-<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>
-<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>
-
-<VarListEntry>
-<Term>Generic classes:</Term>
-<ListItem>
-<Para>
-Generic class declarations allow you to define a class
-whose methods say how to work over an arbitrary data type.
-Then it's really easy to make any new type into an instance of
-the class. This generalises the rather ad-hoc "deriving" feature
-of Haskell 98.
-Details in <XRef LinkEnd="generic-classes">.
-</Para>
-</ListItem>
-</VarListEntry>
-</VariableList>
-</Para>
-
-<Para>
-Before you get too carried away working at the lowest level (e.g.,
-sloshing <Literal>MutableByteArray#</Literal>s around your
-program), you may wish to check if there are libraries that provide a
-“Haskellised veneer” over the features you want. See
-<xref linkend="book-hslibs">.
-</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>
-
-<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
-object. The representation of a Haskell <literal>Int</literal>, for
-example, is a two-word heap object. An <firstterm>unboxed</firstterm>
-type, however, is represented by the value itself, no pointers or heap
-allocation are involved.
-</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>
-(PrimOps) on these types are what you might expect; e.g.,
-<Literal>(+#)</Literal> is addition on
-<Literal>Int#</Literal>s, and is the machine-addition that we all
-know and love—usually one instruction.
-</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>
-
-<Para>
-Primitive values are often represented by a simple bit-pattern, such
-as <Literal>Int#</Literal>, <Literal>Float#</Literal>,
-<Literal>Double#</Literal>. But this is not necessarily the case:
-a primitive value might be represented by a pointer to a
-heap-allocated object. Examples include
-<Literal>Array#</Literal>, the type of primitive arrays. A
-primitive array is heap-allocated because it is too big a value to fit
-in a register, and would be too expensive to copy around; in a sense,
-it is accidental that it is represented by a pointer. If a pointer
-represents a primitive value, then it really does point to that value:
-no unevaluated thunks, no indirections…nothing can be at the
-other end of the pointer than the primitive value.
-</Para>
-
-<Para>
-There are some restrictions on the use of primitive types, the main
-one being that you can't pass a primitive value to a polymorphic
-function or store one in a polymorphic data type. This rules out
-things like <Literal>[Int#]</Literal> (i.e. lists of primitive
-integers). The reason for this restriction is that polymorphic
-arguments and constructor fields are assumed to be pointers: if an
-unboxed integer is stored in one of these, the garbage collector would
-attempt to follow it, leading to unpredictable space leaks. Or a
-<Function>seq</Function> operation on the polymorphic component may
-attempt to dereference the pointer, with disastrous results. Even
-worse, the unboxed value might be larger than a pointer
-(<Literal>Double#</Literal> for instance).
-</Para>
-
-<Para>
-Nevertheless, A numerically-intensive program using unboxed types can
-go a <Emphasis>lot</Emphasis> faster than its “standard”
-counterpart—we saw a threefold speedup on one example.
-</Para>
-
-</sect2>
-
-<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
-unboxed tuple looks like this:
-</Para>
-
-<Para>
-
-<ProgramListing>
-(# e_1, ..., e_n #)
-</ProgramListing>
-
-</Para>
-
-<Para>
-where <Literal>e_1..e_n</Literal> are expressions of any
-type (primitive or non-primitive). The type of an unboxed tuple looks
-the same.
-</Para>
-
-<Para>
-Unboxed tuples are used for functions that need to return multiple
-values, but they avoid the heap allocation normally associated with
-using fully-fledged tuples. When an unboxed tuple is returned, the
-components are put directly into registers or on the stack; the
-unboxed tuple itself does not have a composite representation. Many
-of the primitive operations listed in this section return unboxed
-tuples.
-</Para>
-
-<Para>
-There are some pretty stringent restrictions on the use of unboxed tuples:
-</Para>
-
-<Para>
-
-<ItemizedList>
-<ListItem>
-
-<Para>
- Unboxed tuple types are subject to the same restrictions as
-other unboxed types; i.e. they may not be stored in polymorphic data
-structures or passed to polymorphic functions.
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- Unboxed tuples may only be constructed as the direct result of
-a function, and may only be deconstructed with a <Literal>case</Literal> expression.
-eg. the following are valid:
-
-
-<ProgramListing>
-f x y = (# x+1, y-1 #)
-g x = case f x x of { (# a, b #) -> a + b }
-</ProgramListing>
-
-
-but the following are invalid:
-
-
-<ProgramListing>
-f x y = g (# x, y #)
-g (# x, y #) = x + y
-</ProgramListing>
-
-
-</Para>
-</ListItem>
-<ListItem>
-
-<Para>
- No variable can have an unboxed tuple type. This is illegal:
-
-
-<ProgramListing>
-f :: (# Int, Int #) -> (# Int, Int #)
-f x = x
-</ProgramListing>
-
-
-because <VarName>x</VarName> has an unboxed tuple type.
-
-</Para>
-</ListItem>
-
-</ItemizedList>
-
-</Para>
-
-<Para>
-Note: we may relax some of these restrictions in the future.
-</Para>
-
-<Para>
-The <Literal>IO</Literal> and <Literal>ST</Literal> monads use unboxed tuples to avoid unnecessary
-allocation during sequences of operations.
-</Para>
-
-</Sect2>
+</para>
-<Sect2>
-<Title>Character and numeric types</Title>
+ <variablelist>
-<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>
+ <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>
-<Para>
+ <varlistentry>
+ <term>Type system extensions:</term>
+ <listitem>
+ <para> GHC supports a large number of extensions to Haskell's
+ type system. Specifically:</para>
+
+ <variablelist>
+ <varlistentry>
+ <term>Multi-parameter type classes:</term>
+ <listitem>
+ <para><xref LinkEnd="multi-param-type-classes"></para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term>Functional dependencies:</term>
+ <listitem>
+ <para><xref LinkEnd="functional-dependencies"></para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term>Implicit parameters:</term>
+ <listitem>
+ <para><xref LinkEnd="implicit-parameters"></para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term>Local universal quantification:</term>
+ <listitem>
+ <para><xref LinkEnd="universal-quantification"></para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term>Extistentially quantification in data types:</term>
+ <listitem>
+ <para><xref LinkEnd="existential-quantification"></para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term>Scoped type variables:</term>
+ <listitem>
+ <para>Scoped type variables enable the programmer to
+ supply type signatures for some nested declarations,
+ where this would not be legal in Haskell 98. Details in
+ <xref LinkEnd="scoped-type-variables">.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
+ </listitem>
+ </varlistentry>
-<ProgramListing>
-type Char#
-type Int#
-type Word#
-type Addr#
-type Float#
-type Double#
-type Int64#
-type Word64#
-</ProgramListing>
+ <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>
-<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>
+ <varlistentry>
+ <term>Parallel list comprehensions</term>
+ <listitem>
+ <para>An extension to the list comprehension syntax to support
+ <literal>zipWith</literal>-like functionality. See <xref
+ linkend="parallel-list-comprehensions">.</para>
+ </listitem>
+ </varlistentry>
-<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>
+ <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>
-<Para>
-Literals for these types may be written as follows:
-</Para>
+ <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>
-<Para>
+ <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>
-<ProgramListing>
-1# an Int#
-1.2# a Float#
-1.34## a Double#
-'a'# a Char#; for weird characters, use e.g. '\o<octal>'#
-"a"# an Addr# (a `char *'); only characters '\0'..'\255' allowed
-</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>
+ <varlistentry>
+ <term>Generic classes:</term>
+ <listitem>
+ <para>Generic class declarations allow you to define a class
+ whose methods say how to work over an arbitrary data type.
+ Then it's really easy to make any new type into an instance of
+ the class. This generalises the rather ad-hoc "deriving"
+ feature of Haskell 98. Details in <xref
+ LinkEnd="generic-classes">.</para>
+ </listitem>
+ </varlistentry>
+ </variablelist>
-<Para>
-<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>
+<para>
+Before you get too carried away working at the lowest level (e.g.,
+sloshing <literal>MutableByteArray#</literal>s around your
+program), you may wish to check if there are libraries that provide a
+“Haskellised veneer” over the features you want. See
+<xref linkend="book-hslibs">.
+</para>
-</Sect2>
-
-<Sect2>
-<Title>Synchronizing variables (M-vars)</Title>
+ <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>-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>-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>-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, all
+ 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> With one group of exceptions! You may want to
+ define your own numeric class hierarchy. It completely
+ defeats that purpose if the literal "1" means
+ "<literal>Prelude.fromInteger 1</literal>", which is what
+ the Haskell Report specifies. So the
+ <option>-fno-implicit-prelude</option> flag causes the
+ following pieces of built-in syntax to refer to <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>
+ </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>
+ </itemizedlist>
+
+ <para>Note: Negative literals, such as <literal>-3</literal>, are
+ specified by (a careful reading of) the Haskell Report as
+ meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
+ However, GHC deviates from this slightly, and treats them as meaning
+ <literal>fromInteger (-3)</literal>. One particular effect of this
+ slightly-non-standard reading is that there is no difficulty with
+ the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
+ it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
+ would be <literal>negate (fromInteger 2147483648)</literal>,
+ and the call to <literal>fromInteger</literal> would overflow
+ (at type <literal>Int</literal>, remember).
+ </para>
-<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>
+ </listitem>
+ </varlistentry>
-</Sect2>
+ </variablelist>
+ </sect1>
-</Sect1>
+<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
+&primitives;
-<Sect1 id="glasgow-ST-monad">
-<Title>Primitive state-transformer monad
-</Title>
+<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>
+<indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
+<indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
+</para>
-<Para>
+<para>
This monad underlies our implementation of arrays, mutable and
immutable, and our implementation of I/O, including “C calls”.
-</Para>
+</para>
-<Para>
-The <Literal>ST</Literal> library, which provides access to the
-<Function>ST</Function> monad, is described in <xref
+<para>
+The <literal>ST</literal> library, which provides access to the
+<function>ST</function> monad, is described in <xref
linkend="sec-ST">.
-</Para>
+</para>
-</Sect1>
+</sect1>
-<Sect1 id="glasgow-prim-arrays">
-<Title>Primitive arrays, mutable and otherwise
-</Title>
+<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>
+<indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
+<indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
+</para>
-<Para>
+<para>
GHC knows about quite a few flavours of Large Swathes of Bytes.
-</Para>
+</para>
-<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>
+objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
+<literal>ByteArray#</literal>).
+</para>
-<Para>
+<para>
Second, it distinguishes between…
-<VariableList>
+<variablelist>
-<VarListEntry>
-<Term>Immutable:</Term>
-<ListItem>
-<Para>
+<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>
+</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
+<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>
+</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
+<emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
pointer “stable,” so that the garbage collector won't forget that it
exists. That is, GHC provides a safe way to pass Haskell pointers to
C.
-</Para>
-
-<Para>
-Please see <XRef LinkEnd="sec-stable-pointers"> for more details.
-</Para>
-</ListItem>
-</VarListEntry>
-<VarListEntry>
-<Term>“Foreign objects”:</Term>
-<ListItem>
-<Para>
+</para>
+
+<para>
+Please see <xref LinkEnd="sec-stable-pointers"> for more details.
+</para>
+</listitem>
+</varlistentry>
+<varlistentry>
+<term>“Foreign objects”:</term>
+<listitem>
+<para>
A “foreign object” is a safe way to pass an external object (a
C-allocated pointer, say) to Haskell and have Haskell do the Right
Thing when it no longer references the object. So, for example, C
could pass a large bitmap over to Haskell and say “please free this
memory when you're done with it.”
-</Para>
+</para>
-<Para>
-Please see <XRef LinkEnd="sec-ForeignObj"> for more details.
-</Para>
-</ListItem>
-</VarListEntry>
-</VariableList>
-</Para>
+<para>
+Please see <xref LinkEnd="sec-ForeignObj"> for more details.
+</para>
+</listitem>
+</varlistentry>
+</variablelist>
+</para>
-<Para>
+<para>
The libraries documentatation gives more details on all these
“primitive array” types and the operations on them.
-</Para>
+</para>
-</Sect1>
+</sect1>
-<Sect1 id="pattern-guards">
-<Title>Pattern guards</Title>
+<sect1 id="pattern-guards">
+<title>Pattern guards</title>
-<Para>
-<IndexTerm><Primary>Pattern guards (Glasgow extension)</Primary></IndexTerm>
+<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>
+</para>
+</sect1>
+
+ <sect1 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>
+
+ </sect1>
<sect1 id="sec-ffi">
<title>The foreign interface</title>
<para>The following sections also give some hints and tips on the use
of the foreign function interface in GHC.</para>
-<Sect2 id="glasgow-foreign-headers">
-<Title>Using function headers
-</Title>
+<sect2 id="glasgow-foreign-headers">
+<title>Using function headers
+</title>
-<Para>
-<IndexTerm><Primary>C calls, function headers</Primary></IndexTerm>
-</Para>
+<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
+<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>
+to provide <filename>.h</filename> files containing function headers.
+</para>
-<Para>
+<para>
For example,
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
#include "HsFFI.h"
void initialiseEFS (HsInt size);
HsForeignObj emptyEFS(void);
HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
HsInt lookupEFS (HsForeignObj a, HsInt i);
-</ProgramListing>
-</Para>
+</programlisting>
+</para>
<para>The types <literal>HsInt</literal>,
<literal>HsForeignObj</literal> etc. are described in <xref
- linkend="sec-mapping-table">.</Para>
+ linkend="sec-mapping-table">.</para>
- <Para>Note that this approach is only
- <Emphasis>essential</Emphasis> for returning
- <Literal>float</Literal>s (or if <Literal>sizeof(int) !=
- sizeof(int *)</Literal> on your architecture) but is a Good
+ <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>
+ crazy not to do it.</para>
-</Sect2>
+</sect2>
-</Sect1>
+</sect1>
-<Sect1 id="multi-param-type-classes">
-<Title>Multi-parameter type classes
-</Title>
+<sect1 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>
-<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>
-<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>
+</para>
-<Sect2>
-<Title>Types</Title>
+<sect2>
+<title>Types</title>
-<Para>
+<para>
There are the following restrictions on the form of a qualified
type:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
forall tv1..tvn (c1, ...,cn) => type
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
(Here, I write the "foralls" explicitly, although the Haskell source
language omits them; in Haskell 1.4, all the free type variables of an
explicit source-language type signature are universally quantified,
except for the class type variables in a class declaration. However,
-in GHC, you can give the foralls if you want. See <XRef LinkEnd="universal-quantification">).
-</Para>
+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 mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
The reason for this is that a value with a type that does not obey
this restriction could not be used without introducing
ambiguity. Here, for example, is an illegal type:
-<ProgramListing>
+<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>
+<para>
These restrictions apply to all types, whether declared in a type signature
or inferred.
-</Para>
+</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>
+</sect2>
-<Sect2>
-<Title>Class declarations</Title>
+<sect2>
+<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>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
- <Emphasis>In the signature of a class operation, every constraint
+<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>.
+variable</emphasis>.
Thus:
-<ProgramListing>
+<programlisting>
class Collection c a where
mapC :: Collection c b => (a->b) -> c a -> c b
-</ProgramListing>
+</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:
+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>
+<programlisting>
class C a where
op :: Eq a => (a,b) -> (a,b)
-</ProgramListing>
+</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
+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>
+<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>
-<ListItem>
+</para>
+</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>The type of each class operation must mention <emphasis>all</emphasis> of
+the class type variables</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>
+</sect2>
-<Sect2>
-<Title>Instance declarations</Title>
+<sect2 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
+<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
+option</primary></indexterm> then two overlapping instance declarations are permitted
iff
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
- EITHER <Literal>type1</Literal> and <Literal>type2</Literal> do not unify
-</Para>
-</ListItem>
-<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 <literal>type2</literal> is a substitution instance of <literal>type1</literal>
+(but not identical to <literal>type1</literal>)
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
OR vice versa
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</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>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
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>
+</programlisting>
The "at least one not a type variable" restriction is to ensure that
loop if it wasn't excluded:
-<ProgramListing>
+<programlisting>
instance C a => C a where ...
-</ProgramListing>
+</programlisting>
There are two situations in which the rule is a bit of a pain. First,
something more specific does not:
-<ProgramListing>
+<programlisting>
instance C a where
op = ... -- Default
-</ProgramListing>
+</programlisting>
Second, sometimes you might want to use the following to get the
effect of a "class synonym":
-<ProgramListing>
+<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>
+<programlisting>
f :: C a => ...
-</ProgramListing>
+</programlisting>
instead of
-<ProgramListing>
+<programlisting>
f :: (C1 a, C2 a, C3 a) => ...
-</ProgramListing>
+</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
+<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>
+</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
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
+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>.
+with <option>-fcontext-stack</option><emphasis>N</emphasis>.
-</Para>
-</ListItem>
+</para>
+</listitem>
</OrderedList>
-</Para>
+</para>
+
+</sect2>
+
+</sect1>
+
+<sect1 id="implicit-parameters">
+<title>Implicit parameters
+</title>
+
+<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>
-</Sect2>
+<para>
+There should be more documentation, but there isn't (yet). Yell if you need it.
+</para>
+<itemizedlist>
+<listitem>
+<para> You can't have an implicit parameter in the context of a class or instance
+declaration. For example, both these declarations are illegal:
+<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>
+</listitem>
+
+</itemizedlist>
+
+</sect1>
+
+
+<sect1 id="functional-dependencies">
+<title>Functional dependencies
+</title>
+
+<para> Functional dependencies are implemented as described by Mark Jones
+in "Type Classes with Functional Dependencies", Mark P. Jones,
+In Proceedings of the 9th European Symposium on Programming,
+ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
+</para>
-</Sect1>
+<para>
+There should be more documentation, but there isn't (yet). Yell if you need it.
+</para>
+</sect1>
-<Sect1 id="universal-quantification">
-<Title>Explicit universal quantification
-</Title>
-<Para>
-GHC now allows you to write explicitly quantified types. GHC's
-syntax for this now agrees with Hugs's, namely:
-</Para>
+<sect1 id="universal-quantification">
+<title>Explicit universal quantification
+</title>
-<Para>
+<para>
+GHC's type system supports explicit universal quantification in
+constructor fields and function arguments. This is useful for things
+like defining <literal>runST</literal> from the state-thread world.
+GHC's syntax for this now agrees with Hugs's, namely:
+</para>
-<ProgramListing>
+<para>
+
+<programlisting>
forall a b. (Ord a, Eq b) => a -> b -> a
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-The context is, of course, optional. You can't use <Literal>forall</Literal> as
+<para>
+The context is, of course, optional. You can't use <literal>forall</literal> as
a type variable any more!
-</Para>
+</para>
-<Para>
-Haskell type signatures are implicitly quantified. The <Literal>forall</Literal>
+<para>
+Haskell type signatures are implicitly quantified. The <literal>forall</literal>
allows us to say exactly what this means. For example:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
g :: b -> b
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
means this:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
g :: forall b. (b -> b)
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
The two are treated identically.
-</Para>
+</para>
-<Sect2 id="univ">
-<Title>Universally-quantified data type fields
-</Title>
+<sect2 id="univ">
+<title>Universally-quantified data type fields
+</title>
-<Para>
-In a <Literal>data</Literal> or <Literal>newtype</Literal> declaration one can quantify
+<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>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
data T a = T1 (forall b. b -> b -> b) a
data MonadT m = MkMonad { return :: forall a. a -> m a,
}
newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-The constructors now have so-called <Emphasis>rank 2</Emphasis> polymorphic
+<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>
+</para>
-<Para>
+<para>
-<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>
+</programlisting>
-</Para>
+</para>
-<Para>
-Notice that you don't need to use a <Literal>forall</Literal> if there's an
+<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>
+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>
-<Para>
+<para>
As for type signatures, implicit quantification happens for non-overloaded
types too. So if you write this:
-<ProgramListing>
+<programlisting>
data T a = MkT (Either a b) (b -> b)
-</ProgramListing>
+</programlisting>
it's just as if you had written this:
-<ProgramListing>
+<programlisting>
data T a = MkT (forall b. Either a b) (forall b. b -> b)
-</ProgramListing>
+</programlisting>
-That is, since the type variable <Literal>b</Literal> isn't in scope, it's
+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
+to <emphasis>require</emphasis> explicit quantification on constructor arguments
where that is what is wanted. Feedback welcomed.)
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Construction </Title>
+<sect2>
+<title>Construction </title>
-<Para>
-You construct values of types <Literal>T1, MonadT, Swizzle</Literal> by applying
+<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>
+<para>
-<ProgramListing>
+<programlisting>
(T1 (\xy->x) 3) :: T Int
(MkSwizzle sort) :: Swizzle
Nothing -> Nothing
in
MkMonad r b) :: MonadT Maybe
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<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>
+required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
+does not need the <literal>Ord</literal> constraint.)
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Pattern matching</Title>
+<sect2>
+<title>Pattern matching</title>
-<Para>
+<para>
When you use pattern matching, the bound variables may now have
polymorphic types. For example:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
f :: T a -> a -> (a, Char)
f (T1 f k) x = (f k x, f 'c' 'd')
h m (x:xs) = bind m x $ \y ->
bind m (h m xs) $ \ys ->
return m (y:ys)
-</ProgramListing>
+</programlisting>
-</Para>
+</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
+<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>
-<Para>
+<para>
You cannot pattern-match against an argument that is polymorphic.
For example:
-<ProgramListing>
+<programlisting>
newtype TIM s a = TIM (ST s (Maybe a))
runTIM :: (forall s. TIM s a) -> Maybe a
runTIM (TIM m) = runST m
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<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
+an argument of type <literal>(forall s. TIM s a)</literal>. Instead you
must bind the variable and pattern match in the right hand side:
-<ProgramListing>
+<programlisting>
runTIM :: (forall s. TIM s a) -> Maybe a
runTIM tm = case tm of { TIM m -> runST m }
-</ProgramListing>
+</programlisting>
-The <Literal>tm</Literal> on the right hand side is (invisibly) instantiated, like
+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>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>The partial-application restriction</Title>
+<sect2>
+<title>The partial-application restriction</title>
-<Para>
+<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>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
map MkSwizzle [sort, reverse]
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-The restriction is this: <Emphasis>every subexpression of the program must
+<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>
+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
+<para>
+In the illegal example, the sub-expression <literal>MkSwizzle</literal> has the
+polymorphic type <literal>(Ord b => [b] -> [b]) -> Swizzle</literal> and is not
a sub-expression of an enclosing application. On the other hand, this
expression is OK:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
map (T1 (\a b -> a)) [1,2,3]
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-even though it involves a partial application of <Function>T1</Function>, because
-the sub-expression <Literal>T1 (\a b -> a)</Literal> has type <Literal>Int -> T
-Int</Literal>.
-</Para>
+<para>
+even though it involves a partial application of <function>T1</function>, because
+the sub-expression <literal>T1 (\a b -> a)</literal> has type <literal>Int -> T
+Int</literal>.
+</para>
-</Sect2>
+</sect2>
-<Sect2 id="sigs">
-<Title>Type signatures
-</Title>
+<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>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
mkTs f x y = [T1 f x, T1 f y]
-</ProgramListing>
+</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
+<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>
-<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
+type signature for <emphasis>ordinary</emphasis> functions (not only data
constructors), thus:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
mkTs :: (forall b. b -> b -> b) -> a -> [T a]
mkTs f x y = [T1 f x, T1 f y]
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-This type signature tells the compiler to attribute <Literal>f</Literal> with
-the polymorphic type <Literal>(forall b. b -> b -> b)</Literal> when type
-checking the body of <Function>mkTs</Function>, so now the application of
-<Function>T1</Function> is fine.
-</Para>
+<para>
+This type signature tells the compiler to attribute <literal>f</literal> with
+the polymorphic type <literal>(forall b. b -> b -> b)</literal> when type
+checking the body of <function>mkTs</function>, so now the application of
+<function>T1</function> is fine.
+</para>
-<Para>
+<para>
There are two restrictions:
-</Para>
+</para>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
You can only define a rank 2 type, specified by the following
grammar:
-<ProgramListing>
+<programlisting>
rank2type ::= [forall tyvars .] [context =>] funty
funty ::= ([forall tyvars .] [context =>] ty) -> funty
| ty
ty ::= ...current Haskell monotype syntax...
-</ProgramListing>
+</programlisting>
Informally, the universal quantification must all be right at the beginning,
or at the top level of a function argument.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<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:
+matched on the left hand side of the "<literal>=</literal>" sign. You can't
+define <function>mkTs</function> like this:
-<ProgramListing>
+<programlisting>
mkTs :: (forall b. b -> b -> b) -> a -> [T a]
mkTs = \ f x y -> [T1 f x, T1 f y]
-</ProgramListing>
+</programlisting>
The same partial-application rule applies to ordinary functions with
rank-2 types as applied to data constructors.
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2 id="hoist">
-<Title>Type synonyms and hoisting
-</Title>
+<sect2 id="hoist">
+<title>Type synonyms and hoisting
+</title>
-<Para>
-GHC also allows you to write a <Literal>forall</Literal> in a type synonym, thus:
-<ProgramListing>
+<para>
+GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
+<programlisting>
type Discard a = forall b. a -> b -> a
f :: Discard a
f x y = x
-</ProgramListing>
+</programlisting>
However, it is often convenient to use these sort of 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 a. <emphasis>type2</emphasis>
==>
- forall a. <Emphasis>type1</Emphasis> -> <Emphasis>type2</Emphasis>
-</ProgramListing>
+ forall a. <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>
+</sect2>
-</Sect1>
+</sect1>
-<Sect1 id="existential-quantification">
-<Title>Existentially quantified data constructors
-</Title>
+<sect1 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>
+<sect2 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>
+</sect2>
-<Sect2>
-<Title>Type classes</Title>
+<sect2>
+<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>
+</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>
+</sect2>
-<Sect2>
-<Title>Restrictions</Title>
+<sect2>
+<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>
You can only pattern-match
-on an existentially-quantified constructor in a <Literal>case</Literal> expression or
+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>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-</Sect1>
+</sect1>
-<Sect1 id="sec-assertions">
-<Title>Assertions
-<IndexTerm><Primary>Assertions</Primary></IndexTerm>
-</Title>
+<sect1 id="sec-assertions">
+<title>Assertions
+<indexterm><primary>Assertions</primary></indexterm>
+</title>
-<Para>
+<para>
If you want to make use of assertions in your standard Haskell code, you
could define a function like the following:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
assert :: Bool -> a -> a
assert False x = error "assertion failed!"
assert _ x = x
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<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
+<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>
+the source location where <function>assert</function> was used.
+</para>
-<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>
+use of <function>assert</function> in the user's source:
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
kelvinToC :: Double -> Double
kelvinToC k = assert (k >= 0.0) (k+273.15)
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
Ghc will rewrite this to also include the source location where the
assertion was made,
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
assert pred val ==> assertError "Main.hs|15" pred val
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
+<para>
The rewrite is only performed by the compiler when it spots
-applications of <Function>Exception.assert</Function>, so you can still define and
-use your own versions of <Function>assert</Function>, should you so wish. If not,
-import <Literal>Exception</Literal> to make use <Function>assert</Function> in your code.
-</Para>
+applications of <function>Exception.assert</function>, so you can still define and
+use your own versions of <function>assert</function>, should you so wish. If not,
+import <literal>Exception</literal> to make use <function>assert</function> in your code.
+</para>
-<Para>
+<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>
+<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>
+</para>
-</Sect1>
+</sect1>
-<Sect1 id="scoped-type-variables">
-<Title>Scoped Type Variables
-</Title>
+<sect1 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>
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>
-<Sect2>
-<Title>Scope and implicit quantification</Title>
+<sect2>
+<title>Scope and implicit quantification</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<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>.
+the <emphasis>type variables bound by the equation</emphasis>.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
The type variables thus brought into scope may be mentioned
in ordinary type signatures or pattern type signatures anywhere within
their scope.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<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>
-<ListItem>
+</para>
+</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>
+<para>
There is no implicit universal quantification on pattern type
-signatures, nor may one write an explicit <Literal>forall</Literal> type in a pattern
+signatures, nor may one write an explicit <literal>forall</literal> type in a pattern
type signature. The pattern type signature is a monotype.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<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:
+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>
+</sect2>
-<Sect2>
-<Title>Polymorphism</Title>
+<sect2>
+<title>Polymorphism</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<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>
+<programlisting>
f :: [a] -> [a]
f (xs::[b]) = reverse xs
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
The function must be polymorphic in the type variables
bound by all its equations. Operationally, the type variables bound
by one equation must not:
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
- Be unified with a type (such as <Literal>Int</Literal>, or <Literal>[a]</Literal>).
-</Para>
-</ListItem>
-<ListItem>
+<para>
+ Be unified with a type (such as <literal>Int</literal>, or <literal>[a]</literal>).
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
Be unified with a type variable free in the environment.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<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>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
For example, the following all fail to type check:
-<ProgramListing>
+<programlisting>
f (x::a) (y::b) = [x,y] -- a unifies with b
g (x::a) = x + 1::Int -- a unifies with Int
w :: [b] -> [b]
w (x::a) = x -- a unifies with [b]
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
The pattern-bound type variable may, however, be constrained
by the context of the principal type, thus:
-<ProgramListing>
+<programlisting>
f (x::a) (y::a) = x+y*2
-</ProgramListing>
+</programlisting>
-gets the inferred type: <Literal>forall a. Num a => a -> a -> a</Literal>.
-</Para>
-</ListItem>
+gets the inferred type: <literal>forall a. Num a => a -> a -> a</literal>.
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Result type signatures</Title>
+<sect2>
+<title>Result type signatures</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<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>
+</programlisting>
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-<Para>
+<para>
Result type signatures are not yet implemented in Hugs.
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Pattern signatures on other constructs</Title>
+<sect2>
+<title>Pattern signatures on other constructs</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
A pattern type signature can be on an arbitrary sub-pattern, not
just on a variable:
-<ProgramListing>
+<programlisting>
f ((x,y)::(a,b)) = (y,x) :: (b,a)
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
Pattern type signatures, including the result part, can be used
in lambda abstractions:
-<ProgramListing>
+<programlisting>
(\ (x::a, y) :: a -> x)
-</ProgramListing>
+</programlisting>
Type variables bound by these patterns must be polymorphic in
For example:
-<ProgramListing>
+<programlisting>
f1 (x::c) = f1 x -- ok
f2 = \(x::c) -> f2 x -- not ok
-</ProgramListing>
+</programlisting>
-Here, <Function>f1</Function> is OK, but <Function>f2</Function> is not, because <VarName>c</VarName> gets unified
+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
+case, the type of <function>f2</function>, which is in the environment when
the lambda abstraction is checked.
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
Pattern type signatures, including the result part, can be used
-in <Literal>case</Literal> expressions:
+in <literal>case</literal> expressions:
-<ProgramListing>
+<programlisting>
case e of { (x::a, y) :: a -> x }
-</ProgramListing>
+</programlisting>
The pattern-bound type variables must, as usual,
Thus this is OK:
-<ProgramListing>
+<programlisting>
case (True,False) of { (x::a, y) -> x }
-</ProgramListing>
+</programlisting>
Even though the context is that of a pair of booleans,
also OK to say:
-<ProgramListing>
+<programlisting>
case (True,False) of { (x::Bool, y) -> x }
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</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
+<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:
-<ProgramListing>
+<programlisting>
\ x :: a -> b -> x
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
-<ListItem>
+</para>
+</listitem>
+<listitem>
-<Para>
+<para>
Pattern type signatures that bind new type variables
may not be used in pattern bindings at all.
So this is illegal:
-<ProgramListing>
+<programlisting>
f x = let (y, z::a) = x in ...
-</ProgramListing>
+</programlisting>
But these are OK, because they do not bind fresh type variables:
-<ProgramListing>
+<programlisting>
f1 x = let (y, z::Int) = x in ...
f2 (x::(Int,a)) = let (y, z::a) = x in ...
-</ProgramListing>
+</programlisting>
However a single variable is considered a degenerate function binding,
though it binds a type variable:
-<ProgramListing>
+<programlisting>
f :: (b->b) = \(x::b) -> x
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
Such degnerate function bindings do not fall under the monomorphism
restriction. Thus:
-</Para>
+</para>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
g :: a -> a -> Bool = \x y. x==y
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-Here <Function>g</Function> has type <Literal>forall a. Eq a => a -> a -> Bool</Literal>, just as if
-<Function>g</Function> had a separate type signature. Lacking a type signature, <Function>g</Function>
+<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>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>Existentials</Title>
+<sect2>
+<title>Existentials</title>
-<Para>
+<para>
-<ItemizedList>
-<ListItem>
+<itemizedlist>
+<listitem>
-<Para>
+<para>
Pattern type signatures can bind existential type variables.
For example:
-<ProgramListing>
+<programlisting>
data T = forall a. MkT [a]
f :: T -> T
f (MkT [t::a]) = MkT t3
where
t3::[a] = [t,t,t]
-</ProgramListing>
+</programlisting>
-</Para>
-</ListItem>
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-</Sect1>
+</sect1>
-<Sect1 id="pragmas">
-<Title>Pragmas
-</Title>
+<sect1 id="pragmas">
+<title>Pragmas
+</title>
-<Para>
+<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
+<sect2 id="inline-pragma">
+<title>INLINE pragma
-<IndexTerm><Primary>INLINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, INLINE</Primary></IndexTerm></Title>
+<indexterm><primary>INLINE pragma</primary></indexterm>
+<indexterm><primary>pragma, INLINE</primary></indexterm></title>
-<Para>
-GHC (with <Option>-O</Option>, as always) tries to inline (or “unfold”)
+<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>
+<para>
You will probably see these unfoldings (in Core syntax) in your
interface files.
-</Para>
+</para>
-<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>
-<Para>
+<para>
The sledgehammer you can bring to bear is the
-<Literal>INLINE</Literal><IndexTerm><Primary>INLINE pragma</Primary></IndexTerm> pragma, used thusly:
+<literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
-<ProgramListing>
+<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>
+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
+<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>
-<Para>
-An <Literal>INLINE</Literal> pragma for a function can be put anywhere its type
+<para>
+An <literal>INLINE</literal> pragma for a function can be put anywhere its type
signature could be put.
-</Para>
+</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:
-<ProgramListing>
+<programlisting>
#ifdef __GLASGOW_HASKELL__
{-# INLINE thenUs #-}
{-# INLINE returnUs #-}
#endif
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2 id="noinline-pragma">
-<Title>NOINLINE pragma
-</Title>
+<sect2 id="noinline-pragma">
+<title>NOINLINE pragma
+</title>
-<Para>
-<IndexTerm><Primary>NOINLINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, NOINLINE</Primary></IndexTerm>
-</Para>
+<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
+<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>
+</para>
-<Sect2 id="specialize-pragma">
-<Title>SPECIALIZE pragma
-</Title>
+</sect2>
-<Para>
-<IndexTerm><Primary>SPECIALIZE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, SPECIALIZE</Primary></IndexTerm>
-<IndexTerm><Primary>overloading, death to</Primary></IndexTerm>
-</Para>
+ <sect2 id="specialize-pragma">
+ <title>SPECIALIZE pragma</title>
-<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>
+ <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>
-<ProgramListing>
+<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>To get very fancy, you can also specify a named function
+ to use for the specialised value, as in:</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:
+<programlisting>
+{-# RULES hammeredLookup = blah #-}
+</programlisting>
-<ProgramListing>
-{-# SPECIALIZE hammeredLookup :: ...as before... = blah #-}
-</ProgramListing>
+ <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>
-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 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>
-NOTE: the <Literal>=blah</Literal> feature isn't implemented in GHC 4.xx.
-</Para>
+ <para>An example in which using <literal>RULES</literal> for
+ specialisation will Win Big:
-<Para>
-An example in which the <Literal>= blah</Literal> form will Win Big:
-
-<ProgramListing>
+<programlisting>
toDouble :: Real a => a -> Double
toDouble = fromRational . toRational
{-# SPECIALIZE toDouble :: Int -> Double = 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>
+ <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>
+<programlisting>
instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
{-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
-</ProgramListing>
+</programlisting>
Compatible with HBC, by the way.
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2 id="line-pragma">
-<Title>LINE pragma
-</Title>
+<sect2 id="line-pragma">
+<title>LINE pragma
+</title>
-<Para>
-<IndexTerm><Primary>LINE pragma</Primary></IndexTerm>
-<IndexTerm><Primary>pragma, LINE</Primary></IndexTerm>
-</Para>
+<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
+<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>
-<Para>
+<para>
-<ProgramListing>
+<programlisting>
{-# LINE 42 "Foo.vhs" #-}
-</ProgramListing>
+</programlisting>
-</Para>
+</para>
-<Para>
-if you'd generated the current file from something called <Filename>Foo.vhs</Filename>
+<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>
+its error messages to refer to the line/file named in the <literal>LINE</literal>
pragma.
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2>
-<Title>RULES pragma</Title>
+<sect2 id="rules">
+<title>RULES pragma</title>
-<Para>
+<para>
The RULES pragma lets you specify rewrite rules. It is described in
-<XRef LinkEnd="rewrite-rules">.
-</Para>
+<xref LinkEnd="rewrite-rules">.
+</para>
-</Sect2>
+</sect2>
-</Sect1>
+</sect1>
-<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>
+<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>
+ 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
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>"wrong2"</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>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>PrelBase.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>ghc/lib/std/PrelBase.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>PrelList.lhs</filename>.
+</para>
+</listitem>
-</ItemizedList>
+</itemizedlist>
-</Para>
+</para>
-</Sect2>
+</sect2>
-</Sect1>
+</sect1>
-<Sect1 id="generic-classes">
-<Title>Generic classes</Title>
+<sect1 id="generic-classes">
+<title>Generic classes</title>
-<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>
+</para>
+
+<programlisting>
+ import Generics
-<ProgramListing>
class Bin a where
toBin :: a -> [Int]
fromBin :: [Int] -> (a, [Int])
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>
+</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:
-</Para>
-<ProgramListing>
+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>
+</programlisting>
+<para>
Now you can make a data type into an instance of Bin like this:
-<ProgramListing>
+<programlisting>
instance (Bin a, Bin b) => Bin (a,b)
instance Bin a => Bin [a]
-</ProgramListing>
+</programlisting>
That is, just leave off the "where" clasuse. Of course, you can put in the
where clause and over-ride whichever methods you please.
+</para>
-
-<Sect2> <Title> Changes wrt the paper </Title>
-<Para>
-Note that the type constructors <Literal>:+:</Literal> and <Literal>:*:</Literal>
+ <sect2>
+ <title> Using generics </title>
+ <para>To use generics you need to</para>
+ <itemizedlist>
+ <listitem>
+ <para>Use the <option>-fgenerics</option> flag.</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
+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>
+</para>
+</sect2>
-<Sect2> <Title>Terminology and restrictions</Title>
-<Para>
+<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>
+
+<para>
Restrictions:
-<ItemizedList>
-<ListItem> Alas, we do not yet implement the stuff about constructor names and
+<itemizedlist>
+<listitem>
+<para>
+Alas, we do not yet implement the stuff about constructor names and
field labels.
-</ListItem>
+</para>
+</listitem>
-<ListItem> A generic class can have only one parameter; you can't have a generic
+<listitem>
+<para>
+A generic class can have only one parameter; you can't have a generic
multi-parameter class.
-</ListItem>
+</para>
+</listitem>
-<ListItem> A default method must be defined entirely using type patterns, or entirely
+<listitem>
+<para>
+A default method must be defined entirely using type patterns, or entirely
without. So this is illegal:
-<ProgramListing>
+<programlisting>
class Foo a where
op :: a -> (a, Bool)
op {| Unit |} Unit = (Unit, True)
op x = (x, False)
-</ProgramListing>
+</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.
-</ListItem>
+</para>
+</listitem>
-<ListItem> 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>
+<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>
+</programlisting>
+</para>
+</listitem>
-<ListItem> The type patterns in a generic default method must take one of the forms:
-<ProgramListing>
+<listitem>
+<para>
+The type patterns in a generic default method must take one of the forms:
+<programlisting>
a :+: b
a :*: b
Unit
-</ProgramListing>
+</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
+a single type constructor (<literal>:*:</literal>, say) must be identical; they
must use the same type variables. So this is illegal:
-<ProgramListing>
+<programlisting>
class Foo a where
op :: a -> Bool
op {| a :+: b |} (Inl x) = True
op {| p :+: q |} (Inr y) = False
-</ProgramListing>
+</programlisting>
The type patterns must be identical, even in equations for different methods of the class.
So this too is illegal:
-<ProgramListing>
+<programlisting>
class Foo a where
op1 :: a -> Bool
op {| a :*: b |} (Inl x) = True
op2 :: a -> Bool
op {| p :*: q |} (Inr y) = False
-</ProgramListing>
+</programlisting>
(The reason for this restriction is that we gather all the equations for a particular type consructor
into a single generic instance declaration.)
-</ListItem>
-
-<ListItem> A generic method declaration must give a case for each of the three type constructors.
-</ListItem>
+</para>
+</listitem>
-<ListItem> In an instance declaration for a generic class, the idea is that the compiler
+<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> The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
- </ListItem>
- <ListItem> No constructor of the instance type has unboxed fields. </ListItem>
- </ItemizedList>
+ <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>
-</ListItem>
+</itemizedlist>
+</para>
-</ItemizedList>
-<Para>
-The option <Option>-ddump-deriv</Option> dumps incomprehensible stuff giving details of
+<para>
+The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
what the compiler does with generic declarations.
-</Para>
+</para>
-</Sect2>
+</sect2>
-<Sect2> <Title> Another example </Title>
-<Para>
+<sect2> <title> Another example </title>
+<para>
Just to finish with, here's another example I rather like:
-<ProgramListing>
+<programlisting>
class Tag a where
nCons :: a -> Int
nCons {| Unit |} _ = 1
tag {| a :*: b |} _ = 1
tag {| a :+: b |} (Inl x) = tag x
tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
-</ProgramListing>
-</Sect2>
-</Sect1>
+</programlisting>
+</para>
+</sect2>
+</sect1>
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