-<Para>
-<IndexTerm><Primary>language, GHC</Primary></IndexTerm>
-<IndexTerm><Primary>extensions, GHC</Primary></IndexTerm>
+<para>
+<indexterm><primary>language, GHC</primary></indexterm>
+<indexterm><primary>extensions, GHC</primary></indexterm>
As with all known Haskell systems, GHC implements some extensions to
-the language. To use them, you'll need to give a <Option>-fglasgow-exts</Option>
-<IndexTerm><Primary>-fglasgow-exts option</Primary></IndexTerm> option.
-</Para>
+the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
+<indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
+</para>
-<Para>
+<para>
Virtually all of the Glasgow extensions serve to give you access to
the underlying facilities with which we implement Haskell. Thus, you
can get at the Raw Iron, if you are willing to write some non-standard
code at a more primitive level. You need not be “stuck” on
performance because of the implementation costs of Haskell's
“high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
-</Para>
-
-<Para>
-Executive summary of our extensions:
-</Para>
-
-<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>Multi-parameter type classes:</Term>
-<ListItem>
-<Para>
-GHC's type system supports extended type classes with multiple
-parameters. Please see <XRef LinkEnd="multi-param-type-classes">.
-</Para>
-</ListItem>
-</VarListEntry>
-
-<VarListEntry>
-<Term>Local universal quantification:</Term>
-<ListItem>
-<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. See <XRef LinkEnd="universal-quantification">.
-</Para>
-</ListItem>
-</VarListEntry>
-
-<VarListEntry>
-<Term>Extistentially quantification in data types:</Term>
-<ListItem>
-<Para>
-Some or all of the type variables in a datatype declaration may be
-<Emphasis>existentially quantified</Emphasis>. More details in <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>
-
-<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>
-</VariableList>
-</Para>
-
-<Para>
+</para>
+
+<para>
Before you get too carried away working at the lowest level (e.g.,
-sloshing <Literal>MutableByteArray#</Literal>s around your
+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">.
-</Para>
-
-<Sect1 id="primitives">
-<Title>Unboxed types and primitive operations
-</Title>
-<IndexTerm><Primary>PrelGHC module</Primary></IndexTerm>
-
-<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>
+“Haskellised veneer” over the features you want. The
+separate libraries documentation describes all the libraries that come
+with GHC.
+</para>
-<Para>
-<IndexTerm><Primary>Unboxed types (Glasgow extension)</Primary></IndexTerm>
-</Para>
+<!-- LANGUAGE OPTIONS -->
+ <sect1 id="options-language">
+ <title>Language options</title>
+
+ <indexterm><primary>language</primary><secondary>option</secondary>
+ </indexterm>
+ <indexterm><primary>options</primary><secondary>language</secondary>
+ </indexterm>
+ <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
+ </indexterm>
+
+ <para> These flags control what variation of the language are
+ permitted. Leaving out all of them gives you standard Haskell
+ 98.</para>
+
+ <variablelist>
+
+ <varlistentry>
+ <term><option>-fglasgow-exts</option>:</term>
+ <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
+ <listitem>
+ <para>This simultaneously enables all of the extensions to
+ Haskell 98 described in <xref
+ linkend="ghc-language-features">, except where otherwise
+ noted. </para>
+ </listitem>
+ </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>
+ <para> Switch off the Haskell 98 monomorphism restriction.
+ Independent of the <option>-fglasgow-exts</option>
+ flag. </para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fallow-overlapping-instances</option></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>
+ <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
+ <listitem>
+ <para> See <xref LinkEnd="instance-decls">. Only relevant
+ if you also use <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-finline-phase</option></term>
+ <indexterm><primary><option>-finline-phase</option></primary></indexterm>
+ <listitem>
+ <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
+ you also use <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-farrows</option></term>
+ <indexterm><primary><option>-farrows</option></primary></indexterm>
+ <listitem>
+ <para>See <xref LinkEnd="arrow-notation">. Independent of
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fgenerics</option></term>
+ <indexterm><primary><option>-fgenerics</option></primary></indexterm>
+ <listitem>
+ <para>See <xref LinkEnd="generic-classes">. Independent of
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fno-implicit-prelude</option></term>
+ <listitem>
+ <para><indexterm><primary>-fno-implicit-prelude
+ option</primary></indexterm> GHC normally imports
+ <filename>Prelude.hi</filename> files for you. If you'd
+ rather it didn't, then give it a
+ <option>-fno-implicit-prelude</option> option. The idea
+ is that you can then import a Prelude of your own. (But
+ don't call it <literal>Prelude</literal>; the Haskell
+ module namespace is flat, and you must not conflict with
+ any Prelude module.)</para>
+
+ <para>Even though you have not imported the Prelude, most of
+ the built-in syntax still refers to the built-in Haskell
+ Prelude types and values, as specified by the Haskell
+ Report. For example, the type <literal>[Int]</literal>
+ still means <literal>Prelude.[] Int</literal>; tuples
+ continue to refer to the standard Prelude tuples; the
+ translation for list comprehensions continues to use
+ <literal>Prelude.map</literal> etc.</para>
+
+ <para>However, <option>-fno-implicit-prelude</option> does
+ change the handling of certain built-in syntax: see
+ <xref LinkEnd="rebindable-syntax">.</para>
+
+ </listitem>
+ </varlistentry>
+
+ </variablelist>
+ </sect1>
+
+<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
+<!-- included from primitives.sgml -->
+<!-- &primitives; -->
+<sect1 id="primitives">
+ <title>Unboxed types and primitive operations</title>
+
+<para>GHC is built on a raft of primitive data types and operations.
+While you really can use this stuff to write fast code,
+ we generally find it a lot less painful, and more satisfying in the
+ long run, to use higher-level language features and libraries. With
+ any luck, the code you write will be optimised to the efficient
+ unboxed version in any case. And if it isn't, we'd like to know
+ about it.</para>
+
+<para>We do not currently have good, up-to-date documentation about the
+primitives, perhaps because they are mainly intended for internal use.
+There used to be a long section about them here in the User Guide, but it
+became out of date, and wrong information is worse than none.</para>
+
+<para>The Real Truth about what primitive types there are, and what operations
+work over those types, is held in the file
+<filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
+This file is used directly to generate GHC's primitive-operation definitions, so
+it is always correct! It is also intended for processing into text.</para>
+
+<para> Indeed,
+the result of such processing is part of the description of the
+ <ulink
+ url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
+ Core language</ulink>.
+So that document is a good place to look for a type-set version.
+We would be very happy if someone wanted to volunteer to produce an SGML
+back end to the program that processes <filename>primops.txt</filename> so that
+we could include the results here in the User Guide.</para>
+
+<para>What follows here is a brief summary of some main points.</para>
+
+<sect2 id="glasgow-unboxed">
+<title>Unboxed types
+</title>
+
+<para>
+<indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
+</para>
<para>Most types in GHC are <firstterm>boxed</firstterm>, which means
that values of that type are represented by a pointer to a heap
allocation are involved.
</para>
-<Para>
+<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>
+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
+<literal>(+#)</literal> is addition on
+<literal>Int#</literal>s, and is the machine-addition that we all
know and love—usually one instruction.
-</Para>
+</para>
-<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.
-</Para>
+operations have a <literal>#</literal> suffix.
+</para>
-<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:
+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
+<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.
-</Para>
+</para>
-<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
+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
+<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).
-</Para>
+(<literal>Double#</literal> for instance).
+</para>
-<Para>
+<para>
Nevertheless, A numerically-intensive program using unboxed types can
-go a <Emphasis>lot</Emphasis> faster than its “standard”
+go a <emphasis>lot</emphasis> faster than its “standard”
counterpart—we saw a threefold speedup on one example.
-</Para>
+</para>
</sect2>
-<Sect2 id="unboxed-tuples">
-<Title>Unboxed Tuples
-</Title>
+<sect2 id="unboxed-tuples">
+<title>Unboxed Tuples
+</title>
-<Para>
-Unboxed tuples aren't really exported by <Literal>PrelGHC</Literal>,
-they're available by default with <Option>-fglasgow-exts</Option>. An
+<para>
+Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
+they're available by default with <option>-fglasgow-exts</option>. An
unboxed tuple looks like this:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
(# e_1, ..., e_n #)
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-where <Literal>e_1..e_n</Literal> are expressions of any
+<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.
-</Para>
+</para>
-<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
unboxed tuple itself does not have a composite representation. Many
of the primitive operations listed in this section return unboxed
tuples.
-</Para>
+</para>
-<Para>
+<para>
There are some pretty stringent restrictions on the use of unboxed tuples:
-</Para>
+</para>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<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.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<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.
+a function, and may only be deconstructed with a <literal>case</literal> expression.
eg. the following are valid:
-<ProgramListing>
+<programlisting>
f x y = (# x+1, y-1 #)
g x = case f x x of { (# a, b #) -> a + b }
-</ProgramListing>
+</programlisting>
but the following are invalid:
-<ProgramListing>
+<programlisting>
f x y = g (# x, y #)
g (# x, y #) = x + y
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
No variable can have an unboxed tuple type. This is illegal:
-<ProgramListing>
+<programlisting>
f :: (# Int, Int #) -> (# Int, Int #)
f x = x
-</ProgramListing>
+</programlisting>
-because <VarName>x</VarName> has an unboxed tuple type.
+because <literal>x</literal> has an unboxed tuple type.
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-<Para>
+<para>
Note: we may relax some of these restrictions in the future.
-</Para>
-
-<Para>
-The <Literal>IO</Literal> and <Literal>ST</Literal> monads use unboxed tuples to avoid unnecessary
-allocation during sequences of operations.
-</Para>
-
-</Sect2>
-
-<Sect2>
-<Title>Character and numeric types</Title>
-
-<Para>
-<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>
-There are the following obvious primitive types:
-</Para>
-
-<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>
-
-<Para>
-If you really want to know their exact equivalents in C, see
-<Filename>ghc/includes/StgTypes.h</Filename> in the GHC source tree.
-</Para>
-
-<Para>
-Literals for these types may be written as follows:
-</Para>
-
-<Para>
-
-<ProgramListing>
-1# an Int#
-1.2# a Float#
-1.34## a Double#
-'a'# a Char#; for weird characters, use '\o<octal>'#
-"a"# an Addr# (a `char *')
-</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>
-</Para>
-
-<Para>
-
-<ProgramListing>
-{>,>=,==,/=,<,<=}# :: Int# -> Int# -> Bool
-
-{gt,ge,eq,ne,lt,le}Char# :: Char# -> Char# -> Bool
- -- ditto for Word# and Addr#
-</ProgramListing>
-
-<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>
-
-</Sect2>
-
-<Sect2>
-<Title>Primitive-character operations</Title>
-
-<Para>
-<IndexTerm><Primary>characters, primitive operations</Primary></IndexTerm>
-<IndexTerm><Primary>operators, primitive character</Primary></IndexTerm>
-</Para>
-
-<Para>
-
-<ProgramListing>
-ord# :: Char# -> Int#
-chr# :: Int# -> Char#
-</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>
-
-<Para>
-
-<ProgramListing>
-{+,-,*,quotInt,remInt,gcdInt}# :: Int# -> Int# -> Int#
-negateInt# :: Int# -> Int#
-
-iShiftL#, iShiftRA#, iShiftRL# :: Int# -> Int# -> Int#
- -- shift left, right arithmetic, right logical
-
-addIntC#, subIntC#, mulIntC# :: Int# -> Int# -> (# Int#, Int# #)
- -- add, subtract, multiply with carry
-</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>
-
-<Para>
-<IndexTerm><Primary>floating point numbers, primitive</Primary></IndexTerm>
-<IndexTerm><Primary>operators, primitive floating point</Primary></IndexTerm>
-</Para>
-
-<Para>
-
-<ProgramListing>
-{+,-,*,/}## :: Double# -> Double# -> Double#
-{<,<=,==,/=,>=,>}## :: Double# -> Double# -> Bool
-negateDouble# :: Double# -> Double#
-double2Int# :: Double# -> Int#
-int2Double# :: Int# -> Double#
-
-{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#
-</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>
-
-<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>
-
-<Para>
-And a full complement of trigonometric functions:
-</Para>
-
-<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#
-</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>
-
-<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>
+
+<para>
+The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
+tuples to avoid unnecessary allocation during sequences of operations.
+</para>
+
+</sect2>
+</sect1>
+
+
+<!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
+
+<sect1 id="syntax-extns">
+<title>Syntactic extensions</title>
+
+ <!-- ====================== HIERARCHICAL MODULES ======================= -->
-<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="glasgow-stablePtrs"> 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="glasgow-foreignObjs"> 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>
+ <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>It is a common strategy to use the <literal>as</literal>
+ keyword to save some typing when using qualified names with
+ hierarchical modules. For example:</para>
+
+<programlisting>
+import qualified Control.Monad.ST.Strict as ST
+</programlisting>
+
+ <para>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>
+</para>
-<Para>
+<para>
Suppose we have an abstract data type of finite maps, with a
lookup operation:
-<ProgramListing>
+<programlisting>
lookup :: FiniteMap -> Int -> Maybe Int
-</ProgramListing>
+</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,
+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>
+</para>
-<ProgramListing>
+<programlisting>
clunky env var1 var2 | ok1 && ok2 = val1 + val2
| otherwise = var1 + var2
where
ok2 = maybeToBool m2
val1 = expectJust m1
val2 = expectJust m2
-</ProgramListing>
+</programlisting>
-<Para>
+<para>
The auxiliary functions are
-</Para>
+</para>
-<ProgramListing>
+<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>
+</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>
+<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>
+<literal>otherwise</literal> case and returns the sum of its arguments.
+</para>
-<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>
+</para>
-<ProgramListing>
+<programlisting>
clunky env var1 var1 = case lookup env var1 of
Nothing -> fail
Just val1 -> case lookup env var2 of
Just val2 -> val1 + val2
where
fail = val1 + val2
-</ProgramListing>
+</programlisting>
-<Para>
+<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
+are really the same (<function>fail</function>), and the whole expression
tends to become more and more indented.
-</Para>
+</para>
-<Para>
+<para>
Here is how I would write clunky:
-</Para>
+</para>
-<ProgramListing>
+<programlisting>
clunky env var1 var1
| Just val1 <- lookup env var1
, Just val2 <- lookup env var2
= val1 + val2
...other equations for clunky...
-</ProgramListing>
+</programlisting>
-<Para>
+<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
+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
+<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>
-<Para>
+<para>
Just as with list comprehensions, boolean expressions can be freely mixed
with among the pattern guards. For example:
-</Para>
+</para>
-<ProgramListing>
+<programlisting>
f x | [y] <- x
, y > 3
, Just z <- h y
= ...
-</ProgramListing>
+</programlisting>
-<Para>
+<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 language and library support. The former
-is described later in <XRef LinkEnd="ffi">; the latter is outlined below,
-and detailed in the hslibs documentation.
-</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>
-typedef unsigned long *StgForeignObj;
-typedef long StgInt;
-
-void initialiseEFS (StgInt size);
-StgInt terminateEFS (void);
-StgForeignObj emptyEFS(void);
-StgForeignObj updateEFS (StgForeignObj a, StgInt i, StgInt x);
-StgInt lookupEFS (StgForeignObj a, StgInt i);
-</ProgramListing>
-
-</Para>
-
-<Para>
-You can find appropriate definitions for <Literal>StgInt</Literal>, <Literal>StgForeignObj</Literal>,
-etc using <Command>gcc</Command> on your architecture by consulting
-<Filename>ghc/includes/StgTypes.h</Filename>. The following table summarises the
-relationship between Haskell types and C types.
-</Para>
-
-<Para>
-
-<InformalTable>
-<TGroup Cols="2">
-<ColSpec Align="Left" Colsep="0">
-<ColSpec Align="Left" Colsep="0">
-<TBody>
-<Row>
-<Entry><Emphasis>C type name</Emphasis> </Entry>
-<Entry> <Emphasis>Haskell Type</Emphasis> </Entry>
-</Row>
-
-<Row>
-<Entry>
-<Literal>StgChar</Literal> </Entry>
-<Entry> <Literal>Char#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgInt</Literal> </Entry>
-<Entry> <Literal>Int#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgWord</Literal> </Entry>
-<Entry> <Literal>Word#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgAddr</Literal> </Entry>
-<Entry> <Literal>Addr#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgFloat</Literal> </Entry>
-<Entry> <Literal>Float#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgDouble</Literal> </Entry>
-<Entry> <Literal>Double#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgArray</Literal> </Entry>
-<Entry> <Literal>Array#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgByteArray</Literal> </Entry>
-<Entry> <Literal>ByteArray#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgArray</Literal> </Entry>
-<Entry> <Literal>MutableArray#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgByteArray</Literal> </Entry>
-<Entry> <Literal>MutableByteArray#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgStablePtr</Literal> </Entry>
-<Entry> <Literal>StablePtr#</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StgForeignObj</Literal> </Entry>
-<Entry> <Literal>ForeignObj#</Literal></Entry>
-</Row>
-</TBody>
-
-</TGroup>
-</InformalTable>
-</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>
-
-<Sect2 id="glasgow-stablePtrs">
-<Title>Subverting automatic unboxing with “stable pointers”
-</Title>
-
-<Para>
-<IndexTerm><Primary>stable pointers (Glasgow extension)</Primary></IndexTerm>
-</Para>
-
-<Para>
-The arguments of a <Function>_ccall_</Function> automatically unboxed before the
-call. There are two reasons why this is usually the Right Thing to
-do:
-</Para>
-
-<Para>
-
-<ItemizedList>
-<ListItem>
-
-<Para>
-C is a strict language: it would be excessively tedious to pass
-unevaluated arguments and require the C programmer to force their
-evaluation before using them.
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Boxed values are stored on the Haskell heap and may be moved
-within the heap if a garbage collection occurs—that is, pointers
-to boxed objects are not <Emphasis>stable</Emphasis>.
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-</Para>
-
-<Para>
-It is possible to subvert the unboxing process by creating a “stable
-pointer” to a value and passing the stable pointer instead. For
-example, to pass/return an integer lazily to C functions <Function>storeC</Function> and
-<Function>fetchC</Function> might write:
-</Para>
-
-<Para>
-
-<ProgramListing>
-storeH :: Int -> IO ()
-storeH x = makeStablePtr x >>= \ stable_x ->
- _ccall_ storeC stable_x
-
-fetchH :: IO Int
-fetchH x = _ccall_ fetchC >>= \ stable_x ->
- deRefStablePtr stable_x >>= \ x ->
- freeStablePtr stable_x >>
- return x
-</ProgramListing>
-
-</Para>
-
-<Para>
-The garbage collector will refrain from throwing a stable pointer away
-until you explicitly call one of the following from C or Haskell.
-</Para>
-
-<Para>
-
-<ProgramListing>
-void freeStablePointer( StgStablePtr stablePtrToToss )
-freeStablePtr :: StablePtr a -> IO ()
-</ProgramListing>
-
-</Para>
-
-<Para>
-As with the use of <Function>free</Function> in C programs, GREAT CARE SHOULD BE
-EXERCISED to ensure these functions are called at the right time: too
-early and you get dangling references (and, if you're lucky, an error
-message from the runtime system); too late and you get space leaks.
-</Para>
-
-<Para>
-And to force evaluation of the argument within <Function>fooC</Function>, one would
-call one of the following C functions (according to type of argument).
-</Para>
-
-<Para>
-
-<ProgramListing>
-void performIO ( StgStablePtr stableIndex /* StablePtr s (IO ()) */ );
-StgInt enterInt ( StgStablePtr stableIndex /* StablePtr s Int */ );
-StgFloat enterFloat ( StgStablePtr stableIndex /* StablePtr s Float */ );
-</ProgramListing>
-
-</Para>
-
-<Para>
-<IndexTerm><Primary>performIO</Primary></IndexTerm>
-<IndexTerm><Primary>enterInt</Primary></IndexTerm>
-<IndexTerm><Primary>enterFloat</Primary></IndexTerm>
-</Para>
-
-<Para>
-Nota Bene: <Function>_ccall_GC_</Function><IndexTerm><Primary>_ccall_GC_</Primary></IndexTerm> must be used if any of
-these functions are used.
-</Para>
-
-</Sect2>
-
-<Sect2 id="glasgow-foreignObjs">
-<Title>Foreign objects: pointing outside the Haskell heap
-</Title>
-
-<Para>
-<IndexTerm><Primary>foreign objects (Glasgow extension)</Primary></IndexTerm>
-</Para>
-
-<Para>
-There are two types that GHC programs can use to reference
-(heap-allocated) objects outside the Haskell world: <Literal>Addr</Literal> and
-<Literal>ForeignObj</Literal>.
-</Para>
-
-<Para>
-If you use <Literal>Addr</Literal>, it is up to you to the programmer to arrange
-allocation and deallocation of the objects.
-</Para>
-
-<Para>
-If you use <Literal>ForeignObj</Literal>, GHC's garbage collector will call upon the
-user-supplied <Emphasis>finaliser</Emphasis> function to free the object when the
-Haskell world no longer can access the object. (An object is
-associated with a finaliser function when the abstract
-Haskell type <Literal>ForeignObj</Literal> is created). The finaliser function is
-expressed in C, and is passed as argument the object:
-</Para>
-
-<Para>
-
-<ProgramListing>
-void foreignFinaliser ( StgForeignObj fo )
-</ProgramListing>
-
-</Para>
-
-<Para>
-when the Haskell world can no longer access the object. Since
-<Literal>ForeignObj</Literal>s only get released when a garbage collection occurs, we
-provide ways of triggering a garbage collection from within C and from
-within Haskell.
-</Para>
-
-<Para>
-
-<ProgramListing>
-void GarbageCollect()
-performGC :: IO ()
-</ProgramListing>
-
-</Para>
-
-<Para>
-More information on the programmers' interface to <Literal>ForeignObj</Literal> can be
-found in the library documentation.
-</Para>
-
-</Sect2>
-
-<Sect2 id="glasgow-avoiding-monads">
-<Title>Avoiding monads
-</Title>
-
-<Para>
-<IndexTerm><Primary>C calls to `pure C'</Primary></IndexTerm>
-<IndexTerm><Primary>unsafePerformIO</Primary></IndexTerm>
-</Para>
-
-<Para>
-The <Function>_ccall_</Function> construct is part of the <Literal>IO</Literal> monad because 9 out of 10
-uses will be to call imperative functions with side effects such as
-<Function>printf</Function>. Use of the monad ensures that these operations happen in a
-predictable order in spite of laziness and compiler optimisations.
-</Para>
-
-<Para>
-To avoid having to be in the monad to call a C function, it is
-possible to use <Function>unsafePerformIO</Function>, which is available from the
-<Literal>IOExts</Literal> module. There are three situations where one might like to
-call a C function from outside the IO world:
-</Para>
-
-<Para>
-
-<ItemizedList>
-<ListItem>
-
-<Para>
-Calling a function with no side-effects:
-
-<ProgramListing>
-atan2d :: Double -> Double -> Double
-atan2d y x = unsafePerformIO (_ccall_ atan2d y x)
-
-sincosd :: Double -> (Double, Double)
-sincosd x = unsafePerformIO $ do
- da <- newDoubleArray (0, 1)
- _casm_ “sincosd( %0, &((double *)%1[0]), &((double *)%1[1]) );” x da
- s <- readDoubleArray da 0
- c <- readDoubleArray da 1
- return (s, c)
-</ProgramListing>
-
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Calling a set of functions which have side-effects but which can
-be used in a purely functional manner.
-
-For example, an imperative implementation of a purely functional
-lookup-table might be accessed using the following functions.
-
+</para>
+</sect2>
-<ProgramListing>
-empty :: EFS x
-update :: EFS x -> Int -> x -> EFS x
-lookup :: EFS a -> Int -> a
+ <!-- ===================== Recursive do-notation =================== -->
-empty = unsafePerformIO (_ccall_ emptyEFS)
+<sect2 id="mdo-notation">
+<title>The recursive do-notation
+</title>
-update a i x = unsafePerformIO $
- makeStablePtr x >>= \ stable_x ->
- _ccall_ updateEFS a i stable_x
+<para> The recursive do-notation (also known as mdo-notation) is implemented as described in
+"A recursive do for Haskell",
+Levent Erkok, John Launchbury",
+Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
+</para>
+<para>
+The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
+that is, the variables bound in a do-expression are visible only in the textually following
+code block. Compare this to a let-expression, where bound variables are visible in the entire binding
+group. It turns out that several applications can benefit from recursive bindings in
+the do-notation, and this extension provides the necessary syntactic support.
+</para>
+<para>
+Here is a simple (yet contrived) example:
+</para>
+<programlisting>
+import Control.Monad.Fix
+
+justOnes = mdo xs <- Just (1:xs)
+ return xs
+</programlisting>
+<para>
+As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
+</para>
-lookup a i = unsafePerformIO $
- _ccall_ lookupEFS a i >>= \ stable_x ->
- deRefStablePtr stable_x
-</ProgramListing>
+<para>
+The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
+</para>
+<programlisting>
+class Monad m => MonadFix m where
+ mfix :: (a -> m a) -> m a
+</programlisting>
+<para>
+The function <literal>mfix</literal>
+dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
+then that monad must be declared an instance of the <literal>MonadFix</literal> class.
+For details, see the above mentioned reference.
+</para>
+<para>
+The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
+Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
+for Haskell's internal state monad (strict and lazy, respectively).
+</para>
+<para>
+There are three important points in using the recursive-do notation:
+<itemizedlist>
+<listitem><para>
+The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
+than <literal>do</literal>).
+</para></listitem>
+
+<listitem><para>
+You should <literal>import Control.Monad.Fix</literal>.
+(Note: Strictly speaking, this import is required only when you need to refer to the name
+<literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
+are encouraged to always import this module when using the mdo-notation.)
+</para></listitem>
+
+<listitem><para>
+As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
+</para></listitem>
+</itemizedlist>
+</para>
+<para>
+The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
+contains up to date information on recursive monadic bindings.
+</para>
-You will almost always want to use <Literal>ForeignObj</Literal>s with this.
+<para>
+Historical note: The old implementation of the mdo-notation (and most
+of the existing documents) used the name
+<literal>MonadRec</literal> for the class and the corresponding library.
+This name is not supported by GHC.
+</para>
-</Para>
-</ListItem>
-<ListItem>
+</sect2>
-<Para>
- Calling a side-effecting function even though the results will
-be unpredictable. For example the <Function>trace</Function> function is defined by:
+ <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
+
+ <sect2 id="parallel-list-comprehensions">
+ <title>Parallel List Comprehensions</title>
+ <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
+ </indexterm>
+ <indexterm><primary>parallel list comprehensions</primary>
+ </indexterm>
+
+ <para>Parallel list comprehensions are a natural extension to list
+ comprehensions. List comprehensions can be thought of as a nice
+ syntax for writing maps and filters. Parallel comprehensions
+ extend this to include the zipWith family.</para>
+
+ <para>A parallel list comprehension has multiple independent
+ branches of qualifier lists, each separated by a `|' symbol. For
+ example, the following zips together two lists:</para>
+
+<programlisting>
+ [ (x, y) | x <- 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>
+
+ <para>We can define parallel list comprehensions by translation to
+ regular comprehensions. Here's the basic idea:</para>
+
+ <para>Given a parallel comprehension of the form: </para>
+
+<programlisting>
+ [ e | p1 <- e11, p2 <- e12, ...
+ | q1 <- e21, q2 <- e22, ...
+ ...
+ ]
+</programlisting>
+
+ <para>This will be translated to: </para>
+
+<programlisting>
+ [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
+ [(q1,q2) | q1 <- e21, q2 <- e22, ...]
+ ...
+ ]
+</programlisting>
+
+ <para>where `zipN' is the appropriate zip for the given number of
+ branches.</para>
+
+ </sect2>
+
+<sect2 id="rebindable-syntax">
+<title>Rebindable syntax</title>
+
+
+ <para>GHC allows most kinds of built-in syntax to be rebound by
+ the user, to facilitate replacing the <literal>Prelude</literal>
+ with a home-grown version, for example.</para>
+
+ <para>You may want to define your own numeric class
+ hierarchy. It completely defeats that purpose if the
+ literal "1" means "<literal>Prelude.fromInteger
+ 1</literal>", which is what the Haskell Report specifies.
+ So the <option>-fno-implicit-prelude</option> flag causes
+ the following pieces of built-in syntax to refer to
+ <emphasis>whatever is in scope</emphasis>, not the Prelude
+ versions:</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>
+ <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>
+
+ <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>
+
+ <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>
-<ProgramListing>
-trace :: String -> a -> a
-trace string expr
- = unsafePerformIO (
- ((_ccall_ PreTraceHook sTDERR{-msg-}):: IO ()) >>
- fputs sTDERR string >>
- ((_ccall_ PostTraceHook sTDERR{-msg-}):: IO ()) >>
- return expr )
- where
- sTDERR = (“stderr” :: Addr)
-</ProgramListing>
+</sect2>
+</sect1>
-(This kind of use is not highly recommended—it is only really
-useful in debugging code.)
-</Para>
-</ListItem>
+<!-- TYPE SYSTEM EXTENSIONS -->
+<sect1 id="type-extensions">
+<title>Type system extensions</title>
-</ItemizedList>
+<sect2 id="nullary-types">
+<title>Data types with no constructors</title>
-</Para>
+<para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
+a data type with no constructors. For example:</para>
-</Sect2>
-
-<Sect2 id="ccall-gotchas">
-<Title>C-calling “gotchas” checklist
-</Title>
-
-<Para>
-<IndexTerm><Primary>C call dangers</Primary></IndexTerm>
-<IndexTerm><Primary>CCallable</Primary></IndexTerm>
-<IndexTerm><Primary>CReturnable</Primary></IndexTerm>
-</Para>
-
-<Para>
-And some advice, too.
-</Para>
-
-<Para>
-
-<ItemizedList>
-<ListItem>
-
-<Para>
- For modules that use <Function>_ccall_</Function>s, etc., compile with
-<Option>-fvia-C</Option>.<IndexTerm><Primary>-fvia-C option</Primary></IndexTerm> You don't have to, but you should.
-
-Also, use the <Option>-#include "prototypes.h"</Option> flag (hack) to inform the C
-compiler of the fully-prototyped types of all the C functions you
-call. (<XRef LinkEnd="glasgow-foreign-headers"> says more about this…)
-
-This scheme is the <Emphasis>only</Emphasis> way that you will get <Emphasis>any</Emphasis>
-typechecking of your <Function>_ccall_</Function>s. (It shouldn't be that way, but…).
-GHC will pass the flag <Option>-Wimplicit</Option> to <Command>gcc</Command> so that you'll get warnings
-if any <Function>_ccall_</Function>ed functions have no prototypes.
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
-Try to avoid <Function>_ccall_</Function>s to C functions that take <Literal>float</Literal>
-arguments or return <Literal>float</Literal> results. Reason: if you do, you will
-become entangled in (ANSI?) C's rules for when arguments/results are
-promoted to <Literal>doubles</Literal>. It's a nightmare and just not worth it.
-Use <Literal>doubles</Literal> if possible.
-
-If you do use <Literal>floats</Literal>, check and re-check that the right thing is
-happening. Perhaps compile with <Option>-keep-hc-file-too</Option> and look at
-the intermediate C (<Function>.hc</Function>).
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- The compiler uses two non-standard type-classes when
-type-checking the arguments and results of <Function>_ccall_</Function>: the arguments
-(respectively result) of <Function>_ccall_</Function> must be instances of the class
-<Literal>CCallable</Literal> (respectively <Literal>CReturnable</Literal>). Both classes may be
-imported from the module <Literal>CCall</Literal>, but this should only be
-necessary if you want to define a new instance. (Neither class
-defines any methods—their only function is to keep the
-type-checker happy.)
-
-The type checker must be able to figure out just which of the
-C-callable/returnable types is being used. If it can't, you have to
-add type signatures. For example,
-
-
-<ProgramListing>
-f x = _ccall_ foo x
-</ProgramListing>
-
-
-is not good enough, because the compiler can't work out what type <VarName>x</VarName>
-is, nor what type the <Function>_ccall_</Function> returns. You have to write, say:
-
-
-<ProgramListing>
-f :: Int -> IO Double
-f x = _ccall_ foo x
-</ProgramListing>
-
-
-This table summarises the standard instances of these classes.
-
-<InformalTable>
-<TGroup Cols="4">
-<ColSpec Align="Left" Colsep="0">
-<ColSpec Align="Left" Colsep="0">
-<ColSpec Align="Left" Colsep="0">
-<ColSpec Align="Left" Colsep="0">
-<TBody>
-<Row>
-<Entry><Emphasis>Type</Emphasis> </Entry>
-<Entry><Emphasis>CCallable</Emphasis></Entry>
-<Entry><Emphasis>CReturnable</Emphasis> </Entry>
-<Entry><Emphasis>Which is probably…</Emphasis> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Char</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>unsigned char</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Int</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>long int</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Word</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>unsigned long int</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Addr</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>void *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Float</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>float</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Double</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>double</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>()</Literal> </Entry>
-<Entry> No </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>void</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>[Char]</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> No </Entry>
-<Entry> <Literal>char *</Literal> (null-terminated) </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>Array</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> No </Entry>
-<Entry> <Literal>unsigned long *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>ByteArray</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> No </Entry>
-<Entry> <Literal>unsigned long *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>MutableArray</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> No </Entry>
-<Entry> <Literal>unsigned long *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>MutableByteArray</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> No </Entry>
-<Entry> <Literal>unsigned long *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>State</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> nothing!</Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>StablePtr</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> <Literal>unsigned long *</Literal> </Entry>
-</Row>
-<Row>
-<Entry>
-<Literal>ForeignObjs</Literal> </Entry>
-<Entry> Yes </Entry>
-<Entry> Yes </Entry>
-<Entry> see later </Entry>
-</Row>
-
-</TBody>
-
-</TGroup>
-</InformalTable>
-
-Actually, the <Literal>Word</Literal> type is defined as being the same size as a
-pointer on the target architecture, which is <Emphasis>probably</Emphasis>
-<Literal>unsigned long int</Literal>.
-
-The brave and careful programmer can add their own instances of these
-classes for the following types:
-
-
-<ItemizedList>
-<ListItem>
-
-<Para>
-A <Emphasis>boxed-primitive</Emphasis> type may be made an instance of both
-<Literal>CCallable</Literal> and <Literal>CReturnable</Literal>.
-
-A boxed primitive type is any data type with a
-single unary constructor with a single primitive argument. For
-example, the following are all boxed primitive types:
-
-
-<ProgramListing>
-Int
-Double
-data XDisplay = XDisplay Addr#
-data EFS a = EFS# ForeignObj#
-</ProgramListing>
-
-
-
-<ProgramListing>
-instance CCallable (EFS a)
-instance CReturnable (EFS a)
-</ProgramListing>
-
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Any datatype with a single nullary constructor may be made an
-instance of <Literal>CReturnable</Literal>. For example:
-
-
-<ProgramListing>
-data MyVoid = MyVoid
-instance CReturnable MyVoid
-</ProgramListing>
-
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- As at version 2.09, <Literal>String</Literal> (i.e., <Literal>[Char]</Literal>) is still
-not a <Literal>CReturnable</Literal> type.
-
-Also, the now-builtin type <Literal>PackedString</Literal> is neither
-<Literal>CCallable</Literal> nor <Literal>CReturnable</Literal>. (But there are functions in
-the PackedString interface to let you get at the necessary bits…)
-</Para>
-</ListItem>
-
-</ItemizedList>
+<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>
-</ListItem>
-<ListItem>
+<para>Such data types have only one value, namely bottom.
+Nevertheless, they can be useful when defining "phantom types".</para>
+</sect2>
-<Para>
- The code-generator will complain if you attempt to use <Literal>%r</Literal> in
-a <Literal>_casm_</Literal> whose result type is <Literal>IO ()</Literal>; or if you don't use <Literal>%r</Literal>
-<Emphasis>precisely</Emphasis> once for any other result type. These messages are
-supposed to be helpful and catch bugs—please tell us if they wreck
-your life.
+<sect2 id="infix-tycons">
+<title>Infix type constructors</title>
+
+<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>
+
+</itemizedlist>
+</para>
+</sect2>
-</Para>
-</ListItem>
-<ListItem>
+<sect2 id="sec-kinding">
+<title>Explicitly-kinded quantification</title>
+
+<para>
+Haskell infers the kind of each type variable. Sometimes it is nice to be able
+to give the kind explicitly as (machine-checked) documentation,
+just as it is nice to give a type signature for a function. On some occasions,
+it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
+John Hughes had to define the data type:
+<Screen>
+ data Set cxt a = Set [a]
+ | Unused (cxt a -> ())
+</Screen>
+The only use for the <literal>Unused</literal> constructor was to force the correct
+kind for the type variable <literal>cxt</literal>.
+</para>
+<para>
+GHC now instead allows you to specify the kind of a type variable directly, wherever
+a type variable is explicitly bound. Namely:
+<itemizedlist>
+<listitem><para><literal>data</literal> declarations:
+<Screen>
+ data Set (cxt :: * -> *) a = Set [a]
+</Screen></para></listitem>
+<listitem><para><literal>type</literal> declarations:
+<Screen>
+ type T (f :: * -> *) = f Int
+</Screen></para></listitem>
+<listitem><para><literal>class</literal> declarations:
+<Screen>
+ class (Eq a) => C (f :: * -> *) a where ...
+</Screen></para></listitem>
+<listitem><para><literal>forall</literal>'s in type signatures:
+<Screen>
+ f :: forall (cxt :: * -> *). Set cxt Int
+</Screen></para></listitem>
+</itemizedlist>
+</para>
-<Para>
- If you call out to C code which may trigger the Haskell garbage
-collector or create new threads (examples of this later…), then you
-must use the <Function>_ccall_GC_</Function><IndexTerm><Primary>_ccall_GC_ primitive</Primary></IndexTerm> or
-<Function>_casm_GC_</Function><IndexTerm><Primary>_casm_GC_ primitive</Primary></IndexTerm> variant of C-calls. (This
-does not work with the native code generator—use <Option>-fvia-C</Option>.) This
-stuff is hairy with a capital H!
-</Para>
-</ListItem>
+<para>
+The parentheses are required. Some of the spaces are required too, to
+separate the lexemes. If you write <literal>(f::*->*)</literal> you
+will get a parse error, because "<literal>::*->*</literal>" is a
+single lexeme in Haskell.
+</para>
-</ItemizedList>
+<para>
+As part of the same extension, you can put kind annotations in types
+as well. Thus:
+<Screen>
+ f :: (Int :: *) -> Int
+ g :: forall a. a -> (a :: *)
+</Screen>
+The syntax is
+<Screen>
+ atype ::= '(' ctype '::' kind ')
+</Screen>
+The parentheses are required.
+</para>
+</sect2>
-</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>
+With the <option>-fglasgow-exts</option> GHC lifts this restriction.
+</para>
-</Sect1>
+</sect2>
-<Sect1 id="multi-param-type-classes">
-<Title>Multi-parameter type classes
-</Title>
+<sect2 id="multi-param-type-classes">
+<title>Multi-parameter type classes
+</title>
-<Para>
+<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>
+<sect3 id="type-restrictions">
+<title>Types</title>
+
+<para>
+GHC imposes the following restrictions on the form of a qualified
+type, whether declared in a type signature
+or inferred. Consider the type:
+
+<programlisting>
+ forall tv1..tvn (c1, ...,cn) => type
+</programlisting>
-<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>
+in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
+</para>
-<Para>
+<para>
<OrderedList>
-<ListItem>
+<listitem>
-<Para>
- <Emphasis>Each universally quantified type variable
-<Literal>tvi</Literal> must be mentioned (i.e. appear free) in <Literal>type</Literal></Emphasis>.
+<para>
+ <emphasis>Each universally quantified type variable
+<literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
+A type variable is "reachable" if it it is functionally dependent
+(see <xref linkend="functional-dependencies">)
+on the type variables free in <literal>type</literal>.
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:
+ambiguity.
+Here, for example, is an illegal type:
-<ProgramListing>
+<programlisting>
forall a. Eq a => Int
-</ProgramListing>
+</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
+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>.
+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>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>Every constraint <Literal>ci</Literal> must mention at least one of the
-universally quantified type variables <Literal>tvi</Literal></Emphasis>.
+<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>:
+For example, this type is OK because <literal>C a b</literal> mentions the
+universally quantified type variable <literal>b</literal>:
-<ProgramListing>
+<programlisting>
forall a. C a b => burble
-</ProgramListing>
+</programlisting>
-The next type is illegal because the constraint <Literal>Eq b</Literal> does not
-mention <Literal>a</Literal>:
+The next type is illegal because the constraint <literal>Eq b</literal> does not
+mention <literal>a</literal>:
-<ProgramListing>
+<programlisting>
forall a. Eq b => burble
-</ProgramListing>
+</programlisting>
The reason for this restriction is milder than the other one. The
excluding them is a conservative choice; it leaves a patch of
territory free in case we need it later.
-</Para>
-</ListItem>
+</para>
+</listitem>
</OrderedList>
-</Para>
+</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
+<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>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f :: Eq (m a) => [m a] -> [m a]
g :: Eq [a] => ...
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
This choice recovers principal types, a property that Haskell 1.4 does not have.
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Class declarations</Title>
+<sect3>
+<title>Class declarations</title>
-<Para>
+<para>
<OrderedList>
-<ListItem>
+<listitem>
-<Para>
- <Emphasis>Multi-parameter type classes are permitted</Emphasis>. For example:
+<para>
+ <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
-<ProgramListing>
+<programlisting>
class Collection c a where
union :: c a -> c a -> c a
...etc.
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>The class hierarchy must be acyclic</Emphasis>. However, the definition
+<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>
+<programlisting>
class C a where {
op :: D b => a -> b -> b
}
class C a => D a where { ... }
-</ProgramListing>
+</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>.)
+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>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>There are no restrictions on the context in a class declaration
+<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:
+be acyclic</emphasis>. So these class declarations are OK:
-<ProgramListing>
+<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)
-</ProgramListing>
-
-
-is not OK because the constraint <Literal>(Eq a)</Literal> mentions on the class
-type variable <Literal>a</Literal>, but not <Literal>b</Literal>. However, any such
-example is easily fixed by moving the offending context up to the
-superclass context:
-
-
-<ProgramListing>
- class Eq a => C a where
- op ::(a,b) -> (a,b)
-</ProgramListing>
+</programlisting>
-A yet more relaxed rule would allow the context of a class-op signature
-to mention only class type variables. However, that conflicts with
-Rule 1(b) for types above.
+</para>
+</listitem>
-</Para>
-</ListItem>
-<ListItem>
+<listitem>
-<Para>
- <Emphasis>The type of each class operation must mention <Emphasis>all</Emphasis> of
-the class type variables</Emphasis>. For example:
+<para>
+ <emphasis>All of the class type variables must be reachable (in the sense
+mentioned in <xref linkend="type-restrictions">)
+from the free varibles of each method type
+</emphasis>. For example:
-<ProgramListing>
+<programlisting>
class Coll s a where
empty :: s
insert :: s -> a -> s
-</ProgramListing>
+</programlisting>
-is not OK, because the type of <Literal>empty</Literal> doesn't mention
-<Literal>a</Literal>. This rule is a consequence of Rule 1(a), above, for
+is not OK, because the type of <literal>empty</literal> doesn't mention
+<literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
types, and has the same motivation.
Sometimes, offending class declarations exhibit misunderstandings. For
-example, <Literal>Coll</Literal> might be rewritten
+example, <literal>Coll</literal> might be rewritten
-<ProgramListing>
+<programlisting>
class Coll s a where
empty :: s a
insert :: s a -> a -> s a
-</ProgramListing>
+</programlisting>
which makes the connection between the type of a collection of
-<Literal>a</Literal>'s (namely <Literal>(s a)</Literal>) and the element type <Literal>a</Literal>.
+<literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
Occasionally this really doesn't work, in which case you can split the
class like this:
-<ProgramListing>
+<programlisting>
class CollE s where
empty :: s
class CollE s => Coll s a where
insert :: s -> a -> s
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
+</para>
+</listitem>
</OrderedList>
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Instance declarations</Title>
+<sect3 id="instance-decls">
+<title>Instance declarations</title>
-<Para>
+<para>
<OrderedList>
-<ListItem>
+<listitem>
-<Para>
- <Emphasis>Instance declarations may not overlap</Emphasis>. The two instance
+<para>
+ <emphasis>Instance declarations may not overlap</emphasis>. The two instance
declarations
-<ProgramListing>
+<programlisting>
instance context1 => C type1 where ...
instance context2 => C type2 where ...
-</ProgramListing>
+</programlisting>
-"overlap" if <Literal>type1</Literal> and <Literal>type2</Literal> unify
+"overlap" if <literal>type1</literal> and <literal>type2</literal> unify
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
-
-
-<ItemizedList>
-<ListItem>
-
-<Para>
- EITHER <Literal>type1</Literal> and <Literal>type2</Literal> do not unify
-</Para>
-</ListItem>
-<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
-</Para>
-</ListItem>
+<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
+option</primary></indexterm> then overlapping instance declarations are permitted.
+However, GHC arranges never to commit to using an instance declaration
+if another instance declaration also applies, either now or later.
-</ItemizedList>
+<itemizedlist>
+<listitem>
+<para>
+ EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
+</para>
+</listitem>
+<listitem>
+<para>
+ OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
+(but not identical to <literal>type1</literal>), or vice versa.
+</para>
+</listitem>
+</itemizedlist>
Notice that these rules
+<itemizedlist>
+<listitem>
-
-<ItemizedList>
-<ListItem>
-
-<Para>
+<para>
make it clear which instance decl to use
(pick the most specific one that matches)
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- do not mention the contexts <Literal>context1</Literal>, <Literal>context2</Literal>
+<para>
+ do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
Reason: you can pick which instance decl
"matches" based on the type.
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-
+</para>
+</listitem>
+
+</itemizedlist>
+However the rules are over-conservative. Two instance declarations can overlap,
+but it can still be clear in particular situations which to use. For example:
+<programlisting>
+ instance C (Int,a) where ...
+ instance C (a,Bool) where ...
+</programlisting>
+These are rejected by GHC's rules, but it is clear what to do when trying
+to solve the constraint <literal>C (Int,Int)</literal> because the second instance
+cannot apply. Yell if this restriction bites you.
+</para>
+<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
imported by the one being compiled, so it can "see" all instance decls
-when it is compiling <Literal>Main</Literal>. However, it currently chooses not
+when it is compiling <literal>Main</literal>. However, it currently chooses not
to look at ones that can't possibly be of use in the module currently
being compiled, in the interests of efficiency. (Perhaps we should
-change that decision, at least for <Literal>Main</Literal>.)
+change that decision, at least for <literal>Main</literal>.)
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>There are no restrictions on the type in an instance
-<Emphasis>head</Emphasis>, except that at least one must not be a type variable</Emphasis>.
+<para>
+ <emphasis>There are no restrictions on the type in an instance
+<emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
The instance "head" is the bit after the "=>" in an instance decl. For
example, these are OK:
-<ProgramListing>
+<programlisting>
instance C Int a where ...
instance D (Int, Int) where ...
instance E [[a]] where ...
-</ProgramListing>
+</programlisting>
-Note that instance heads <Emphasis>may</Emphasis> contain repeated type variables.
+Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
For example, this is OK:
-<ProgramListing>
+<programlisting>
instance Stateful (ST s) (MutVar s) where ...
-</ProgramListing>
-
-
-The "at least one not a type variable" restriction is to ensure that
-context reduction terminates: each reduction step removes one type
-constructor. For example, the following would make the type checker
-loop if it wasn't excluded:
-
-
-<ProgramListing>
- instance C a => C a where ...
-</ProgramListing>
-
-
-There are two situations in which the rule is a bit of a pain. First,
-if one allows overlapping instance declarations then it's quite
-convenient to have a "default instance" declaration that applies if
-something more specific does not:
-
-
-<ProgramListing>
- instance C a where
- op = ... -- Default
-</ProgramListing>
-
-
-Second, sometimes you might want to use the following to get the
-effect of a "class synonym":
-
-
-<ProgramListing>
- class (C1 a, C2 a, C3 a) => C a where { }
-
- instance (C1 a, C2 a, C3 a) => C a where { }
-</ProgramListing>
-
+</programlisting>
-This allows you to write shorter signatures:
-
-
-<ProgramListing>
- f :: C a => ...
-</ProgramListing>
-
-
-instead of
-
-
-<ProgramListing>
- f :: (C1 a, C2 a, C3 a) => ...
-</ProgramListing>
-
-
-I'm on the lookout for a simple rule that preserves decidability while
-allowing these idioms. The experimental flag
-<Option>-fallow-undecidable-instances</Option><IndexTerm><Primary>-fallow-undecidable-instances
-option</Primary></IndexTerm> lifts this restriction, allowing all the types in an
-instance head to be type variables.
-
-</Para>
-</ListItem>
-<ListItem>
+See <xref linkend="undecidable-instances"> for an experimental
+extension to lift this restriction.
+</para>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>Unlike Haskell 1.4, instance heads may use type
-synonyms</Emphasis>. As always, using a type synonym is just shorthand for
+<para>
+ <emphasis>Unlike Haskell 1.4, instance heads may use type
+synonyms</emphasis>. As always, using a type synonym is just shorthand for
writing the RHS of the type synonym definition. For example:
-<ProgramListing>
+<programlisting>
type Point = (Int,Int)
instance C Point where ...
instance C [Point] where ...
-</ProgramListing>
+</programlisting>
is legal. However, if you added
-<ProgramListing>
+<programlisting>
instance C (Int,Int) where ...
-</ProgramListing>
+</programlisting>
as well, then the compiler will complain about the overlapping
must be fully applied. You cannot, for example, write:
-<ProgramListing>
+<programlisting>
type P a = [[a]]
instance Monad P where ...
-</ProgramListing>
+</programlisting>
This design decision is independent of all the others, and easily
reversed, but it makes sense to me.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
-<Emphasis>The types in an instance-declaration <Emphasis>context</Emphasis> must all
-be type variables</Emphasis>. Thus
+<para>
+<emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
+be type variables</emphasis>. Thus
-<ProgramListing>
+<programlisting>
instance C a b => Eq (a,b) where ...
-</ProgramListing>
+</programlisting>
is OK, but
-<ProgramListing>
+<programlisting>
instance C Int b => Foo b where ...
-</ProgramListing>
+</programlisting>
-is not OK. Again, the intent here is to make sure that context
-reduction terminates.
+is not OK. See <xref linkend="undecidable-instances"> for an experimental
+extension to lift this restriction.
-Voluminous correspondence on the Haskell mailing list has convinced me
-that it's worth experimenting with a more liberal rule. If you use
-the flag <Option>-fallow-undecidable-instances</Option> can use arbitrary
-types in an instance context. Termination is ensured by having a
-fixed-depth recursion stack. If you exceed the stack depth you get a
-sort of backtrace, and the opportunity to increase the stack depth
-with <Option>-fcontext-stack</Option><Emphasis>N</Emphasis>.
-</Para>
-</ListItem>
+
+</para>
+</listitem>
</OrderedList>
-</Para>
+</para>
-</Sect2>
+</sect3>
-</Sect1>
+</sect2>
-<Sect1 id="universal-quantification">
-<Title>Explicit universal quantification
-</Title>
+<sect2 id="undecidable-instances">
+<title>Undecidable instances</title>
+
+<para>The rules for instance declarations state that:
+<itemizedlist>
+<listitem><para>At least one of the types in the <emphasis>head</emphasis> of
+an instance declaration <emphasis>must not</emphasis> be a type variable.
+</para></listitem>
+<listitem><para>All of the types in the <emphasis>context</emphasis> of
+an instance declaration <emphasis>must</emphasis> be type variables.
+</para></listitem>
+</itemizedlist>
+These restrictions ensure that
+context reduction terminates: each reduction step removes one type
+constructor. For example, the following would make the type checker
+loop if it wasn't excluded:
+<programlisting>
+ instance C a => C a where ...
+</programlisting>
+There are two situations in which the rule is a bit of a pain. First,
+if one allows overlapping instance declarations then it's quite
+convenient to have a "default instance" declaration that applies if
+something more specific does not:
-<Para>
-GHC now allows you to write explicitly quantified types. GHC's
-syntax for this now agrees with Hugs's, namely:
-</Para>
-<Para>
+<programlisting>
+ instance C a where
+ op = ... -- Default
+</programlisting>
-<ProgramListing>
- forall a b. (Ord a, Eq b) => a -> b -> a
-</ProgramListing>
-</Para>
+Second, sometimes you might want to use the following to get the
+effect of a "class synonym":
-<Para>
-The context is, of course, optional. You can't use <Literal>forall</Literal> as
-a type variable any more!
-</Para>
-<Para>
-Haskell type signatures are implicitly quantified. The <Literal>forall</Literal>
-allows us to say exactly what this means. For example:
-</Para>
+<programlisting>
+ class (C1 a, C2 a, C3 a) => C a where { }
-<Para>
+ instance (C1 a, C2 a, C3 a) => C a where { }
+</programlisting>
-<ProgramListing>
- g :: b -> b
-</ProgramListing>
-</Para>
+This allows you to write shorter signatures:
-<Para>
-means this:
-</Para>
-<Para>
+<programlisting>
+ f :: C a => ...
+</programlisting>
-<ProgramListing>
- g :: forall b. (b -> b)
-</ProgramListing>
-</Para>
+instead of
-<Para>
-The two are treated identically.
-</Para>
-<Sect2 id="univ">
-<Title>Universally-quantified data type fields
-</Title>
+<programlisting>
+ f :: (C1 a, C2 a, C3 a) => ...
+</programlisting>
-<Para>
-In a <Literal>data</Literal> or <Literal>newtype</Literal> declaration one can quantify
-the types of the constructor arguments. Here are several examples:
-</Para>
-<Para>
+Voluminous correspondence on the Haskell mailing list has convinced me
+that it's worth experimenting with more liberal rules. If you use
+the experimental flag <option>-fallow-undecidable-instances</option>
+<indexterm><primary>-fallow-undecidable-instances
+option</primary></indexterm>, you can use arbitrary
+types in both an instance context and instance head. Termination is ensured by having a
+fixed-depth recursion stack. If you exceed the stack depth you get a
+sort of backtrace, and the opportunity to increase the stack depth
+with <option>-fcontext-stack</option><emphasis>N</emphasis>.
+</para>
+<para>
+I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
+allowing these idioms interesting idioms.
+</para>
+</sect2>
-<ProgramListing>
-data T a = T1 (forall b. b -> b -> b) a
+<sect2 id="implicit-parameters">
+<title>Implicit parameters
+</title>
-data MonadT m = MkMonad { return :: forall a. a -> m a,
- bind :: forall a b. m a -> (a -> m b) -> m b
- }
+<para> Implicit paramters are implemented as described in
+"Implicit parameters: dynamic scoping with static types",
+J Lewis, MB Shields, E Meijer, J Launchbury,
+27th ACM Symposium on Principles of Programming Languages (POPL'00),
+Boston, Jan 2000.
+</para>
+<para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
+<para>
+A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
+context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
+context. In Haskell, all variables are statically bound. Dynamic
+binding of variables is a notion that goes back to Lisp, but was later
+discarded in more modern incarnations, such as Scheme. Dynamic binding
+can be very confusing in an untyped language, and unfortunately, typed
+languages, in particular Hindley-Milner typed languages like Haskell,
+only support static scoping of variables.
+</para>
+<para>
+However, by a simple extension to the type class system of Haskell, we
+can support dynamic binding. Basically, we express the use of a
+dynamically bound variable as a constraint on the type. These
+constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
+function uses a dynamically-bound variable <literal>?x</literal>
+of type <literal>t'</literal>". For
+example, the following expresses the type of a sort function,
+implicitly parameterized by a comparison function named <literal>cmp</literal>.
+<programlisting>
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+</programlisting>
+The dynamic binding constraints are just a new form of predicate in the type class system.
+</para>
+<para>
+An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
+where <literal>x</literal> is
+any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
+Use of this construct also introduces a new
+dynamic-binding constraint in the type of the expression.
+For example, the following definition
+shows how we can define an implicitly parameterized sort function in
+terms of an explicitly parameterized <literal>sortBy</literal> function:
+<programlisting>
+ sortBy :: (a -> a -> Bool) -> [a] -> [a]
+
+ sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
+ sort = sortBy ?cmp
+</programlisting>
+</para>
-newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
-</ProgramListing>
+<sect3>
+<title>Implicit-parameter type constraints</title>
+<para>
+Dynamic binding constraints behave just like other type class
+constraints in that they are automatically propagated. Thus, when a
+function is used, its implicit parameters are inherited by the
+function that called it. For example, our <literal>sort</literal> function might be used
+to pick out the least value in a list:
+<programlisting>
+ least :: (?cmp :: a -> a -> Bool) => [a] -> a
+ least xs = fst (sort xs)
+</programlisting>
+Without lifting a finger, the <literal>?cmp</literal> parameter is
+propagated to become a parameter of <literal>least</literal> as well. With explicit
+parameters, the default is that parameters must always be explicit
+propagated. With implicit parameters, the default is to always
+propagate them.
+</para>
+<para>
+An implicit-parameter type constraint differs from other type class constraints in the
+following way: All uses of a particular implicit parameter must have
+the same type. This means that the type of <literal>(?x, ?x)</literal>
+is <literal>(?x::a) => (a,a)</literal>, and not
+<literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
+class constraints.
+</para>
-</Para>
+<para> You can't have an implicit parameter in the context of a class or instance
+declaration. For example, both these declarations are illegal:
+<programlisting>
+ class (?x::Int) => C a where ...
+ instance (?x::a) => Foo [a] where ...
+</programlisting>
+Reason: exactly which implicit parameter you pick up depends on exactly where
+you invoke a function. But the ``invocation'' of instance declarations is done
+behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
+Easiest thing is to outlaw the offending types.</para>
+<para>
+Implicit-parameter constraints do not cause ambiguity. For example, consider:
+<programlisting>
+ f :: (?x :: [a]) => Int -> Int
+ f n = n + length ?x
+
+ g :: (Read a, Show a) => String -> String
+ g s = show (read s)
+</programlisting>
+Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
+is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
+quite unambiguous, and fixes the type <literal>a</literal>.
+</para>
+</sect3>
+
+<sect3>
+<title>Implicit-parameter bindings</title>
+
+<para>
+An implicit parameter is <emphasis>bound</emphasis> using the standard
+<literal>let</literal> or <literal>where</literal> binding forms.
+For example, we define the <literal>min</literal> function by binding
+<literal>cmp</literal>.
+<programlisting>
+ min :: [a] -> a
+ min = let ?cmp = (<=) in least
+</programlisting>
+</para>
+<para>
+A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
+bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
+(including in a list comprehension, or do-notation, or pattern guards),
+or a <literal>where</literal> clause.
+Note the following points:
+<itemizedlist>
+<listitem><para>
+An implicit-parameter binding group must be a
+collection of simple bindings to implicit-style variables (no
+function-style bindings, and no type signatures); these bindings are
+neither polymorphic or recursive.
+</para></listitem>
+<listitem><para>
+You may not mix implicit-parameter bindings with ordinary bindings in a
+single <literal>let</literal>
+expression; use two nested <literal>let</literal>s instead.
+(In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
+</para></listitem>
+
+<listitem><para>
+You may put multiple implicit-parameter bindings in a
+single binding group; but they are <emphasis>not</emphasis> treated
+as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
+Instead they are treated as a non-recursive group, simultaneously binding all the implicit
+parameter. The bindings are not nested, and may be re-ordered without changing
+the meaning of the program.
+For example, consider:
+<programlisting>
+ f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
+</programlisting>
+The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
+the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
+<programlisting>
+ f :: (?x::Int) => Int -> Int
+</programlisting>
+</para></listitem>
+</itemizedlist>
+</para>
-<Para>
-The constructors now have so-called <Emphasis>rank 2</Emphasis> polymorphic
-types, in which there is a for-all in the argument types.:
-</Para>
+</sect3>
+</sect2>
-<Para>
+<sect2 id="linear-implicit-parameters">
+<title>Linear implicit parameters
+</title>
+<para>
+Linear implicit parameters are an idea developed by Koen Claessen,
+Mark Shields, and Simon PJ. They address the long-standing
+problem that monads seem over-kill for certain sorts of problem, notably:
+</para>
+<itemizedlist>
+<listitem> <para> distributing a supply of unique names </para> </listitem>
+<listitem> <para> distributing a suppply of random numbers </para> </listitem>
+<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
+</itemizedlist>
+
+<para>
+Linear implicit parameters are just like ordinary implicit parameters,
+except that they are "linear" -- that is, they cannot be copied, and
+must be explicitly "split" instead. Linear implicit parameters are
+written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
+(The '/' in the '%' suggests the split!)
+</para>
+<para>
+For example:
+<programlisting>
+ import GHC.Exts( Splittable )
+
+ data NameSupply = ...
+
+ splitNS :: NameSupply -> (NameSupply, NameSupply)
+ newName :: NameSupply -> Name
+
+ instance Splittable NameSupply where
+ split = splitNS
+
+
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+ ...more equations for f...
+</programlisting>
+Notice that the implicit parameter %ns is consumed
+<itemizedlist>
+<listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
+<listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
+</itemizedlist>
+</para>
+<para>
+So the translation done by the type checker makes
+the parameter explicit:
+<programlisting>
+ f :: NameSupply -> Env -> Expr -> Expr
+ f ns env (Lam x e) = Lam x' (f ns1 env e)
+ where
+ (ns1,ns2) = splitNS ns
+ x' = newName ns2
+ env = extend env x x'
+</programlisting>
+Notice the call to 'split' introduced by the type checker.
+How did it know to use 'splitNS'? Because what it really did
+was to introduce a call to the overloaded function 'split',
+defined by the class <literal>Splittable</literal>:
+<programlisting>
+ class Splittable a where
+ split :: a -> (a,a)
+</programlisting>
+The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
+split for name supplies. But we can simply write
+<programlisting>
+ g x = (x, %ns, %ns)
+</programlisting>
+and GHC will infer
+<programlisting>
+ g :: (Splittable a, %ns :: a) => b -> (b,a,a)
+</programlisting>
+The <literal>Splittable</literal> class is built into GHC. It's exported by module
+<literal>GHC.Exts</literal>.
+</para>
+<para>
+Other points:
+<itemizedlist>
+<listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
+are entirely distinct implicit parameters: you
+ can use them together and they won't intefere with each other. </para>
+</listitem>
+
+<listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
+
+<listitem> <para>You cannot have implicit parameters (whether linear or not)
+ in the context of a class or instance declaration. </para></listitem>
+</itemizedlist>
+</para>
-<ProgramListing>
-T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
-MkMonad :: forall m. (forall a. a -> m a)
- -> (forall a b. m a -> (a -> m b) -> m b)
- -> MonadT m
-MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
-</ProgramListing>
-
-</Para>
-
-<Para>
-Notice that you don't need to use a <Literal>forall</Literal> if there's an
-explicit context. For example in the first argument of the
-constructor <Function>MkSwizzle</Function>, an implicit "<Literal>forall a.</Literal>" is
-prefixed to the argument type. The implicit <Literal>forall</Literal>
-quantifies all type variables that are not already in scope, and are
-mentioned in the type quantified over.
-</Para>
-
-<Para>
-As for type signatures, implicit quantification happens for non-overloaded
-types too. So if you write this:
-
-<ProgramListing>
- data T a = MkT (Either a b) (b -> b)
-</ProgramListing>
-
-it's just as if you had written this:
-
-<ProgramListing>
- data T a = MkT (forall b. Either a b) (forall b. b -> b)
-</ProgramListing>
-
-That is, since the type variable <Literal>b</Literal> isn't in scope, it's
-implicitly universally quantified. (Arguably, it would be better
-to <Emphasis>require</Emphasis> explicit quantification on constructor arguments
-where that is what is wanted. Feedback welcomed.)
-</Para>
-
-</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>
-
-<Para>
-
-<ProgramListing>
-(T1 (\xy->x) 3) :: T Int
-
-(MkSwizzle sort) :: Swizzle
-(MkSwizzle reverse) :: Swizzle
-
-(let r x = Just x
- b m k = case m of
- Just y -> k y
- Nothing -> Nothing
- in
- MkMonad r b) :: MonadT Maybe
-</ProgramListing>
-
-</Para>
-
-<Para>
-The type of the argument can, as usual, be more general than the type
-required, as <Literal>(MkSwizzle reverse)</Literal> shows. (<Function>reverse</Function>
-does not need the <Literal>Ord</Literal> constraint.)
-</Para>
-
-</Sect2>
-
-<Sect2>
-<Title>Pattern matching</Title>
-
-<Para>
-When you use pattern matching, the bound variables may now have
-polymorphic types. For example:
-</Para>
-
-<Para>
-
-<ProgramListing>
- f :: T a -> a -> (a, Char)
- f (T1 f k) x = (f k x, f 'c' 'd')
-
- g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
- g (MkSwizzle s) xs f = s (map f (s xs))
-
- h :: MonadT m -> [m a] -> m [a]
- h m [] = return m []
- h m (x:xs) = bind m x $ \y ->
- bind m (h m xs) $ \ys ->
- return m (y:ys)
-</ProgramListing>
-
-</Para>
-
-<Para>
-In the function <Function>h</Function> we use the record selectors <Literal>return</Literal>
-and <Literal>bind</Literal> to extract the polymorphic bind and return functions
-from the <Literal>MonadT</Literal> data structure, rather than using pattern
-matching.
-</Para>
-
-<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>Warnings</title>
+
+<para>
+The monomorphism restriction is even more important than usual.
+Consider the example above:
+<programlisting>
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+</programlisting>
+If we replaced the two occurrences of x' by (newName %ns), which is
+usually a harmless thing to do, we get:
+<programlisting>
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam (newName %ns) (f env e)
+ where
+ env' = extend env x (newName %ns)
+</programlisting>
+But now the name supply is consumed in <emphasis>three</emphasis> places
+(the two calls to newName,and the recursive call to f), so
+the result is utterly different. Urk! We don't even have
+the beta rule.
+</para>
+<para>
+Well, this is an experimental change. With implicit
+parameters we have already lost beta reduction anyway, and
+(as John Launchbury puts it) we can't sensibly reason about
+Haskell programs without knowing their typing.
+</para>
-<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:
+</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>
-<ProgramListing>
- runTIM :: (forall s. TIM s a) -> Maybe a
- runTIM tm = case tm of { TIM m -> runST m }
-</ProgramListing>
+</sect2>
-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.
-</Para>
-
-</Sect2>
+<sect2 id="functional-dependencies">
+<title>Functional dependencies
+</title>
-<Sect2>
-<Title>The partial-application restriction</Title>
+<para> Functional dependencies are implemented as described by Mark Jones
+in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
+In Proceedings of the 9th European Symposium on Programming,
+ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
+.
+</para>
+<para>
+Functional dependencies are introduced by a vertical bar in the syntax of a
+class declaration; e.g.
+<programlisting>
+ class (Monad m) => MonadState s m | m -> s where ...
+
+ class Foo a b c | a b -> c where ...
+</programlisting>
+There should be more documentation, but there isn't (yet). Yell if you need it.
+</para>
+</sect2>
-<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:
-</Para>
-<Para>
+<sect2 id="universal-quantification">
+<title>Arbitrary-rank polymorphism
+</title>
-<ProgramListing>
- map MkSwizzle [sort, reverse]
-</ProgramListing>
+<para>
+Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
+allows us to say exactly what this means. For example:
+</para>
+<para>
+<programlisting>
+ g :: b -> b
+</programlisting>
+means this:
+<programlisting>
+ g :: forall b. (b -> b)
+</programlisting>
+The two are treated identically.
+</para>
-</Para>
+<para>
+However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
+explicit universal quantification in
+types.
+For example, all the following types are legal:
+<programlisting>
+ f1 :: forall a b. a -> b -> a
+ g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
+
+ f2 :: (forall a. a->a) -> Int -> Int
+ g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
+
+ f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
+</programlisting>
+Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
+can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
+The <literal>forall</literal> makes explicit the universal quantification that
+is implicitly added by Haskell.
+</para>
+<para>
+The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
+the <literal>forall</literal> is on the left of a function 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>
+ 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 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>
+<sect3 id="univ">
+<title>Examples
+</title>
-<Para>
+<para>
+In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
+the types of the constructor arguments. Here are several examples:
+</para>
-<ProgramListing>
- map (T1 (\a b -> a)) [1,2,3]
-</ProgramListing>
+<para>
-</Para>
+<programlisting>
+data T a = T1 (forall b. b -> b -> b) a
-<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>.
-</Para>
+data MonadT m = MkMonad { return :: forall a. a -> m a,
+ bind :: forall a b. m a -> (a -> m b) -> m b
+ }
-</Sect2>
+newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
+</programlisting>
-<Sect2 id="sigs">
-<Title>Type signatures
-</Title>
+</para>
-<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>
+<para>
+The constructors have rank-2 types:
+</para>
-<Para>
+<para>
-<ProgramListing>
- mkTs f x y = [T1 f x, T1 f y]
-</ProgramListing>
+<programlisting>
+T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
+MkMonad :: forall m. (forall a. a -> m a)
+ -> (forall a b. m a -> (a -> m b) -> m b)
+ -> MonadT m
+MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
+</programlisting>
-</Para>
+</para>
-<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>
+<para>
+Notice that you don't need to use a <literal>forall</literal> if there's an
+explicit context. For example in the first argument of the
+constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
+prefixed to the argument type. The implicit <literal>forall</literal>
+quantifies all type variables that are not already in scope, and are
+mentioned in the type quantified over.
+</para>
-<Para>
-The 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:
-</Para>
+<para>
+As for type signatures, implicit quantification happens for non-overloaded
+types too. So if you write this:
-<Para>
+<programlisting>
+ data T a = MkT (Either a b) (b -> b)
+</programlisting>
-<ProgramListing>
- mkTs :: (forall b. b -> b -> b) -> a -> [T a]
- mkTs f x y = [T1 f x, T1 f y]
-</ProgramListing>
+it's just as if you had written this:
-</Para>
+<programlisting>
+ data T a = MkT (forall b. Either a b) (forall b. b -> b)
+</programlisting>
-<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.
-</Para>
+That is, since the type variable <literal>b</literal> isn't in scope, it's
+implicitly universally quantified. (Arguably, it would be better
+to <emphasis>require</emphasis> explicit quantification on constructor arguments
+where that is what is wanted. Feedback welcomed.)
+</para>
-<Para>
-There are two restrictions:
-</Para>
+<para>
+You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
+the constructor to suitable values, just as usual. For example,
+</para>
-<Para>
+<para>
+
+<programlisting>
+ a1 :: T Int
+ a1 = T1 (\xy->x) 3
+
+ a2, a3 :: Swizzle
+ a2 = MkSwizzle sort
+ a3 = MkSwizzle reverse
+
+ a4 :: MonadT Maybe
+ a4 = let r x = Just x
+ b m k = case m of
+ Just y -> k y
+ Nothing -> Nothing
+ in
+ MkMonad r b
+
+ mkTs :: (forall b. b -> b -> b) -> a -> [T a]
+ mkTs f x y = [T1 f x, T1 f y]
+</programlisting>
-<ItemizedList>
-<ListItem>
+</para>
-<Para>
- You can only define a rank 2 type, specified by the following
-grammar:
+<para>
+The type of the argument can, as usual, be more general than the type
+required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
+does not need the <literal>Ord</literal> constraint.)
+</para>
+<para>
+When you use pattern matching, the bound variables may now have
+polymorphic types. For example:
+</para>
-<ProgramListing>
-rank2type ::= [forall tyvars .] [context =>] funty
-funty ::= ([forall tyvars .] [context =>] ty) -> funty
- | ty
-ty ::= ...current Haskell monotype syntax...
-</ProgramListing>
+<para>
+<programlisting>
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
-Informally, the universal quantification must all be right at the beginning,
-or at the top level of a function argument.
+ g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
+ g (MkSwizzle s) xs f = s (map f (s xs))
-</Para>
-</ListItem>
-<ListItem>
+ 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>
- 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:
+</para>
+<para>
+In the function <function>h</function> we use the record selectors <literal>return</literal>
+and <literal>bind</literal> to extract the polymorphic bind and return functions
+from the <literal>MonadT</literal> data structure, rather than using pattern
+matching.
+</para>
+</sect3>
-<ProgramListing>
-mkTs :: (forall b. b -> b -> b) -> a -> [T a]
-mkTs = \ f x y -> [T1 f x, T1 f y]
-</ProgramListing>
+<sect3>
+<title>Type inference</title>
+<para>
+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>
+<para>
+<emphasis>For a lambda-bound or case-bound variable, x, either the programmer
+provides an explicit polymorphic type for x, or GHC's type inference will assume
+that x's type has no foralls in it</emphasis>.
+</para>
+<para>
+What does it mean to "provide" an explicit type for x? You can do that by
+giving a type signature for x directly, using a pattern type signature
+(<xref linkend="scoped-type-variables">), thus:
+<programlisting>
+ \ f :: (forall a. a->a) -> (f True, f 'c')
+</programlisting>
+Alternatively, you can give a type signature to the enclosing
+context, which GHC can "push down" to find the type for the variable:
+<programlisting>
+ (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
+</programlisting>
+Here the type signature on the expression can be pushed inwards
+to give a type signature for f. Similarly, and more commonly,
+one can give a type signature for the function itself:
+<programlisting>
+ h :: (forall a. a->a) -> (Bool,Char)
+ h f = (f True, f 'c')
+</programlisting>
+You don't need to give a type signature if the lambda bound variable
+is a constructor argument. Here is an example we saw earlier:
+<programlisting>
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
+</programlisting>
+Here we do not need to give a type signature to <literal>w</literal>, because
+it is an argument of constructor <literal>T1</literal> and that tells GHC all
+it needs to know.
+</para>
+</sect3>
-The same partial-application rule applies to ordinary functions with
-rank-2 types as applied to data constructors.
-</Para>
-</ListItem>
+<sect3 id="implicit-quant">
+<title>Implicit quantification</title>
-</ItemizedList>
+<para>
+GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
+user-written types, if and only if there is no explicit <literal>forall</literal>,
+GHC finds all the type variables mentioned in the type that are not already
+in scope, and universally quantifies them.</emphasis> For example, the following pairs are
+equivalent:
+<programlisting>
+ f :: a -> a
+ f :: forall a. a -> a
+
+ g (x::a) = let
+ h :: a -> b -> b
+ h x y = y
+ in ...
+ g (x::a) = let
+ h :: forall b. a -> b -> b
+ h x y = y
+ in ...
+</programlisting>
+</para>
+<para>
+Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
+point. For example:
+<programlisting>
+ f :: (a -> a) -> Int
+ -- MEANS
+ f :: forall a. (a -> a) -> Int
+ -- NOT
+ f :: (forall a. a -> a) -> Int
+
+
+ g :: (Ord a => a -> a) -> Int
+ -- MEANS the illegal type
+ g :: forall a. (Ord a => a -> a) -> Int
+ -- NOT
+ g :: (forall a. Ord a => a -> a) -> Int
+</programlisting>
+The latter produces an illegal type, which you might think is silly,
+but at least the rule is simple. If you want the latter type, you
+can write your for-alls explicitly. Indeed, doing so is strongly advised
+for rank-2 types.
+</para>
+</sect3>
+</sect2>
-</Para>
+<sect2 id="type-synonyms">
+<title>Liberalised type synonyms
+</title>
-</Sect2>
+<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 write a <literal>forall</literal> (including overloading)
+in a type synonym, thus:
+<programlisting>
+ type Discard a = forall b. Show b => a -> b -> (a, String)
+ f :: Discard a
+ f x y = (x, show y)
-<Sect2 id="hoist">
-<Title>Type synonyms and hoisting
-</Title>
+ g :: Discard Int -> (Int,Bool) -- A rank-2 type
+ g f = f Int True
+</programlisting>
+</para>
+</listitem>
+
+<listitem><para>
+You can write an unboxed tuple in a type synonym:
+<programlisting>
+ type Pr = (# Int, Int #)
+
+ h :: Int -> Pr
+ h x = (# x, x #)
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+You can apply a type synonym to a forall type:
+<programlisting>
+ type Foo a = a -> a -> Bool
+
+ f :: Foo (forall b. b->b)
+</programlisting>
+After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
+<programlisting>
+ f :: (forall b. b->b) -> (forall b. b->b) -> Bool
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+You can apply a type synonym to a partially applied type synonym:
+<programlisting>
+ type Generic i o = forall x. i x -> o x
+ type Id x = x
+
+ foo :: Generic Id []
+</programlisting>
+After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
+<programlisting>
+ foo :: forall x. x -> [x]
+</programlisting>
+</para></listitem>
+
+</itemizedlist>
+</para>
-<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
+<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>
- f :: Discard a
- f x y = x
-</ProgramListing>
-However, it is often convenient to use these sort of synonyms at the right hand
+<sect2 id="hoist">
+<title>For-all hoisting</title>
+<para>
+It is often convenient to use generalised type synonyms at the right hand
end of an arrow, thus:
-<ProgramListing>
+<programlisting>
type Discard a = forall b. a -> b -> a
g :: Int -> Discard Int
g x y z = x+y
-</ProgramListing>
+</programlisting>
Simply expanding the type synonym would give
-<ProgramListing>
+<programlisting>
g :: Int -> (forall b. Int -> b -> Int)
-</ProgramListing>
-but GHC "hoists" the <Literal>forall</Literal> to give the isomorphic type
-<ProgramListing>
+</programlisting>
+but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
+<programlisting>
g :: forall b. Int -> Int -> b -> Int
-</ProgramListing>
-In general, the rule is this: <Emphasis>to determine the type specified by any explicit
+</programlisting>
+In general, the rule is this: <emphasis>to determine the type specified by any explicit
user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
-performs the transformation:</Emphasis>
-<ProgramListing>
- <Emphasis>type1</Emphasis> -> forall a. <Emphasis>type2</Emphasis>
+performs the transformation:</emphasis>
+<programlisting>
+ <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
==>
- forall a. <Emphasis>type1</Emphasis> -> <Emphasis>type2</Emphasis>
-</ProgramListing>
+ forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
+</programlisting>
(In fact, GHC tries to retain as much synonym information as possible for use in
error messages, but that is a usability issue.) This rule applies, of course, whether
-or not the <Literal>forall</Literal> comes from a synonym. For example, here is another
-valid way to write <Literal>g</Literal>'s type signature:
-<ProgramListing>
+or not the <literal>forall</literal> comes from a synonym. For example, here is another
+valid way to write <literal>g</literal>'s type signature:
+<programlisting>
g :: Int -> Int -> forall b. b -> Int
-</ProgramListing>
-</Para>
-</Sect2>
+</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">
-<Title>Existentially quantified data constructors
-</Title>
+<sect2 id="existential-quantification">
+<title>Existentially quantified data constructors
+</title>
-<Para>
+<para>
The idea of using existential quantification in data type declarations
was suggested by Laufer (I believe, thought doubtless someone will
correct me), and implemented in Hope+. It's been in Lennart
Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
proved very useful. Here's the idea. Consider the declaration:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
data Foo = forall a. MkFoo a (a -> Bool)
| Nil
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-The data type <Literal>Foo</Literal> has two constructors with types:
-</Para>
+<para>
+The data type <literal>Foo</literal> has two constructors with types:
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
MkFoo :: forall a. a -> (a -> Bool) -> Foo
Nil :: Foo
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-Notice that the type variable <Literal>a</Literal> in the type of <Function>MkFoo</Function>
-does not appear in the data type itself, which is plain <Literal>Foo</Literal>.
+<para>
+Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
+does not appear in the data type itself, which is plain <literal>Foo</literal>.
For example, the following expression is fine:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
[MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-Here, <Literal>(MkFoo 3 even)</Literal> packages an integer with a function
-<Function>even</Function> that maps an integer to <Literal>Bool</Literal>; and <Function>MkFoo 'c'
-isUpper</Function> packages a character with a compatible function. These
-two things are each of type <Literal>Foo</Literal> and can be put in a list.
-</Para>
+<para>
+Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
+<function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
+isUpper</function> packages a character with a compatible function. These
+two things are each of type <literal>Foo</literal> and can be put in a list.
+</para>
-<Para>
-What can we do with a value of type <Literal>Foo</Literal>?. In particular,
-what happens when we pattern-match on <Function>MkFoo</Function>?
-</Para>
+<para>
+What can we do with a value of type <literal>Foo</literal>?. In particular,
+what happens when we pattern-match on <function>MkFoo</function>?
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f (MkFoo val fn) = ???
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-Since all we know about <Literal>val</Literal> and <Function>fn</Function> is that they
+<para>
+Since all we know about <literal>val</literal> and <function>fn</function> is that they
are compatible, the only (useful) thing we can do with them is to
-apply <Function>fn</Function> to <Literal>val</Literal> to get a boolean. For example:
-</Para>
+apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f :: Foo -> Bool
f (MkFoo val fn) = fn val
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
What this allows us to do is to package heterogenous values
together with a bunch of functions that manipulate them, and then treat
that collection of packages in a uniform manner. You can express
quite a bit of object-oriented-like programming this way.
-</Para>
+</para>
-<Sect2 id="existential">
-<Title>Why existential?
-</Title>
+<sect3 id="existential">
+<title>Why existential?
+</title>
-<Para>
-What has this to do with <Emphasis>existential</Emphasis> quantification?
-Simply that <Function>MkFoo</Function> has the (nearly) isomorphic type
-</Para>
+<para>
+What has this to do with <emphasis>existential</emphasis> quantification?
+Simply that <function>MkFoo</function> has the (nearly) isomorphic type
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
MkFoo :: (exists a . (a, a -> Bool)) -> Foo
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
But Haskell programmers can safely think of the ordinary
-<Emphasis>universally</Emphasis> quantified type given above, thereby avoiding
+<emphasis>universally</emphasis> quantified type given above, thereby avoiding
adding a new existential quantification construct.
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Type classes</Title>
+<sect3>
+<title>Type classes</title>
-<Para>
+<para>
An easy extension (implemented in <Command>hbc</Command>) is to allow
arbitrary contexts before the constructor. For example:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
data Baz = forall a. Eq a => Baz1 a a
| forall b. Show b => Baz2 b (b -> b)
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
The two constructors have the types you'd expect:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
Baz1 :: forall a. Eq a => a -> a -> Baz
Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-But when pattern matching on <Function>Baz1</Function> the matched values can be compared
-for equality, and when pattern matching on <Function>Baz2</Function> the first matched
+<para>
+But when pattern matching on <function>Baz1</function> the matched values can be compared
+for equality, and when pattern matching on <function>Baz2</function> the first matched
value can be converted to a string (as well as applying the function to it).
So this program is legal:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f :: Baz -> String
f (Baz1 p q) | p == q = "Yes"
| otherwise = "No"
- f (Baz1 v fn) = show (fn v)
-</ProgramListing>
+ f (Baz2 v fn) = show (fn v)
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
Operationally, in a dictionary-passing implementation, the
-constructors <Function>Baz1</Function> and <Function>Baz2</Function> must store the
-dictionaries for <Literal>Eq</Literal> and <Literal>Show</Literal> respectively, and
+constructors <function>Baz1</function> and <function>Baz2</function> must store the
+dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
extract it on pattern matching.
-</Para>
+</para>
-<Para>
+<para>
Notice the way that the syntax fits smoothly with that used for
universal quantification earlier.
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Restrictions</Title>
+<sect3>
+<title>Restrictions</title>
-<Para>
+<para>
There are several restrictions on the ways in which existentially-quantified
constructors can be use.
-</Para>
+</para>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
When pattern matching, each pattern match introduces a new,
distinct, type for each existential type variable. These types cannot
be unified with any other type, nor can they escape from the scope of
the pattern match. For example, these fragments are incorrect:
-<ProgramListing>
+<programlisting>
f1 (MkFoo a f) = a
-</ProgramListing>
+</programlisting>
-Here, the type bound by <Function>MkFoo</Function> "escapes", because <Literal>a</Literal>
-is the result of <Function>f1</Function>. One way to see why this is wrong is to
-ask what type <Function>f1</Function> has:
+Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
+is the result of <function>f1</function>. One way to see why this is wrong is to
+ask what type <function>f1</function> has:
-<ProgramListing>
+<programlisting>
f1 :: Foo -> a -- Weird!
-</ProgramListing>
+</programlisting>
-What is this "<Literal>a</Literal>" in the result type? Clearly we don't mean
+What is this "<literal>a</literal>" in the result type? Clearly we don't mean
this:
-<ProgramListing>
+<programlisting>
f1 :: forall a. Foo -> a -- Wrong!
-</ProgramListing>
+</programlisting>
The original program is just plain wrong. Here's another sort of error
-<ProgramListing>
+<programlisting>
f2 (Baz1 a b) (Baz1 p q) = a==q
-</ProgramListing>
+</programlisting>
-It's ok to say <Literal>a==b</Literal> or <Literal>p==q</Literal>, but
-<Literal>a==q</Literal> is wrong because it equates the two distinct types arising
-from the two <Function>Baz1</Function> constructors.
+It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
+<literal>a==q</literal> is wrong because it equates the two distinct types arising
+from the two <function>Baz1</function> constructors.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
You can't pattern-match on an existentially quantified
-constructor in a <Literal>let</Literal> or <Literal>where</Literal> group of
+constructor in a <literal>let</literal> or <literal>where</literal> group of
bindings. So this is illegal:
-<ProgramListing>
+<programlisting>
f3 x = a==b where { Baz1 a b = x }
-</ProgramListing>
+</programlisting>
+
+Instead, use a <literal>case</literal> expression:
+<programlisting>
+ f3 x = case x of Baz1 a b -> a==b
+</programlisting>
-You can only pattern-match
-on an existentially-quantified constructor in a <Literal>case</Literal> expression or
+In general, you can only pattern-match
+on an existentially-quantified constructor in a <literal>case</literal> expression or
in the patterns of a function definition.
The reason for this restriction is really an implementation one.
So for now, there's a simple-to-state restriction. We'll see how
annoying it is.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
-You can't use existential quantification for <Literal>newtype</Literal>
+<para>
+You can't use existential quantification for <literal>newtype</literal>
declarations. So this is illegal:
-<ProgramListing>
+<programlisting>
newtype T = forall a. Ord a => MkT a
-</ProgramListing>
+</programlisting>
-Reason: a value of type <Literal>T</Literal> must be represented as a pair
-of a dictionary for <Literal>Ord t</Literal> and a value of type <Literal>t</Literal>.
-That contradicts the idea that <Literal>newtype</Literal> should have no
+Reason: a value of type <literal>T</literal> must be represented as a pair
+of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
+That contradicts the idea that <literal>newtype</literal> should have no
concrete representation. You can get just the same efficiency and effect
-by using <Literal>data</Literal> instead of <Literal>newtype</Literal>. If there is no
+by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
overloading involved, then there is more of a case for allowing
-an existentially-quantified <Literal>newtype</Literal>, because the <Literal>data</Literal>
-because the <Literal>data</Literal> version does carry an implementation cost,
+an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
+because the <literal>data</literal> version does carry an implementation cost,
but single-field existentially quantified constructors aren't much
-use. So the simple restriction (no existential stuff on <Literal>newtype</Literal>)
+use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
stands, unless there are convincing reasons to change it.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- You can't use <Literal>deriving</Literal> to define instances of a
+<para>
+ You can't use <literal>deriving</literal> to define instances of a
data type with existentially quantified data constructors.
Reason: in most cases it would not make sense. For example:#
-<ProgramListing>
+<programlisting>
data T = forall a. MkT [a] deriving( Eq )
-</ProgramListing>
+</programlisting>
-To derive <Literal>Eq</Literal> in the standard way we would need to have equality
-between the single component of two <Function>MkT</Function> constructors:
+To derive <literal>Eq</literal> in the standard way we would need to have equality
+between the single component of two <function>MkT</function> constructors:
-<ProgramListing>
+<programlisting>
instance Eq T where
(MkT a) == (MkT b) = ???
-</ProgramListing>
+</programlisting>
But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
It's just about possible to imagine examples in which the derived instance
would make sense, but it seems altogether simpler simply to prohibit such
declarations. Define your own instances!
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-</Para>
-
-</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 &gt;= 0.0) (k+273.15)
-</ProgramListing>
-
-</Para>
-
-<Para>
-Ghc will rewrite this to also include the source location where the
-assertion was made,
-</Para>
-
-<Para>
-
-<ProgramListing>
-assert pred val ==> assertError "Main.hs|15" pred val
-</ProgramListing>
-
-</Para>
+</para>
+</listitem>
-<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>
+</itemizedlist>
-<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>
-<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
-</Title>
+<sect2 id="scoped-type-variables">
+<title>Scoped type variables
+</title>
-<Para>
-A <Emphasis>pattern type signature</Emphasis> can introduce a <Emphasis>scoped type
-variable</Emphasis>. For example
-</Para>
+<para>
+A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
+variable</emphasis>. For example
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f (xs::[a]) = ys ++ ys
where
ys :: [a]
ys = reverse xs
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-The pattern <Literal>(xs::[a])</Literal> includes a type signature for <VarName>xs</VarName>.
-This brings the type variable <Literal>a</Literal> into scope; it scopes over
-all the patterns and right hand sides for this equation for <Function>f</Function>.
+<para>
+The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
+This brings the type variable <literal>a</literal> into scope; it scopes over
+all the patterns and right hand sides for this equation for <function>f</function>.
In particular, it is in scope at the type signature for <VarName>y</VarName>.
-</Para>
+</para>
-<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
+mentioned in the type signature <emphasis>that are not in scope</emphasis> are
implicitly universally quantified. (If there are no type variables in
scope, all type variables mentioned in the signature are universally
quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
it becomes possible to do so.
-</Para>
+</para>
-<Para>
+<para>
Scoped type variables are implemented in both GHC and Hugs. Where the
implementations differ from the specification below, those differences
are noted.
-</Para>
+</para>
-<Para>
+<para>
So much for the basic idea. Here are the details.
-</Para>
+</para>
+
+<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>
-<Sect2>
-<Title>Scope and implicit quantification</Title>
+</sect3>
-<Para>
+<sect3>
+<title>Scope and implicit quantification</title>
-<ItemizedList>
-<ListItem>
+<para>
-<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>.
+<itemizedlist>
+<listitem>
+
+<para>
+All the type variables mentioned in a pattern,
+that are not already in scope,
+are brought into scope by the pattern. We describe this set as
+the <emphasis>type variables bound by the pattern</emphasis>.
+For example:
+<programlisting>
+ f (x::a) = let g (y::(a,b)) = fst y
+ in
+ g (x,True)
+</programlisting>
+The pattern <literal>(x::a)</literal> brings the type variable
+<literal>a</literal> into scope, as well as the term
+variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
+contains an occurrence of the already-in-scope type variable <literal>a</literal>,
+and brings into scope the type variable <literal>b</literal>.
+</para>
+</listitem>
+
+<listitem>
+<para>
+The type variable(s) bound by the pattern have the same scope
+as the term variable(s) bound by the pattern. For example:
+<programlisting>
+ let
+ f (x::a) = <...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>
-</Para>
-</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.
+<listitem>
+<para>
+The type variables bound by the pattern may be
+mentioned in ordinary type signatures or pattern
+type signatures anywhere within their scope.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
-<Para>
+<listitem>
+<para>
In ordinary type signatures, any type variable mentioned in the
-signature that is in scope is <Emphasis>not</Emphasis> universally quantified.
+signature that is in scope is <emphasis>not</emphasis> universally quantified.
+
+</para>
+</listitem>
-</Para>
-</ListItem>
-<ListItem>
+<listitem>
-<Para>
+<para>
Ordinary type signatures do not bring any new type variables
into scope (except in the type signature itself!). So this is illegal:
-
-<ProgramListing>
+<programlisting>
f :: a -> a
f x = x::a
-</ProgramListing>
+</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>;
+It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
+so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
and that is an incorrect typing.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+
+<listitem>
+<para>
+The pattern type signature is a monotype:
+</para>
+
+<itemizedlist>
+<listitem> <para>
+A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
+</para> </listitem>
+
+<listitem> <para>
+The type variables bound by a pattern type signature can only be instantiated to monotypes,
+not to type schemes.
+</para> </listitem>
-<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.
+<listitem> <para>
+There is no implicit universal quantification on pattern type signatures (in contrast to
+ordinary type signatures).
+</para> </listitem>
-</Para>
-</ListItem>
-<ListItem>
+</itemizedlist>
-<Para>
+</listitem>
-The type variables in the head of a <Literal>class</Literal> or <Literal>instance</Literal> declaration
-scope over the methods defined in the <Literal>where</Literal> part. For example:
+<listitem>
+<para>
+The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
+scope over the methods defined in the <literal>where</literal> part. For example:
-<ProgramListing>
+
+<programlisting>
class C a where
op :: [a] -> a
ys = reverse xs
in
head ys
-</ProgramListing>
+</programlisting>
(Not implemented in Hugs yet, Dec 98).
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Polymorphism</Title>
+<sect3>
+<title>Where a pattern type signature can occur</title>
-<Para>
+<para>
+A pattern type signature can occur in any pattern. For example:
+<itemizedlist>
-<ItemizedList>
-<ListItem>
+<listitem>
+<para>
+A pattern type signature can be on an arbitrary sub-pattern, not
+ust on a variable:
-<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.
+<programlisting>
+ f ((x,y)::(a,b)) = (y,x) :: (b,a)
+</programlisting>
-<ProgramListing>
- f :: [a] -> [a]
- f (xs::[b]) = reverse xs
-</ProgramListing>
+</para>
+</listitem>
+<listitem>
-</Para>
-</ListItem>
-<ListItem>
+<para>
+ Pattern type signatures, including the result part, can be used
+in lambda abstractions:
-<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:
+<programlisting>
+ (\ (x::a, y) :: a -> x)
+</programlisting>
+</para>
+</listitem>
+<listitem>
+<para>
+ Pattern type signatures, including the result part, can be used
+in <literal>case</literal> expressions:
-<ItemizedList>
-<ListItem>
-<Para>
- Be unified with a type (such as <Literal>Int</Literal>, or <Literal>[a]</Literal>).
-</Para>
-</ListItem>
-<ListItem>
+<programlisting>
+ case e of { (x::a, y) :: a -> x }
+</programlisting>
-<Para>
- Be unified with a type variable free in the environment.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
-<Para>
- Be unified with each other. (They may unify with the type variables
-bound by another equation for the same function, of course.)
-</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:
-</ItemizedList>
+<programlisting>
+ \ x :: a -> b -> x
+</programlisting>
-For example, the following all fail to type check:
+</para>
+</listitem>
-<ProgramListing>
- f (x::a) (y::b) = [x,y] -- a unifies with b
+<listitem>
- g (x::a) = x + 1::Int -- a unifies with Int
+<para>
+ Pattern type signatures can bind existential type variables.
+For example:
- 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 = ...
+<programlisting>
+ data T = forall a. MkT [a]
- w :: [b] -> [b]
- w (x::a) = x -- a unifies with [b]
-</ProgramListing>
+ f :: T -> T
+ f (MkT [t::a]) = MkT t3
+ where
+ t3::[a] = [t,t,t]
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
-<Para>
- The pattern-bound type variable may, however, be constrained
-by the context of the principal type, thus:
+<listitem>
-<ProgramListing>
- f (x::a) (y::a) = x+y*2
-</ProgramListing>
+<para>
+Pattern type signatures
+can be used in pattern bindings:
+<programlisting>
+ f x = let (y, z::a) = x in ...
+ f1 x = let (y, z::Int) = x in ...
+ f2 (x::(Int,a)) = let (y, z::a) = x in ...
+ f3 :: (b->b) = \x -> x
+</programlisting>
+
+In all such cases, the binding is not generalised over the pattern-bound
+type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
+has type <literal>b -> 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>
-
-</Sect2>
-
-<Sect2>
-<Title>Result type signatures</Title>
+</para>
+</listitem>
+</itemizedlist>
+</para>
-<Para>
+</sect3>
-<ItemizedList>
-<ListItem>
+<sect3>
+<title>Result type signatures</title>
-<Para>
- The result type of a function can be given a signature,
-thus:
+<para>
+The result type of a function can be given a signature, thus:
-<ProgramListing>
+<programlisting>
f (x::a) :: [a] = [x,x,x]
-</ProgramListing>
+</programlisting>
-The final <Literal>:: [a]</Literal> after all the patterns gives a signature to the
+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>
+<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>
+</programlisting>
-</ItemizedList>
-
-</Para>
+</para>
+<para>
+The type variables bound in a result type signature scope over the right hand side
+of the definition. However, consider this corner-case:
+<programlisting>
+ rev1 :: [a] -> [a] = \xs -> reverse xs
+
+ foo ys = rev (ys::[a])
+</programlisting>
+The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
+type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
+itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
+In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
+is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
+</para>
+<para>
+As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
+For example, the following program would be rejected, because it claims that <literal>rev1</literal>
+is polymorphic:
+<programlisting>
+ rev1 :: [b] -> [b]
+ rev1 :: [a] -> [a] = \xs -> reverse xs
+</programlisting>
+</para>
-<Para>
+<para>
Result type signatures are not yet implemented in Hugs.
-</Para>
+</para>
-</Sect2>
+</sect3>
-<Sect2>
-<Title>Pattern signatures on other constructs</Title>
+</sect2>
-<Para>
+<sect2 id="newtype-deriving">
+<title>Generalised derived instances for newtypes</title>
-<ItemizedList>
-<ListItem>
+<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
-<Para>
- A pattern type signature can be on an arbitrary sub-pattern, not
-just on a variable:
+<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>
- f ((x,y)::(a,b)) = (y,x) :: (b,a)
-</ProgramListing>
+<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>
-</Para>
-</ListItem>
-<ListItem>
+<sect3> <title> Generalising the deriving clause </title>
+<para>
+GHC now permits such instances to be derived instead, so one can write
+<programlisting>
+ newtype Dollars = Dollars Int deriving (Eq,Show,Num)
+</programlisting>
-<Para>
- Pattern type signatures, including the result part, can be used
-in lambda abstractions:
+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>
-<ProgramListing>
- (\ (x::a, y) :: a -> x)
-</ProgramListing>
+which just adds or removes the <literal>newtype</literal> constructor according to the type.
+</para>
+<para>
+
+We can also derive instances of constructor classes in a similar
+way. For example, suppose we have implemented state and failure monad
+transformers, such that
+
+<programlisting>
+ instance Monad m => Monad (State s m)
+ instance Monad m => Monad (Failure m)
+</programlisting>
+In Haskell 98, we can define a parsing monad by
+<programlisting>
+ type Parser tok m a = State [tok] (Failure m) a
+</programlisting>
+
+which is automatically a monad thanks to the instance declarations
+above. With the extension, we can make the parser type abstract,
+without needing to write an instance of class <literal>Monad</literal>, via
+
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving Monad
+</programlisting>
+In this case the derived instance declaration is of the form
+<programlisting>
+ instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
+</programlisting>
+
+Notice that, since <literal>Monad</literal> is a constructor class, the
+instance is a <emphasis>partial application</emphasis> of the new type, not the
+entire left hand side. We can imagine that the type declaration is
+``eta-converted'' to generate the context of the instance
+declaration.
+</para>
+<para>
+
+We can even derive instances of multi-parameter classes, provided the
+newtype is the last class parameter. In this case, a ``partial
+application'' of the class appears in the <literal>deriving</literal>
+clause. For example, given the class
+
+<programlisting>
+ class StateMonad s m | m -> s where ...
+ instance Monad m => StateMonad s (State s m) where ...
+</programlisting>
+then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving (Monad, StateMonad [tok])
+</programlisting>
+
+The derived instance is obtained by completing the application of the
+class to the new type:
+
+<programlisting>
+ instance StateMonad [tok] (State [tok] (Failure m)) =>
+ StateMonad [tok] (Parser tok m)
+</programlisting>
+</para>
+<para>
+As a result of this extension, all derived instances in newtype
+declarations are treated uniformly (and implemented just by reusing
+the dictionary for the representation type), <emphasis>except</emphasis>
+<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
+the newtype and its representation.
+</para>
+</sect3>
+
+<sect3> <title> A more precise specification </title>
+<para>
+Derived instance declarations are constructed as follows. Consider the
+declaration (after expansion of any type synonyms)
+
+<programlisting>
+ newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
+</programlisting>
+
+where
+ <itemizedlist>
+<listitem><para>
+ <literal>S</literal> is a type constructor,
+</para></listitem>
+<listitem><para>
+ <literal>t1...tk</literal> are types,
+</para></listitem>
+<listitem><para>
+ <literal>vk+1...vn</literal> are type variables which do not occur in any of
+ the <literal>ti</literal>, and
+</para></listitem>
+<listitem><para>
+ the <literal>ci</literal> are partial applications of
+ classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
+ is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
+</para></listitem>
+</itemizedlist>
+Then, for each <literal>ci</literal>, the derived instance
+declaration is:
+<programlisting>
+ instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
+</programlisting>
+where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
+right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
+</para>
+<para>
+
+As an example which does <emphasis>not</emphasis> work, consider
+<programlisting>
+ newtype NonMonad m s = NonMonad (State s m s) deriving Monad
+</programlisting>
+Here we cannot derive the instance
+<programlisting>
+ instance Monad (State s m) => Monad (NonMonad m)
+</programlisting>
+
+because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
+and so cannot be "eta-converted" away. It is a good thing that this
+<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
+not, in fact, a monad --- for the same reason. Try defining
+<literal>>>=</literal> with the correct type: you won't be able to.
+</para>
+<para>
-Type variables bound by these patterns must be polymorphic in
-the sense defined above.
-For example:
+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>
-<ProgramListing>
- f1 (x::c) = f1 x -- ok
- f2 = \(x::c) -> f2 x -- not ok
-</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>
+</sect3>
+</sect2>
-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>
-</ListItem>
-<ListItem>
+</sect1>
+<!-- ==================== End of type system extensions ================= -->
+
+<!-- ====================== TEMPLATE HASKELL ======================= -->
-<Para>
- Pattern type signatures, including the result part, can be used
-in <Literal>case</Literal> expressions:
+<sect1 id="template-haskell">
+<title>Template Haskell</title>
+<para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
+the main technical innovations are discussed in "<ulink
+url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
+Template Meta-programming for Haskell</ulink>", in
+Proc Haskell Workshop 2002.
+</para>
-<ProgramListing>
- case e of { (x::a, y) :: a -> x }
-</ProgramListing>
+<para> The first example from that paper is set out below as a worked example to help get you started.
+</para>
+<para>
+The documentation here describes the realisation in GHC. (It's rather sketchy just now;
+Tim Sheard is going to expand it.)
+</para>
-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:
+<sect2> <title> Syntax </title>
+<para>
+ Template Haskell has the following new syntactic constructions. You need to use the flag
+ <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
+
+ <itemizedlist>
+ <listitem><para>
+ A splice is written <literal>$x</literal>, where <literal>x</literal> is an
+ identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
+ There must be no space between the "$" and the identifier or parenthesis. This use
+ of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
+ of "." as an infix operator. If you want the infix operator, put spaces around it.
+ </para>
+ <para> A splice can occur in place of
+ <itemizedlist>
+ <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
+ <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
+ <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
+ </itemizedlist>
+ (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
+ the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
+ as in the paper.)
+ </para></listitem>
+
+
+ <listitem><para>
+ A expression quotation is written in Oxford brackets, thus:
+ <itemizedlist>
+ <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
+ the quotation has type <literal>Expr</literal>.</para></listitem>
+ <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
+ the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
+ <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
+ the quotation has type <literal>Type</literal>.</para></listitem>
+ </itemizedlist></para></listitem>
+
+ <listitem><para>
+ Reification is written thus:
+ <itemizedlist>
+ <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
+ has type <literal>Dec</literal>. </para></listitem>
+ <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
+ <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
+ <listitem><para> Still to come: fixities </para></listitem>
+
+ </itemizedlist></para>
+ </listitem>
+
+
+ </itemizedlist>
+</para>
+</sect2>
+<sect2> <title> Using Template Haskell </title>
+<para>
+<itemizedlist>
+ <listitem><para>
+ The data types and monadic constructor functions for Template Haskell are in the library
+ <literal>Language.Haskell.THSyntax</literal>.
+ </para></listitem>
+
+ <listitem><para>
+ You can only run a function at compile time if it is imported from another module. That is,
+ you can't define a function in a module, and call it from within a splice in the same module.
+ (It would make sense to do so, but it's hard to implement.)
+ </para></listitem>
+
+ <listitem><para>
+ The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
+ </para></listitem>
+ <listitem><para>
+ If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
+ run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
+ compiles and runs a program, and then looks at the result. So it's important that
+ the program it compiles produces results whose representations are identical to
+ those of the compiler itself.
+ </para></listitem>
+</itemizedlist>
+</para>
+<para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
+ or file-at-a-time). There used to be a restriction to the former two, but that restriction
+ has been lifted.
+</para>
+</sect2>
+
+<sect2> <title> A Template Haskell Worked Example </title>
+<para>To help you get over the confidence barrier, try out this skeletal worked example.
+ First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
+
+<programlisting>
+{- Main.hs -}
+module Main where
+
+-- Import our template "pr"
+import Printf ( pr )
+
+-- The splice operator $ takes the Haskell source code
+-- generated at compile time by "pr" and splices it into
+-- the argument of "putStrLn".
+main = putStrLn ( $(pr "Hello") )
+</programlisting>
+
+<programlisting>
+{- Printf.hs -}
+module Printf where
+
+-- Skeletal printf from the paper.
+-- It needs to be in a separate module to the one where
+-- you intend to use it.
+
+-- Import some Template Haskell syntax
+import Language.Haskell.THSyntax
+
+-- Describe a format string
+data Format = D | S | L String
+
+-- Parse a format string. This is left largely to you
+-- as we are here interested in building our first ever
+-- Template Haskell program and not in building printf.
+parse :: String -> [Format]
+parse s = [ L s ]
+
+-- Generate Haskell source code from a parsed representation
+-- of the format string. This code will be spliced into
+-- the module which calls "pr", at compile time.
+gen :: [Format] -> Expr
+gen [D] = [| \n -> show n |]
+gen [S] = [| \s -> s |]
+gen [L s] = string s
+
+-- Here we generate the Haskell code for the splice
+-- from an input format string.
+pr :: String -> Expr
+pr s = gen (parse s)
+</programlisting>
+
+<para>Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
+</para>
+<programlisting>
+ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
+</programlisting>
-<ProgramListing>
- case (True,False) of { (x::a, y) -> x }
-</ProgramListing>
+<para>Run "main.exe" and here is your output:
+</para>
+<programlisting>
+$ ./main
+Hello
+</programlisting>
-Even though the context is that of a pair of booleans,
-the alternative itself is polymorphic. Of course, it is
-also OK to say:
+</sect2>
+
+</sect1>
+<!-- ===================== Arrow notation =================== -->
-<ProgramListing>
- case (True,False) of { (x::Bool, y) -> x }
-</ProgramListing>
+<sect1 id="arrow-notation">
+<title>Arrow notation
+</title>
+<para>Arrows are a generalization of monads introduced by John Hughes.
+For more details, see
+<itemizedlist>
-</Para>
-</ListItem>
-<ListItem>
+<listitem>
+<para>
+“Generalising Monads to Arrows”,
+John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
+pp67–111, May 2000.
+</para>
+</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:
+<listitem>
+<para>
+“<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
+Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
+</para>
+</listitem>
+<listitem>
+<para>
+“<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
+Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
+Palgrave, 2003.
+</para>
+</listitem>
+
+</itemizedlist>
+and the arrows web page at
+<ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
+With the <option>-farrows</option> flag, GHC supports the arrow
+notation described in the second of these papers.
+What follows is a brief introduction to the notation;
+it won't make much sense unless you've read Hughes's paper.
+This notation is translated to ordinary Haskell,
+using combinators from the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module.
+</para>
-<ProgramListing>
- \ x :: a -> b -> x
-</ProgramListing>
+<para>The extension adds a new kind of expression for defining arrows,
+of the form <literal>proc pat -> cmd</literal>,
+where <literal>proc</literal> is a new keyword.
+The variables of the pattern are bound in the body of the
+<literal>proc</literal>-expression,
+which is a new sort of thing called a <firstterm>command</firstterm>.
+The syntax of commands is as follows:
+<screen>
+cmd ::= exp1 -< exp2
+ | exp1 -<< exp2
+ | do { cstmt1 .. cstmtn ; cmd }
+ | let decls in cmd
+ | if exp then cmd1 else cmd2
+ | case exp of { calts }
+ | cmd1 qop cmd2
+ | (| exp |) cmd1 .. cmdn
+ | \ pat1 .. patn -> cmd
+ | ( cmd )
+
+cstmt ::= let decls
+ | pat <- cmd
+ | rec { cstmt1 .. cstmtn }
+ | cmd
+</screen>
+Commands produce values, but (like monadic computations)
+may yield more than one value,
+or none, and may do other things as well.
+For the most part, familiarity with monadic notation is a good guide to
+using commands.
+However the values of expressions, even monadic ones,
+are determined by the values of the variables they contain;
+this is not necessarily the case for commands.
+</para>
+<para>
+A simple example of the new notation is the expression
+<screen>
+proc x -> f -< x+1
+</screen>
+We call this a <firstterm>procedure</firstterm> or
+<firstterm>arrow abstraction</firstterm>.
+As with a lambda expression, the variable <literal>x</literal>
+is a new variable bound within the <literal>proc</literal>-expression.
+It refers to the input to the arrow.
+In the above example, <literal>-<</literal> is not an identifier but an
+new reserved symbol used for building commands from an expression of arrow
+type and an expression to be fed as input to that arrow.
+(The weird look will make more sense later.)
+It may be read as analogue of application for arrows.
+The above example is equivalent to the Haskell expression
+<screen>
+arr (\ x -> x+1) >>> f
+</screen>
+That would make no sense if the expression to the left of
+<literal>-<</literal> involves the bound variable <literal>x</literal>.
+More generally, the expression to the left of <literal>-<</literal>
+may not involve any <firstterm>local variable</firstterm>,
+i.e. a variable bound in the current arrow abstraction.
+For such a situation there is a variant <literal>-<<</literal>, as in
+<screen>
+proc x -> f x -<< x+1
+</screen>
+which is equivalent to
+<screen>
+arr (\ x -> (f, x+1)) >>> app
+</screen>
+so in this case the arrow must belong to the <literal>ArrowApply</literal>
+class.
+Such an arrow is equivalent to a monad, so if you're using this form
+you may find a monadic formulation more convenient.
+</para>
-</Para>
-</ListItem>
-<ListItem>
+<sect2>
+<title>do-notation for commands</title>
+
+<para>
+Another form of command is a form of <literal>do</literal>-notation.
+For example, you can write
+<screen>
+proc x -> do
+ y <- f -< x+1
+ g -< 2*y
+ let z = x+y
+ t <- h -< x*z
+ returnA -< t+z
+</screen>
+You can read this much like ordinary <literal>do</literal>-notation,
+but with commands in place of monadic expressions.
+The first line sends the value of <literal>x+1</literal> as an input to
+the arrow <literal>f</literal>, and matches its output against
+<literal>y</literal>.
+In the next line, the output is discarded.
+The arrow <literal>returnA</literal> is defined in the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module as <literal>arr id</literal>.
+The above example is treated as an abbreviation for
+<screen>
+arr (\ x -> (x, x)) >>>
+ first (arr (\ x -> x+1) >>> f) >>>
+ arr (\ (y, x) -> (y, (x, y))) >>>
+ first (arr (\ y -> 2*y) >>> g) >>>
+ arr snd >>>
+ arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
+ first (arr (\ (x, z) -> x*z) >>> h) >>>
+ arr (\ (t, z) -> t+z) >>>
+ returnA
+</screen>
+Note that variables not used later in the composition are projected out.
+After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
+defined in the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module, this reduces to
+<screen>
+arr (\ x -> (x+1, x)) >>>
+ first f >>>
+ arr (\ (y, x) -> (2*y, (x, y))) >>>
+ first g >>>
+ arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
+ first h >>>
+ arr (\ (t, z) -> t+z)
+</screen>
+which is what you might have written by hand.
+With arrow notation, GHC keeps track of all those tuples of variables for you.
+</para>
-<Para>
- Pattern type signatures that bind new type variables
-may not be used in pattern bindings at all.
-So this is illegal:
+<para>
+Note that although the above translation suggests that
+<literal>let</literal>-bound variables like <literal>z</literal> must be
+monomorphic, the actual translation produces Core,
+so polymorphic variables are allowed.
+</para>
+<para>
+It's also possible to have mutually recursive bindings,
+using the new <literal>rec</literal> keyword, as in the following example:
+<screen>
+counter :: ArrowCircuit a => a Bool Int
+counter = proc reset -> do
+ rec output <- returnA -< if reset then 0 else next
+ next <- delay 0 -< output+1
+ returnA -< output
+</screen>
+The translation of such forms uses the <literal>loop</literal> combinator,
+so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
+</para>
-<ProgramListing>
- f x = let (y, z::a) = x in ...
-</ProgramListing>
+</sect2>
+<sect2>
+<title>Conditional commands</title>
+
+<para>
+In the previous example, we used a conditional expression to construct the
+input for an arrow.
+Sometimes we want to conditionally execute different commands, as in
+<screen>
+proc (x,y) ->
+ if f x y
+ then g -< x+1
+ else h -< y+2
+</screen>
+which is translated to
+<screen>
+arr (\ (x,y) -> if f x y then Left x else Right y) >>>
+ (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
+</screen>
+Since the translation uses <literal>|||</literal>,
+the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
+</para>
-But these are OK, because they do not bind fresh type variables:
+<para>
+There are also <literal>case</literal> commands, like
+<screen>
+case input of
+ [] -> f -< ()
+ [x] -> g -< x+1
+ x1:x2:xs -> do
+ y <- h -< (x1, x2)
+ ys <- k -< xs
+ returnA -< y:ys
+</screen>
+The syntax is the same as for <literal>case</literal> expressions,
+except that the bodies of the alternatives are commands rather than expressions.
+The translation is similar to that of <literal>if</literal> commands.
+</para>
+</sect2>
-<ProgramListing>
- f1 x = let (y, z::Int) = x in ...
- f2 (x::(Int,a)) = let (y, z::a) = x in ...
-</ProgramListing>
+<sect2>
+<title>Defining your own control structures</title>
+
+<para>
+As we're seen, arrow notation provides constructs,
+modelled on those for expressions,
+for sequencing, value recursion and conditionals.
+But suitable combinators,
+which you can define in ordinary Haskell,
+may also be used to build new commands out of existing ones.
+The basic idea is that a command defines an arrow from environments to values.
+These environments assign values to the free local variables of the command.
+Thus combinators that produce arrows from arrows
+may also be used to build commands from commands.
+For example, the <literal>ArrowChoice</literal> class includes a combinator
+<programlisting>
+ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
+</programlisting>
+so we can use it to build commands:
+<programlisting>
+expr' = proc x ->
+ returnA -< x
+ <+> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y
+ <+> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y
+</programlisting>
+This is equivalent to
+<programlisting>
+expr' = (proc x -> returnA -< x)
+ <+> (proc x -> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y)
+ <+> (proc x -> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y)
+</programlisting>
+It is essential that this operator be polymorphic in <literal>e</literal>
+(representing the environment input to the command
+and thence to its subcommands)
+and satisfy the corresponding naturality property
+<screen>
+arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
+</screen>
+at least for strict <literal>k</literal>.
+(This should be automatic if you're not using <literal>seq</literal>.)
+This ensures that environments seen by the subcommands are environments
+of the whole command,
+and also allows the translation to safely trim these environments.
+The operator must also not use any variable defined within the current
+arrow abstraction.
+</para>
+<para>
+We could define our own operator
+<programlisting>
+untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
+untilA body cond = proc x ->
+ if cond x then returnA -< ()
+ else do
+ body -< x
+ untilA body cond -< x
+</programlisting>
+and use it in the same way.
+Of course this infix syntax only makes sense for binary operators;
+there is also a more general syntax involving special brackets:
+<screen>
+proc x -> do
+ y <- f -< x+1
+ (|untilA|) (increment -< x+y) (within 0.5 -< x)
+</screen>
+</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>
+Some operators will need to pass additional inputs to their subcommands.
+For example, in an arrow type supporting exceptions,
+the operator that attaches an exception handler will wish to pass the
+exception that occurred to the handler.
+Such an operator might have a type
+<screen>
+handleA :: ... => a e c -> a (e,Ex) c -> a e c
+</screen>
+where <literal>Ex</literal> is the type of exceptions handled.
+You could then use this with arrow notation by writing a command
+<screen>
+body `handleA` \ ex -> handler
+</screen>
+so that if an exception is raised in the command <literal>body</literal>,
+the variable <literal>ex</literal> is bound to the value of the exception
+and the command <literal>handler</literal>,
+which typically refers to <literal>ex</literal>, is entered.
+Though the syntax here looks like a functional lambda,
+we are talking about commands, and something different is going on.
+The input to the arrow represented by a command consists of values for
+the free local variables in the command, plus a stack of anonymous values.
+In all the prior examples, this stack was empty.
+In the second argument to <literal>handleA</literal>,
+this stack consists of one value, the value of the exception.
+The command form of lambda merely gives this value a name.
+</para>
+<para>
+More concretely,
+the values on the stack are paired to the right of the environment.
+So when designing operators like <literal>handleA</literal> that pass
+extra inputs to their subcommands,
+More precisely, the type of each argument of the operator (and its result)
+should have the form
+<screen>
+a (...(e,t1), ... tn) t
+</screen>
+where <replaceable>e</replaceable> is the polymorphic variable
+(representing the environment)
+and <replaceable>ti</replaceable> are the types of the values on the stack,
+with <replaceable>t1</replaceable> being the <quote>top</quote>.
+The polymorphic variable <replaceable>e</replaceable> must not occur in
+<replaceable>a</replaceable>, <replaceable>ti</replaceable> or
+<replaceable>t</replaceable>.
+However the arrows involved need not be the same.
+Here are some more examples of suitable operators:
+<screen>
+bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
+runReader :: ... => a e c -> a' (e,State) c
+runState :: ... => a e c -> a' (e,State) (c,State)
+</screen>
+How can we supply the extra input required by the last two?
+We can define yet another operator, a counterpart of the monadic
+<literal>>>=</literal> operator:
+<programlisting>
+bind :: Arrow a => a e b -> a (e,b) c -> a e c
+u `bind` f = returnA &&& u >>> f
+</programlisting>
+and then build commands like
+<screen>
+proc x ->
+ (mkState -< x) `bind` (|runReader|) (do { ... })
+</screen>
+which uses the arrow <literal>mkState</literal> to create a state,
+and then provides this as an extra input to the command built using
+<literal>runReader</literal>.
+</para>
-<ProgramListing>
- f :: (b->b) = \(x::b) -> x
-</ProgramListing>
+</sect2>
+<sect2>
+<title>Differences with the paper</title>
-</Para>
-</ListItem>
+<itemizedlist>
-</ItemizedList>
+<listitem>
+<para>Instead of a single form of arrow application (arrow tail) with two
+translations, the implementation provides two forms
+<quote><literal>-<</literal></quote> (first-order)
+and <quote><literal>-<<</literal></quote> (higher-order).
+</para>
+</listitem>
-Such degnerate function bindings do not fall under the monomorphism
-restriction. Thus:
-</Para>
+<listitem>
+<para>User-defined operators are flagged with banana brackets instead of
+a new <literal>form</literal> keyword.
+</para>
+</listitem>
-<Para>
+</itemizedlist>
-<ProgramListing>
- g :: a -> a -> Bool = \x y. x==y
-</ProgramListing>
+</sect2>
-</Para>
+<sect2>
+<title>Portability</title>
+
+<para>
+Although only GHC implements arrow notation directly,
+there is also a preprocessor
+(available from the
+<ulink url="http://www.haskell.org/arrows/">arrows web page></ulink>)
+that translates arrow notation into Haskell 98
+for use with other Haskell systems.
+You would still want to check arrow programs with GHC;
+tracing type errors in the preprocessor output is not easy.
+Modules intended for both GHC and the preprocessor must observe some
+additional restrictions:
+<itemizedlist>
+
+<listitem>
+<para>
+The module must import
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
+</para>
+</listitem>
-<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>
+<listitem>
+<para>
+The preprocessor cannot cope with other Haskell extensions.
+These would have to go in separate modules.
+</para>
+</listitem>
-</Sect2>
+<listitem>
+<para>
+Because the preprocessor targets Haskell (rather than Core),
+<literal>let</literal>-bound variables are monomorphic.
+</para>
+</listitem>
-<Sect2>
-<Title>Existentials</Title>
+</itemizedlist>
+</para>
-<Para>
+</sect2>
-<ItemizedList>
-<ListItem>
+</sect1>
-<Para>
- Pattern type signatures can bind existential type variables.
-For example:
+<!-- ==================== ASSERTIONS ================= -->
+<sect1 id="sec-assertions">
+<title>Assertions
+<indexterm><primary>Assertions</primary></indexterm>
+</title>
-<ProgramListing>
- data T = forall a. MkT [a]
+<para>
+If you want to make use of assertions in your standard Haskell code, you
+could define a function like the following:
+</para>
- f :: T -> T
- f (MkT [t::a]) = MkT t3
- where
- t3::[a] = [t,t,t]
-</ProgramListing>
+<para>
+<programlisting>
+assert :: Bool -> a -> a
+assert False x = error "assertion failed!"
+assert _ x = x
+</programlisting>
-</Para>
-</ListItem>
+</para>
-</ItemizedList>
+<para>
+which works, but gives you back a less than useful error message --
+an assertion failed, but which and where?
+</para>
-</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>
-</Sect2>
+<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>
-</Sect1>
+<para>
-<Sect1 id="pragmas">
-<Title>Pragmas
-</Title>
+<programlisting>
+kelvinToC :: Double -> Double
+kelvinToC k = assert (k >= 0.0) (k+273.15)
+</programlisting>
-<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>
+</para>
-<Sect2 id="inline-pragma">
-<Title>INLINE pragma
+<para>
+Ghc will rewrite this to also include the source location where the
+assertion was made,
+</para>
-<IndexTerm><Primary>INLINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, INLINE</Primary></IndexTerm></Title>
+<para>
+
+<programlisting>
+assert pred val ==> assertError "Main.hs|15" pred val
+</programlisting>
-<Para>
-GHC (with <Option>-O</Option>, as always) tries to inline (or “unfold”)
-functions/values that are “small enough,” thus avoiding the call
-overhead and possibly exposing other more-wonderful optimisations.
-</Para>
+</para>
-<Para>
-You will probably see these unfoldings (in Core syntax) in your
-interface files.
-</Para>
+<para>
+The rewrite is only performed by the compiler when it spots
+applications of <function>Control.Exception.assert</function>, so you
+can still define and use your own versions of
+<function>assert</function>, should you so wish. If not, import
+<literal>Control.Exception</literal> to make use
+<function>assert</function> in your code.
+</para>
-<Para>
-Normally, if GHC decides a function is “too expensive” to inline, it
-will not do so, nor will it export that unfolding for other modules to
-use.
-</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>
-The sledgehammer you can bring to bear is the
-<Literal>INLINE</Literal><IndexTerm><Primary>INLINE pragma</Primary></IndexTerm> pragma, used thusly:
+<para>
+Assertion failures can be caught, see the documentation for the
+<literal>Control.Exception</literal> library for the details.
+</para>
-<ProgramListing>
+</sect1>
+
+
+<!-- =============================== PRAGMAS =========================== -->
+
+ <sect1 id="pragmas">
+ <title>Pragmas</title>
+
+ <indexterm><primary>pragma</primary></indexterm>
+
+ <para>GHC supports several pragmas, or instructions to the
+ compiler placed in the source code. Pragmas don't normally affect
+ the meaning of the program, but they might affect the efficiency
+ of the generated code.</para>
+
+ <para>Pragmas all take the form
+
+<literal>{-# <replaceable>word</replaceable> ... #-}</literal>
+
+ where <replaceable>word</replaceable> indicates the type of
+ pragma, and is followed optionally by information specific to that
+ type of pragma. Case is ignored in
+ <replaceable>word</replaceable>. The various values for
+ <replaceable>word</replaceable> that GHC understands are described
+ in the following sections; any pragma encountered with an
+ unrecognised <replaceable>word</replaceable> is (silently)
+ ignored.</para>
+
+ <sect2 id="deprecated-pragma">
+ <title>DEPRECATED pragma</title>
+ <indexterm><primary>DEPRECATED</primary>
+ </indexterm>
+
+ <para>The DEPRECATED pragma lets you specify that a particular
+ function, class, or type, is deprecated. There are two
+ forms.</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>
+
+ <sect2 id="inline-noinline-pragma">
+ <title>INLINE and NOINLINE pragmas</title>
+
+ <para>These pragmas control the inlining of function
+ definitions.</para>
+
+ <sect3 id="inline-pragma">
+ <title>INLINE pragma</title>
+ <indexterm><primary>INLINE</primary></indexterm>
+
+ <para>GHC (with <option>-O</option>, as always) tries to
+ inline (or “unfold”) functions/values that are
+ “small enough,” thus avoiding the call overhead
+ and possibly exposing other more-wonderful optimisations.
+ Normally, if GHC decides a function is “too
+ expensive” to inline, it will not do so, nor will it
+ export that unfolding for other modules to use.</para>
+
+ <para>The sledgehammer you can bring to bear is the
+ <literal>INLINE</literal><indexterm><primary>INLINE
+ pragma</primary></indexterm> pragma, used thusly:</para>
+
+<programlisting>
key_function :: Int -> String -> (Bool, Double)
#ifdef __GLASGOW_HASKELL__
{-# INLINE key_function #-}
#endif
-</ProgramListing>
+</programlisting>
-(You don't need to do the C pre-processor carry-on unless you're going
-to stick the code through HBC—it doesn't like <Literal>INLINE</Literal> pragmas.)
-</Para>
+ <para>(You don't need to do the C pre-processor carry-on
+ unless you're going to stick the code through HBC—it
+ doesn't like <literal>INLINE</literal> pragmas.)</para>
-<Para>
-The major effect of an <Literal>INLINE</Literal> pragma is to declare a function's
-“cost” to be very low. The normal unfolding machinery will then be
-very keen to inline it.
-</Para>
+ <para>The major effect of an <literal>INLINE</literal> pragma
+ is to declare a function's “cost” to be very low.
+ The normal unfolding machinery will then be very keen to
+ inline it.</para>
-<Para>
-An <Literal>INLINE</Literal> pragma for a function can be put anywhere its type
-signature could be put.
-</Para>
+ <para>Syntactially, an <literal>INLINE</literal> pragma for a
+ function can be put anywhere its type signature could be
+ put.</para>
-<Para>
-<Literal>INLINE</Literal> pragmas are a particularly good idea for the
-<Literal>then</Literal>/<Literal>return</Literal> (or <Literal>bind</Literal>/<Literal>unit</Literal>) functions in a monad.
-For example, in GHC's own <Literal>UniqueSupply</Literal> monad code, we have:
+ <para><literal>INLINE</literal> pragmas are a particularly
+ good idea for the
+ <literal>then</literal>/<literal>return</literal> (or
+ <literal>bind</literal>/<literal>unit</literal>) functions in
+ a monad. For example, in GHC's own
+ <literal>UniqueSupply</literal> monad code, we have:</para>
-<ProgramListing>
+<programlisting>
#ifdef __GLASGOW_HASKELL__
{-# INLINE thenUs #-}
{-# INLINE returnUs #-}
#endif
-</ProgramListing>
-
-</Para>
-
-</Sect2>
-
-<Sect2 id="noinline-pragma">
-<Title>NOINLINE pragma
-</Title>
-
-<Para>
-<IndexTerm><Primary>NOINLINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, NOINLINE</Primary></IndexTerm>
-</Para>
-
-<Para>
-The <Literal>NOINLINE</Literal> pragma does exactly what you'd expect: it stops the
-named function from being inlined by the compiler. You shouldn't ever
-need to do this, unless you're very cautious about code size.
-</Para>
-
-</Sect2>
-
-<Sect2 id="specialize-pragma">
-<Title>SPECIALIZE pragma
-</Title>
-
-<Para>
-<IndexTerm><Primary>SPECIALIZE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, SPECIALIZE</Primary></IndexTerm>
-<IndexTerm><Primary>overloading, death to</Primary></IndexTerm>
-</Para>
-
-<Para>
-(UK spelling also accepted.) For key overloaded functions, you can
-create extra versions (NB: more code space) specialised to particular
-types. Thus, if you have an overloaded function:
-</Para>
-
-<Para>
-
-<ProgramListing>
+</programlisting>
+
+ <para>See also the <literal>NOINLINE</literal> pragma (<xref
+ linkend="noinline-pragma">).</para>
+ </sect3>
+
+ <sect3 id="noinline-pragma">
+ <title>NOINLINE pragma</title>
+
+ <indexterm><primary>NOINLINE</primary></indexterm>
+ <indexterm><primary>NOTINLINE</primary></indexterm>
+
+ <para>The <literal>NOINLINE</literal> pragma does exactly what
+ you'd expect: it stops the named function from being inlined
+ by the compiler. You shouldn't ever need to do this, unless
+ you're very cautious about code size.</para>
+
+ <para><literal>NOTINLINE</literal> is a synonym for
+ <literal>NOINLINE</literal> (<literal>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>
+ </sect3>
+
+ <sect3 id="phase-control">
+ <title>Phase control</title>
+
+ <para> Sometimes you want to control exactly when in GHC's
+ pipeline the INLINE pragma is switched on. Inlining happens
+ only during runs of the <emphasis>simplifier</emphasis>. Each
+ run of the simplifier has a different <emphasis>phase
+ number</emphasis>; the phase number decreases towards zero.
+ If you use <option>-dverbose-core2core</option> you'll see the
+ sequence of phase numbers for successive runs of the
+ simpifier. In an INLINE pragma you can optionally specify a
+ phase number, thus:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>You can say "inline <literal>f</literal> in Phase 2
+ and all subsequent phases":
+<programlisting>
+ {-# INLINE [2] f #-}
+</programlisting>
+ </para>
+ </listitem>
+
+ <listitem>
+ <para>You can say "inline <literal>g</literal> in all
+ phases up to, but not including, Phase 3":
+<programlisting>
+ {-# INLINE [~3] g #-}
+</programlisting>
+ </para>
+ </listitem>
+
+ <listitem>
+ <para>If you omit the phase indicator, you mean "inline in
+ all phases".</para>
+ </listitem>
+ </itemizedlist>
+
+ <para>You can use a phase number on a NOINLINE pragma too:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>You can say "do not inline <literal>f</literal>
+ until Phase 2; in Phase 2 and subsequently behave as if
+ there was no pragma at all":
+<programlisting>
+ {-# NOINLINE [2] f #-}
+</programlisting>
+ </para>
+ </listitem>
+
+ <listitem>
+ <para>You can say "do not inline <literal>g</literal> in
+ Phase 3 or any subsequent phase; before that, behave as if
+ there was no pragma":
+<programlisting>
+ {-# NOINLINE [~3] g #-}
+</programlisting>
+ </para>
+ </listitem>
+
+ <listitem>
+ <para>If you omit the phase indicator, you mean "never
+ inline this function".</para>
+ </listitem>
+ </itemizedlist>
+
+ <para>The same phase-numbering control is available for RULES
+ (<xref LinkEnd="rewrite-rules">).</para>
+ </sect3>
+ </sect2>
+
+ <sect2 id="line-pragma">
+ <title>LINE pragma</title>
+
+ <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
+ <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
+ <para>This pragma is similar to C's <literal>#line</literal>
+ pragma, and is mainly for use in automatically generated Haskell
+ code. It lets you specify the line number and filename of the
+ original code; for example</para>
+
+<programlisting>
+{-# LINE 42 "Foo.vhs" #-}
+</programlisting>
+
+ <para>if you'd generated the current file from something called
+ <filename>Foo.vhs</filename> and this line corresponds to line
+ 42 in the original. GHC will adjust its error messages to refer
+ to the line/file named in the <literal>LINE</literal>
+ pragma.</para>
+ </sect2>
+
+ <sect2 id="options-pragma">
+ <title>OPTIONS pragma</title>
+ <indexterm><primary>OPTIONS</primary>
+ </indexterm>
+ <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
+ </indexterm>
+
+ <para>The <literal>OPTIONS</literal> pragma is used to specify
+ additional options that are given to the compiler when compiling
+ this source file. See <xref linkend="source-file-options"> for
+ details.</para>
+ </sect2>
+
+ <sect2 id="rules">
+ <title>RULES pragma</title>
+
+ <para>The RULES pragma lets you specify rewrite rules. It is
+ described in <xref LinkEnd="rewrite-rules">.</para>
+ </sect2>
+
+ <sect2 id="specialize-pragma">
+ <title>SPECIALIZE pragma</title>
+
+ <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
+ <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
+ <indexterm><primary>overloading, death to</primary></indexterm>
+
+ <para>(UK spelling also accepted.) For key overloaded
+ functions, you can create extra versions (NB: more code space)
+ specialised to particular types. Thus, if you have an
+ overloaded function:</para>
+
+<programlisting>
hammeredLookup :: Ord key => [(key, value)] -> key -> value
-</ProgramListing>
-
-</Para>
+</programlisting>
-<Para>
-If it is heavily used on lists with <Literal>Widget</Literal> keys, you could
-specialise it as follows:
+ <para>If it is heavily used on lists with
+ <literal>Widget</literal> keys, you could specialise it as
+ follows:</para>
-<ProgramListing>
+<programlisting>
{-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
-</ProgramListing>
+</programlisting>
-</Para>
+ <para>A <literal>SPECIALIZE</literal> pragma for a function can
+ be put anywhere its type signature could be put.</para>
-<Para>
-To get very fancy, you can also specify a named function to use for
-the specialised value, by adding <Literal>= blah</Literal>, as in:
+ <para>To get very fancy, you can also specify a named function
+ to use for the specialised value, as in:</para>
-<ProgramListing>
-{-# SPECIALIZE hammeredLookup :: ...as before... = blah #-}
-</ProgramListing>
+<programlisting>
+{-# RULES "hammeredLookup" hammeredLookup = blah #-}
+</programlisting>
-It's <Emphasis>Your Responsibility</Emphasis> to make sure that <Function>blah</Function> really
-behaves as a specialised version of <Function>hammeredLookup</Function>!!!
-</Para>
+ <para>where <literal>blah</literal> is an implementation of
+ <literal>hammerdLookup</literal> written specialy for
+ <literal>Widget</literal> lookups. It's <emphasis>Your
+ Responsibility</emphasis> to make sure that
+ <function>blah</function> really behaves as a specialised
+ version of <function>hammeredLookup</function>!!!</para>
-<Para>
-NOTE: the <Literal>=blah</Literal> feature isn't implemented in GHC 4.xx.
-</Para>
+ <para>Note we use the <literal>RULE</literal> pragma here to
+ indicate that <literal>hammeredLookup</literal> applied at a
+ certain type should be replaced by <literal>blah</literal>. See
+ <xref linkend="rules"> for more information on
+ <literal>RULES</literal>.</para>
-<Para>
-An example in which the <Literal>= blah</Literal> form will Win Big:
+ <para>An example in which using <literal>RULES</literal> for
+ specialisation will Win Big:
-<ProgramListing>
+<programlisting>
toDouble :: Real a => a -> Double
toDouble = fromRational . toRational
-{-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
+{-# RULES "toDouble/Int" toDouble = i2d #-}
i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
-</ProgramListing>
-
-The <Function>i2d</Function> function is virtually one machine instruction; the
-default conversion—via an intermediate <Literal>Rational</Literal>—is obscenely
-expensive by comparison.
-</Para>
+</programlisting>
-<Para>
-By using the US spelling, your <Literal>SPECIALIZE</Literal> pragma will work with
-HBC, too. Note that HBC doesn't support the <Literal>= blah</Literal> form.
-</Para>
+ The <function>i2d</function> function is virtually one machine
+ instruction; the default conversion—via an intermediate
+ <literal>Rational</literal>—is obscenely expensive by
+ comparison.</para>
-<Para>
-A <Literal>SPECIALIZE</Literal> pragma for a function can be put anywhere its type
-signature could be put.
-</Para>
+ </sect2>
-</Sect2>
+<sect2 id="specialize-instance-pragma">
+<title>SPECIALIZE instance pragma
+</title>
-<Sect2 id="specialize-instance-pragma">
-<Title>SPECIALIZE instance pragma
-</Title>
-
-<Para>
-<IndexTerm><Primary>SPECIALIZE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>overloading, death to</Primary></IndexTerm>
+<para>
+<indexterm><primary>SPECIALIZE pragma</primary></indexterm>
+<indexterm><primary>overloading, death to</primary></indexterm>
Same idea, except for instance declarations. For example:
-<ProgramListing>
-instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
-
-{-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
-</ProgramListing>
-
-Compatible with HBC, by the way.
-</Para>
-
-</Sect2>
-
-<Sect2 id="line-pragma">
-<Title>LINE pragma
-</Title>
-
-<Para>
-<IndexTerm><Primary>LINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, LINE</Primary></IndexTerm>
-</Para>
-
-<Para>
-This pragma is similar to C's <Literal>#line</Literal> pragma, and is mainly for use in
-automatically generated Haskell code. It lets you specify the line
-number and filename of the original code; for example
-</Para>
-
-<Para>
-
-<ProgramListing>
-{-# LINE 42 "Foo.vhs" #-}
-</ProgramListing>
-
-</Para>
-
-<Para>
-if you'd generated the current file from something called <Filename>Foo.vhs</Filename>
-and this line corresponds to line 42 in the original. GHC will adjust
-its error messages to refer to the line/file named in the <Literal>LINE</Literal>
-pragma.
-</Para>
+<programlisting>
+instance (Eq a) => Eq (Foo a) where {
+ {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
+ ... usual stuff ...
+ }
+</programlisting>
+The pragma must occur inside the <literal>where</literal> part
+of the instance declaration.
+</para>
+<para>
+Compatible with HBC, by the way, except perhaps in the placement
+of the pragma.
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>RULES pragma</Title>
-<Para>
-The RULES pragma lets you specify rewrite rules. It is described in
-<XRef LinkEnd="rewrite-rules">.
-</Para>
-</Sect2>
+</sect1>
-</Sect1>
+<!-- ======================= REWRITE RULES ======================== -->
-<Sect1 id="rewrite-rules">
-<Title>Rewrite rules
+<sect1 id="rewrite-rules">
+<title>Rewrite rules
-<IndexTerm><Primary>RULES pagma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, RULES</Primary></IndexTerm>
-<IndexTerm><Primary>rewrite rules</Primary></IndexTerm></Title>
+<indexterm><primary>RULES pagma</primary></indexterm>
+<indexterm><primary>pragma, RULES</primary></indexterm>
+<indexterm><primary>rewrite rules</primary></indexterm></title>
-<Para>
+<para>
The programmer can specify rewrite rules as part of the source program
(in a pragma). GHC applies these rewrite rules wherever it can.
-</Para>
+</para>
-<Para>
+<para>
Here is an example:
-<ProgramListing>
+<programlisting>
{-# RULES
"map/map" forall f g xs. map f (map g xs) = map (f.g) xs
#-}
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Sect2>
-<Title>Syntax</Title>
+<sect2>
+<title>Syntax</title>
-<Para>
+<para>
From a syntactic point of view:
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
+
+<para>
+ There may be zero or more rules in a <literal>RULES</literal> pragma.
+</para>
+</listitem>
+
+<listitem>
-<Para>
+<para>
Each rule has a name, enclosed in double quotes. The name itself has
no significance at all. It is only used when reporting how many times the rule fired.
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- There may be zero or more rules in a <Literal>RULES</Literal> pragma.
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Layout applies in a <Literal>RULES</Literal> pragma. Currently no new indentation level
+</para>
+</listitem>
+
+<listitem>
+<para>
+A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
+immediately after the name of the rule. Thus:
+<programlisting>
+ {-# RULES
+ "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
+ #-}
+</programlisting>
+The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
+notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
+Phase 2.
+</para>
+</listitem>
+
+
+<listitem>
+
+<para>
+ Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
is set, so you must lay out your rules starting in the same column as the
enclosing definitions.
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Each variable mentioned in a rule must either be in scope (e.g. <Function>map</Function>),
-or bound by the <Literal>forall</Literal> (e.g. <Function>f</Function>, <Function>g</Function>, <Function>xs</Function>). The variables bound by
-the <Literal>forall</Literal> are called the <Emphasis>pattern</Emphasis> variables. They are separated
-by spaces, just like in a type <Literal>forall</Literal>.
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
+</para>
+</listitem>
+
+<listitem>
+
+<para>
+ Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
+or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
+the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
+by spaces, just like in a type <literal>forall</literal>.
+</para>
+</listitem>
+<listitem>
+
+<para>
A pattern variable may optionally have a type signature.
-If the type of the pattern variable is polymorphic, it <Emphasis>must</Emphasis> have a type signature.
-For example, here is the <Literal>foldr/build</Literal> rule:
+If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
+For example, here is the <literal>foldr/build</literal> rule:
-<ProgramListing>
+<programlisting>
"fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
foldr k z (build g) = g k z
-</ProgramListing>
+</programlisting>
-Since <Function>g</Function> has a polymorphic type, it must have a type signature.
+Since <function>g</function> has a polymorphic type, it must have a type signature.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
The left hand side of a rule must consist of a top-level variable applied
-to arbitrary expressions. For example, this is <Emphasis>not</Emphasis> OK:
+to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
-<ProgramListing>
+<programlisting>
"wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
"wrong2" forall f. f True = True
-</ProgramListing>
+</programlisting>
-In <Literal>"wrong1"</Literal>, the LHS is not an application; in <Literal>"wrong1"</Literal>, the LHS has a pattern variable
+In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
in the head.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
A rule does not need to be in the same module as (any of) the
variables it mentions, though of course they need to be in scope.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
Rules are automatically exported from a module, just as instance declarations are.
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Semantics</Title>
+<sect2>
+<title>Semantics</title>
-<Para>
+<para>
From a semantic point of view:
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
-Rules are only applied if you use the <Option>-O</Option> flag.
-</Para>
-</ListItem>
+<para>
+Rules are only applied if you use the <option>-O</option> flag.
+</para>
+</listitem>
-<ListItem>
-<Para>
+<listitem>
+<para>
Rules are regarded as left-to-right rewrite rules.
When GHC finds an expression that is a substitution instance of the LHS
of a rule, it replaces the expression by the (appropriately-substituted) RHS.
By "a substitution instance" we mean that the LHS can be made equal to the
expression by substituting for the pattern variables.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
The LHS and RHS of a rule are typechecked, and must have the
same type.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
GHC makes absolutely no attempt to verify that the LHS and RHS
of a rule have the same meaning. That is undecideable in general, and
infeasible in most interesting cases. The responsibility is entirely the programmer's!
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
GHC makes no attempt to make sure that the rules are confluent or
terminating. For example:
-<ProgramListing>
+<programlisting>
"loop" forall x,y. f x y = f y x
-</ProgramListing>
+</programlisting>
This rule will cause the compiler to go into an infinite loop.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
If more than one rule matches a call, GHC will choose one arbitrarily to apply.
-</Para>
-</ListItem>
-<ListItem>
-<Para>
+</para>
+</listitem>
+<listitem>
+<para>
GHC currently uses a very simple, syntactic, matching algorithm
for matching a rule LHS with an expression. It seeks a substitution
which makes the LHS and expression syntactically equal modulo alpha
conversion. The pattern (rule), but not the expression, is eta-expanded if
necessary. (Eta-expanding the epression can lead to laziness bugs.)
But not beta conversion (that's called higher-order matching).
-</Para>
+</para>
-<Para>
+<para>
Matching is carried out on GHC's intermediate language, which includes
type abstractions and applications. So a rule only matches if the
-types match too. See <XRef LinkEnd="rule-spec"> below.
-</Para>
-</ListItem>
-<ListItem>
+types match too. See <xref LinkEnd="rule-spec"> below.
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
GHC keeps trying to apply the rules as it optimises the program.
For example, consider:
-<ProgramListing>
+<programlisting>
let s = map f
t = map g
in
s (t xs)
-</ProgramListing>
+</programlisting>
-The expression <Literal>s (t xs)</Literal> does not match the rule <Literal>"map/map"</Literal>, but GHC
+The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
not be substituted, and the rule would not fire.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- In the earlier phases of compilation, GHC inlines <Emphasis>nothing
-that appears on the LHS of a rule</Emphasis>, because once you have substituted
+<para>
+ In the earlier phases of compilation, GHC inlines <emphasis>nothing
+that appears on the LHS of a rule</emphasis>, because once you have substituted
for something you can't match against it (given the simple minded
matching). So if you write the rule
-<ProgramListing>
+<programlisting>
"map/map" forall f,g. map f . map g = map (f.g)
-</ProgramListing>
+</programlisting>
-this <Emphasis>won't</Emphasis> match the expression <Literal>map f (map g xs)</Literal>.
+this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
It will only match something written with explicit use of ".".
-Well, not quite. It <Emphasis>will</Emphasis> match the expression
+Well, not quite. It <emphasis>will</emphasis> match the expression
-<ProgramListing>
+<programlisting>
wibble f g xs
-</ProgramListing>
+</programlisting>
-where <Function>wibble</Function> is defined:
+where <function>wibble</function> is defined:
-<ProgramListing>
+<programlisting>
wibble f g = map f . map g
-</ProgramListing>
+</programlisting>
-because <Function>wibble</Function> will be inlined (it's small).
+because <function>wibble</function> will be inlined (it's small).
Later on in compilation, GHC starts inlining even things on the
LHS of rules, but still leaves the rules enabled. This inlining
-policy is controlled by the per-simplification-pass flag <Option>-finline-phase</Option><Emphasis>n</Emphasis>.
+policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
All rules are implicitly exported from the module, and are therefore
in force in any module that imports the module that defined the rule, directly
or indirectly. (That is, if A imports B, which imports C, then C's rules are
in force when compiling A.) The situation is very similar to that for instance
declarations.
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>List fusion</Title>
+<sect2>
+<title>List fusion</title>
-<Para>
+<para>
The RULES mechanism is used to implement fusion (deforestation) of common list functions.
If a "good consumer" consumes an intermediate list constructed by a "good producer", the
intermediate list should be eliminated entirely.
-</Para>
+</para>
-<Para>
+<para>
The following are good producers:
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
List comprehensions
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Enumerations of <Literal>Int</Literal> and <Literal>Char</Literal> (e.g. <Literal>['a'..'z']</Literal>).
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Explicit lists (e.g. <Literal>[True, False]</Literal>)
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- The cons constructor (e.g <Literal>3:4:[]</Literal>)
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>++</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>map</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>filter</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>iterate</Function>, <Function>repeat</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>zip</Function>, <Function>zipWith</Function>
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-</Para>
-
-<Para>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
+</para>
+</listitem>
+<listitem>
+
+<para>
+ Explicit lists (e.g. <literal>[True, False]</literal>)
+</para>
+</listitem>
+<listitem>
+
+<para>
+ The cons constructor (e.g <literal>3:4:[]</literal>)
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>++</function>
+</para>
+</listitem>
+
+<listitem>
+<para>
+ <function>map</function>
+</para>
+</listitem>
+
+<listitem>
+<para>
+ <function>filter</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>iterate</function>, <function>repeat</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>zip</function>, <function>zipWith</function>
+</para>
+</listitem>
+
+</itemizedlist>
+
+</para>
+
+<para>
The following are good consumers:
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
List comprehensions
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>array</Function> (on its second argument)
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>length</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>++</Function> (on its first argument)
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>map</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>filter</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>concat</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>unzip</Function>, <Function>unzip2</Function>, <Function>unzip3</Function>, <Function>unzip4</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>zip</Function>, <Function>zipWith</Function> (but on one argument only; if both are good producers, <Function>zip</Function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>array</function> (on its second argument)
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>length</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>++</function> (on its first argument)
+</para>
+</listitem>
+
+<listitem>
+<para>
+ <function>foldr</function>
+</para>
+</listitem>
+
+<listitem>
+<para>
+ <function>map</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>filter</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>concat</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
will fuse with one but not the other)
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>partition</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>head</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>and</Function>, <Function>or</Function>, <Function>any</Function>, <Function>all</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>sequence_</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>msum</Function>
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- <Function>sortBy</Function>
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-</Para>
-
-<Para>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>partition</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>head</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>sequence_</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>msum</function>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <function>sortBy</function>
+</para>
+</listitem>
+
+</itemizedlist>
+
+</para>
+
+<para>
So, for example, the following should generate no intermediate lists:
-<ProgramListing>
+<programlisting>
array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
This list could readily be extended; if there are Prelude functions that you use
a lot which are not included, please tell us.
-</Para>
+</para>
-<Para>
+<para>
If you want to write your own good consumers or producers, look at the
Prelude definitions of the above functions to see how to do so.
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2 id="rule-spec">
-<Title>Specialisation
-</Title>
+<sect2 id="rule-spec">
+<title>Specialisation
+</title>
-<Para>
+<para>
Rewrite rules can be used to get the same effect as a feature
present in earlier version of GHC:
-<ProgramListing>
+<programlisting>
{-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
-</ProgramListing>
+</programlisting>
-This told GHC to use <Function>int8ToInt16</Function> instead of <Function>fromIntegral</Function> whenever
-the latter was called with type <Literal>Int8 -> Int16</Literal>. That is, rather than
-specialising the original definition of <Function>fromIntegral</Function> the programmer is
-promising that it is safe to use <Function>int8ToInt16</Function> instead.
-</Para>
+This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
+the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
+specialising the original definition of <function>fromIntegral</function> the programmer is
+promising that it is safe to use <function>int8ToInt16</function> instead.
+</para>
-<Para>
+<para>
This feature is no longer in GHC. But rewrite rules let you do the
same thing:
-<ProgramListing>
+<programlisting>
{-# RULES
"fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
#-}
-</ProgramListing>
+</programlisting>
-This slightly odd-looking rule instructs GHC to replace <Function>fromIntegral</Function>
-by <Function>int8ToInt16</Function> <Emphasis>whenever the types match</Emphasis>. Speaking more operationally,
+This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
+by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
GHC adds the type and dictionary applications to get the typed rule
-<ProgramListing>
+<programlisting>
forall (d1::Integral Int8) (d2::Num Int16) .
fromIntegral Int8 Int16 d1 d2 = int8ToInt16
-</ProgramListing>
+</programlisting>
What is more,
this rule does not need to be in the same file as fromIntegral,
-unlike the <Literal>SPECIALISE</Literal> pragmas which currently do (so that they
+unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
have an original definition available to specialise).
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Controlling what's going on</Title>
+<sect2>
+<title>Controlling what's going on</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
- Use <Option>-ddump-rules</Option> to see what transformation rules GHC is using.
-</Para>
-</ListItem>
-<ListItem>
+<para>
+ Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
+</para>
+</listitem>
+<listitem>
-<Para>
- Use <Option>-ddump-simpl-stats</Option> to see what rules are being fired.
-If you add <Option>-dppr-debug</Option> you get a more detailed listing.
-</Para>
-</ListItem>
-<ListItem>
+<para>
+ Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
+If you add <option>-dppr-debug</option> you get a more detailed listing.
+</para>
+</listitem>
+<listitem>
-<Para>
- The defintion of (say) <Function>build</Function> in <FileName>PrelBase.lhs</FileName> looks llike this:
+<para>
+ The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
-<ProgramListing>
+<programlisting>
build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
{-# INLINE build #-}
build g = g (:) []
-</ProgramListing>
+</programlisting>
-Notice the <Literal>INLINE</Literal>! That prevents <Literal>(:)</Literal> from being inlined when compiling
-<Literal>PrelBase</Literal>, so that an importing module will “see” the <Literal>(:)</Literal>, and can
-match it on the LHS of a rule. <Literal>INLINE</Literal> prevents any inlining happening
-in the RHS of the <Literal>INLINE</Literal> thing. I regret the delicacy of this.
+Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
+<literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
+match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
+in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- In <Filename>ghc/lib/std/PrelBase.lhs</Filename> look at the rules for <Function>map</Function> to
+<para>
+ In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
see how to write rules that will do fusion and yet give an efficient
-program even if fusion doesn't happen. More rules in <Filename>PrelList.lhs</Filename>.
-</Para>
-</ListItem>
+program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
+</para>
+</listitem>
+
+</itemizedlist>
+
+</para>
+
+</sect2>
-</ItemizedList>
+<sect2 id="core-pragma">
+ <title>CORE pragma</title>
-</Para>
+ <indexterm><primary>CORE pragma</primary></indexterm>
+ <indexterm><primary>pragma, CORE</primary></indexterm>
+ <indexterm><primary>core, annotation</primary></indexterm>
+
+<para>
+ The external core format supports <quote>Note</quote> annotations;
+ the <literal>CORE</literal> pragma gives a way to specify what these
+ should be in your Haskell source code. Syntactically, core
+ annotations are attached to expressions and take a Haskell string
+ literal as an argument. The following function definition shows an
+ example:
+
+<programlisting>
+f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
+</programlisting>
+
+ Sematically, this is equivalent to:
+
+<programlisting>
+g x = show x
+</programlisting>
+</para>
+
+<para>
+ However, when external for is generated (via
+ <option>-fext-core</option>), there will be Notes attached to the
+ expressions <function>show</function> and <VarName>x</VarName>.
+ The core function declaration for <function>f</function> is:
+</para>
+
+<programlisting>
+ f :: %forall a . GHCziShow.ZCTShow a ->
+ a -> GHCziBase.ZMZN GHCziBase.Char =
+ \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
+ (%note "foo"
+ %case zddShow %of (tpl::GHCziShow.ZCTShow a)
+ {GHCziShow.ZCDShow
+ (tpl1::GHCziBase.Int ->
+ a ->
+ GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
+r)
+ (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
+ (tpl3::GHCziBase.ZMZN a ->
+ GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
+r) ->
+ tpl2})
+ (%note "foo"
+ eta);
+</programlisting>
+
+<para>
+ Here, we can see that the function <function>show</function> (which
+ has been expanded out to a case expression over the Show dictionary)
+ has a <literal>%note</literal> attached to it, as does the
+ expression <VarName>eta</VarName> (which used to be called
+ <VarName>x</VarName>).
+</para>
+
+</sect2>
+
+</sect1>
+
+<sect1 id="generic-classes">
+<title>Generic classes</title>
+
+ <para>(Note: support for generic classes is currently broken in
+ GHC 5.02).</para>
+
+<para>
+The ideas behind this extension are described in detail in "Derivable type classes",
+Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
+An example will give the idea:
+</para>
+
+<programlisting>
+ import Generics
+
+ class Bin a where
+ toBin :: a -> [Int]
+ fromBin :: [Int] -> (a, [Int])
+
+ toBin {| Unit |} Unit = []
+ toBin {| a :+: b |} (Inl x) = 0 : toBin x
+ toBin {| a :+: b |} (Inr y) = 1 : toBin y
+ toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
+
+ fromBin {| Unit |} bs = (Unit, bs)
+ fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
+ fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
+ fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
+ (y,bs'') = fromBin bs'
+</programlisting>
+<para>
+This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
+work for arbitrary data types. They do so by giving cases for unit, product, and sum,
+which are defined thus in the library module <literal>Generics</literal>:
+</para>
+<programlisting>
+ data Unit = Unit
+ data a :+: b = Inl a | Inr b
+ data a :*: b = a :*: b
+</programlisting>
+<para>
+Now you can make a data type into an instance of Bin like this:
+<programlisting>
+ instance (Bin a, Bin b) => Bin (a,b)
+ instance Bin a => Bin [a]
+</programlisting>
+That is, just leave off the "where" clause. Of course, you can put in the
+where clause and over-ride whichever methods you please.
+</para>
+
+ <sect2>
+ <title> Using generics </title>
+ <para>To use generics you need to</para>
+ <itemizedlist>
+ <listitem>
+ <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
+ <option>-fgenerics</option> (to generate extra per-data-type code),
+ and <option>-package lang</option> (to make the <literal>Generics</literal> library
+ available. </para>
+ </listitem>
+ <listitem>
+ <para>Import the module <literal>Generics</literal> from the
+ <literal>lang</literal> package. This import brings into
+ scope the data types <literal>Unit</literal>,
+ <literal>:*:</literal>, and <literal>:+:</literal>. (You
+ don't need this import if you don't mention these types
+ explicitly; for example, if you are simply giving instance
+ declarations.)</para>
+ </listitem>
+ </itemizedlist>
+ </sect2>
+
+<sect2> <title> Changes wrt the paper </title>
+<para>
+Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
+can be written infix (indeed, you can now use
+any operator starting in a colon as an infix type constructor). Also note that
+the type constructors are not exactly as in the paper (Unit instead of 1, etc).
+Finally, note that the syntax of the type patterns in the class declaration
+uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
+alone would ambiguous when they appear on right hand sides (an extension we
+anticipate wanting).
+</para>
+</sect2>
+
+<sect2> <title>Terminology and restrictions</title>
+<para>
+Terminology. A "generic default method" in a class declaration
+is one that is defined using type patterns as above.
+A "polymorphic default method" is a default method defined as in Haskell 98.
+A "generic class declaration" is a class declaration with at least one
+generic default method.
+</para>
+
+<para>
+Restrictions:
+<itemizedlist>
+<listitem>
+<para>
+Alas, we do not yet implement the stuff about constructor names and
+field labels.
+</para>
+</listitem>
+
+<listitem>
+<para>
+A generic class can have only one parameter; you can't have a generic
+multi-parameter class.
+</para>
+</listitem>
+
+<listitem>
+<para>
+A default method must be defined entirely using type patterns, or entirely
+without. So this is illegal:
+<programlisting>
+ class Foo a where
+ op :: a -> (a, Bool)
+ op {| Unit |} Unit = (Unit, True)
+ op x = (x, False)
+</programlisting>
+However it is perfectly OK for some methods of a generic class to have
+generic default methods and others to have polymorphic default methods.
+</para>
+</listitem>
+
+<listitem>
+<para>
+The type variable(s) in the type pattern for a generic method declaration
+scope over the right hand side. So this is legal (note the use of the type variable ``p'' in a type signature on the right hand side:
+<programlisting>
+ class Foo a where
+ op :: a -> Bool
+ op {| p :*: q |} (x :*: y) = op (x :: p)
+ ...
+</programlisting>
+</para>
+</listitem>
+
+<listitem>
+<para>
+The type patterns in a generic default method must take one of the forms:
+<programlisting>
+ a :+: b
+ a :*: b
+ Unit
+</programlisting>
+where "a" and "b" are type variables. Furthermore, all the type patterns for
+a single type constructor (<literal>:*:</literal>, say) must be identical; they
+must use the same type variables. So this is illegal:
+<programlisting>
+ class Foo a where
+ op :: a -> Bool
+ op {| a :+: b |} (Inl x) = True
+ op {| p :+: q |} (Inr y) = False
+</programlisting>
+The type patterns must be identical, even in equations for different methods of the class.
+So this too is illegal:
+<programlisting>
+ class Foo a where
+ op1 :: a -> Bool
+ op1 {| a :*: b |} (x :*: y) = True
+
+ op2 :: a -> Bool
+ op2 {| p :*: q |} (x :*: y) = False
+</programlisting>
+(The reason for this restriction is that we gather all the equations for a particular type consructor
+into a single generic instance declaration.)
+</para>
+</listitem>
+
+<listitem>
+<para>
+A generic method declaration must give a case for each of the three type constructors.
+</para>
+</listitem>
+
+<listitem>
+<para>
+The type for a generic method can be built only from:
+ <itemizedlist>
+ <listitem> <para> Function arrows </para> </listitem>
+ <listitem> <para> Type variables </para> </listitem>
+ <listitem> <para> Tuples </para> </listitem>
+ <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
+ </itemizedlist>
+Here are some example type signatures for generic methods:
+<programlisting>
+ op1 :: a -> Bool
+ op2 :: Bool -> (a,Bool)
+ op3 :: [Int] -> a -> a
+ op4 :: [a] -> Bool
+</programlisting>
+Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
+inside a list.
+</para>
+<para>
+This restriction is an implementation restriction: we just havn't got around to
+implementing the necessary bidirectional maps over arbitrary type constructors.
+It would be relatively easy to add specific type constructors, such as Maybe and list,
+to the ones that are allowed.</para>
+</listitem>
+
+<listitem>
+<para>
+In an instance declaration for a generic class, the idea is that the compiler
+will fill in the methods for you, based on the generic templates. However it can only
+do so if
+ <itemizedlist>
+ <listitem>
+ <para>
+ The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
+ </para>
+ </listitem>
+ <listitem>
+ <para>
+ No constructor of the instance type has unboxed fields.
+ </para>
+ </listitem>
+ </itemizedlist>
+(Of course, these things can only arise if you are already using GHC extensions.)
+However, you can still give an instance declarations for types which break these rules,
+provided you give explicit code to override any generic default methods.
+</para>
+</listitem>
+
+</itemizedlist>
+</para>
+
+<para>
+The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
+what the compiler does with generic declarations.
+</para>
+
+</sect2>
+
+<sect2> <title> Another example </title>
+<para>
+Just to finish with, here's another example I rather like:
+<programlisting>
+ class Tag a where
+ nCons :: a -> Int
+ nCons {| Unit |} _ = 1
+ nCons {| a :*: b |} _ = 1
+ nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
+
+ tag :: a -> Int
+ tag {| Unit |} _ = 1
+ tag {| a :*: b |} _ = 1
+ tag {| a :+: b |} (Inl x) = tag x
+ tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
+</programlisting>
+</para>
+</sect2>
+</sect1>
-</Sect2>
-</Sect1>
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