary><literal>decodeDouble#</literal></primary></indexterm>
-</para>
-
-<para>
-(And the same for <literal>Float#</literal>s.)
-</para>
-
-</sect2>
-
-<sect2 id="integer-operations">
-<title>Operations on/for <literal>Integers</literal> (interface to GMP)
-</title>
-
-<para>
-<indexterm><primary>arbitrary precision integers</primary></indexterm>
-<indexterm><primary>Integer, operations on</primary></indexterm>
-</para>
-
-<para>
-We implement <literal>Integers</literal> (arbitrary-precision
-integers) using the GNU multiple-precision (GMP) package (version
-2.0.2).
-</para>
-
-<para>
-The data type for <literal>Integer</literal> is either a small
-integer, represented by an <literal>Int</literal>, or a large integer
-represented using the pieces required by GMP's
-<literal>MP_INT</literal> in <filename>gmp.h</filename> (see
-<filename>gmp.info</filename> in
-<filename>ghc/includes/runtime/gmp</filename>). It comes out as:
-</para>
-
-<para>
-
-<programlisting>
-data Integer = S# Int# -- small integers
- | J# Int# ByteArray# -- large integers
-</programlisting>
-
-<indexterm><primary>Integer type</primary></indexterm> The primitive
-ops to support large <literal>Integers</literal> use the
-“pieces” of the representation, and are as follows:
-</para>
-
-<para>
-
-<programlisting>
-negateInteger# :: Int# -> ByteArray# -> Integer
-
-{plus,minus,times}Integer#, gcdInteger#,
- quotInteger#, remInteger#, divExactInteger#
- :: Int# -> ByteArray#
- -> Int# -> ByteArray#
- -> (# Int#, ByteArray# #)
-
-cmpInteger#
- :: Int# -> ByteArray#
- -> Int# -> ByteArray#
- -> Int# -- -1 for <; 0 for ==; +1 for >
-
-cmpIntegerInt#
- :: Int# -> ByteArray#
- -> Int#
- -> Int# -- -1 for <; 0 for ==; +1 for >
-
-gcdIntegerInt# ::
- :: Int# -> ByteArray#
- -> Int#
- -> Int#
-
-divModInteger#, quotRemInteger#
- :: Int# -> ByteArray#
- -> Int# -> ByteArray#
- -> (# Int#, ByteArray#,
- Int#, ByteArray# #)
-
-integer2Int# :: Int# -> ByteArray# -> Int#
-
-int2Integer# :: Int# -> Integer -- NB: no error-checking on these two!
-word2Integer# :: Word# -> Integer
-
-addr2Integer# :: Addr# -> Integer
- -- the Addr# is taken to be a `char *' string
- -- to be converted into an Integer.
-</programlisting>
-
-<indexterm><primary><literal>negateInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>plusInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>minusInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>timesInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>quotInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>remInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>gcdInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>gcdIntegerInt#</literal></primary></indexterm>
-<indexterm><primary><literal>divExactInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>cmpInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>divModInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>quotRemInteger#</literal></primary></indexterm>
-<indexterm><primary><literal>integer2Int#</literal></primary></indexterm>
-<indexterm><primary><literal>int2Integer#</literal></primary></indexterm>
-<indexterm><primary><literal>word2Integer#</literal></primary></indexterm>
-<indexterm><primary><literal>addr2Integer#</literal></primary></indexterm>
-</para>
-
-</sect2>
-
-<sect2>
-<title>Words and addresses</title>
-
-<para>
-<indexterm><primary>word, primitive type</primary></indexterm>
-<indexterm><primary>address, primitive type</primary></indexterm>
-<indexterm><primary>unsigned integer, primitive type</primary></indexterm>
-<indexterm><primary>pointer, primitive type</primary></indexterm>
-</para>
-
-<para>
-A <literal>Word#</literal> is used for bit-twiddling operations.
-It is the same size as an <literal>Int#</literal>, but has no sign
-nor any arithmetic operations.
-
-<programlisting>
-type Word# -- Same size/etc as Int# but *unsigned*
-type Addr# -- A pointer from outside the "Haskell world" (from C, probably);
- -- described under "arrays"
-</programlisting>
-
-<indexterm><primary><literal>Word#</literal></primary></indexterm>
-<indexterm><primary><literal>Addr#</literal></primary></indexterm>
-</para>
-
-<para>
-<literal>Word#</literal>s and <literal>Addr#</literal>s have
-the usual comparison operations. Other
-unboxed-<literal>Word</literal> ops (bit-twiddling and coercions):
-</para>
-
-<para>
-
-<programlisting>
-{gt,ge,eq,ne,lt,le}Word# :: Word# -> Word# -> Bool
-
-and#, or#, xor# :: Word# -> Word# -> Word#
- -- standard bit ops.
-
-quotWord#, remWord# :: Word# -> Word# -> Word#
- -- word (i.e. unsigned) versions are different from int
- -- versions, so we have to provide these explicitly.
-
-not# :: Word# -> Word#
-
-shiftL#, shiftRL# :: Word# -> Int# -> Word#
- -- shift left, right logical
-
-int2Word# :: Int# -> Word# -- just a cast, really
-word2Int# :: Word# -> Int#
-</programlisting>
-
-<indexterm><primary>bit operations, Word and Addr</primary></indexterm>
-<indexterm><primary><literal>gtWord#</literal></primary></indexterm>
-<indexterm><primary><literal>geWord#</literal></primary></indexterm>
-<indexterm><primary><literal>eqWord#</literal></primary></indexterm>
-<indexterm><primary><literal>neWord#</literal></primary></indexterm>
-<indexterm><primary><literal>ltWord#</literal></primary></indexterm>
-<indexterm><primary><literal>leWord#</literal></primary></indexterm>
-<indexterm><primary><literal>and#</literal></primary></indexterm>
-<indexterm><primary><literal>or#</literal></primary></indexterm>
-<indexterm><primary><literal>xor#</literal></primary></indexterm>
-<indexterm><primary><literal>not#</literal></primary></indexterm>
-<indexterm><primary><literal>quotWord#</literal></primary></indexterm>
-<indexterm><primary><literal>remWord#</literal></primary></indexterm>
-<indexterm><primary><literal>shiftL#</literal></primary></indexterm>
-<indexterm><primary><literal>shiftRA#</literal></primary></indexterm>
-<indexterm><primary><literal>shiftRL#</literal></primary></indexterm>
-<indexterm><primary><literal>int2Word#</literal></primary></indexterm>
-<indexterm><primary><literal>word2Int#</literal></primary></indexterm>
-</para>
-
-<para>
-Unboxed-<literal>Addr</literal> ops (C casts, really):
-
-<programlisting>
-{gt,ge,eq,ne,lt,le}Addr# :: Addr# -> Addr# -> Bool
-
-int2Addr# :: Int# -> Addr#
-addr2Int# :: Addr# -> Int#
-addr2Integer# :: Addr# -> (# Int#, ByteArray# #)
-</programlisting>
-
-<indexterm><primary><literal>gtAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>geAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>eqAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>neAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>ltAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>leAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>int2Addr#</literal></primary></indexterm>
-<indexterm><primary><literal>addr2Int#</literal></primary></indexterm>
-<indexterm><primary><literal>addr2Integer#</literal></primary></indexterm>
-</para>
-
-<para>
-The casts between <literal>Int#</literal>,
-<literal>Word#</literal> and <literal>Addr#</literal>
-correspond to null operations at the machine level, but are required
-to keep the Haskell type checker happy.
-</para>
-
-<para>
-Operations for indexing off of C pointers
-(<literal>Addr#</literal>s) to snatch values are listed under
-“arrays”.
-</para>
-
-</sect2>
-
-<sect2>
-<title>Arrays</title>
-
-<para>
-<indexterm><primary>arrays, primitive</primary></indexterm>
-</para>
-
-<para>
-The type <literal>Array# elt</literal> is the type of primitive,
-unpointed arrays of values of type <literal>elt</literal>.
-</para>
-
-<para>
-
-<programlisting>
-type Array# elt
-</programlisting>
-
-<indexterm><primary><literal>Array#</literal></primary></indexterm>
-</para>
-
-<para>
-<literal>Array#</literal> is more primitive than a Haskell
-array—indeed, the Haskell <literal>Array</literal> interface is
-implemented using <literal>Array#</literal>—in that an
-<literal>Array#</literal> is indexed only by
-<literal>Int#</literal>s, starting at zero. It is also more
-primitive by virtue of being unboxed. That doesn't mean that it isn't
-a heap-allocated object—of course, it is. Rather, being unboxed
-means that it is represented by a pointer to the array itself, and not
-to a thunk which will evaluate to the array (or to bottom). The
-components of an <literal>Array#</literal> are themselves boxed.
-</para>
-
-<para>
-The type <literal>ByteArray#</literal> is similar to
-<literal>Array#</literal>, except that it contains just a string
-of (non-pointer) bytes.
-</para>
-
-<para>
-
-<programlisting>
-type ByteArray#
-</programlisting>
-
-<indexterm><primary><literal>ByteArray#</literal></primary></indexterm>
-</para>
-
-<para>
-Arrays of these types are useful when a Haskell program wishes to
-construct a value to pass to a C procedure. It is also possible to use
-them to build (say) arrays of unboxed characters for internal use in a
-Haskell program. Given these uses, <literal>ByteArray#</literal>
-is deliberately a bit vague about the type of its components.
-Operations are provided to extract values of type
-<literal>Char#</literal>, <literal>Int#</literal>,
-<literal>Float#</literal>, <literal>Double#</literal>, and
-<literal>Addr#</literal> from arbitrary offsets within a
-<literal>ByteArray#</literal>. (For type
-<literal>Foo#</literal>, the $i$th offset gets you the $i$th
-<literal>Foo#</literal>, not the <literal>Foo#</literal> at
-byte-position $i$. Mumble.) (If you want a
-<literal>Word#</literal>, grab an <literal>Int#</literal>,
-then coerce it.)
-</para>
-
-<para>
-Lastly, we have static byte-arrays, of type
-<literal>Addr#</literal> [mentioned previously]. (Remember
-the duality between arrays and pointers in C.) Arrays of this types
-are represented by a pointer to an array in the world outside Haskell,
-so this pointer is not followed by the garbage collector. In other
-respects they are just like <literal>ByteArray#</literal>. They
-are only needed in order to pass values from C to Haskell.
-</para>
-
-</sect2>
-
-<sect2>
-<title>Reading and writing</title>
-
-<para>
-Primitive arrays are linear, and indexed starting at zero.
-</para>
-
-<para>
-The size and indices of a <literal>ByteArray#</literal>, <literal>Addr#</literal>, and
-<literal>MutableByteArray#</literal> are all in bytes. It's up to the program to
-calculate the correct byte offset from the start of the array. This
-allows a <literal>ByteArray#</literal> to contain a mixture of values of different
-type, which is often needed when preparing data for and unpicking
-results from C. (Umm…not true of indices…WDP 95/09)
-</para>
-
-<para>
-<emphasis>Should we provide some <literal>sizeOfDouble#</literal> constants?</emphasis>
-</para>
-
-<para>
-Out-of-range errors on indexing should be caught by the code which
-uses the primitive operation; the primitive operations themselves do
-<emphasis>not</emphasis> check for out-of-range indexes. The intention is that the
-primitive ops compile to one machine instruction or thereabouts.
-</para>
-
-<para>
-We use the terms “reading” and “writing” to refer to accessing
-<emphasis>mutable</emphasis> arrays (see <xref LinkEnd="sect-mutable">), and
-“indexing” to refer to reading a value from an <emphasis>immutable</emphasis>
-array.
-</para>
-
-<para>
-Immutable byte arrays are straightforward to index (all indices in bytes):
-
-<programlisting>
-indexCharArray# :: ByteArray# -> Int# -> Char#
-indexIntArray# :: ByteArray# -> Int# -> Int#
-indexAddrArray# :: ByteArray# -> Int# -> Addr#
-indexFloatArray# :: ByteArray# -> Int# -> Float#
-indexDoubleArray# :: ByteArray# -> Int# -> Double#
-
-indexCharOffAddr# :: Addr# -> Int# -> Char#
-indexIntOffAddr# :: Addr# -> Int# -> Int#
-indexFloatOffAddr# :: Addr# -> Int# -> Float#
-indexDoubleOffAddr# :: Addr# -> Int# -> Double#
-indexAddrOffAddr# :: Addr# -> Int# -> Addr#
- -- Get an Addr# from an Addr# offset
-</programlisting>
-
-<indexterm><primary><literal>indexCharArray#</literal></primary></indexterm>
-<indexterm><primary><literal>indexIntArray#</literal></primary></indexterm>
-<indexterm><primary><literal>indexAddrArray#</literal></primary></indexterm>
-<indexterm><primary><literal>indexFloatArray#</literal></primary></indexterm>
-<indexterm><primary><literal>indexDoubleArray#</literal></primary></indexterm>
-<indexterm><primary><literal>indexCharOffAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>indexIntOffAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>indexFloatOffAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>indexDoubleOffAddr#</literal></primary></indexterm>
-<indexterm><primary><literal>indexAddrOffAddr#</literal></primary></indexterm>
-</para>
-
-<para>
-The last of these, <function>indexAddrOffAddr#</function>, extracts an <literal>Addr#</literal> using an offset
-from another <literal>Addr#</literal>, thereby providing the ability to follow a chain of
-C pointers.
-</para>
-
-<para>
-Something a bit more interesting goes on when indexing arrays of boxed
-objects, because the result is simply the boxed object. So presumably
-it should be entered—we never usually return an unevaluated
-object! This is a pain: primitive ops aren't supposed to do
-complicated things like enter objects. The current solution is to
-return a single element unboxed tuple (see <xref LinkEnd="unboxed-tuples">).
-</para>
-
-<para>
-
-<programlisting>
-indexArray# :: Array# elt -> Int# -> (# elt #)
-</programlisting>
-
-<indexterm><primary><literal>indexArray#</literal></primary></indexterm>
-</para>
-
-</sect2>
-
-<sect2>
-<title>The state type</title>
-
-<para>
-<indexterm><primary><literal>state, primitive type</literal></primary></indexterm>
-<indexterm><primary><literal>State#</literal></primary></indexterm>
-</para>
-
-<para>
-The primitive type <literal>State#</literal> represents the state of a state
-transformer. It is parameterised on the desired type of state, which
-serves to keep states from distinct threads distinct from one another.
-But the <emphasis>only</emphasis> effect of this parameterisation is in the type
-system: all values of type <literal>State#</literal> are represented in the same way.
-Indeed, they are all represented by nothing at all! The code
-generator “knows” to generate no code, and allocate no registers
-etc, for primitive states.
-</para>
-
-<para>
-
-<programlisting>
-type State# s
-</programlisting>
-
-</para>
-
-<para>
-The type <literal>GHC.RealWorld</literal> is truly opaque: there are no values defined
-of this type, and no operations over it. It is “primitive” in that
-sense - but it is <emphasis>not unlifted!</emphasis> Its only role in life is to be
-the type which distinguishes the <literal>IO</literal> state transformer.
-</para>
-
-<para>
-
-<programlisting>
-data RealWorld
-</programlisting>
-
-</para>
-
-</sect2>
-
-<sect2>
-<title>State of the world</title>
-
-<para>
-A single, primitive, value of type <literal>State# RealWorld</literal> is provided.
-</para>
-
-<para>
-
-<programlisting>
-realWorld# :: State# RealWorld
-</programlisting>
-
-<indexterm><primary>realWorld# state object</primary></indexterm>
-</para>
-
-<para>
-(Note: in the compiler, not a <literal>PrimOp</literal>; just a mucho magic
-<literal>Id</literal>. Exported from <literal>GHC</literal>, though).
-</para>
-
-</sect2>
-
-<sect2 id="sect-mutable">
-<title>Mutable arrays</title>
-
-<para>
-<indexterm><primary>mutable arrays</primary></indexterm>
-<indexterm><primary>arrays, mutable</primary></indexterm>
-Corresponding to <literal>Array#</literal> and <literal>ByteArray#</literal>, we have the types of
-mutable versions of each. In each case, the representation is a
-pointer to a suitable block of (mutable) heap-allocated storage.
-</para>
-
-<para>
-
-<programlisting>
-type MutableArray# s elt
-type MutableByteArray# s
-</programlisting>
-
-<indexterm><primary><literal>MutableArray#</literal></primary></indexterm>
-<indexterm><primary><literal>MutableByteArray#</literal></primary></indexterm>
-</para>
-
-<sect3>
-<title>Allocation</title>
-
-<para>
-<indexterm><primary>mutable arrays, allocation</primary></indexterm>
-<indexterm><primary>arrays, allocation</primary></indexterm>
-<indexterm><primary>allocation, of mutable arrays</primary></indexterm>
-</para>
-
-<para>
-Mutable arrays can be allocated. Only pointer-arrays are initialised;
-arrays of non-pointers are filled in by “user code” rather than by
-the array-allocation primitive. Reason: only the pointer case has to
-worry about GC striking with a partly-initialised array.
-</para>
-
-<para>
-
-<programlisting>
-newArray# :: Int# -> elt -> State# s -> (# State# s, MutableArray# s elt #)
-
-newCharArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
-newIntArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
-newAddrArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
-newFloatArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
-newDoubleArray# :: Int# -> State# s -> (# State# s, MutableByteArray# s elt #)
-</programlisting>
-
-<indexterm><primary><literal>newArray#</literal></primary></indexterm>
-<indexterm><primary><literal>newCharArray#</literal></primary></indexterm>
-<indexterm><primary><literal>newIntArray#</literal></primary></indexterm>
-<indexterm><primary><literal>newAddrArray#</literal></primary></indexterm>
-<indexterm><primary><literal>newFloatArray#</literal></primary></indexterm>
-<indexterm><primary><literal>newDoubleArray#</literal></primary></indexterm>
-</para>
-
-<para>
-The size of a <literal>ByteArray#</literal> is given in bytes.
-</para>
-
-</sect3>
-
-<sect3>
-<title>Reading and writing</title>
-
-<para>
-<indexterm><primary>arrays, reading and writing</primary></indexterm>
-</para>
-
-<para>
-
-<programlisting>
-readArray# :: MutableArray# s elt -> Int# -> State# s -> (# State# s, elt #)
-readCharArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Char# #)
-readIntArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Int# #)
-readAddrArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Addr# #)
-readFloatArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Float# #)
-readDoubleArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Double# #)
-
-writeArray# :: MutableArray# s elt -> Int# -> elt -> State# s -> State# s
-writeCharArray# :: MutableByteArray# s -> Int# -> Char# -> State# s -> State# s
-writeIntArray# :: MutableByteArray# s -> Int# -> Int# -> State# s -> State# s
-writeAddrArray# :: MutableByteArray# s -> Int# -> Addr# -> State# s -> State# s
-writeFloatArray# :: MutableByteArray# s -> Int# -> Float# -> State# s -> State# s
-writeDoubleArray# :: MutableByteArray# s -> Int# -> Double# -> State# s -> State# s
-</programlisting>
-
-<indexterm><primary><literal>readArray#</literal></primary></indexterm>
-<indexterm><primary><literal>readCharArray#</literal></primary></indexterm>
-<indexterm><primary><literal>readIntArray#</literal></primary></indexterm>
-<indexterm><primary><literal>readAddrArray#</literal></primary></indexterm>
-<indexterm><primary><literal>readFloatArray#</literal></primary></indexterm>
-<indexterm><primary><literal>readDoubleArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeCharArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeIntArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeAddrArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeFloatArray#</literal></primary></indexterm>
-<indexterm><primary><literal>writeDoubleArray#</literal></primary></indexterm>
-</para>
-
-</sect3>
-
-<sect3>
-<title>Equality</title>
-
-<para>
-<indexterm><primary>arrays, testing for equality</primary></indexterm>
-</para>
-
-<para>
-One can take “equality” of mutable arrays. What is compared is the
-<emphasis>name</emphasis> or reference to the mutable array, not its contents.
-</para>
-
-<para>
-
-<programlisting>
-sameMutableArray# :: MutableArray# s elt -> MutableArray# s elt -> Bool
-sameMutableByteArray# :: MutableByteArray# s -> MutableByteArray# s -> Bool
-</programlisting>
-
-<indexterm><primary><literal>sameMutableArray#</literal></primary></indexterm>
-<indexterm><primary><literal>sameMutableByteArray#</literal></primary></indexterm>
-</para>
-
-</sect3>
-
-<sect3>
-<title>Freezing mutable arrays</title>
-
-<para>
-<indexterm><primary>arrays, freezing mutable</primary></indexterm>
-<indexterm><primary>freezing mutable arrays</primary></indexterm>
-<indexterm><primary>mutable arrays, freezing</primary></indexterm>
-</para>
-
-<para>
-Only unsafe-freeze has a primitive. (Safe freeze is done directly in Haskell
-by copying the array and then using <function>unsafeFreeze</function>.)
-</para>
-
-<para>
-
-<programlisting>
-unsafeFreezeArray# :: MutableArray# s elt -> State# s -> (# State# s, Array# s elt #)
-unsafeFreezeByteArray# :: MutableByteArray# s -> State# s -> (# State# s, ByteArray# #)
-</programlisting>
-
-<indexterm><primary><literal>unsafeFreezeArray#</literal></primary></indexterm>
-<indexterm><primary><literal>unsafeFreezeByteArray#</literal></primary></indexterm>
-</para>
-
-</sect3>
-
-</sect2>
-
-<sect2>
-<title>Synchronizing variables (M-vars)</title>
-
-<para>
-<indexterm><primary>synchronising variables (M-vars)</primary></indexterm>
-<indexterm><primary>M-Vars</primary></indexterm>
-</para>
-
-<para>
-Synchronising variables are the primitive type used to implement
-Concurrent Haskell's MVars (see the Concurrent Haskell paper for
-the operational behaviour of these operations).
-</para>
-
-<para>
-
-<programlisting>
-type MVar# s elt -- primitive
-
-newMVar# :: State# s -> (# State# s, MVar# s elt #)
-takeMVar# :: SynchVar# s elt -> State# s -> (# State# s, elt #)
-putMVar# :: SynchVar# s elt -> State# s -> State# s
-</programlisting>
-
-<indexterm><primary><literal>SynchVar#</literal></primary></indexterm>
-<indexterm><primary><literal>newSynchVar#</literal></primary></indexterm>
-<indexterm><primary><literal>takeMVar</literal></primary></indexterm>
-<indexterm><primary><literal>putMVar</literal></primary></indexterm>
-</para>
-
-</sect2>
-
-</sect1>
-
-<sect1 id="glasgow-ST-monad">
-<title>Primitive state-transformer monad
-</title>
-
-<para>
-<indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
-<indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
-</para>
-
-<para>
-This monad underlies our implementation of arrays, mutable and
-immutable, and our implementation of I/O, including “C calls”.
-</para>
-
-<para>
-The <literal>ST</literal> library, which provides access to the
-<function>ST</function> monad, is described in <xref
-linkend="sec-ST">.
-</para>
-
-</sect1>
-
-<sect1 id="glasgow-prim-arrays">
-<title>Primitive arrays, mutable and otherwise
-</title>
-
-<para>
-<indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
-<indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
-</para>
-
-<para>
-GHC knows about quite a few flavours of Large Swathes of Bytes.
-</para>
-
-<para>
-First, GHC distinguishes between primitive arrays of (boxed) Haskell
-objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
-<literal>ByteArray#</literal>).
-</para>
-
-<para>
-Second, it distinguishes between…
-<variablelist>
-
-<varlistentry>
-<term>Immutable:</term>
-<listitem>
-<para>
-Arrays that do not change (as with “standard” Haskell arrays); you
-can only read from them. Obviously, they do not need the care and
-attention of the state-transformer monad.
-</para>
-</listitem>
-</varlistentry>
-<varlistentry>
-<term>Mutable:</term>
-<listitem>
-<para>
-Arrays that may be changed or “mutated.” All the operations on them
-live within the state-transformer monad and the updates happen
-<emphasis>in-place</emphasis>.
-</para>
-</listitem>
-</varlistentry>
-<varlistentry>
-<term>“Static” (in C land):</term>
-<listitem>
-<para>
-A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
-are then primitive operations with which you may merrily grab values
-over in C land, by indexing off the “static” pointer.
-</para>
-</listitem>
-</varlistentry>
-<varlistentry>
-<term>“Stable” pointers:</term>
-<listitem>
-<para>
-If, for some reason, you wish to hand a Haskell pointer (i.e.,
-<emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
-pointer “stable,” so that the garbage collector won't forget that it
-exists. That is, GHC provides a safe way to pass Haskell pointers to
-C.
-</para>
-
-<para>
-Please see <xref LinkEnd="sec-stable-pointers"> for more details.
-</para>
-</listitem>
-</varlistentry>
-<varlistentry>
-<term>“Foreign objects”:</term>
-<listitem>
-<para>
-A “foreign object” is a safe way to pass an external object (a
-C-allocated pointer, say) to Haskell and have Haskell do the Right
-Thing when it no longer references the object. So, for example, C
-could pass a large bitmap over to Haskell and say “please free this
-memory when you're done with it.”
-</para>
-
-<para>
-Please see <xref LinkEnd="sec-ForeignObj"> for more details.
-</para>
-</listitem>
-</varlistentry>
-</variablelist>
-</para>
-
-<para>
-The libraries documentatation gives more details on all these
-“primitive array” types and the operations on them.
-</para>
-
-</sect1>
-
-
-<sect1 id="pattern-guards">
-<title>Pattern guards</title>
-
-<para>
-<indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
-The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
-</para>
-
-<para>
-Suppose we have an abstract data type of finite maps, with a
-lookup operation:
-
-<programlisting>
-lookup :: FiniteMap -> Int -> Maybe Int
-</programlisting>
-
-The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
-where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
-</para>
-
-<programlisting>
-clunky env var1 var2 | ok1 && ok2 = val1 + val2
-| otherwise = var1 + var2
-where
- m1 = lookup env var1
- m2 = lookup env var2
- ok1 = maybeToBool m1
- ok2 = maybeToBool m2
- val1 = expectJust m1
- val2 = expectJust m2
-</programlisting>
-
-<para>
-The auxiliary functions are
-</para>
-
-<programlisting>
-maybeToBool :: Maybe a -> Bool
-maybeToBool (Just x) = True
-maybeToBool Nothing = False
-
-expectJust :: Maybe a -> a
-expectJust (Just x) = x
-expectJust Nothing = error "Unexpected Nothing"
-</programlisting>
-
-<para>
-What is <function>clunky</function> doing? The guard <literal>ok1 &&
-ok2</literal> checks that both lookups succeed, using
-<function>maybeToBool</function> to convert the <function>Maybe</function>
-types to booleans. The (lazily evaluated) <function>expectJust</function>
-calls extract the values from the results of the lookups, and binds the
-returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
-respectively. If either lookup fails, then clunky takes the
-<literal>otherwise</literal> case and returns the sum of its arguments.
-</para>
-
-<para>
-This is certainly legal Haskell, but it is a tremendously verbose and
-un-obvious way to achieve the desired effect. Arguably, a more direct way
-to write clunky would be to use case expressions:
-</para>
-
-<programlisting>
-clunky env var1 var1 = case lookup env var1 of
- Nothing -> fail
- Just val1 -> case lookup env var2 of
- Nothing -> fail
- Just val2 -> val1 + val2
-where
- fail = val1 + val2
-</programlisting>
-
-<para>
-This is a bit shorter, but hardly better. Of course, we can rewrite any set
-of pattern-matching, guarded equations as case expressions; that is
-precisely what the compiler does when compiling equations! The reason that
-Haskell provides guarded equations is because they allow us to write down
-the cases we want to consider, one at a time, independently of each other.
-This structure is hidden in the case version. Two of the right-hand sides
-are really the same (<function>fail</function>), and the whole expression
-tends to become more and more indented.
-</para>
-
-<para>
-Here is how I would write clunky:
-</para>
-
-<programlisting>
-clunky env var1 var1
- | Just val1 <- lookup env var1
- , Just val2 <- lookup env var2
- = val1 + val2
-...other equations for clunky...
-</programlisting>
-
-<para>
-The semantics should be clear enough. The qualifers 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
-tried. If it succeeds, then the appropriate binding takes place, and the
-next qualifier is matched, in the augmented environment. Unlike list
-comprehensions, however, the type of the expression to the right of the
-<literal><-</literal> is the same as the type of the pattern to its
-left. The bindings introduced by pattern guards scope over all the
-remaining guard qualifiers, and over the right hand side of the equation.
-</para>
-
-<para>
-Just as with list comprehensions, boolean expressions can be freely mixed
-with among the pattern guards. For example:
-</para>
-
-<programlisting>
-f x | [y] <- x
- , y > 3
- , Just z <- h y
- = ...
-</programlisting>
-
-<para>
-Haskell's current guards therefore emerge as a special case, in which the
-qualifier list has just one element, a boolean expression.
-</para>
-</sect1>
-
- <sect1 id="sec-ffi">
- <title>The foreign interface</title>
-
- <para>The foreign interface consists of the following components:</para>
-
- <itemizedlist>
- <listitem>
- <para>The Foreign Function Interface language specification
- (included in this manual, in <xref linkend="ffi">).</para>
- </listitem>
-
- <listitem>
- <para>The <literal>Foreign</literal> module (see <xref
- linkend="sec-Foreign">) collects together several interfaces
- which are useful in specifying foreign language
- interfaces, including the following:</para>
-
- <itemizedlist>
- <listitem>
- <para>The <literal>ForeignObj</literal> module (see <xref
- linkend="sec-ForeignObj">), for managing pointers from
- Haskell into the outside world.</para>
- </listitem>
-
- <listitem>
- <para>The <literal>StablePtr</literal> module (see <xref
- linkend="sec-stable-pointers">), for managing pointers
- into Haskell from the outside world.</para>
- </listitem>
-
- <listitem>
- <para>The <literal>CTypes</literal> module (see <xref
- linkend="sec-CTypes">) gives Haskell equivalents for the
- standard C datatypes, for use in making Haskell bindings
- to existing C libraries.</para>
- </listitem>
-
- <listitem>
- <para>The <literal>CTypesISO</literal> module (see <xref
- linkend="sec-CTypesISO">) gives Haskell equivalents for C
- types defined by the ISO C standard.</para>
- </listitem>
-
- <listitem>
- <para>The <literal>Storable</literal> library, for
- primitive marshalling of data types between Haskell and
- the foreign language.</para>
- </listitem>
- </itemizedlist>
-
- </listitem>
- </itemizedlist>
-
-<para>The following sections also give some hints and tips on the use
-of the foreign function interface in GHC.</para>
-
-<sect2 id="glasgow-foreign-headers">
-<title>Using function headers
-</title>
-
-<para>
-<indexterm><primary>C calls, function headers</primary></indexterm>
-</para>
-
-<para>
-When generating C (using the <option>-fvia-C</option> directive), one can assist the
-C compiler in detecting type errors by using the <Command>-#include</Command> directive
-to provide <filename>.h</filename> files containing function headers.
-</para>
-
-<para>
-For example,
-</para>
-
-<para>
-
-<programlisting>
-#include "HsFFI.h"
-
-void initialiseEFS (HsInt size);
-HsInt terminateEFS (void);
-HsForeignObj emptyEFS(void);
-HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
-HsInt lookupEFS (HsForeignObj a, HsInt i);
-</programlisting>
-</para>
-
- <para>The types <literal>HsInt</literal>,
- <literal>HsForeignObj</literal> etc. are described in <xref
- linkend="sec-mapping-table">.</para>
-
- <para>Note that this approach is only
- <emphasis>essential</emphasis> for returning
- <literal>float</literal>s (or if <literal>sizeof(int) !=
- sizeof(int *)</literal> on your architecture) but is a Good
- Thing for anyone who cares about writing solid code. You're
- crazy not to do it.</para>
-
-</sect2>
-
-</sect1>
-
-<sect1 id="multi-param-type-classes">
-<title>Multi-parameter type classes
-</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
-classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
-Jones, Erik Meijer).
-</para>
-
-<para>
-I'd like to thank people who reported shorcomings in the GHC 3.02
-implementation. Our default decisions were all conservative ones, and
-the experience of these heroic pioneers has given useful concrete
-examples to support several generalisations. (These appear below as
-design choices not implemented in 3.02.)
-</para>
-
-<para>
-I've discussed these notes with Mark Jones, and I believe that Hugs
-will migrate towards the same design choices as I outline here.
-Thanks to him, and to many others who have offered very useful
-feedback.
-</para>
-
-<sect2>
-<title>Types</title>
-
-<para>
-There are the following restrictions on the form of a qualified
-type:
-</para>
-
-<para>
-
-<programlisting>
- forall tv1..tvn (c1, ...,cn) => type
-</programlisting>
-
-</para>
-
-<para>
-(Here, I write the "foralls" explicitly, although the Haskell source
-language omits them; in Haskell 1.4, all the free type variables of an
-explicit source-language type signature are universally quantified,
-except for the class type variables in a class declaration. However,
-in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
-</para>
-
-<para>
-
-<OrderedList>
-<listitem>
-
-<para>
- <emphasis>Each universally quantified type variable
-<literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
-
-The reason for this is that a value with a type that does not obey
-this restriction could not be used without introducing
-ambiguity. Here, for example, is an illegal type:
-
-
-<programlisting>
- forall a. Eq a => Int
-</programlisting>
-
-
-When a value with this type was used, the constraint <literal>Eq tv</literal>
-would be introduced where <literal>tv</literal> is a fresh type variable, and
-(in the dictionary-translation implementation) the value would be
-applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
-can never know which instance of <literal>Eq</literal> to use because we never
-get any more information about <literal>tv</literal>.
-
-</para>
-</listitem>
-<listitem>
-
-<para>
- <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
-universally quantified type variables <literal>tvi</literal></emphasis>.
-
-For example, this type is OK because <literal>C a b</literal> mentions the
-universally quantified type variable <literal>b</literal>:
-
-
-<programlisting>
- forall a. C a b => burble
-</programlisting>
-
-
-The next type is illegal because the constraint <literal>Eq b</literal> does not
-mention <literal>a</literal>:
-
-
-<programlisting>
- forall a. Eq b => burble
-</programlisting>
-
-
-The reason for this restriction is milder than the other one. The
-excluded types are never useful or necessary (because the offending
-context doesn't need to be witnessed at this point; it can be floated
-out). Furthermore, floating them out increases sharing. Lastly,
-excluding them is a conservative choice; it leaves a patch of
-territory free in case we need it later.
-
-</para>
-</listitem>
-
-</OrderedList>
-
-</para>
-
-<para>
-These restrictions apply to all types, whether declared in a type signature
-or inferred.
-</para>
-
-<para>
-Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
-the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
-are perfectly OK
-</para>
-
-<para>
-
-<programlisting>
- f :: Eq (m a) => [m a] -> [m a]
- g :: Eq [a] => ...
-</programlisting>
-
-</para>
-
-<para>
-This choice recovers principal types, a property that Haskell 1.4 does not have.
-</para>
-
-</sect2>
-
-<sect2>
-<title>Class declarations</title>
-
-<para>
-
-<OrderedList>
-<listitem>
-
-<para>
- <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
-
-
-<programlisting>
- class Collection c a where
- union :: c a -> c a -> c a
- ...etc.
-</programlisting>
-
-
-
-</para>
-</listitem>
-<listitem>
-
-<para>
- <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
-of "acyclic" involves only the superclass relationships. For example,
-this is OK:
-
-
-<programlisting>
- class C a where {
- op :: D b => a -> b -> b
- }
-
- class C a => D a where { ... }
-</programlisting>
-
-
-Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
-class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
-would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
-
-</para>
-</listitem>
-<listitem>
-
-<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
-</programlisting>
-
-
-</para>
-</listitem>
-<listitem>
-
-<para>
- <emphasis>In the signature of a class operation, every constraint
-must mention at least one type variable that is not a class type
-variable</emphasis>.
-
-Thus:
-
-
-<programlisting>
- class Collection c a where
- mapC :: Collection c b => (a->b) -> c a -> c b
-</programlisting>
-
-
-is OK because the constraint <literal>(Collection a b)</literal> mentions
-<literal>b</literal>, even though it also mentions the class variable
-<literal>a</literal>. On the other hand:
-
-
-<programlisting>
- class C a where
- op :: Eq a => (a,b) -> (a,b)
+ class C a where
+ op :: Eq a => (a,b) -> (a,b)
</programlisting>
</para>
-</sect2>
+</sect3>
-<sect2 id="instance-decls">
+<sect3 id="instance-decls">
<title>Instance declarations</title>
<para>
However, if you give the command line option
<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
-option</primary></indexterm> then two overlapping instance declarations are permitted
-iff
-
+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>
<para>
OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
-(but not identical to <literal>type1</literal>)
-</para>
-</listitem>
-<listitem>
-
-<para>
- OR vice versa
+(but not identical to <literal>type1</literal>), or vice versa.
</para>
</listitem>
-
</itemizedlist>
-
-
Notice that these rules
-
-
<itemizedlist>
<listitem>
</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>
+<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
+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
</para>
-</sect2>
+</sect3>
-</sect1>
+</sect2>
-<sect1 id="implicit-parameters">
+<sect2 id="implicit-parameters">
<title>Implicit parameters
</title>
27th ACM Symposium on Principles of Programming Languages (POPL'00),
Boston, Jan 2000.
</para>
+<para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
+<para>
+A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
+context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
+context. In Haskell, all variables are statically bound. Dynamic
+binding of variables is a notion that goes back to Lisp, but was later
+discarded in more modern incarnations, such as Scheme. Dynamic binding
+can be very confusing in an untyped language, and unfortunately, typed
+languages, in particular Hindley-Milner typed languages like Haskell,
+only support static scoping of variables.
+</para>
+<para>
+However, by a simple extension to the type class system of Haskell, we
+can support dynamic binding. Basically, we express the use of a
+dynamically bound variable as a constraint on the type. These
+constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
+function uses a dynamically-bound variable <literal>?x</literal>
+of type <literal>t'</literal>". For
+example, the following expresses the type of a sort function,
+implicitly parameterized by a comparison function named <literal>cmp</literal>.
+<programlisting>
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+</programlisting>
+The dynamic binding constraints are just a new form of predicate in the type class system.
+</para>
+<para>
+An implicit parameter is introduced by the special form <literal>?x</literal>,
+where <literal>x</literal> is
+any valid identifier. Use if this construct also introduces new
+dynamic binding constraints. For example, the following definition
+shows how we can define an implicitly parameterized sort function in
+terms of an explicitly parameterized <literal>sortBy</literal> function:
+<programlisting>
+ sortBy :: (a -> a -> Bool) -> [a] -> [a]
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+ sort = sortBy ?cmp
+</programlisting>
+Dynamic binding constraints behave just like other type class
+constraints in that they are automatically propagated. Thus, when a
+function is used, its implicit parameters are inherited by the
+function that called it. For example, our <literal>sort</literal> function might be used
+to pick out the least value in a list:
+<programlisting>
+ least :: (?cmp :: a -> a -> Bool) => [a] -> a
+ least xs = fst (sort xs)
+</programlisting>
+Without lifting a finger, the <literal>?cmp</literal> parameter is
+propagated to become a parameter of <literal>least</literal> as well. With explicit
+parameters, the default is that parameters must always be explicit
+propagated. With implicit parameters, the default is to always
+propagate them.
+</para>
<para>
-There should be more documentation, but there isn't (yet). Yell if you need it.
+An implicit parameter differs from other type class constraints in the
+following way: All uses of a particular implicit parameter must have
+the same type. This means that the type of <literal>(?x, ?x)</literal>
+is <literal>(?x::a) => (a,a)</literal>, and not
+<literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
+class constraints.
</para>
+<para>
+An implicit parameter is bound using the standard
+<literal>let</literal> binding form, where the bindings must be a
+collection of simple bindings to implicit-style variables (no
+function-style bindings, and no type signatures); these bindings are
+neither polymorphic or recursive. This form binds the implicit
+parameters arising in the body, not the free variables as a
+<literal>let</literal> or <literal>where</literal> would do. For
+example, we define the <literal>min</literal> function by binding
+<literal>cmp</literal>.</para>
+<programlisting>
+ min :: [a] -> a
+ min = let ?cmp = (<=) in least
+</programlisting>
+<para>
+Note the following points:
<itemizedlist>
+<listitem><para>
+You may not mix implicit-parameter bindings with ordinary bindings in a
+single <literal>let</literal>
+expression; use two nested <literal>let</literal>s instead.
+</para></listitem>
+
+<listitem><para>
+You may put multiple implicit-parameter bindings in a
+single <literal>let</literal> expression; they are <emphasis>not</emphasis> treated
+as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
+Instead they are treated as a non-recursive group, each scoping over the bindings that
+follow. For example, consider:
+<programlisting>
+ f y = let { ?x = y; ?x = ?x+1 } in ?x
+</programlisting>
+This function adds one to its argument.
+</para></listitem>
+
+<listitem><para>
+You may not have an implicit-parameter binding in a <literal>where</literal> clause,
+only in a <literal>let</literal> binding.
+</para></listitem>
+
<listitem>
<para> You can't have an implicit parameter in the context of a class or instance
declaration. For example, both these declarations are illegal:
behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
Easiest thing is to outlaw the offending types.</para>
</listitem>
-
</itemizedlist>
+</para>
-</sect1>
-
+</sect2>
-<sect1 id="functional-dependencies">
-<title>Functional dependencies
+<sect2 id="linear-implicit-parameters">
+<title>Linear implicit parameters
</title>
-
-<para> Functional dependencies are implemented as described by Mark Jones
-in "Type Classes with Functional Dependencies", Mark P. Jones,
-In Proceedings of the 9th European Symposium on Programming,
-ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
+<para>
+Linear implicit parameters are an idea developed by Koen Claessen,
+Mark Shields, and Simon PJ. They address the long-standing
+problem that monads seem over-kill for certain sorts of problem, notably:
</para>
+<itemizedlist>
+<listitem> <para> distributing a supply of unique names </para> </listitem>
+<listitem> <para> distributing a suppply of random numbers </para> </listitem>
+<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
+</itemizedlist>
<para>
-There should be more documentation, but there isn't (yet). Yell if you need it.
+Linear implicit parameters are just like ordinary implicit parameters,
+except that they are "linear" -- that is, they cannot be copied, and
+must be explicitly "split" instead. Linear implicit parameters are
+written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
+(The '/' in the '%' suggests the split!)
</para>
-</sect1>
+<para>
+For example:
+<programlisting>
+ import GHC.Exts( Splittable )
+ data NameSupply = ...
+
+ splitNS :: NameSupply -> (NameSupply, NameSupply)
+ newName :: NameSupply -> Name
+
+ instance Splittable NameSupply where
+ split = splitNS
-<sect1 id="universal-quantification">
-<title>Explicit universal quantification
-</title>
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+ ...more equations for f...
+</programlisting>
+Notice that the implicit parameter %ns is consumed
+<itemizedlist>
+<listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
+<listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
+</itemizedlist>
+</para>
+<para>
+So the translation done by the type checker makes
+the parameter explicit:
+<programlisting>
+ f :: NameSupply -> Env -> Expr -> Expr
+ f ns env (Lam x e) = Lam x' (f ns1 env e)
+ where
+ (ns1,ns2) = splitNS ns
+ x' = newName ns2
+ env = extend env x x'
+</programlisting>
+Notice the call to 'split' introduced by the type checker.
+How did it know to use 'splitNS'? Because what it really did
+was to introduce a call to the overloaded function 'split',
+defined by the class <literal>Splittable</literal>:
+<programlisting>
+ class Splittable a where
+ split :: a -> (a,a)
+</programlisting>
+The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
+split for name supplies. But we can simply write
+<programlisting>
+ g x = (x, %ns, %ns)
+</programlisting>
+and GHC will infer
+<programlisting>
+ g :: (Splittable a, %ns :: a) => b -> (b,a,a)
+</programlisting>
+The <literal>Splittable</literal> class is built into GHC. It's exported by module
+<literal>GHC.Exts</literal>.
+</para>
<para>
-GHC's type system supports explicit universal quantification in
-constructor fields and function arguments. This is useful for things
-like defining <literal>runST</literal> from the state-thread world.
-GHC's syntax for this now agrees with Hugs's, namely:
+Other points:
+<itemizedlist>
+<listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
+are entirely distinct implicit parameters: you
+ can use them together and they won't intefere with each other. </para>
+</listitem>
+
+<listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
+
+<listitem> <para>You cannot have implicit parameters (whether linear or not)
+ in the context of a class or instance declaration. </para></listitem>
+</itemizedlist>
</para>
-<para>
+<sect3><title>Warnings</title>
+<para>
+The monomorphism restriction is even more important than usual.
+Consider the example above:
+<programlisting>
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+</programlisting>
+If we replaced the two occurrences of x' by (newName %ns), which is
+usually a harmless thing to do, we get:
<programlisting>
- forall a b. (Ord a, Eq b) => a -> b -> a
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam (newName %ns) (f env e)
+ where
+ env' = extend env x (newName %ns)
</programlisting>
+But now the name supply is consumed in <emphasis>three</emphasis> places
+(the two calls to newName,and the recursive call to f), so
+the result is utterly different. Urk! We don't even have
+the beta rule.
+</para>
+<para>
+Well, this is an experimental change. With implicit
+parameters we have already lost beta reduction anyway, and
+(as John Launchbury puts it) we can't sensibly reason about
+Haskell programs without knowing their typing.
+</para>
+
+</sect3>
+
+<sect3><title>Recursive functions</title>
+<para>Linear implicit parameters can be particularly tricky when you have a recursive function
+Consider
+<programlisting>
+ foo :: %x::T => Int -> [Int]
+ foo 0 = []
+ foo n = %x : foo (n-1)
+</programlisting>
+where T is some type in class Splittable.</para>
+<para>
+Do you get a list of all the same T's or all different T's
+(assuming that split gives two distinct T's back)?
+</para><para>
+If you supply the type signature, taking advantage of polymorphic
+recursion, you get what you'd probably expect. Here's the
+translated term, where the implicit param is made explicit:
+<programlisting>
+ foo x 0 = []
+ foo x n = let (x1,x2) = split x
+ in x1 : foo x2 (n-1)
+</programlisting>
+But if you don't supply a type signature, GHC uses the Hindley
+Milner trick of using a single monomorphic instance of the function
+for the recursive calls. That is what makes Hindley Milner type inference
+work. So the translation becomes
+<programlisting>
+ foo x = let
+ foom 0 = []
+ foom n = x : foom (n-1)
+ in
+ foom
+</programlisting>
+Result: 'x' is not split, and you get a list of identical T's. So the
+semantics of the program depends on whether or not foo has a type signature.
+Yikes!
+</para><para>
+You may say that this is a good reason to dislike linear implicit parameters
+and you'd be right. That is why they are an experimental feature.
+</para>
+</sect3>
+
+</sect2>
+
+<sect2 id="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>
-The context is, of course, optional. You can't use <literal>forall</literal> as
-a type variable any more!
+There should be more documentation, but there isn't (yet). Yell if you need it.
</para>
+</sect2>
+
+
+<sect2 id="universal-quantification">
+<title>Arbitrary-rank polymorphism
+</title>
<para>
-Haskell type signatures are implicitly quantified. The <literal>forall</literal>
+Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
allows us to say exactly what this means. For example:
</para>
-
<para>
-
<programlisting>
g :: b -> b
</programlisting>
+means this:
+<programlisting>
+ g :: forall b. (b -> b)
+</programlisting>
+The two are treated identically.
+</para>
+
+<para>
+However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
+explicit universal quantification in
+types.
+For example, all the following types are legal:
+<programlisting>
+ f1 :: forall a b. a -> b -> a
+ g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
+
+ f2 :: (forall a. a->a) -> Int -> Int
+ g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
+ f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
+</programlisting>
+Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
+can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
+The <literal>forall</literal> makes explicit the universal quantification that
+is implicitly added by Haskell.
</para>
-
<para>
-means this:
+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>
+shows, the polymorphic type on the left of the function arrow can be overloaded.
</para>
-
<para>
-
+The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
+they have rank-2 types on the left of a function arrow.
+</para>
+<para>
+GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
+arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
+that restriction has now been lifted.)
+In particular, a forall-type (also called a "type scheme"),
+including an operational type class context, is legal:
+<itemizedlist>
+<listitem> <para> On the left of a function arrow </para> </listitem>
+<listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
+<listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
+example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
+field type signatures.</para> </listitem>
+<listitem> <para> As the type of an implicit parameter </para> </listitem>
+<listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
+</itemizedlist>
+There is one place you cannot put a <literal>forall</literal>:
+you cannot instantiate a type variable with a forall-type. So you cannot
+make a forall-type the argument of a type constructor. So these types are illegal:
<programlisting>
- g :: forall b. (b -> b)
+ x1 :: [forall a. a->a]
+ x2 :: (forall a. a->a, Int)
+ x3 :: Maybe (forall a. a->a)
</programlisting>
-
+Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
+a type variable any more!
</para>
-<para>
-The two are treated identically.
-</para>
-<sect2 id="univ">
-<title>Universally-quantified data type fields
+<sect3 id="univ">
+<title>Examples
</title>
<para>
</para>
<para>
-The constructors now have so-called <emphasis>rank 2</emphasis> polymorphic
-types, in which there is a for-all in the argument types.:
+The constructors have rank-2 types:
</para>
<para>
where that is what is wanted. Feedback welcomed.)
</para>
-</sect2>
-
-<sect2>
-<title>Construction </title>
-
<para>
You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
the constructor to suitable values, just as usual. For example,
<para>
<programlisting>
-(T1 (\xy->x) 3) :: T Int
-
-(MkSwizzle sort) :: Swizzle
-(MkSwizzle reverse) :: Swizzle
+ a1 :: T Int
+ a1 = T1 (\xy->x) 3
+
+ a2, a3 :: Swizzle
+ a2 = MkSwizzle sort
+ a3 = MkSwizzle reverse
+
+ a4 :: MonadT Maybe
+ a4 = let r x = Just x
+ b m k = case m of
+ Just y -> k y
+ Nothing -> Nothing
+ in
+ MkMonad r b
-(let r x = Just x
- b m k = case m of
- Just y -> k y
- Nothing -> Nothing
- in
- MkMonad r b) :: MonadT Maybe
+ mkTs :: (forall b. b -> b -> b) -> a -> [T a]
+ mkTs f x y = [T1 f x, T1 f y]
</programlisting>
</para>
does not need the <literal>Ord</literal> constraint.)
</para>
-</sect2>
-
-<sect2>
-<title>Pattern matching</title>
-
<para>
When you use pattern matching, the bound variables may now have
polymorphic types. For example:
<para>
<programlisting>
- f :: T a -> a -> (a, Char)
- f (T1 f k) x = (f k x, f 'c' 'd')
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
- g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
- g (MkSwizzle s) xs f = s (map f (s xs))
+ g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
+ g (MkSwizzle s) xs f = s (map f (s xs))
- h :: MonadT m -> [m a] -> m [a]
- h m [] = return m []
- h m (x:xs) = bind m x $ \y ->
- bind m (h m xs) $ \ys ->
- return m (y:ys)
+ h :: MonadT m -> [m a] -> m [a]
+ h m [] = return m []
+ h m (x:xs) = bind m x $ \y ->
+ bind m (h m xs) $ \ys ->
+ return m (y:ys)
</programlisting>
</para>
from the <literal>MonadT</literal> data structure, rather than using pattern
matching.
</para>
+</sect3>
-<para>
-You cannot pattern-match against an argument that is polymorphic.
-For example:
-
-<programlisting>
- newtype TIM s a = TIM (ST s (Maybe a))
-
- runTIM :: (forall s. TIM s a) -> Maybe a
- runTIM (TIM m) = runST m
-</programlisting>
-
-</para>
+<sect3>
+<title>Type inference</title>
<para>
-Here the pattern-match fails, because you can't pattern-match against
-an argument of type <literal>(forall s. TIM s a)</literal>. Instead you
-must bind the variable and pattern match in the right hand side:
-
-<programlisting>
- runTIM :: (forall s. TIM s a) -> Maybe a
- runTIM tm = case tm of { TIM m -> runST m }
-</programlisting>
-
-The <literal>tm</literal> on the right hand side is (invisibly) instantiated, like
-any polymorphic value at its occurrence site, and now you can pattern-match
-against it.
+In general, type inference for arbitrary-rank types is undecideable.
+GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
+to get a decidable algorithm by requiring some help from the programmer.
+We do not yet have a formal specification of "some help" but the rule is this:
</para>
-
-</sect2>
-
-<sect2>
-<title>The partial-application restriction</title>
-
<para>
-There is really only one way in which data structures with polymorphic
-components might surprise you: you must not partially apply them.
-For example, this is illegal:
+<emphasis>For a lambda-bound or case-bound variable, x, either the programmer
+provides an explicit polymorphic type for x, or GHC's type inference will assume
+that x's type has no foralls in it</emphasis>.
</para>
-
<para>
-
+What does it mean to "provide" an explicit type for x? You can do that by
+giving a type signature for x directly, using a pattern type signature
+(<xref linkend="scoped-type-variables">), thus:
<programlisting>
- map MkSwizzle [sort, reverse]
+ \ f :: (forall a. a->a) -> (f True, f 'c')
</programlisting>
-
-</para>
-
-<para>
-The restriction is this: <emphasis>every subexpression of the program must
-have a type that has no for-alls, except that in a function
-application (f e1…en) the partial applications are not subject to
-this rule</emphasis>. The restriction makes type inference feasible.
-</para>
-
-<para>
-In the illegal example, the sub-expression <literal>MkSwizzle</literal> has the
-polymorphic type <literal>(Ord b => [b] -> [b]) -> Swizzle</literal> and is not
-a sub-expression of an enclosing application. On the other hand, this
-expression is OK:
-</para>
-
-<para>
-
+Alternatively, you can give a type signature to the enclosing
+context, which GHC can "push down" to find the type for the variable:
<programlisting>
- map (T1 (\a b -> a)) [1,2,3]
+ (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
</programlisting>
-
-</para>
-
-<para>
-even though it involves a partial application of <function>T1</function>, because
-the sub-expression <literal>T1 (\a b -> a)</literal> has type <literal>Int -> T
-Int</literal>.
+Here the type signature on the expression can be pushed inwards
+to give a type signature for f. Similarly, and more commonly,
+one can give a type signature for the function itself:
+<programlisting>
+ h :: (forall a. a->a) -> (Bool,Char)
+ h f = (f True, f 'c')
+</programlisting>
+You don't need to give a type signature if the lambda bound variable
+is a constructor argument. Here is an example we saw earlier:
+<programlisting>
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
+</programlisting>
+Here we do not need to give a type signature to <literal>w</literal>, because
+it is an argument of constructor <literal>T1</literal> and that tells GHC all
+it needs to know.
</para>
-</sect2>
+</sect3>
-<sect2 id="sigs">
-<title>Type signatures
-</title>
-<para>
-Once you have data constructors with universally-quantified fields, or
-constants such as <Constant>runST</Constant> that have rank-2 types, it isn't long
-before you discover that you need more! Consider:
-</para>
+<sect3 id="implicit-quant">
+<title>Implicit quantification</title>
<para>
-
+GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
+user-written types, if and only if there is no explicit <literal>forall</literal>,
+GHC finds all the type variables mentioned in the type that are not already
+in scope, and universally quantifies them.</emphasis> For example, the following pairs are
+equivalent:
<programlisting>
- mkTs f x y = [T1 f x, T1 f y]
-</programlisting>
-
-</para>
-
-<para>
-<function>mkTs</function> is a fuction that constructs some values of type
-<literal>T</literal>, using some pieces passed to it. The trouble is that since
-<literal>f</literal> is a function argument, Haskell assumes that it is
-monomorphic, so we'll get a type error when applying <function>T1</function> to
-it. This is a rather silly example, but the problem really bites in
-practice. Lots of people trip over the fact that you can't make
-"wrappers functions" for <Constant>runST</Constant> for exactly the same reason.
-In short, it is impossible to build abstractions around functions with
-rank-2 types.
-</para>
+ f :: a -> a
+ f :: forall a. a -> a
-<para>
-The solution is fairly clear. We provide the ability to give a rank-2
-type signature for <emphasis>ordinary</emphasis> functions (not only data
-constructors), thus:
+ g (x::a) = let
+ h :: a -> b -> b
+ h x y = y
+ in ...
+ g (x::a) = let
+ h :: forall b. a -> b -> b
+ h x y = y
+ in ...
+</programlisting>
</para>
-
<para>
-
+Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
+point. For example:
<programlisting>
- mkTs :: (forall b. b -> b -> b) -> a -> [T a]
- mkTs f x y = [T1 f x, T1 f y]
-</programlisting>
+ f :: (a -> a) -> Int
+ -- MEANS
+ f :: forall a. (a -> a) -> Int
+ -- NOT
+ f :: (forall a. a -> a) -> Int
-</para>
-<para>
-This type signature tells the compiler to attribute <literal>f</literal> with
-the polymorphic type <literal>(forall b. b -> b -> b)</literal> when type
-checking the body of <function>mkTs</function>, so now the application of
-<function>T1</function> is fine.
+ g :: (Ord a => a -> a) -> Int
+ -- MEANS the illegal type
+ g :: forall a. (Ord a => a -> a) -> Int
+ -- NOT
+ g :: (forall a. Ord a => a -> a) -> Int
+</programlisting>
+The latter produces an illegal type, which you might think is silly,
+but at least the rule is simple. If you want the latter type, you
+can write your for-alls explicitly. Indeed, doing so is strongly advised
+for rank-2 types.
</para>
+</sect3>
+</sect2>
-<para>
-There are two restrictions:
-</para>
+<sect2 id="type-synonyms">
+<title>Liberalised type synonyms
+</title>
<para>
-
+Type synonmys are like macros at the type level, and
+GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
+That means that GHC can be very much more liberal about type synonyms than Haskell 98:
<itemizedlist>
-<listitem>
-
-<para>
- You can only define a rank 2 type, specified by the following
-grammar:
-
-
+<listitem> <para>You can write a <literal>forall</literal> (including overloading)
+in a type synonym, thus:
<programlisting>
-rank2type ::= [forall tyvars .] [context =>] funty
-funty ::= ([forall tyvars .] [context =>] ty) -> funty
- | ty
-ty ::= ...current Haskell monotype syntax...
-</programlisting>
+ type Discard a = forall b. Show b => a -> b -> (a, String)
+ f :: Discard a
+ f x y = (x, show y)
-Informally, the universal quantification must all be right at the beginning,
-or at the top level of a function argument.
-
+ g :: Discard Int -> (Int,Bool) -- A rank-2 type
+ g f = f Int True
+</programlisting>
</para>
</listitem>
-<listitem>
-<para>
- There is a restriction on the definition of a function whose
-type signature is a rank-2 type: the polymorphic arguments must be
-matched on the left hand side of the "<literal>=</literal>" sign. You can't
-define <function>mkTs</function> like this:
+<listitem><para>
+You can write an unboxed tuple in a type synonym:
+<programlisting>
+ type Pr = (# Int, Int #)
+ h :: Int -> Pr
+ h x = (# x, x #)
+</programlisting>
+</para></listitem>
+<listitem><para>
+You can apply a type synonym to a forall type:
<programlisting>
-mkTs :: (forall b. b -> b -> b) -> a -> [T a]
-mkTs = \ f x y -> [T1 f x, T1 f y]
+ type Foo a = a -> a -> Bool
+
+ f :: Foo (forall b. b->b)
</programlisting>
+After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
+<programlisting>
+ f :: (forall b. b->b) -> (forall b. b->b) -> Bool
+</programlisting>
+</para></listitem>
+<listitem><para>
+You can apply a type synonym to a partially applied type synonym:
+<programlisting>
+ type Generic i o = forall x. i x -> o x
+ type Id x = x
+
+ foo :: Generic Id []
+</programlisting>
+After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
+<programlisting>
+ foo :: forall x. x -> [x]
+</programlisting>
+</para></listitem>
-
-The same partial-application rule applies to ordinary functions with
-rank-2 types as applied to data constructors.
-
+</itemizedlist>
</para>
-</listitem>
+<para>
+GHC currently does kind checking before expanding synonyms (though even that
+could be changed.)
+</para>
+<para>
+After expanding type synonyms, GHC does validity checking on types, looking for
+the following mal-formedness which isn't detected simply by kind checking:
+<itemizedlist>
+<listitem><para>
+Type constructor applied to a type involving for-alls.
+</para></listitem>
+<listitem><para>
+Unboxed tuple on left of an arrow.
+</para></listitem>
+<listitem><para>
+Partially-applied type synonym.
+</para></listitem>
</itemizedlist>
+So, for example,
+this will be rejected:
+<programlisting>
+ type Pr = (# Int, Int #)
+ h :: Pr -> Int
+ h x = ...
+</programlisting>
+because GHC does not allow unboxed tuples on the left of a function arrow.
</para>
-
</sect2>
-
<sect2 id="hoist">
-<title>Type synonyms and hoisting
-</title>
-
+<title>For-all hoisting</title>
<para>
-GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
-<programlisting>
- type Discard a = forall b. a -> b -> a
-
- f :: Discard a
- f x y = x
-</programlisting>
-However, it is often convenient to use these sort of synonyms at the right hand
+It is often convenient to use generalised type synonyms at the right hand
end of an arrow, thus:
<programlisting>
type Discard a = forall b. a -> b -> a
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 a. <emphasis>type2</emphasis>
+ <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
==>
- forall a. <emphasis>type1</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
g :: Int -> Int -> forall b. b -> Int
</programlisting>
</para>
+<para>
+When doing this hoisting operation, GHC eliminates duplicate constraints. For
+example:
+<programlisting>
+ type Foo a = (?x::Int) => Bool -> a
+ g :: Foo (Foo Int)
+</programlisting>
+means
+<programlisting>
+ g :: (?x::Int) => Bool -> Bool -> Int
+</programlisting>
+</para>
</sect2>
-</sect1>
-<sect1 id="existential-quantification">
+<sect2 id="existential-quantification">
<title>Existentially quantified data constructors
</title>
quite a bit of object-oriented-like programming this way.
</para>
-<sect2 id="existential">
+<sect3 id="existential">
<title>Why existential?
</title>
adding a new existential quantification construct.
</para>
-</sect2>
+</sect3>
-<sect2>
+<sect3>
<title>Type classes</title>
<para>
f :: Baz -> String
f (Baz1 p q) | p == q = "Yes"
| otherwise = "No"
- f (Baz1 v fn) = show (fn v)
+ f (Baz2 v fn) = show (fn v)
</programlisting>
</para>
universal quantification earlier.
</para>
-</sect2>
+</sect3>
-<sect2>
+<sect3>
<title>Restrictions</title>
<para>
</para>
-</sect2>
-
-</sect1>
-
-<sect1 id="sec-assertions">
-<title>Assertions
-<indexterm><primary>Assertions</primary></indexterm>
-</title>
-
-<para>
-If you want to make use of assertions in your standard Haskell code, you
-could define a function like the following:
-</para>
-
-<para>
-
-<programlisting>
-assert :: Bool -> a -> a
-assert False x = error "assertion failed!"
-assert _ x = x
-</programlisting>
-
-</para>
-
-<para>
-which works, but gives you back a less than useful error message --
-an assertion failed, but which and where?
-</para>
-
-<para>
-One way out is to define an extended <function>assert</function> function which also
-takes a descriptive string to include in the error message and
-perhaps combine this with the use of a pre-processor which inserts
-the source location where <function>assert</function> was used.
-</para>
-
-<para>
-Ghc offers a helping hand here, doing all of this for you. For every
-use of <function>assert</function> in the user's source:
-</para>
-
-<para>
-
-<programlisting>
-kelvinToC :: Double -> Double
-kelvinToC k = assert (k >= 0.0) (k+273.15)
-</programlisting>
-
-</para>
-
-<para>
-Ghc will rewrite this to also include the source location where the
-assertion was made,
-</para>
-
-<para>
-
-<programlisting>
-assert pred val ==> assertError "Main.hs|15" pred val
-</programlisting>
-
-</para>
-
-<para>
-The rewrite is only performed by the compiler when it spots
-applications of <function>Exception.assert</function>, so you can still define and
-use your own versions of <function>assert</function>, should you so wish. If not,
-import <literal>Exception</literal> to make use <function>assert</function> in your code.
-</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 <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
-</para>
-
-<para>
-Assertion failures can be caught, see the documentation for the
-<literal>Exception</literal> library (<xref linkend="sec-Exception">)
-for the details.
-</para>
+</sect3>
-</sect1>
+</sect2>
-<sect1 id="scoped-type-variables">
-<title>Scoped Type Variables
+<sect2 id="scoped-type-variables">
+<title>Scoped type variables
</title>
<para>
</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
So much for the basic idea. Here are the details.
</para>
-<sect2>
+<sect3>
+<title>What a pattern type signature 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
+of the same name mean the same type. For example:
+<programlisting>
+ f :: [Int] -> Int -> Int
+ f (xs::[a]) (y::a) = (head xs + y) :: a
+</programlisting>
+The pattern type signatures on the left hand side of
+<literal>f</literal> express the fact that <literal>xs</literal>
+must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
+must have this same type. The type signature on the expression <literal>(head xs)</literal>
+specifies that this expression must have the same type <literal>a</literal>.
+<emphasis>There is no requirement that the type named by "<literal>a</literal>" is
+in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
+<literal>Int</literal>. (This is a slight liberalisation from the original rather complex
+rules, which specified that a pattern-bound type variable should be universally quantified.)
+For example, all of these are legal:</para>
+
+<programlisting>
+ t (x::a) (y::a) = x+y*2
+
+ f (x::a) (y::b) = [x,y] -- a unifies with b
+
+ g (x::a) = x + 1::Int -- a unifies with Int
+
+ h x = let k (y::a) = [x,y] -- a is free in the
+ in k x -- environment
+
+ k (x::a) True = ... -- a unifies with Int
+ k (x::Int) False = ...
+
+ w :: [b] -> [b]
+ w (x::a) = x -- a unifies with [b]
+</programlisting>
+
+</sect3>
+
+<sect3>
<title>Scope and implicit quantification</title>
<para>
<listitem>
<para>
- All the type variables mentioned in the patterns for a single
-function definition equation, that are not already in scope,
-are brought into scope by the patterns. We describe this set as
-the <emphasis>type variables bound by the equation</emphasis>.
-
+All the type variables mentioned in a pattern,
+that are not already in scope,
+are brought into scope by the pattern. We describe this set as
+the <emphasis>type variables bound by the pattern</emphasis>.
+For example:
+<programlisting>
+ f (x::a) = let g (y::(a,b)) = fst y
+ in
+ g (x,True)
+</programlisting>
+The pattern <literal>(x::a)</literal> brings the type variable
+<literal>a</literal> into scope, as well as the term
+variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
+contains an occurrence of the already-in-scope type variable <literal>a</literal>,
+and brings into scope the type variable <literal>b</literal>.
+</para>
+</listitem>
+
+<listitem>
+<para>
+The type variable(s) bound by the pattern have the same scope
+as the term variable(s) bound by the pattern. For example:
+<programlisting>
+ let
+ f (x::a) = <...rhs of f...>
+ (p::b, q::b) = (1,2)
+ in <...body of let...>
+</programlisting>
+Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
+just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
+body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
+just like <literal>p</literal> and <literal>q</literal> do.
+Indeed, the newly bound type variables also scope over any ordinary, separate
+type signatures in the <literal>let</literal> group.
</para>
</listitem>
-<listitem>
+
+<listitem>
<para>
- The type variables thus brought into scope may be mentioned
-in ordinary type signatures or pattern type signatures anywhere within
-their scope.
+The type variables bound by the pattern may be
+mentioned in ordinary type signatures or pattern
+type signatures anywhere within their scope.
</para>
</listitem>
-<listitem>
+<listitem>
<para>
In ordinary type signatures, any type variable mentioned in the
signature that is in scope is <emphasis>not</emphasis> universally quantified.
</para>
</listitem>
+
<listitem>
<para>
Ordinary type signatures do not bring any new type variables
into scope (except in the type signature itself!). So this is illegal:
-
<programlisting>
f :: a -> a
f x = x::a
</programlisting>
-
It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
and that is an incorrect typing.
</para>
</listitem>
-<listitem>
+<listitem>
<para>
- There is no implicit universal quantification on pattern type
-signatures, nor may one write an explicit <literal>forall</literal> type in a pattern
-type signature. The pattern type signature is a monotype.
-
+The pattern type signature is a monotype:
</para>
+
+<itemizedlist>
+<listitem> <para>
+A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
+</para> </listitem>
+
+<listitem> <para>
+The type variables bound by a pattern type signature can only be instantiated to monotypes,
+not to type schemes.
+</para> </listitem>
+
+<listitem> <para>
+There is no implicit universal quantification on pattern type signatures (in contrast to
+ordinary type signatures).
+</para> </listitem>
+
+</itemizedlist>
+
</listitem>
-<listitem>
+<listitem>
<para>
The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
</para>
-</sect2>
+</sect3>
-<sect2>
-<title>Polymorphism</title>
+<sect3>
+<title>Result type signatures</title>
<para>
<listitem>
<para>
- Pattern type signatures are completely orthogonal to ordinary, separate
-type signatures. The two can be used independently or together. There is
-no scoping associated with the names of the type variables in a separate type signature.
+ The result type of a function can be given a signature,
+thus:
<programlisting>
- f :: [a] -> [a]
- f (xs::[b]) = reverse xs
+ f (x::a) :: [a] = [x,x,x]
+</programlisting>
+
+
+The final <literal>:: [a]</literal> after all the patterns gives a signature to the
+result type. Sometimes this is the only way of naming the type variable
+you want:
+
+
+<programlisting>
+ f :: Int -> [a] -> [a]
+ f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
+ in \xs -> map g (reverse xs `zip` xs)
</programlisting>
</para>
</listitem>
-<listitem>
+
+</itemizedlist>
+
+</para>
<para>
- The function must be polymorphic in the type variables
-bound by all its equations. Operationally, the type variables bound
-by one equation must not:
+Result type signatures are not yet implemented in Hugs.
+</para>
+</sect3>
+
+<sect3>
+<title>Where a pattern type signature can occur</title>
+<para>
+A pattern type signature can occur in any pattern. For example:
<itemizedlist>
-<listitem>
+<listitem>
<para>
- Be unified with a type (such as <literal>Int</literal>, or <literal>[a]</literal>).
+A pattern type signature can be on an arbitrary sub-pattern, not
+ust on a variable:
+
+
+<programlisting>
+ f ((x,y)::(a,b)) = (y,x) :: (b,a)
+</programlisting>
+
+
</para>
</listitem>
<listitem>
<para>
- Be unified with a type variable free in the environment.
+ Pattern type signatures, including the result part, can be used
+in lambda abstractions:
+
+<programlisting>
+ (\ (x::a, y) :: a -> x)
+</programlisting>
</para>
</listitem>
<listitem>
<para>
- Be unified with each other. (They may unify with the type variables
-bound by another equation for the same function, of course.)
+ Pattern type signatures, including the result part, can be used
+in <literal>case</literal> expressions:
+
+
+<programlisting>
+ case e of { (x::a, y) :: a -> x }
+</programlisting>
+
</para>
</listitem>
-</itemizedlist>
+<listitem>
+<para>
+To avoid ambiguity, the type after the “<literal>::</literal>” in a result
+pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
+token or a parenthesised type of some sort). To see why,
+consider how one would parse this:
-For example, the following all fail to type check:
+<programlisting>
+ \ x :: a -> b -> x
+</programlisting>
-<programlisting>
- f (x::a) (y::b) = [x,y] -- a unifies with b
+</para>
+</listitem>
- g (x::a) = x + 1::Int -- a unifies with Int
+<listitem>
- h x = let k (y::a) = [x,y] -- a is free in the
- in k x -- environment
+<para>
+ Pattern type signatures can bind existential type variables.
+For example:
- k (x::a) True = ... -- a unifies with Int
- k (x::Int) False = ...
- w :: [b] -> [b]
- w (x::a) = x -- a unifies with [b]
+<programlisting>
+ data T = forall a. MkT [a]
+
+ f :: T -> T
+ f (MkT [t::a]) = MkT t3
+ where
+ t3::[a] = [t,t,t]
</programlisting>
</para>
</listitem>
+
+
<listitem>
<para>
- The pattern-bound type variable may, however, be constrained
-by the context of the principal type, thus:
-
+Pattern type signatures
+can be used in pattern bindings:
<programlisting>
- f (x::a) (y::a) = x+y*2
+ f x = let (y, z::a) = x in ...
+ f1 x = let (y, z::Int) = x in ...
+ f2 (x::(Int,a)) = let (y, z::a) = x in ...
+ f3 :: (b->b) = \x -> x
</programlisting>
+In all such cases, the binding is not generalised over the pattern-bound
+type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
+has type <literal>b -> b</literal> for some type <literal>b</literal>,
+and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
+In contrast, the binding
+<programlisting>
+ f4 :: b->b
+ f4 = \x -> x
+</programlisting>
+makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
+in <literal>f4</literal>'s scope.
-gets the inferred type: <literal>forall a. Num a => a -> a -> a</literal>.
</para>
</listitem>
-
</itemizedlist>
-
</para>
+</sect3>
</sect2>
-<sect2>
-<title>Result type signatures</title>
-<para>
+</sect1>
+<!-- ==================== End of type system extensions ================= -->
+
-<itemizedlist>
-<listitem>
+<!-- ==================== ASSERTIONS ================= -->
+
+<sect1 id="sec-assertions">
+<title>Assertions
+<indexterm><primary>Assertions</primary></indexterm>
+</title>
<para>
- The result type of a function can be given a signature,
-thus:
+If you want to make use of assertions in your standard Haskell code, you
+could define a function like the following:
+</para>
+<para>
<programlisting>
- f (x::a) :: [a] = [x,x,x]
+assert :: Bool -> a -> a
+assert False x = error "assertion failed!"
+assert _ x = x
</programlisting>
+</para>
-The final <literal>:: [a]</literal> after all the patterns gives a signature to the
-result type. Sometimes this is the only way of naming the type variable
-you want:
+<para>
+which works, but gives you back a less than useful error message --
+an assertion failed, but which and where?
+</para>
+
+<para>
+One way out is to define an extended <function>assert</function> function which also
+takes a descriptive string to include in the error message and
+perhaps combine this with the use of a pre-processor which inserts
+the source location where <function>assert</function> was used.
+</para>
+
+<para>
+Ghc offers a helping hand here, doing all of this for you. For every
+use of <function>assert</function> in the user's source:
+</para>
+<para>
<programlisting>
- f :: Int -> [a] -> [a]
- f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
- in \xs -> map g (reverse xs `zip` xs)
+kelvinToC :: Double -> Double
+kelvinToC k = assert (k >= 0.0) (k+273.15)
</programlisting>
+</para>
+<para>
+Ghc will rewrite this to also include the source location where the
+assertion was made,
</para>
-</listitem>
-</itemizedlist>
+<para>
+
+<programlisting>
+assert pred val ==> assertError "Main.hs|15" pred val
+</programlisting>
</para>
<para>
-Result type signatures are not yet implemented in Hugs.
+The rewrite is only performed by the compiler when it spots
+applications of <function>Control.Exception.assert</function>, so you
+can still define and use your own versions of
+<function>assert</function>, should you so wish. If not, import
+<literal>Control.Exception</literal> to make use
+<function>assert</function> in your code.
</para>
-</sect2>
-
-<sect2>
-<title>Pattern signatures on other constructs</title>
+<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
+<literal>assert pred e</literal> will be rewritten to
+<literal>e</literal>.
+</para>
<para>
+Assertion failures can be caught, see the documentation for the
+<literal>Control.Exception</literal> library for the details.
+</para>
-<itemizedlist>
-<listitem>
+</sect1>
+
+
+<sect1 id="syntax-extns">
+<title>Syntactic extensions</title>
+
+<!-- ====================== HIERARCHICAL MODULES ======================= -->
+
+ <sect2 id="hierarchical-modules">
+ <title>Hierarchical Modules</title>
+
+ <para>GHC supports a small extension to the syntax of module
+ names: a module name is allowed to contain a dot
+ <literal>‘.’</literal>. This is also known as the
+ “hierarchical module namespace” extension, because
+ it extends the normally flat Haskell module namespace into a
+ more flexible hierarchy of modules.</para>
+
+ <para>This extension has very little impact on the language
+ itself; modules names are <emphasis>always</emphasis> fully
+ qualified, so you can just think of the fully qualified module
+ name as <quote>the module name</quote>. In particular, this
+ means that the full module name must be given after the
+ <literal>module</literal> keyword at the beginning of the
+ module; for example, the module <literal>A.B.C</literal> must
+ begin</para>
+
+<programlisting>module A.B.C</programlisting>
-<para>
- A pattern type signature can be on an arbitrary sub-pattern, not
-just on a variable:
+ <para>It is a common strategy to use the <literal>as</literal>
+ keyword to save some typing when using qualified names with
+ hierarchical modules. For example:</para>
<programlisting>
- f ((x,y)::(a,b)) = (y,x) :: (b,a)
+import qualified Control.Monad.ST.Strict as ST
</programlisting>
+ <para>Hierarchical modules have an impact on the way that GHC
+ searches for files. For a description, see <xref
+ linkend="finding-hierarchical-modules">.</para>
+
+ <para>GHC comes with a large collection of libraries arranged
+ hierarchically; see the accompanying library documentation.
+ There is an ongoing project to create and maintain a stable set
+ of <quote>core</quote> libraries used by several Haskell
+ compilers, and the libraries that GHC comes with represent the
+ current status of that project. For more details, see <ulink
+ url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
+ Libraries</ulink>.</para>
+
+ </sect2>
+
+<!-- ====================== PATTERN GUARDS ======================= -->
+
+<sect2 id="pattern-guards">
+<title>Pattern guards</title>
+<para>
+<indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
+The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
</para>
-</listitem>
-<listitem>
<para>
- Pattern type signatures, including the result part, can be used
-in lambda abstractions:
+Suppose we have an abstract data type of finite maps, with a
+lookup operation:
+<programlisting>
+lookup :: FiniteMap -> Int -> Maybe Int
+</programlisting>
+
+The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
+where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
+</para>
<programlisting>
- (\ (x::a, y) :: a -> x)
+clunky env var1 var2 | ok1 && ok2 = val1 + val2
+| otherwise = var1 + var2
+where
+ m1 = lookup env var1
+ m2 = lookup env var2
+ ok1 = maybeToBool m1
+ ok2 = maybeToBool m2
+ val1 = expectJust m1
+ val2 = expectJust m2
</programlisting>
+<para>
+The auxiliary functions are
+</para>
-Type variables bound by these patterns must be polymorphic in
-the sense defined above.
-For example:
+<programlisting>
+maybeToBool :: Maybe a -> Bool
+maybeToBool (Just x) = True
+maybeToBool Nothing = False
+
+expectJust :: Maybe a -> a
+expectJust (Just x) = x
+expectJust Nothing = error "Unexpected Nothing"
+</programlisting>
+
+<para>
+What is <function>clunky</function> doing? The guard <literal>ok1 &&
+ok2</literal> checks that both lookups succeed, using
+<function>maybeToBool</function> to convert the <function>Maybe</function>
+types to booleans. The (lazily evaluated) <function>expectJust</function>
+calls extract the values from the results of the lookups, and binds the
+returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
+respectively. If either lookup fails, then clunky takes the
+<literal>otherwise</literal> case and returns the sum of its arguments.
+</para>
+<para>
+This is certainly legal Haskell, but it is a tremendously verbose and
+un-obvious way to achieve the desired effect. Arguably, a more direct way
+to write clunky would be to use case expressions:
+</para>
<programlisting>
- f1 (x::c) = f1 x -- ok
- f2 = \(x::c) -> f2 x -- not ok
+clunky env var1 var1 = case lookup env var1 of
+ Nothing -> fail
+ Just val1 -> case lookup env var2 of
+ Nothing -> fail
+ Just val2 -> val1 + val2
+where
+ fail = val1 + val2
</programlisting>
-
-Here, <function>f1</function> is OK, but <function>f2</function> is not, because <VarName>c</VarName> gets unified
-with a type variable free in the environment, in this
-case, the type of <function>f2</function>, which is in the environment when
-the lambda abstraction is checked.
-
+<para>
+This is a bit shorter, but hardly better. Of course, we can rewrite any set
+of pattern-matching, guarded equations as case expressions; that is
+precisely what the compiler does when compiling equations! The reason that
+Haskell provides guarded equations is because they allow us to write down
+the cases we want to consider, one at a time, independently of each other.
+This structure is hidden in the case version. Two of the right-hand sides
+are really the same (<function>fail</function>), and the whole expression
+tends to become more and more indented.
</para>
-</listitem>
-<listitem>
<para>
- Pattern type signatures, including the result part, can be used
-in <literal>case</literal> expressions:
-
+Here is how I would write clunky:
+</para>
<programlisting>
- case e of { (x::a, y) :: a -> x }
+clunky env var1 var1
+ | Just val1 <- lookup env var1
+ , Just val2 <- lookup env var2
+ = val1 + val2
+...other equations for clunky...
</programlisting>
+<para>
+The semantics should be clear enough. The qualifers 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
+tried. If it succeeds, then the appropriate binding takes place, and the
+next qualifier is matched, in the augmented environment. Unlike list
+comprehensions, however, the type of the expression to the right of the
+<literal><-</literal> is the same as the type of the pattern to its
+left. The bindings introduced by pattern guards scope over all the
+remaining guard qualifiers, and over the right hand side of the equation.
+</para>
-The pattern-bound type variables must, as usual,
-be polymorphic in the following sense: each case alternative,
-considered as a lambda abstraction, must be polymorphic.
-Thus this is OK:
-
+<para>
+Just as with list comprehensions, boolean expressions can be freely mixed
+with among the pattern guards. For example:
+</para>
<programlisting>
- case (True,False) of { (x::a, y) -> x }
+f x | [y] <- x
+ , y > 3
+ , Just z <- h y
+ = ...
</programlisting>
+<para>
+Haskell's current guards therefore emerge as a special case, in which the
+qualifier list has just one element, a boolean expression.
+</para>
+</sect2>
-Even though the context is that of a pair of booleans,
-the alternative itself is polymorphic. Of course, it is
-also OK to say:
+<!-- ===================== Recursive do-notation =================== -->
+<sect2 id="mdo-notation">
+<title>The recursive do-notation
+</title>
+<para> The recursive do-notation (also known as mdo-notation) is implemented as described in
+"A recursive do for Haskell",
+Levent Erkok, John Launchbury",
+Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
+</para>
+<para>
+The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
+that is, the variables bound in a do-expression are visible only in the textually following
+code block. Compare this to a let-expression, where bound variables are visible in the entire binding
+group. It turns out that several applications can benefit from recursive bindings in
+the do-notation, and this extension provides the necessary syntactic support.
+</para>
+<para>
+Here is a simple (yet contrived) example:
+</para>
<programlisting>
- case (True,False) of { (x::Bool, y) -> x }
+justOnes = mdo xs <- Just (1:xs)
+ return xs
</programlisting>
-
-
+<para>
+As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
</para>
-</listitem>
-<listitem>
<para>
-To avoid ambiguity, the type after the “<literal>::</literal>” in a result
-pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
-token or a parenthesised type of some sort). To see why,
-consider how one would parse this:
-
-
+The MonadFix library introduces the <literal>MonadFix</literal> class. It's definition is:
+</para>
<programlisting>
- \ x :: a -> b -> x
+class Monad m => MonadFix m where
+ mfix :: (a -> m a) -> m a
</programlisting>
+<para>
+The function <literal>mfix</literal>
+dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
+then that monad must be declared an instance of the <literal>MonadFix</literal> class.
+For details, see the above mentioned reference.
+</para>
+<para>
+The <literal>MonadFix</literal> library automatically declares List, Maybe, IO, and
+state monads (both lazy and strict) as instances of the <literal>MonadFix</literal> class.
+</para>
+<para>
+There are three important points in using the recursive-do notation:
+<itemizedlist>
+<listitem><para>
+The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
+than <literal>do</literal>).
+</para></listitem>
+
+<listitem><para>
+If you want to declare an instance of the <literal>MonadFix</literal> class for one of
+your own monads, or you need to refer to the class name <literal>MonadFix</literal> in any other way (for instance in
+writing a type constraint), then your program should <literal>import Control.Monad.MonadFix</literal>.
+Otherwise, you don't need to import any special libraries to use the mdo-notation. That is,
+as long as you only use the predefined instances mentioned above, the mdo-notation will
+be automatically available. (Note: This differs from the Hugs implementation, where
+<literal>MonadFix</literal> should always be imported.)
+</para></listitem>
+
+<listitem><para>
+As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
+</para></listitem>
+</itemizedlist>
+</para>
-
+<para>
+Historical note: The originial implementation of the mdo-notation, and most
+of the existing documents, use the names
+<literal>MonadRec</literal> for the class, and
+<literal>Control.Monad.MonadRec</literal> for the library. These names
+are no longer supported.
</para>
-</listitem>
-<listitem>
<para>
- Pattern type signatures that bind new type variables
-may not be used in pattern bindings at all.
-So this is illegal:
+The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
+contains up to date information on recursive monadic bindings.
+</para>
+</sect2>
-<programlisting>
- f x = let (y, z::a) = x in ...
-</programlisting>
+<!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
+ <sect2 id="parallel-list-comprehensions">
+ <title>Parallel List Comprehensions</title>
+ <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
+ </indexterm>
+ <indexterm><primary>parallel list comprehensions</primary>
+ </indexterm>
-But these are OK, because they do not bind fresh type variables:
+ <para>Parallel list comprehensions are a natural extension to list
+ comprehensions. List comprehensions can be thought of as a nice
+ syntax for writing maps and filters. Parallel comprehensions
+ extend this to include the zipWith family.</para>
+ <para>A parallel list comprehension has multiple independent
+ branches of qualifier lists, each separated by a `|' symbol. For
+ example, the following zips together two lists:</para>
<programlisting>
- f1 x = let (y, z::Int) = x in ...
- f2 (x::(Int,a)) = let (y, z::a) = x in ...
+ [ (x, y) | x <- xs | y <- ys ]
</programlisting>
+ <para>The behavior of parallel list comprehensions follows that of
+ zip, in that the resulting list will have the same length as the
+ shortest branch.</para>
-However a single variable is considered a degenerate function binding,
-rather than a degerate pattern binding, so this is permitted, even
-though it binds a type variable:
+ <para>We can define parallel list comprehensions by translation to
+ regular comprehensions. Here's the basic idea:</para>
+ <para>Given a parallel comprehension of the form: </para>
<programlisting>
- f :: (b->b) = \(x::b) -> x
+ [ e | p1 <- e11, p2 <- e12, ...
+ | q1 <- e21, q2 <- e22, ...
+ ...
+ ]
</programlisting>
-
-</para>
-</listitem>
-
-</itemizedlist>
-
-Such degnerate function bindings do not fall under the monomorphism
-restriction. Thus:
-</para>
-
-<para>
+ <para>This will be translated to: </para>
<programlisting>
- g :: a -> a -> Bool = \x y. x==y
+ [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
+ [(q1,q2) | q1 <- e21, q2 <- e22, ...]
+ ...
+ ]
</programlisting>
-</para>
+ <para>where `zipN' is the appropriate zip for the given number of
+ branches.</para>
-<para>
-Here <function>g</function> has type <literal>forall a. Eq a => a -> a -> Bool</literal>, just as if
-<function>g</function> had a separate type signature. Lacking a type signature, <function>g</function>
-would get a monomorphic type.
-</para>
+ </sect2>
-</sect2>
+<sect2 id="rebindable-syntax">
+<title>Rebindable syntax</title>
-<sect2>
-<title>Existentials</title>
-<para>
+ <para>GHC allows most kinds of built-in syntax to be rebound by
+ the user, to facilitate replacing the <literal>Prelude</literal>
+ with a home-grown version, for example.</para>
-<itemizedlist>
-<listitem>
+ <para>You may want to define your own numeric class
+ hierarchy. It completely defeats that purpose if the
+ literal "1" means "<literal>Prelude.fromInteger
+ 1</literal>", which is what the Haskell Report specifies.
+ So the <option>-fno-implicit-prelude</option> flag causes
+ the following pieces of built-in syntax to refer to
+ <emphasis>whatever is in scope</emphasis>, not the Prelude
+ versions:</para>
-<para>
- Pattern type signatures can bind existential type variables.
-For example:
+ <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>
+ <listitem>
+ <para>Negation (e.g. "<literal>- (f x)</literal>")
+ means "<literal>negate (f x)</literal>" (not
+ <literal>Prelude.negate</literal>).</para>
+ </listitem>
-<programlisting>
- data T = forall a. MkT [a]
+ <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>
- f :: T -> T
- f (MkT [t::a]) = MkT t3
- where
- t3::[a] = [t,t,t]
-</programlisting>
+ <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
+ 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>
-</para>
-</listitem>
+</sect2>
+</sect1>
-</itemizedlist>
+<!-- =============================== PRAGMAS =========================== -->
-</para>
+ <sect1 id="pragmas">
+ <title>Pragmas</title>
-</sect2>
+ <indexterm><primary>pragma</primary></indexterm>
-</sect1>
+ <para>GHC supports several pragmas, or instructions to the
+ compiler placed in the source code. Pragmas don't normally affect
+ the meaning of the program, but they might affect the efficiency
+ of the generated code.</para>
-<sect1 id="pragmas">
-<title>Pragmas
-</title>
+ <para>Pragmas all take the form
-<para>
-GHC supports several pragmas, or instructions to the compiler placed
-in the source code. Pragmas don't affect the meaning of the program,
-but they might affect the efficiency of the generated code.
-</para>
+<literal>{-# <replaceable>word</replaceable> ... #-}</literal>
+
+ where <replaceable>word</replaceable> indicates the type of
+ pragma, and is followed optionally by information specific to that
+ type of pragma. Case is ignored in
+ <replaceable>word</replaceable>. The various values for
+ <replaceable>word</replaceable> that GHC understands are described
+ in the following sections; any pragma encountered with an
+ unrecognised <replaceable>word</replaceable> is (silently)
+ ignored.</para>
<sect2 id="inline-pragma">
<title>INLINE pragma
<title>NOINLINE pragma
</title>
-<para>
<indexterm><primary>NOINLINE pragma</primary></indexterm>
-<indexterm><primary>pragma, NOINLINE</primary></indexterm>
-</para>
+<indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
+<indexterm><primary>NOTINLINE pragma</primary></indexterm>
+<indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
<para>
-The <literal>NOINLINE</literal> pragma does exactly what you'd expect: it stops the
-named function from being inlined by the compiler. You shouldn't ever
-need to do this, unless you're very cautious about code size.
+The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
+it stops the named function from being inlined by the compiler. You
+shouldn't ever need to do this, unless you're very cautious about code
+size.
</para>
+<para><literal>NOTINLINE</literal> is a synonym for
+<literal>NOINLINE</literal> (<literal>NOTINLINE</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>
+
</sect2>
<sect2 id="specialize-pragma">
Same idea, except for instance declarations. For example:
<programlisting>
-instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
-
-{-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
+instance (Eq a) => Eq (Foo a) where {
+ {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
+ ... usual stuff ...
+ }
</programlisting>
-
-Compatible with HBC, by the way.
+The pragma must occur inside the <literal>where</literal> part
+of the instance declaration.
+</para>
+<para>
+Compatible with HBC, by the way, except perhaps in the placement
+of the pragma.
</para>
</sect2>
</sect2>
+<sect2 id="deprecated-pragma">
+<title>DEPRECATED pragma</title>
+
+<para>
+The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
+There are two forms.
+</para>
+<itemizedlist>
+<listitem><para>
+You can deprecate an entire module thus:</para>
+<programlisting>
+ module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
+ ...
+</programlisting>
+<para>
+When you compile any module that import <literal>Wibble</literal>, GHC will print
+the specified message.</para>
+</listitem>
+
+<listitem>
+<para>
+You can deprecate a function, class, or type, 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 message.
+</para>
+</listitem>
+</itemizedlist>
+<para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
+
+</sect2>
+
</sect1>
+<!-- ======================= REWRITE RULES ======================== -->
+
<sect1 id="rewrite-rules">
<title>Rewrite rules
<function>++</function>
</para>
</listitem>
-<listitem>
+<listitem>
<para>
<function>map</function>
</para>
</listitem>
-<listitem>
+<listitem>
<para>
<function>filter</function>
</para>
<function>++</function> (on its first argument)
</para>
</listitem>
+
<listitem>
+<para>
+ <function>foldr</function>
+</para>
+</listitem>
+<listitem>
<para>
<function>map</function>
</para>
<sect1 id="generic-classes">
<title>Generic classes</title>
+ <para>(Note: support for generic classes is currently broken in
+ GHC 5.02).</para>
+
<para>
The ideas behind this extension are described in detail in "Derivable type classes",
Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
<para>To use generics you need to</para>
<itemizedlist>
<listitem>
- <para>Use the <option>-fgenerics</option> flag.</para>
+ <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
+ <option>-fgenerics</option> (to generate extra per-data-type code),
+ and <option>-package lang</option> (to make the <literal>Generics</literal> library
+ available. </para>
</listitem>
<listitem>
<para>Import the module <literal>Generics</literal> from the
any operator starting in a colon as an infix type constructor). Also note that
the type constructors are not exactly as in the paper (Unit instead of 1, etc).
Finally, note that the syntax of the type patterns in the class declaration
-uses "<literal>{|</literal>" and "<literal>{|</literal>" brackets; curly braces
+uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
alone would ambiguous when they appear on right hand sides (an extension we
anticipate wanting).
</para>
<programlisting>
class Foo a where
op1 :: a -> Bool
- op {| a :*: b |} (Inl x) = True
+ op1 {| a :*: b |} (x :*: y) = True
op2 :: a -> Bool
- op {| p :*: q |} (Inr y) = False
+ op2 {| p :*: q |} (x :*: y) = False
</programlisting>
(The reason for this restriction is that we gather all the equations for a particular type consructor
into a single generic instance declaration.)
</sect2>
</sect1>
+<sect1 id="newtype-deriving">
+<title>Generalised derived instances for newtypes</title>
+
+<para>
+When you define an abstract type using <literal>newtype</literal>, you may want
+the new type to inherit some instances from its representation. In
+Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
+other classes you have to write an explicit instance declaration. For
+example, if you define
+
+<programlisting>
+ newtype Dollars = Dollars Int
+</programlisting>
+
+and you want to use arithmetic on <literal>Dollars</literal>, you have to
+explicitly define an instance of <literal>Num</literal>:
+
+<programlisting>
+ instance Num Dollars where
+ Dollars a + Dollars b = Dollars (a+b)
+ ...
+</programlisting>
+All the instance does is apply and remove the <literal>newtype</literal>
+constructor. It is particularly galling that, since the constructor
+doesn't appear at run-time, this instance declaration defines a
+dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
+dictionary, only slower!
+</para>
+
+<sect2> <title> Generalising the deriving clause </title>
+<para>
+GHC now permits such instances to be derived instead, so one can write
+<programlisting>
+ newtype Dollars = Dollars Int deriving (Eq,Show,Num)
+</programlisting>
+
+and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
+for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
+derives an instance declaration of the form
+
+<programlisting>
+ instance Num Int => Num Dollars
+</programlisting>
+
+which just adds or removes the <literal>newtype</literal> constructor according to the type.
+</para>
+<para>
+
+We can also derive instances of constructor classes in a similar
+way. For example, suppose we have implemented state and failure monad
+transformers, such that
+
+<programlisting>
+ instance Monad m => Monad (State s m)
+ instance Monad m => Monad (Failure m)
+</programlisting>
+In Haskell 98, we can define a parsing monad by
+<programlisting>
+ type Parser tok m a = State [tok] (Failure m) a
+</programlisting>
+
+which is automatically a monad thanks to the instance declarations
+above. With the extension, we can make the parser type abstract,
+without needing to write an instance of class <literal>Monad</literal>, via
+
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving Monad
+</programlisting>
+In this case the derived instance declaration is of the form
+<programlisting>
+ instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
+</programlisting>
+
+Notice that, since <literal>Monad</literal> is a constructor class, the
+instance is a <emphasis>partial application</emphasis> of the new type, not the
+entire left hand side. We can imagine that the type declaration is
+``eta-converted'' to generate the context of the instance
+declaration.
+</para>
+<para>
+
+We can even derive instances of multi-parameter classes, provided the
+newtype is the last class parameter. In this case, a ``partial
+application'' of the class appears in the <literal>deriving</literal>
+clause. For example, given the class
+
+<programlisting>
+ class StateMonad s m | m -> s where ...
+ instance Monad m => StateMonad s (State s m) where ...
+</programlisting>
+then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving (Monad, StateMonad [tok])
+</programlisting>
+
+The derived instance is obtained by completing the application of the
+class to the new type:
+
+<programlisting>
+ instance StateMonad [tok] (State [tok] (Failure m)) =>
+ StateMonad [tok] (Parser tok m)
+</programlisting>
+</para>
+<para>
+
+As a result of this extension, all derived instances in newtype
+declarations are treated uniformly (and implemented just by reusing
+the dictionary for the representation type), <emphasis>except</emphasis>
+<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
+the newtype and its representation.
+</para>
+</sect2>
+
+<sect2> <title> A more precise specification </title>
+<para>
+Derived instance declarations are constructed as follows. Consider the
+declaration (after expansion of any type synonyms)
+
+<programlisting>
+ newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
+</programlisting>
+
+where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
+types,
+<literal>vk+1...vn</literal> are type variables which do not occur in any of
+the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
+classes of the form <literal>C t1'...tj'</literal>. The derived instance
+declarations are, for each <literal>ci</literal>,
+
+<programlisting>
+ instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
+</programlisting>
+where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
+right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
+</para>
+<para>
+
+As an example which does <emphasis>not</emphasis> work, consider
+<programlisting>
+ newtype NonMonad m s = NonMonad (State s m s) deriving Monad
+</programlisting>
+Here we cannot derive the instance
+<programlisting>
+ instance Monad (State s m) => Monad (NonMonad m)
+</programlisting>
+
+because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
+and so cannot be "eta-converted" away. It is a good thing that this
+<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
+not, in fact, a monad --- for the same reason. Try defining
+<literal>>>=</literal> with the correct type: you won't be able to.
+</para>
+<para>
+
+Notice also that the <emphasis>order</emphasis> of class parameters becomes
+important, since we can only derive instances for the last one. If the
+<literal>StateMonad</literal> class above were instead defined as
+
+<programlisting>
+ class StateMonad m s | m -> s where ...
+</programlisting>
+
+then we would not have been able to derive an instance for the
+<literal>Parser</literal> type above. We hypothesise that multi-parameter
+classes usually have one "main" parameter for which deriving new
+instances is most interesting.
+</para>
+</sect2>
+
+</sect1>
+
+
+
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