</varlistentry>
<varlistentry>
- <term><option>-fwith</option>:</term>
- <indexterm><primary><option>-fwith</option></primary></indexterm>
- <listitem>
- <para>This option enables the deprecated <literal>with</literal>
- keyword for implicit parameters; it is merely provided for backwards
- compatibility.
- It is independent of the <option>-fglasgow-exts</option>
- flag. </para>
- </listitem>
- </varlistentry>
-
- <varlistentry>
<term><option>-fno-monomorphism-restriction</option>:</term>
<indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
<listitem>
</varlistentry>
<varlistentry>
+ <term><option>-farrows</option></term>
+ <indexterm><primary><option>-farrows</option></primary></indexterm>
+ <listitem>
+ <para>See <xref LinkEnd="arrow-notation">. Independent of
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
<term><option>-fgenerics</option></term>
<indexterm><primary><option>-fgenerics</option></primary></indexterm>
<listitem>
</listitem>
</varlistentry>
- <varlistentry>
- <term><option>-fno-implicit-prelude</option></term>
- <listitem>
- <para><indexterm><primary>-fno-implicit-prelude
- option</primary></indexterm> GHC normally imports
- <filename>Prelude.hi</filename> files for you. If you'd
- rather it didn't, then give it a
- <option>-fno-implicit-prelude</option> option. The idea
- is that you can then import a Prelude of your own. (But
- don't call it <literal>Prelude</literal>; the Haskell
- module namespace is flat, and you must not conflict with
- any Prelude module.)</para>
-
- <para>Even though you have not imported the Prelude, most of
- the built-in syntax still refers to the built-in Haskell
- Prelude types and values, as specified by the Haskell
- Report. For example, the type <literal>[Int]</literal>
- still means <literal>Prelude.[] Int</literal>; tuples
- continue to refer to the standard Prelude tuples; the
- translation for list comprehensions continues to use
- <literal>Prelude.map</literal> etc.</para>
-
- <para>However, <option>-fno-implicit-prelude</option> does
- change the handling of certain built-in syntax: see
- <xref LinkEnd="rebindable-syntax">.</para>
+ <varlistentry>
+ <term><option>-fno-implicit-prelude</option></term>
+ <listitem>
+ <para><indexterm><primary>-fno-implicit-prelude
+ option</primary></indexterm> GHC normally imports
+ <filename>Prelude.hi</filename> files for you. If you'd
+ rather it didn't, then give it a
+ <option>-fno-implicit-prelude</option> option. The idea is
+ that you can then import a Prelude of your own. (But don't
+ call it <literal>Prelude</literal>; the Haskell module
+ namespace is flat, and you must not conflict with any
+ Prelude module.)</para>
+
+ <para>Even though you have not imported the Prelude, most of
+ the built-in syntax still refers to the built-in Haskell
+ Prelude types and values, as specified by the Haskell
+ Report. For example, the type <literal>[Int]</literal>
+ still means <literal>Prelude.[] Int</literal>; tuples
+ continue to refer to the standard Prelude tuples; the
+ translation for list comprehensions continues to use
+ <literal>Prelude.map</literal> etc.</para>
+
+ <para>However, <option>-fno-implicit-prelude</option> does
+ change the handling of certain built-in syntax: see <xref
+ LinkEnd="rebindable-syntax">.</para>
+ </listitem>
+ </varlistentry>
- </listitem>
- </varlistentry>
+ <varlistentry>
+ <term><option>-fth</option></term>
+ <listitem>
+ <para>Enables Template Haskell (see <xref
+ linkend="template-haskell">). Currently also implied by
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
+
+ <varlistentry>
+ <term><option>-fimplicit-params</option></term>
+ <listitem>
+ <para>Enables implicit parameters (see <xref
+ linkend="implicit-parameters">). Currently also implied by
+ <option>-fglasgow-exts</option>.</para>
+ </listitem>
+ </varlistentry>
</variablelist>
</sect1>
<!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
<!-- included from primitives.sgml -->
-&primitives;
-
-
-<!-- TYPE SYSTEM EXTENSIONS -->
-<sect1 id="type-extensions">
-<title>Type system extensions</title>
-
-<sect2 id="nullary-types">
-<title>Data types with no constructors</title>
-
-<para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
-a data type with no constructors. For example:</para>
-
-<programlisting>
- data S -- S :: *
- data T a -- T :: * -> *
-</programlisting>
-
-<para>Syntactically, the declaration lacks the "= constrs" part. The
-type can be parameterised over types of any kind, but if the kind is
-not <literal>*</literal> then an explicit kind annotation must be used
-(see <xref linkend="sec-kinding">).</para>
-
-<para>Such data types have only one value, namely bottom.
-Nevertheless, they can be useful when defining "phantom types".</para>
-</sect2>
-
-<sect2 id="infix-tycons">
-<title>Infix type constructors</title>
+<!-- &primitives; -->
+<sect1 id="primitives">
+ <title>Unboxed types and primitive operations</title>
+
+<para>GHC is built on a raft of primitive data types and operations.
+While you really can use this stuff to write fast code,
+ we generally find it a lot less painful, and more satisfying in the
+ long run, to use higher-level language features and libraries. With
+ any luck, the code you write will be optimised to the efficient
+ unboxed version in any case. And if it isn't, we'd like to know
+ about it.</para>
+
+<para>We do not currently have good, up-to-date documentation about the
+primitives, perhaps because they are mainly intended for internal use.
+There used to be a long section about them here in the User Guide, but it
+became out of date, and wrong information is worse than none.</para>
+
+<para>The Real Truth about what primitive types there are, and what operations
+work over those types, is held in the file
+<filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
+This file is used directly to generate GHC's primitive-operation definitions, so
+it is always correct! It is also intended for processing into text.</para>
+
+<para> Indeed,
+the result of such processing is part of the description of the
+ <ulink
+ url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
+ Core language</ulink>.
+So that document is a good place to look for a type-set version.
+We would be very happy if someone wanted to volunteer to produce an SGML
+back end to the program that processes <filename>primops.txt</filename> so that
+we could include the results here in the User Guide.</para>
+
+<para>What follows here is a brief summary of some main points.</para>
+
+<sect2 id="glasgow-unboxed">
+<title>Unboxed types
+</title>
<para>
-GHC allows type constructors to be operators, and to be written infix, very much
-like expressions. More specifically:
-<itemizedlist>
-<listitem><para>
- A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
- The lexical syntax is the same as that for data constructors.
- </para></listitem>
-<listitem><para>
- Types can be written infix. For example <literal>Int :*: Bool</literal>.
- </para></listitem>
-<listitem><para>
- Back-quotes work
- as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
- <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
- </para></listitem>
-<listitem><para>
- Fixities may be declared for type constructors just as for data constructors. However,
- one cannot distinguish between the two in a fixity declaration; a fixity declaration
- sets the fixity for a data constructor and the corresponding type constructor. For example:
-<screen>
- infixl 7 T, :*:
-</screen>
- sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
- and similarly for <literal>:*:</literal>.
- <literal>Int `a` Bool</literal>.
- </para></listitem>
-<listitem><para>
- Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
- </para></listitem>
-<listitem><para>
- Data type and type-synonym declarations can be written infix. E.g.
-<screen>
- data a :*: b = Foo a b
- type a :+: b = Either a b
-</screen>
- </para></listitem>
-<listitem><para>
- The only thing that differs between operators in types and operators in expressions is that
- ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
- are not allowed in types. Reason: the uniform thing to do would be to make them type
- variables, but that's not very useful. A less uniform but more useful thing would be to
- allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
- lists. So for now we just exclude them.
- </para></listitem>
-
-</itemizedlist>
+<indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
</para>
-</sect2>
-
-<sect2 id="sec-kinding">
-<title>Explicitly-kinded quantification</title>
-<para>
-Haskell infers the kind of each type variable. Sometimes it is nice to be able
-to give the kind explicitly as (machine-checked) documentation,
-just as it is nice to give a type signature for a function. On some occasions,
-it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
-John Hughes had to define the data type:
-<Screen>
- data Set cxt a = Set [a]
- | Unused (cxt a -> ())
-</Screen>
-The only use for the <literal>Unused</literal> constructor was to force the correct
-kind for the type variable <literal>cxt</literal>.
+<para>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>
-GHC now instead allows you to specify the kind of a type variable directly, wherever
-a type variable is explicitly bound. Namely:
-<itemizedlist>
-<listitem><para><literal>data</literal> declarations:
-<Screen>
- data Set (cxt :: * -> *) a = Set [a]
-</Screen></para></listitem>
-<listitem><para><literal>type</literal> declarations:
-<Screen>
- type T (f :: * -> *) = f Int
-</Screen></para></listitem>
-<listitem><para><literal>class</literal> declarations:
-<Screen>
- class (Eq a) => C (f :: * -> *) a where ...
-</Screen></para></listitem>
-<listitem><para><literal>forall</literal>'s in type signatures:
-<Screen>
- f :: forall (cxt :: * -> *). Set cxt Int
-</Screen></para></listitem>
-</itemizedlist>
+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>
-The parentheses are required. Some of the spaces are required too, to
-separate the lexemes. If you write <literal>(f::*->*)</literal> you
-will get a parse error, because "<literal>::*->*</literal>" is a
-single lexeme in Haskell.
+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>
-As part of the same extension, you can put kind annotations in types
-as well. Thus:
-<Screen>
- f :: (Int :: *) -> Int
- g :: forall a. a -> (a :: *)
-</Screen>
-The syntax is
-<Screen>
- atype ::= '(' ctype '::' kind ')
-</Screen>
-The parentheses are required.
+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>
-</sect2>
-
-<sect2 id="class-method-types">
-<title>Class method types
-</title>
<para>
-Haskell 98 prohibits class method types to mention constraints on the
-class type variable, thus:
-<programlisting>
- class Seq s a where
- fromList :: [a] -> s a
- elem :: Eq a => a -> s a -> Bool
-</programlisting>
-The type of <literal>elem</literal> is illegal in Haskell 98, because it
-contains the constraint <literal>Eq a</literal>, constrains only the
-class type variable (in this case <literal>a</literal>).
+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>
-With the <option>-fglasgow-exts</option> GHC lifts this restriction.
+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="multi-param-type-classes">
-<title>Multi-parameter type classes
+<sect2 id="unboxed-tuples">
+<title>Unboxed Tuples
</title>
<para>
-This section documents GHC's implementation of multi-parameter type
-classes. There's lots of background in the paper <ULink
-URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
-classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
-Jones, Erik Meijer).
+Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
+they're available by default with <option>-fglasgow-exts</option>. An
+unboxed tuple looks like this:
</para>
<para>
-I'd like to thank people who reported shorcomings in the GHC 3.02
-implementation. Our default decisions were all conservative ones, and
-the experience of these heroic pioneers has given useful concrete
-examples to support several generalisations. (These appear below as
-design choices not implemented in 3.02.)
-</para>
-<para>
-I've discussed these notes with Mark Jones, and I believe that Hugs
-will migrate towards the same design choices as I outline here.
-Thanks to him, and to many others who have offered very useful
-feedback.
-</para>
+<programlisting>
+(# e_1, ..., e_n #)
+</programlisting>
-<sect3>
-<title>Types</title>
+</para>
<para>
-There are the following restrictions on the form of a qualified
-type:
+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>
-
-<programlisting>
- forall tv1..tvn (c1, ...,cn) => type
-</programlisting>
-
+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>
-(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">).
+There are some pretty stringent restrictions on the use of unboxed tuples:
</para>
<para>
-<OrderedList>
+<itemizedlist>
<listitem>
<para>
- <emphasis>Each universally quantified type variable
-<literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
-
-The reason for this is that a value with a type that does not obey
-this restriction could not be used without introducing
-ambiguity. Here, for example, is an illegal type:
-
-
-<programlisting>
- forall a. Eq a => Int
-</programlisting>
-
-
-When a value with this type was used, the constraint <literal>Eq tv</literal>
-would be introduced where <literal>tv</literal> is a fresh type variable, and
-(in the dictionary-translation implementation) the value would be
-applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
-can never know which instance of <literal>Eq</literal> to use because we never
-get any more information about <literal>tv</literal>.
+ 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>
- <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>:
+ 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>
- forall a. C a b => burble
+f x y = (# x+1, y-1 #)
+g x = case f x x of { (# a, b #) -> a + b }
</programlisting>
-The next type is illegal because the constraint <literal>Eq b</literal> does not
-mention <literal>a</literal>:
+but the following are invalid:
<programlisting>
- forall a. Eq b => burble
+f x y = g (# x, y #)
+g (# x, y #) = x + y
</programlisting>
-The reason for this restriction is milder than the other one. The
-excluded types are never useful or necessary (because the offending
-context doesn't need to be witnessed at this point; it can be floated
-out). Furthermore, floating them out increases sharing. Lastly,
-excluding them is a conservative choice; it leaves a patch of
-territory free in case we need it later.
-
</para>
</listitem>
-
-</OrderedList>
-
-</para>
-
-<para>
-These restrictions apply to all types, whether declared in a type signature
-or inferred.
-</para>
+<listitem>
<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>
+ No variable can have an unboxed tuple type. This is illegal:
-<para>
<programlisting>
- f :: Eq (m a) => [m a] -> [m a]
- g :: Eq [a] => ...
+f :: (# Int, Int #) -> (# Int, Int #)
+f x = x
</programlisting>
-</para>
-<para>
-This choice recovers principal types, a property that Haskell 1.4 does not have.
+because <literal>x</literal> has an unboxed tuple type.
+
</para>
+</listitem>
-</sect3>
+</itemizedlist>
-<sect3>
-<title>Class declarations</title>
+</para>
<para>
-
-<OrderedList>
-<listitem>
+Note: we may relax some of these restrictions in the future.
+</para>
<para>
- <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
+The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
+tuples to avoid unnecessary allocation during sequences of operations.
+</para>
-
-<programlisting>
- class Collection c a where
- union :: c a -> c a -> c a
- ...etc.
-</programlisting>
+</sect2>
+</sect1>
+<!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
-</para>
-</listitem>
-<listitem>
+<sect1 id="syntax-extns">
+<title>Syntactic extensions</title>
+
+ <!-- ====================== HIERARCHICAL MODULES ======================= -->
-<para>
- <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
-of "acyclic" involves only the superclass relationships. For example,
-this is OK:
+ <sect2 id="hierarchical-modules">
+ <title>Hierarchical Modules</title>
+ <para>GHC supports a small extension to the syntax of module
+ names: a module name is allowed to contain a dot
+ <literal>‘.’</literal>. This is also known as the
+ “hierarchical module namespace” extension, because
+ it extends the normally flat Haskell module namespace into a
+ more flexible hierarchy of modules.</para>
-<programlisting>
- class C a where {
- op :: D b => a -> b -> b
- }
+ <para>This extension has very little impact on the language
+ itself; modules names are <emphasis>always</emphasis> fully
+ qualified, so you can just think of the fully qualified module
+ name as <quote>the module name</quote>. In particular, this
+ means that the full module name must be given after the
+ <literal>module</literal> keyword at the beginning of the
+ module; for example, the module <literal>A.B.C</literal> must
+ begin</para>
- class C a => D a where { ... }
-</programlisting>
+<programlisting>module A.B.C</programlisting>
-Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
-class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
-would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
+ <para>It is a common strategy to use the <literal>as</literal>
+ keyword to save some typing when using qualified names with
+ hierarchical modules. For example:</para>
-</para>
-</listitem>
-<listitem>
+<programlisting>
+import qualified Control.Monad.ST.Strict as ST
+</programlisting>
-<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:
+ <para>For details on how GHC searches for source and interface
+ files in the presence of hierarchical modules, see <xref
+ linkend="search-path">.</para>
+ <para>GHC comes with a large collection of libraries arranged
+ hierarchically; see the accompanying library documentation.
+ There is an ongoing project to create and maintain a stable set
+ of <quote>core</quote> libraries used by several Haskell
+ compilers, and the libraries that GHC comes with represent the
+ current status of that project. For more details, see <ulink
+ url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
+ Libraries</ulink>.</para>
-<programlisting>
- class Functor (m k) => FiniteMap m k where
- ...
+ </sect2>
- class (Monad m, Monad (t m)) => Transform t m where
- lift :: m a -> (t m) a
-</programlisting>
+ <!-- ====================== PATTERN GUARDS ======================= -->
+<sect2 id="pattern-guards">
+<title>Pattern guards</title>
+<para>
+<indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
+The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
</para>
-</listitem>
-<listitem>
<para>
- <emphasis>In the signature of a class operation, every constraint
-must mention at least one type variable that is not a class type
-variable</emphasis>.
-
-Thus:
-
+Suppose we have an abstract data type of finite maps, with a
+lookup operation:
<programlisting>
- class Collection c a where
- mapC :: Collection c b => (a->b) -> c a -> c b
+lookup :: FiniteMap -> Int -> Maybe Int
</programlisting>
+The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
+where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
+</para>
-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>
+clunky env var1 var2 | ok1 && ok2 = val1 + val2
+| otherwise = var1 + var2
+where
+ m1 = lookup env var1
+ m2 = lookup env var2
+ ok1 = maybeToBool m1
+ ok2 = maybeToBool m2
+ val1 = expectJust m1
+ val2 = expectJust m2
+</programlisting>
+<para>
+The auxiliary functions are
+</para>
<programlisting>
- class C a where
- op :: Eq a => (a,b) -> (a,b)
-</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>
-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:
+<para>
+What is <function>clunky</function> doing? The guard <literal>ok1 &&
+ok2</literal> checks that both lookups succeed, using
+<function>maybeToBool</function> to convert the <function>Maybe</function>
+types to booleans. The (lazily evaluated) <function>expectJust</function>
+calls extract the values from the results of the lookups, and binds the
+returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
+respectively. If either lookup fails, then clunky takes the
+<literal>otherwise</literal> case and returns the sum of its arguments.
+</para>
+<para>
+This is certainly legal Haskell, but it is a tremendously verbose and
+un-obvious way to achieve the desired effect. Arguably, a more direct way
+to write clunky would be to use case expressions:
+</para>
<programlisting>
- class Eq a => C a where
- op ::(a,b) -> (a,b)
+clunky env var1 var1 = case lookup env var1 of
+ Nothing -> fail
+ Just val1 -> case lookup env var2 of
+ Nothing -> fail
+ Just val2 -> val1 + val2
+where
+ fail = val1 + val2
</programlisting>
-
-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>
+This is a bit shorter, but hardly better. Of course, we can rewrite any set
+of pattern-matching, guarded equations as case expressions; that is
+precisely what the compiler does when compiling equations! The reason that
+Haskell provides guarded equations is because they allow us to write down
+the cases we want to consider, one at a time, independently of each other.
+This structure is hidden in the case version. Two of the right-hand sides
+are really the same (<function>fail</function>), and the whole expression
+tends to become more and more indented.
</para>
-</listitem>
-<listitem>
<para>
- <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
-the class type variables</emphasis>. For example:
-
+Here is how I would write clunky:
+</para>
<programlisting>
- class Coll s a where
- empty :: s
- insert :: s -> a -> s
+clunky env var1 var1
+ | Just val1 <- lookup env var1
+ , Just val2 <- lookup env var2
+ = val1 + val2
+...other equations for clunky...
</programlisting>
+<para>
+The semantics should be clear enough. The qualifers are matched in order.
+For a <literal><-</literal> qualifier, which I call a pattern guard, the
+right hand side is evaluated and matched against the pattern on the left.
+If the match fails then the whole guard fails and the next equation is
+tried. If it succeeds, then the appropriate binding takes place, and the
+next qualifier is matched, in the augmented environment. Unlike list
+comprehensions, however, the type of the expression to the right of the
+<literal><-</literal> is the same as the type of the pattern to its
+left. The bindings introduced by pattern guards scope over all the
+remaining guard qualifiers, and over the right hand side of the equation.
+</para>
-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
-
+<para>
+Just as with list comprehensions, boolean expressions can be freely mixed
+with among the pattern guards. For example:
+</para>
<programlisting>
- class Coll s a where
- empty :: s a
- insert :: s a -> a -> s a
+f x | [y] <- x
+ , y > 3
+ , Just z <- h y
+ = ...
</programlisting>
+<para>
+Haskell's current guards therefore emerge as a special case, in which the
+qualifier list has just one element, a boolean expression.
+</para>
+</sect2>
-which makes the connection between the type of a collection of
-<literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
-Occasionally this really doesn't work, in which case you can split the
-class like this:
+ <!-- ===================== Recursive do-notation =================== -->
+<sect2 id="mdo-notation">
+<title>The recursive do-notation
+</title>
+<para> The recursive do-notation (also known as mdo-notation) is implemented as described in
+"A recursive do for Haskell",
+Levent Erkok, John Launchbury",
+Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
+</para>
+<para>
+The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
+that is, the variables bound in a do-expression are visible only in the textually following
+code block. Compare this to a let-expression, where bound variables are visible in the entire binding
+group. It turns out that several applications can benefit from recursive bindings in
+the do-notation, and this extension provides the necessary syntactic support.
+</para>
+<para>
+Here is a simple (yet contrived) example:
+</para>
<programlisting>
- class CollE s where
- empty :: s
+import Control.Monad.Fix
- class CollE s => Coll s a where
- insert :: s -> a -> s
+justOnes = mdo xs <- Just (1:xs)
+ return xs
</programlisting>
+<para>
+As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
+</para>
+
+<para>
+The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
+</para>
+<programlisting>
+class Monad m => MonadFix m where
+ mfix :: (a -> m a) -> m a
+</programlisting>
+<para>
+The function <literal>mfix</literal>
+dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
+then that monad must be declared an instance of the <literal>MonadFix</literal> class.
+For details, see the above mentioned reference.
+</para>
+<para>
+The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
+Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
+for Haskell's internal state monad (strict and lazy, respectively).
+</para>
+<para>
+There are three important points in using the recursive-do notation:
+<itemizedlist>
+<listitem><para>
+The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
+than <literal>do</literal>).
+</para></listitem>
+<listitem><para>
+You should <literal>import Control.Monad.Fix</literal>.
+(Note: Strictly speaking, this import is required only when you need to refer to the name
+<literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
+are encouraged to always import this module when using the mdo-notation.)
+</para></listitem>
+<listitem><para>
+As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
+</para></listitem>
+</itemizedlist>
</para>
-</listitem>
-</OrderedList>
+<para>
+The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
+contains up to date information on recursive monadic bindings.
+</para>
+<para>
+Historical note: The old implementation of the mdo-notation (and most
+of the existing documents) used the name
+<literal>MonadRec</literal> for the class and the corresponding library.
+This name is not supported by GHC.
</para>
-</sect3>
+</sect2>
-<sect3 id="instance-decls">
-<title>Instance declarations</title>
-<para>
+ <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
-<OrderedList>
-<listitem>
+ <sect2 id="parallel-list-comprehensions">
+ <title>Parallel List Comprehensions</title>
+ <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
+ </indexterm>
+ <indexterm><primary>parallel list comprehensions</primary>
+ </indexterm>
-<para>
- <emphasis>Instance declarations may not overlap</emphasis>. The two instance
-declarations
+ <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>
- instance context1 => C type1 where ...
- instance context2 => C type2 where ...
+ [ (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>
-"overlap" if <literal>type1</literal> and <literal>type2</literal> unify
+ <para>We can define parallel list comprehensions by translation to
+ regular comprehensions. Here's the basic idea:</para>
-However, if you give the command line option
-<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
+ <para>Given a parallel comprehension of the form: </para>
+
+<programlisting>
+ [ e | p1 <- e11, p2 <- e12, ...
+ | q1 <- e21, q2 <- e22, ...
+ ...
+ ]
+</programlisting>
+
+ <para>This will be translated to: </para>
+
+<programlisting>
+ [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
+ [(q1,q2) | q1 <- e21, q2 <- e22, ...]
+ ...
+ ]
+</programlisting>
+
+ <para>where `zipN' is the appropriate zip for the given number of
+ branches.</para>
+
+ </sect2>
+
+<sect2 id="rebindable-syntax">
+<title>Rebindable syntax</title>
+
+
+ <para>GHC allows most kinds of built-in syntax to be rebound by
+ the user, to facilitate replacing the <literal>Prelude</literal>
+ with a home-grown version, for example.</para>
+
+ <para>You may want to define your own numeric class
+ hierarchy. It completely defeats that purpose if the
+ literal "1" means "<literal>Prelude.fromInteger
+ 1</literal>", which is what the Haskell Report specifies.
+ So the <option>-fno-implicit-prelude</option> flag causes
+ the following pieces of built-in syntax to refer to
+ <emphasis>whatever is in scope</emphasis>, not the Prelude
+ versions:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>Integer and fractional literals mean
+ "<literal>fromInteger 1</literal>" and
+ "<literal>fromRational 3.2</literal>", not the
+ Prelude-qualified versions; both in expressions and in
+ patterns. </para>
+ <para>However, the standard Prelude <literal>Eq</literal> class
+ is still used for the equality test necessary for literal patterns.</para>
+ </listitem>
+
+ <listitem>
+ <para>Negation (e.g. "<literal>- (f x)</literal>")
+ means "<literal>negate (f x)</literal>" (not
+ <literal>Prelude.negate</literal>).</para>
+ </listitem>
+
+ <listitem>
+ <para>In an n+k pattern, the standard Prelude
+ <literal>Ord</literal> class is still used for comparison,
+ but the necessary subtraction uses whatever
+ "<literal>(-)</literal>" is in scope (not
+ "<literal>Prelude.(-)</literal>").</para>
+ </listitem>
+
+ <listitem>
+ <para>"Do" notation is translated using whatever
+ functions <literal>(>>=)</literal>,
+ <literal>(>>)</literal>, <literal>fail</literal>, and
+ <literal>return</literal>, are in scope (not the Prelude
+ versions). List comprehensions, and parallel array
+ comprehensions, are unaffected. </para></listitem>
+ </itemizedlist>
+
+ <para>Be warned: this is an experimental facility, with fewer checks than
+ usual. In particular, it is essential that the functions GHC finds in scope
+ must have the appropriate types, namely:
+ <screen>
+ fromInteger :: forall a. (...) => Integer -> a
+ fromRational :: forall a. (...) => Rational -> a
+ negate :: forall a. (...) => a -> a
+ (-) :: forall a. (...) => a -> a -> a
+ (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
+ (>>) :: forall m a. (...) => m a -> m b -> m b
+ return :: forall m a. (...) => a -> m a
+ fail :: forall m a. (...) => String -> m a
+ </screen>
+ (The (...) part can be any context including the empty context; that part
+ is up to you.)
+ If the functions don't have the right type, very peculiar things may
+ happen. Use <literal>-dcore-lint</literal> to
+ typecheck the desugared program. If Core Lint is happy you should be all right.</para>
+
+</sect2>
+</sect1>
+
+
+<!-- TYPE SYSTEM EXTENSIONS -->
+<sect1 id="type-extensions">
+<title>Type system extensions</title>
+
+
+<sect2>
+<title>Data types and type synonyms</title>
+
+<sect3 id="nullary-types">
+<title>Data types with no constructors</title>
+
+<para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
+a data type with no constructors. For example:</para>
+
+<programlisting>
+ data S -- S :: *
+ data T a -- T :: * -> *
+</programlisting>
+
+<para>Syntactically, the declaration lacks the "= constrs" part. The
+type can be parameterised over types of any kind, but if the kind is
+not <literal>*</literal> then an explicit kind annotation must be used
+(see <xref linkend="sec-kinding">).</para>
+
+<para>Such data types have only one value, namely bottom.
+Nevertheless, they can be useful when defining "phantom types".</para>
+</sect3>
+
+<sect3 id="infix-tycons">
+<title>Infix type constructors</title>
+
+<para>
+GHC allows type constructors to be operators, and to be written infix, very much
+like expressions. More specifically:
+<itemizedlist>
+<listitem><para>
+ A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
+ The lexical syntax is the same as that for data constructors.
+ </para></listitem>
+<listitem><para>
+ Types can be written infix. For example <literal>Int :*: Bool</literal>.
+ </para></listitem>
+<listitem><para>
+ Back-quotes work
+ as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
+ <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
+ </para></listitem>
+<listitem><para>
+ Fixities may be declared for type constructors just as for data constructors. However,
+ one cannot distinguish between the two in a fixity declaration; a fixity declaration
+ sets the fixity for a data constructor and the corresponding type constructor. For example:
+<screen>
+ infixl 7 T, :*:
+</screen>
+ sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
+ and similarly for <literal>:*:</literal>.
+ <literal>Int `a` Bool</literal>.
+ </para></listitem>
+<listitem><para>
+ Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
+ </para></listitem>
+<listitem><para>
+ Data type and type-synonym declarations can be written infix. E.g.
+<screen>
+ data a :*: b = Foo a b
+ type a :+: b = Either a b
+</screen>
+ </para></listitem>
+<listitem><para>
+ The only thing that differs between operators in types and operators in expressions is that
+ ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
+ are not allowed in types. Reason: the uniform thing to do would be to make them type
+ variables, but that's not very useful. A less uniform but more useful thing would be to
+ allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
+ lists. So for now we just exclude them.
+ </para></listitem>
+
+</itemizedlist>
+</para>
+</sect3>
+
+<sect3 id="type-synonyms">
+<title>Liberalised type synonyms</title>
+
+<para>
+Type synonmys are like macros at the type level, and
+GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
+That means that GHC can be very much more liberal about type synonyms than Haskell 98:
+<itemizedlist>
+<listitem> <para>You can write a <literal>forall</literal> (including overloading)
+in a type synonym, thus:
+<programlisting>
+ type Discard a = forall b. Show b => a -> b -> (a, String)
+
+ f :: Discard a
+ f x y = (x, show y)
+
+ g :: Discard Int -> (Int,Bool) -- A rank-2 type
+ g f = f Int True
+</programlisting>
+</para>
+</listitem>
+
+<listitem><para>
+You can write an unboxed tuple in a type synonym:
+<programlisting>
+ type Pr = (# Int, Int #)
+
+ h :: Int -> Pr
+ h x = (# x, x #)
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+You can apply a type synonym to a forall type:
+<programlisting>
+ type Foo a = a -> a -> Bool
+
+ f :: Foo (forall b. b->b)
+</programlisting>
+After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
+<programlisting>
+ f :: (forall b. b->b) -> (forall b. b->b) -> Bool
+</programlisting>
+</para></listitem>
+
+<listitem><para>
+You can apply a type synonym to a partially applied type synonym:
+<programlisting>
+ type Generic i o = forall x. i x -> o x
+ type Id x = x
+
+ foo :: Generic Id []
+</programlisting>
+After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
+<programlisting>
+ foo :: forall x. x -> [x]
+</programlisting>
+</para></listitem>
+
+</itemizedlist>
+</para>
+
+<para>
+GHC currently does kind checking before expanding synonyms (though even that
+could be changed.)
+</para>
+<para>
+After expanding type synonyms, GHC does validity checking on types, looking for
+the following mal-formedness which isn't detected simply by kind checking:
+<itemizedlist>
+<listitem><para>
+Type constructor applied to a type involving for-alls.
+</para></listitem>
+<listitem><para>
+Unboxed tuple on left of an arrow.
+</para></listitem>
+<listitem><para>
+Partially-applied type synonym.
+</para></listitem>
+</itemizedlist>
+So, for example,
+this will be rejected:
+<programlisting>
+ type Pr = (# Int, Int #)
+
+ h :: Pr -> Int
+ h x = ...
+</programlisting>
+because GHC does not allow unboxed tuples on the left of a function arrow.
+</para>
+</sect3>
+
+
+<sect3 id="existential-quantification">
+<title>Existentially quantified data constructors
+</title>
+
+<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>
+
+<programlisting>
+ data Foo = forall a. MkFoo a (a -> Bool)
+ | Nil
+</programlisting>
+
+</para>
+
+<para>
+The data type <literal>Foo</literal> has two constructors with types:
+</para>
+
+<para>
+
+<programlisting>
+ MkFoo :: forall a. a -> (a -> Bool) -> Foo
+ Nil :: Foo
+</programlisting>
+
+</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>.
+For example, the following expression is fine:
+</para>
+
+<para>
+
+<programlisting>
+ [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
+</programlisting>
+
+</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>
+
+<programlisting>
+ f (MkFoo val fn) = ???
+</programlisting>
+
+</para>
+
+<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>
+
+<para>
+
+<programlisting>
+ f :: Foo -> Bool
+ f (MkFoo val fn) = fn val
+</programlisting>
+
+</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>
+
+<sect4 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>
+
+<programlisting>
+ MkFoo :: (exists a . (a, a -> Bool)) -> Foo
+</programlisting>
+
+</para>
+
+<para>
+But Haskell programmers can safely think of the ordinary
+<emphasis>universally</emphasis> quantified type given above, thereby avoiding
+adding a new existential quantification construct.
+</para>
+
+</sect4>
+
+<sect4>
+<title>Type classes</title>
+
+<para>
+An easy extension (implemented in <Command>hbc</Command>) is to allow
+arbitrary contexts before the constructor. For example:
+</para>
+
+<para>
+
+<programlisting>
+data Baz = forall a. Eq a => Baz1 a a
+ | forall b. Show b => Baz2 b (b -> b)
+</programlisting>
+
+</para>
+
+<para>
+The two constructors have the types you'd expect:
+</para>
+
+<para>
+
+<programlisting>
+Baz1 :: forall a. Eq a => a -> a -> Baz
+Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
+</programlisting>
+
+</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
+value can be converted to a string (as well as applying the function to it).
+So this program is legal:
+</para>
+
+<para>
+
+<programlisting>
+ f :: Baz -> String
+ f (Baz1 p q) | p == q = "Yes"
+ | otherwise = "No"
+ f (Baz2 v fn) = show (fn v)
+</programlisting>
+
+</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
+extract it on pattern matching.
+</para>
+
+<para>
+Notice the way that the syntax fits smoothly with that used for
+universal quantification earlier.
+</para>
+
+</sect4>
+
+<sect4>
+<title>Restrictions</title>
+
+<para>
+There are several restrictions on the ways in which existentially-quantified
+constructors can be use.
+</para>
+
+<para>
+
+<itemizedlist>
+<listitem>
+
+<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>
+f1 (MkFoo a f) = a
+</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:
+
+
+<programlisting>
+ f1 :: Foo -> a -- Weird!
+</programlisting>
+
+
+What is this "<literal>a</literal>" in the result type? Clearly we don't mean
+this:
+
+
+<programlisting>
+ f1 :: forall a. Foo -> a -- Wrong!
+</programlisting>
+
+
+The original program is just plain wrong. Here's another sort of error
+
+
+<programlisting>
+ f2 (Baz1 a b) (Baz1 p q) = a==q
+</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.
+
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+You can't pattern-match on an existentially quantified
+constructor in a <literal>let</literal> or <literal>where</literal> group of
+bindings. So this is illegal:
+
+
+<programlisting>
+ f3 x = a==b where { Baz1 a b = x }
+</programlisting>
+
+Instead, use a <literal>case</literal> expression:
+
+<programlisting>
+ f3 x = case x of Baz1 a b -> a==b
+</programlisting>
+
+In general, you can only pattern-match
+on an existentially-quantified constructor in a <literal>case</literal> expression or
+in the patterns of a function definition.
+
+The reason for this restriction is really an implementation one.
+Type-checking binding groups is already a nightmare without
+existentials complicating the picture. Also an existential pattern
+binding at the top level of a module doesn't make sense, because it's
+not clear how to prevent the existentially-quantified type "escaping".
+So for now, there's a simple-to-state restriction. We'll see how
+annoying it is.
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+You can't use existential quantification for <literal>newtype</literal>
+declarations. So this is illegal:
+
+
+<programlisting>
+ newtype T = forall a. Ord a => MkT a
+</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 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 overloading involved, then there is more of a case for
+allowing an existentially-quantified <literal>newtype</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>) stands, unless there
+are convincing reasons to change it.
+
+
+</para>
+</listitem>
+<listitem>
+
+<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>
+data T = forall a. MkT [a] deriving( Eq )
+</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:
+
+<programlisting>
+instance Eq T where
+ (MkT a) == (MkT b) = ???
+</programlisting>
+
+But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
+It's just about possible to imagine examples in which the derived instance
+would make sense, but it seems altogether simpler simply to prohibit such
+declarations. Define your own instances!
+</para>
+</listitem>
+
+</itemizedlist>
+
+</para>
+
+</sect4>
+</sect3>
+
+</sect2>
+
+
+
+<sect2 id="multi-param-type-classes">
+<title>Class declarations</title>
+
+<para>
+This section documents GHC's implementation of multi-parameter type
+classes. There's lots of background in the paper <ULink
+URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
+classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
+Jones, Erik Meijer).
+</para>
+<para>
+There are the following constraints on class declarations:
+<OrderedList>
+<listitem>
+
+<para>
+ <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
+
+
+<programlisting>
+ class Collection c a where
+ union :: c a -> c a -> c a
+ ...etc.
+</programlisting>
+
+
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
+of "acyclic" involves only the superclass relationships. For example,
+this is OK:
+
+
+<programlisting>
+ class C a where {
+ op :: D b => a -> b -> b
+ }
+
+ class C a => D a where { ... }
+</programlisting>
+
+
+Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
+class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
+would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <emphasis>There are no restrictions on the context in a class declaration
+(which introduces superclasses), except that the class hierarchy must
+be acyclic</emphasis>. So these class declarations are OK:
+
+
+<programlisting>
+ class Functor (m k) => FiniteMap m k where
+ ...
+
+ class (Monad m, Monad (t m)) => Transform t m where
+ lift :: m a -> (t m) a
+</programlisting>
+
+
+</para>
+</listitem>
+
+<listitem>
+
+<para>
+ <emphasis>All of the class type variables must be reachable (in the sense
+mentioned in <xref linkend="type-restrictions">)
+from the free varibles of each method type
+</emphasis>. For example:
+
+
+<programlisting>
+ class Coll s a where
+ empty :: s
+ insert :: s -> a -> s
+</programlisting>
+
+
+is not OK, because the type of <literal>empty</literal> doesn't mention
+<literal>a</literal>. 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
+
+
+<programlisting>
+ class Coll s a where
+ empty :: s a
+ insert :: s a -> a -> s a
+</programlisting>
+
+
+which makes the connection between the type of a collection of
+<literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
+Occasionally this really doesn't work, in which case you can split the
+class like this:
+
+
+<programlisting>
+ class CollE s where
+ empty :: s
+
+ class CollE s => Coll s a where
+ insert :: s -> a -> s
+</programlisting>
+
+
+</para>
+</listitem>
+
+</OrderedList>
+</para>
+
+<sect3 id="class-method-types">
+<title>Class method types</title>
+<para>
+Haskell 98 prohibits class method types to mention constraints on the
+class type variable, thus:
+<programlisting>
+ class Seq s a where
+ fromList :: [a] -> s a
+ elem :: Eq a => a -> s a -> Bool
+</programlisting>
+The type of <literal>elem</literal> is illegal in Haskell 98, because it
+contains the constraint <literal>Eq a</literal>, constrains only the
+class type variable (in this case <literal>a</literal>).
+</para>
+<para>
+With the <option>-fglasgow-exts</option> GHC lifts this restriction.
+</para>
+
+</sect3>
+
+</sect2>
+
+<sect2 id="type-restrictions">
+<title>Type signatures</title>
+
+<sect3><title>The context of a type signature</title>
+<para>
+Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
+the form <emphasis>(class type-variable)</emphasis> or
+<emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
+these type signatures are perfectly OK
+<programlisting>
+ g :: Eq [a] => ...
+ g :: Ord (T a ()) => ...
+</programlisting>
+</para>
+<para>
+GHC imposes the following restrictions on the constraints in a type signature.
+Consider the type:
+
+<programlisting>
+ forall tv1..tvn (c1, ...,cn) => type
+</programlisting>
+
+(Here, we write the "foralls" explicitly, although the Haskell source
+language omits them; in Haskell 98, all the free type variables of an
+explicit source-language type signature are universally quantified,
+except for the class type variables in a class declaration. However,
+in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
+</para>
+
+<para>
+
+<OrderedList>
+<listitem>
+
+<para>
+ <emphasis>Each universally quantified type variable
+<literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
+
+A type variable is "reachable" if it it is functionally dependent
+(see <xref linkend="functional-dependencies">)
+on the type variables free in <literal>type</literal>.
+The reason for this is that a value with a type that does not obey
+this restriction could not be used without introducing
+ambiguity.
+Here, for example, is an illegal type:
+
+
+<programlisting>
+ forall a. Eq a => Int
+</programlisting>
+
+
+When a value with this type was used, the constraint <literal>Eq tv</literal>
+would be introduced where <literal>tv</literal> is a fresh type variable, and
+(in the dictionary-translation implementation) the value would be
+applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
+can never know which instance of <literal>Eq</literal> to use because we never
+get any more information about <literal>tv</literal>.
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+ <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
+universally quantified type variables <literal>tvi</literal></emphasis>.
+
+For example, this type is OK because <literal>C a b</literal> mentions the
+universally quantified type variable <literal>b</literal>:
+
+
+<programlisting>
+ forall a. C a b => burble
+</programlisting>
+
+
+The next type is illegal because the constraint <literal>Eq b</literal> does not
+mention <literal>a</literal>:
+
+
+<programlisting>
+ forall a. Eq b => burble
+</programlisting>
+
+
+The reason for this restriction is milder than the other one. The
+excluded types are never useful or necessary (because the offending
+context doesn't need to be witnessed at this point; it can be floated
+out). Furthermore, floating them out increases sharing. Lastly,
+excluding them is a conservative choice; it leaves a patch of
+territory free in case we need it later.
+
+</para>
+</listitem>
+
+</OrderedList>
+
+</para>
+</sect3>
+
+<sect3 id="hoist">
+<title>For-all hoisting</title>
+<para>
+It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
+end of an arrow, thus:
+<programlisting>
+ type Discard a = forall b. a -> b -> a
+
+ g :: Int -> Discard Int
+ g x y z = x+y
+</programlisting>
+Simply expanding the type synonym would give
+<programlisting>
+ g :: Int -> (forall b. Int -> b -> Int)
+</programlisting>
+but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
+<programlisting>
+ g :: forall b. Int -> Int -> b -> Int
+</programlisting>
+In general, the rule is this: <emphasis>to determine the type specified by any explicit
+user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
+performs the transformation:</emphasis>
+<programlisting>
+ <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
+==>
+ forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
+</programlisting>
+(In fact, GHC tries to retain as much synonym information as possible for use in
+error messages, but that is a usability issue.) This rule applies, of course, whether
+or not the <literal>forall</literal> comes from a synonym. For example, here is another
+valid way to write <literal>g</literal>'s type signature:
+<programlisting>
+ g :: Int -> Int -> forall b. b -> Int
+</programlisting>
+</para>
+<para>
+When doing this hoisting operation, GHC eliminates duplicate constraints. For
+example:
+<programlisting>
+ type Foo a = (?x::Int) => Bool -> a
+ g :: Foo (Foo Int)
+</programlisting>
+means
+<programlisting>
+ g :: (?x::Int) => Bool -> Bool -> Int
+</programlisting>
+</para>
+</sect3>
+
+
+</sect2>
+
+<sect2 id="instance-decls">
+<title>Instance declarations</title>
+
+<sect3>
+<title>Overlapping instances</title>
+<para>
+In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
+declarations
+
+
+<programlisting>
+ instance context1 => C type1 where ...
+ instance context2 => C type2 where ...
+</programlisting>
+
+"overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
+</para>
+<para>
+However, if you give the command line option
+<option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
option</primary></indexterm> then overlapping instance declarations are permitted.
However, GHC arranges never to commit to using an instance declaration
if another instance declaration also applies, either now or later.
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>.)
-
</para>
-</listitem>
-<listitem>
+</sect3>
+
+<sect3>
+<title>Type synonyms in the instance head</title>
<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:
+<emphasis>Unlike Haskell 98, instance heads may use type
+synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
+As always, using a type synonym is just shorthand for
+writing the RHS of the type synonym definition. For example:
<programlisting>
+ type Point = (Int,Int)
+ instance C Point where ...
+ instance C [Point] where ...
+</programlisting>
+
+
+is legal. However, if you added
+
+
+<programlisting>
+ instance C (Int,Int) where ...
+</programlisting>
+
+
+as well, then the compiler will complain about the overlapping
+(actually, identical) instance declarations. As always, type synonyms
+must be fully applied. You cannot, for example, write:
+
+
+<programlisting>
+ type P a = [[a]]
+ instance Monad P where ...
+</programlisting>
+
+
+This design decision is independent of all the others, and easily
+reversed, but it makes sense to me.
+
+</para>
+</sect3>
+
+<sect3 id="undecidable-instances">
+<title>Undecidable instances</title>
+
+<para>An instance declaration must normally obey the following rules:
+<orderedlist>
+<listitem><para>At least one of the types in the <emphasis>head</emphasis> of
+an instance declaration <emphasis>must not</emphasis> be a type variable.
+For example, these are OK:
+
+<programlisting>
instance C Int a where ...
instance D (Int, Int) where ...
instance E [[a]] where ...
</programlisting>
-
-
+but this is not:
+<programlisting>
+ instance F a where ...
+</programlisting>
Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
For example, this is OK:
-
-
<programlisting>
instance Stateful (ST s) (MutVar s) where ...
</programlisting>
+</para>
+</listitem>
-The "at least one not a type variable" restriction is to ensure that
+<listitem>
+<para>All of the types in the <emphasis>context</emphasis> of
+an instance declaration <emphasis>must</emphasis> be type variables.
+Thus
+<programlisting>
+instance C a b => Eq (a,b) where ...
+</programlisting>
+is OK, but
+<programlisting>
+instance C Int b => Foo b where ...
+</programlisting>
+is not OK.
+</para>
+</listitem>
+</OrderedList>
+These restrictions ensure that
context reduction terminates: each reduction step removes one type
constructor. For example, the following would make the type checker
loop if it wasn't excluded:
-
-
<programlisting>
instance C a => C a where ...
</programlisting>
-
-
There are two situations in which the rule is a bit of a pain. First,
if one allows overlapping instance declarations then it's quite
convenient to have a "default instance" declaration that applies if
</programlisting>
-I'm on the lookout for a simple rule that preserves decidability while
-allowing these idioms. The experimental flag
-<option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
-option</primary></indexterm> lifts this restriction, allowing all the types in an
-instance head to be type variables.
-
-</para>
-</listitem>
-<listitem>
-
-<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>
- type Point = (Int,Int)
- instance C Point where ...
- instance C [Point] where ...
-</programlisting>
-
-
-is legal. However, if you added
-
-
-<programlisting>
- instance C (Int,Int) where ...
-</programlisting>
-
-
-as well, then the compiler will complain about the overlapping
-(actually, identical) instance declarations. As always, type synonyms
-must be fully applied. You cannot, for example, write:
-
-
-<programlisting>
- type P a = [[a]]
- instance Monad P where ...
-</programlisting>
-
-
-This design decision is independent of all the others, and easily
-reversed, but it makes sense to me.
-
-</para>
-</listitem>
-<listitem>
-
-<para>
-<emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
-be type variables</emphasis>. Thus
-
-
-<programlisting>
-instance C a b => Eq (a,b) where ...
-</programlisting>
-
-
-is OK, but
-
-
-<programlisting>
-instance C Int b => Foo b where ...
-</programlisting>
-
-
-is not OK. Again, the intent here is to make sure that context
-reduction terminates.
-
Voluminous correspondence on the Haskell mailing list has convinced me
-that it's worth experimenting with a more liberal rule. If you use
-the flag <option>-fallow-undecidable-instances</option> can use arbitrary
-types in an instance context. Termination is ensured by having a
+that it's worth experimenting with more liberal rules. If you use
+the experimental flag <option>-fallow-undecidable-instances</option>
+<indexterm><primary>-fallow-undecidable-instances
+option</primary></indexterm>, you can use arbitrary
+types in both an instance context and instance head. Termination is ensured by having a
fixed-depth recursion stack. If you exceed the stack depth you get a
sort of backtrace, and the opportunity to increase the stack depth
with <option>-fcontext-stack</option><emphasis>N</emphasis>.
-
</para>
-</listitem>
-
-</OrderedList>
-
+<para>
+I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
+allowing these idioms interesting idioms.
</para>
-
</sect3>
+
</sect2>
<sect2 id="implicit-parameters">
-<title>Implicit parameters
-</title>
+<title>Implicit parameters</title>
<para> Implicit paramters are implemented as described in
"Implicit parameters: dynamic scoping with static types",
27th ACM Symposium on Principles of Programming Languages (POPL'00),
Boston, Jan 2000.
</para>
-<para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
+
+<para>(Most of the following, stil rather incomplete, documentation is
+due to Jeff Lewis.)</para>
+
+<para>Implicit parameter support is enabled with the option
+<option>-fimplicit-params</option>.</para>
+
<para>
A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
The dynamic binding constraints are just a new form of predicate in the type class system.
</para>
<para>
-An implicit parameter is introduced by the special form <literal>?x</literal>,
+An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
where <literal>x</literal> is
-any valid identifier. Use if this construct also introduces new
-dynamic binding constraints. For example, the following definition
+any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
+Use of this construct also introduces a new
+dynamic-binding constraint in the type of the expression.
+For example, the following definition
shows how we can define an implicitly parameterized sort function in
terms of an explicitly parameterized <literal>sortBy</literal> function:
<programlisting>
sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
sort = sortBy ?cmp
</programlisting>
+</para>
+
+<sect3>
+<title>Implicit-parameter type constraints</title>
+<para>
Dynamic binding constraints behave just like other type class
constraints in that they are automatically propagated. Thus, when a
function is used, its implicit parameters are inherited by the
propagate them.
</para>
<para>
-An implicit parameter differs from other type class constraints in the
+An implicit-parameter type constraint differs from other type class constraints in the
following way: All uses of a particular implicit parameter must have
the same type. This means that the type of <literal>(?x, ?x)</literal>
is <literal>(?x::a) => (a,a)</literal>, and not
<literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
class constraints.
</para>
-<para>
-An implicit parameter is bound using the standard
-<literal>let</literal> binding form, where the bindings must be a
-collection of simple bindings to implicit-style variables (no
-function-style bindings, and no type signatures); these bindings are
-neither polymorphic or recursive. This form binds the implicit
-parameters arising in the body, not the free variables as a
-<literal>let</literal> or <literal>where</literal> would do. For
-example, we define the <literal>min</literal> function by binding
-<literal>cmp</literal>.</para>
-<programlisting>
- min :: [a] -> a
- min = let ?cmp = (<=) in least
-</programlisting>
-<para>
-Note the following additional constraints:
-<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>
-</para>
-
-</sect2>
-
-<sect2 id="linear-implicit-parameters">
-<title>Linear implicit parameters
-</title>
-<para>
-Linear implicit parameters are an idea developed by Koen Claessen,
-Mark Shields, and Simon PJ. They address the long-standing
-problem that monads seem over-kill for certain sorts of problem, notably:
-</para>
-<itemizedlist>
-<listitem> <para> distributing a supply of unique names </para> </listitem>
-<listitem> <para> distributing a suppply of random numbers </para> </listitem>
-<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
-</itemizedlist>
-
-<para>
-Linear implicit parameters are just like ordinary implicit parameters,
-except that they are "linear" -- that is, they cannot be copied, and
-must be explicitly "split" instead. Linear implicit parameters are
-written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
-(The '/' in the '%' suggests the split!)
-</para>
-<para>
-For example:
-<programlisting>
- import GHC.Exts( Splittable )
-
- data NameSupply = ...
-
- splitNS :: NameSupply -> (NameSupply, NameSupply)
- newName :: NameSupply -> Name
-
- instance Splittable NameSupply where
- split = splitNS
-
-
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam x' (f env e)
- where
- x' = newName %ns
- env' = extend env x x'
- ...more equations for f...
-</programlisting>
-Notice that the implicit parameter %ns is consumed
-<itemizedlist>
-<listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
-<listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
-</itemizedlist>
-</para>
-<para>
-So the translation done by the type checker makes
-the parameter explicit:
-<programlisting>
- f :: NameSupply -> Env -> Expr -> Expr
- f ns env (Lam x e) = Lam x' (f ns1 env e)
- where
- (ns1,ns2) = splitNS ns
- x' = newName ns2
- env = extend env x x'
-</programlisting>
-Notice the call to 'split' introduced by the type checker.
-How did it know to use 'splitNS'? Because what it really did
-was to introduce a call to the overloaded function 'split',
-defined by the class <literal>Splittable</literal>:
-<programlisting>
- class Splittable a where
- split :: a -> (a,a)
-</programlisting>
-The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
-split for name supplies. But we can simply write
-<programlisting>
- g x = (x, %ns, %ns)
-</programlisting>
-and GHC will infer
-<programlisting>
- g :: (Splittable a, %ns :: a) => b -> (b,a,a)
-</programlisting>
-The <literal>Splittable</literal> class is built into GHC. It's exported by module
-<literal>GHC.Exts</literal>.
-</para>
-<para>
-Other points:
-<itemizedlist>
-<listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
-are entirely distinct implicit parameters: you
- can use them together and they won't intefere with each other. </para>
-</listitem>
-
-<listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
-
-<listitem> <para>You cannot have implicit parameters (whether linear or not)
- in the context of a class or instance declaration. </para></listitem>
-</itemizedlist>
-</para>
-
-<sect3><title>Warnings</title>
-
-<para>
-The monomorphism restriction is even more important than usual.
-Consider the example above:
-<programlisting>
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam x' (f env e)
- where
- x' = newName %ns
- env' = extend env x x'
-</programlisting>
-If we replaced the two occurrences of x' by (newName %ns), which is
-usually a harmless thing to do, we get:
-<programlisting>
- f :: (%ns :: NameSupply) => Env -> Expr -> Expr
- f env (Lam x e) = Lam (newName %ns) (f env e)
- where
- env' = extend env x (newName %ns)
-</programlisting>
-But now the name supply is consumed in <emphasis>three</emphasis> places
-(the two calls to newName,and the recursive call to f), so
-the result is utterly different. Urk! We don't even have
-the beta rule.
-</para>
-<para>
-Well, this is an experimental change. With implicit
-parameters we have already lost beta reduction anyway, and
-(as John Launchbury puts it) we can't sensibly reason about
-Haskell programs without knowing their typing.
-</para>
-
-</sect3>
-
-</sect2>
-
-<sect2 id="functional-dependencies">
-<title>Functional dependencies
-</title>
-
-<para> Functional dependencies are implemented as described by Mark Jones
-in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
-In Proceedings of the 9th European Symposium on Programming,
-ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
-.
-</para>
-
-<para>
-There should be more documentation, but there isn't (yet). Yell if you need it.
-</para>
-</sect2>
-
-
-<sect2 id="universal-quantification">
-<title>Arbitrary-rank polymorphism
-</title>
-
-<para>
-Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
-allows us to say exactly what this means. For example:
-</para>
-<para>
-<programlisting>
- g :: b -> b
-</programlisting>
-means this:
-<programlisting>
- g :: forall b. (b -> b)
-</programlisting>
-The two are treated identically.
-</para>
-
-<para>
-However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
-explicit universal quantification in
-types.
-For example, all the following types are legal:
-<programlisting>
- f1 :: forall a b. a -> b -> a
- g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
-
- f2 :: (forall a. a->a) -> Int -> Int
- g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
-
- f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
-</programlisting>
-Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
-can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
-The <literal>forall</literal> makes explicit the universal quantification that
-is implicitly added by Haskell.
-</para>
-<para>
-The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
-the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
-shows, the polymorphic type on the left of the function arrow can be overloaded.
-</para>
-<para>
-The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
-they have rank-2 types on the left of a function arrow.
-</para>
-<para>
-GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
-arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
-that restriction has now been lifted.)
-In particular, a forall-type (also called a "type scheme"),
-including an operational type class context, is legal:
-<itemizedlist>
-<listitem> <para> On the left of a function arrow </para> </listitem>
-<listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
-<listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
-example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
-field type signatures.</para> </listitem>
-<listitem> <para> As the type of an implicit parameter </para> </listitem>
-<listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
-</itemizedlist>
-There is one place you cannot put a <literal>forall</literal>:
-you cannot instantiate a type variable with a forall-type. So you cannot
-make a forall-type the argument of a type constructor. So these types are illegal:
-<programlisting>
- x1 :: [forall a. a->a]
- x2 :: (forall a. a->a, Int)
- x3 :: Maybe (forall a. a->a)
-</programlisting>
-Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
-a type variable any more!
-</para>
-
-
-<sect3 id="univ">
-<title>Examples
-</title>
-
-<para>
-In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
-the types of the constructor arguments. Here are several examples:
-</para>
+<para> You can't have an implicit parameter in the context of a class or instance
+declaration. For example, both these declarations are illegal:
+<programlisting>
+ class (?x::Int) => C a where ...
+ instance (?x::a) => Foo [a] where ...
+</programlisting>
+Reason: exactly which implicit parameter you pick up depends on exactly where
+you invoke a function. But the ``invocation'' of instance declarations is done
+behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
+Easiest thing is to outlaw the offending types.</para>
<para>
-
+Implicit-parameter constraints do not cause ambiguity. For example, consider:
<programlisting>
-data T a = T1 (forall b. b -> b -> b) a
-
-data MonadT m = MkMonad { return :: forall a. a -> m a,
- bind :: forall a b. m a -> (a -> m b) -> m b
- }
+ f :: (?x :: [a]) => Int -> Int
+ f n = n + length ?x
-newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
+ g :: (Read a, Show a) => String -> String
+ g s = show (read s)
</programlisting>
-
+Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
+is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
+quite unambiguous, and fixes the type <literal>a</literal>.
</para>
+</sect3>
-<para>
-The constructors have rank-2 types:
-</para>
+<sect3>
+<title>Implicit-parameter bindings</title>
<para>
-
+An implicit parameter is <emphasis>bound</emphasis> using the standard
+<literal>let</literal> or <literal>where</literal> binding forms.
+For example, we define the <literal>min</literal> function by binding
+<literal>cmp</literal>.
<programlisting>
-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
+ min :: [a] -> a
+ min = let ?cmp = (<=) in least
</programlisting>
-
</para>
-
-<para>
-Notice that you don't need to use a <literal>forall</literal> if there's an
-explicit context. For example in the first argument of the
-constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
-prefixed to the argument type. The implicit <literal>forall</literal>
-quantifies all type variables that are not already in scope, and are
-mentioned in the type quantified over.
-</para>
-
<para>
-As for type signatures, implicit quantification happens for non-overloaded
-types too. So if you write this:
+A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
+bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
+(including in a list comprehension, or do-notation, or pattern guards),
+or a <literal>where</literal> clause.
+Note the following points:
+<itemizedlist>
+<listitem><para>
+An implicit-parameter binding group must be a
+collection of simple bindings to implicit-style variables (no
+function-style bindings, and no type signatures); these bindings are
+neither polymorphic or recursive.
+</para></listitem>
+<listitem><para>
+You may not mix implicit-parameter bindings with ordinary bindings in a
+single <literal>let</literal>
+expression; use two nested <literal>let</literal>s instead.
+(In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
+</para></listitem>
+<listitem><para>
+You may put multiple implicit-parameter bindings in a
+single binding group; but they are <emphasis>not</emphasis> treated
+as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
+Instead they are treated as a non-recursive group, simultaneously binding all the implicit
+parameter. The bindings are not nested, and may be re-ordered without changing
+the meaning of the program.
+For example, consider:
<programlisting>
- data T a = MkT (Either a b) (b -> b)
+ f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
</programlisting>
-
-it's just as if you had written this:
-
+The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
+the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
<programlisting>
- data T a = MkT (forall b. Either a b) (forall b. b -> b)
+ f :: (?x::Int) => Int -> Int
</programlisting>
-
-That is, since the type variable <literal>b</literal> isn't in scope, it's
-implicitly universally quantified. (Arguably, it would be better
-to <emphasis>require</emphasis> explicit quantification on constructor arguments
-where that is what is wanted. Feedback welcomed.)
-</para>
-
-<para>
-You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
-the constructor to suitable values, just as usual. For example,
+</para></listitem>
+</itemizedlist>
</para>
-<para>
-
-<programlisting>
- a1 :: T Int
- a1 = T1 (\xy->x) 3
-
- a2, a3 :: Swizzle
- a2 = MkSwizzle sort
- a3 = MkSwizzle reverse
-
- a4 :: MonadT Maybe
- a4 = let r x = Just x
- b m k = case m of
- Just y -> k y
- Nothing -> Nothing
- in
- MkMonad r b
-
- mkTs :: (forall b. b -> b -> b) -> a -> [T a]
- mkTs f x y = [T1 f x, T1 f y]
-</programlisting>
-
-</para>
+</sect3>
+</sect2>
+<sect2 id="linear-implicit-parameters">
+<title>Linear implicit parameters</title>
<para>
-The type of the argument can, as usual, be more general than the type
-required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
-does not need the <literal>Ord</literal> constraint.)
+Linear implicit parameters are an idea developed by Koen Claessen,
+Mark Shields, and Simon PJ. They address the long-standing
+problem that monads seem over-kill for certain sorts of problem, notably:
</para>
+<itemizedlist>
+<listitem> <para> distributing a supply of unique names </para> </listitem>
+<listitem> <para> distributing a suppply of random numbers </para> </listitem>
+<listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
+</itemizedlist>
<para>
-When you use pattern matching, the bound variables may now have
-polymorphic types. For example:
+Linear implicit parameters are just like ordinary implicit parameters,
+except that they are "linear" -- that is, they cannot be copied, and
+must be explicitly "split" instead. Linear implicit parameters are
+written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
+(The '/' in the '%' suggests the split!)
</para>
-
<para>
-
+For example:
<programlisting>
- f :: T a -> a -> (a, Char)
- f (T1 w k) x = (w k x, w 'c' 'd')
-
- g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
- g (MkSwizzle s) xs f = s (map f (s xs))
-
- h :: MonadT m -> [m a] -> m [a]
- h m [] = return m []
- h m (x:xs) = bind m x $ \y ->
- bind m (h m xs) $ \ys ->
- return m (y:ys)
-</programlisting>
+ import GHC.Exts( Splittable )
-</para>
+ data NameSupply = ...
+
+ splitNS :: NameSupply -> (NameSupply, NameSupply)
+ newName :: NameSupply -> Name
-<para>
-In the function <function>h</function> we use the record selectors <literal>return</literal>
-and <literal>bind</literal> to extract the polymorphic bind and return functions
-from the <literal>MonadT</literal> data structure, rather than using pattern
-matching.
-</para>
-</sect3>
+ instance Splittable NameSupply where
+ split = splitNS
-<sect3>
-<title>Type inference</title>
-<para>
-In general, type inference for arbitrary-rank types is undecideable.
-GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
-to get a decidable algorithm by requiring some help from the programmer.
-We do not yet have a formal specification of "some help" but the rule is this:
-</para>
-<para>
-<emphasis>For a lambda-bound or case-bound variable, x, either the programmer
-provides an explicit polymorphic type for x, or GHC's type inference will assume
-that x's type has no foralls in it</emphasis>.
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+ ...more equations for f...
+</programlisting>
+Notice that the implicit parameter %ns is consumed
+<itemizedlist>
+<listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
+<listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
+</itemizedlist>
</para>
<para>
-What does it mean to "provide" an explicit type for x? You can do that by
-giving a type signature for x directly, using a pattern type signature
-(<xref linkend="scoped-type-variables">), thus:
+So the translation done by the type checker makes
+the parameter explicit:
<programlisting>
- \ f :: (forall a. a->a) -> (f True, f 'c')
+ f :: NameSupply -> Env -> Expr -> Expr
+ f ns env (Lam x e) = Lam x' (f ns1 env e)
+ where
+ (ns1,ns2) = splitNS ns
+ x' = newName ns2
+ env = extend env x x'
</programlisting>
-Alternatively, you can give a type signature to the enclosing
-context, which GHC can "push down" to find the type for the variable:
+Notice the call to 'split' introduced by the type checker.
+How did it know to use 'splitNS'? Because what it really did
+was to introduce a call to the overloaded function 'split',
+defined by the class <literal>Splittable</literal>:
<programlisting>
- (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
+ class Splittable a where
+ split :: a -> (a,a)
</programlisting>
-Here the type signature on the expression can be pushed inwards
-to give a type signature for f. Similarly, and more commonly,
-one can give a type signature for the function itself:
+The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
+split for name supplies. But we can simply write
<programlisting>
- h :: (forall a. a->a) -> (Bool,Char)
- h f = (f True, f 'c')
+ g x = (x, %ns, %ns)
</programlisting>
-You don't need to give a type signature if the lambda bound variable
-is a constructor argument. Here is an example we saw earlier:
+and GHC will infer
<programlisting>
- f :: T a -> a -> (a, Char)
- f (T1 w k) x = (w k x, w 'c' 'd')
+ g :: (Splittable a, %ns :: a) => b -> (b,a,a)
</programlisting>
-Here we do not need to give a type signature to <literal>w</literal>, because
-it is an argument of constructor <literal>T1</literal> and that tells GHC all
-it needs to know.
+The <literal>Splittable</literal> class is built into GHC. It's exported by module
+<literal>GHC.Exts</literal>.
</para>
+<para>
+Other points:
+<itemizedlist>
+<listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
+are entirely distinct implicit parameters: you
+ can use them together and they won't intefere with each other. </para>
+</listitem>
-</sect3>
+<listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
+<listitem> <para>You cannot have implicit parameters (whether linear or not)
+ in the context of a class or instance declaration. </para></listitem>
+</itemizedlist>
+</para>
-<sect3 id="implicit-quant">
-<title>Implicit quantification</title>
+<sect3><title>Warnings</title>
<para>
-GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
-user-written types, if and only if there is no explicit <literal>forall</literal>,
-GHC finds all the type variables mentioned in the type that are not already
-in scope, and universally quantifies them.</emphasis> For example, the following pairs are
-equivalent:
+The monomorphism restriction is even more important than usual.
+Consider the example above:
<programlisting>
- f :: a -> a
- f :: forall a. a -> a
-
- g (x::a) = let
- h :: a -> b -> b
- h x y = y
- in ...
- g (x::a) = let
- h :: forall b. a -> b -> b
- h x y = y
- in ...
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam x' (f env e)
+ where
+ x' = newName %ns
+ env' = extend env x x'
+</programlisting>
+If we replaced the two occurrences of x' by (newName %ns), which is
+usually a harmless thing to do, we get:
+<programlisting>
+ f :: (%ns :: NameSupply) => Env -> Expr -> Expr
+ f env (Lam x e) = Lam (newName %ns) (f env e)
+ where
+ env' = extend env x (newName %ns)
</programlisting>
+But now the name supply is consumed in <emphasis>three</emphasis> places
+(the two calls to newName,and the recursive call to f), so
+the result is utterly different. Urk! We don't even have
+the beta rule.
</para>
<para>
-Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
-point. For example:
-<programlisting>
- f :: (a -> a) -> Int
- -- MEANS
- f :: forall a. (a -> a) -> Int
- -- NOT
- f :: (forall a. a -> a) -> Int
+Well, this is an experimental change. With implicit
+parameters we have already lost beta reduction anyway, and
+(as John Launchbury puts it) we can't sensibly reason about
+Haskell programs without knowing their typing.
+</para>
+</sect3>
- g :: (Ord a => a -> a) -> Int
- -- MEANS the illegal type
- g :: forall a. (Ord a => a -> a) -> Int
- -- NOT
- g :: (forall a. Ord a => a -> a) -> Int
-</programlisting>
-The latter produces an illegal type, which you might think is silly,
-but at least the rule is simple. If you want the latter type, you
-can write your for-alls explicitly. Indeed, doing so is strongly advised
-for rank-2 types.
+<sect3><title>Recursive functions</title>
+<para>Linear implicit parameters can be particularly tricky when you have a recursive function
+Consider
+<programlisting>
+ foo :: %x::T => Int -> [Int]
+ foo 0 = []
+ foo n = %x : foo (n-1)
+</programlisting>
+where T is some type in class Splittable.</para>
+<para>
+Do you get a list of all the same T's or all different T's
+(assuming that split gives two distinct T's back)?
+</para><para>
+If you supply the type signature, taking advantage of polymorphic
+recursion, you get what you'd probably expect. Here's the
+translated term, where the implicit param is made explicit:
+<programlisting>
+ foo x 0 = []
+ foo x n = let (x1,x2) = split x
+ in x1 : foo x2 (n-1)
+</programlisting>
+But if you don't supply a type signature, GHC uses the Hindley
+Milner trick of using a single monomorphic instance of the function
+for the recursive calls. That is what makes Hindley Milner type inference
+work. So the translation becomes
+<programlisting>
+ foo x = let
+ foom 0 = []
+ foom n = x : foom (n-1)
+ in
+ foom
+</programlisting>
+Result: 'x' is not split, and you get a list of identical T's. So the
+semantics of the program depends on whether or not foo has a type signature.
+Yikes!
+</para><para>
+You may say that this is a good reason to dislike linear implicit parameters
+and you'd be right. That is why they are an experimental feature.
</para>
</sect3>
+
</sect2>
-<sect2 id="type-synonyms">
-<title>Liberalised type synonyms
+<sect2 id="functional-dependencies">
+<title>Functional dependencies
</title>
+<para> Functional dependencies are implemented as described by Mark Jones
+in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
+In Proceedings of the 9th European Symposium on Programming,
+ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
+.
+</para>
<para>
-Type synonmys are like macros at the type level, and
-GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
-That means that GHC can be very much more liberal about type synonyms than Haskell 98:
-<itemizedlist>
-<listitem> <para>You can write a <literal>forall</literal> (including overloading)
-in a type synonym, thus:
+Functional dependencies are introduced by a vertical bar in the syntax of a
+class declaration; e.g.
<programlisting>
- type Discard a = forall b. Show b => a -> b -> (a, String)
-
- f :: Discard a
- f x y = (x, show y)
+ class (Monad m) => MonadState s m | m -> s where ...
- g :: Discard Int -> (Int,Bool) -- A rank-2 type
- g f = f Int True
+ class Foo a b c | a b -> c where ...
</programlisting>
+There should be more documentation, but there isn't (yet). Yell if you need it.
</para>
-</listitem>
-
-<listitem><para>
-You can write an unboxed tuple in a type synonym:
-<programlisting>
- type Pr = (# Int, Int #)
-
- h :: Int -> Pr
- h x = (# x, x #)
-</programlisting>
-</para></listitem>
+</sect2>
-<listitem><para>
-You can apply a type synonym to a forall type:
-<programlisting>
- type Foo a = a -> a -> Bool
-
- f :: Foo (forall b. b->b)
-</programlisting>
-After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
-<programlisting>
- f :: (forall b. b->b) -> (forall b. b->b) -> Bool
-</programlisting>
-</para></listitem>
-<listitem><para>
-You can apply a type synonym to a partially applied type synonym:
-<programlisting>
- type Generic i o = forall x. i x -> o x
- type Id x = x
-
- foo :: Generic Id []
-</programlisting>
-After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
-<programlisting>
- foo :: forall x. x -> [x]
-</programlisting>
-</para></listitem>
-</itemizedlist>
-</para>
+<sect2 id="sec-kinding">
+<title>Explicitly-kinded quantification</title>
<para>
-GHC currently does kind checking before expanding synonyms (though even that
-could be changed.)
+Haskell infers the kind of each type variable. Sometimes it is nice to be able
+to give the kind explicitly as (machine-checked) documentation,
+just as it is nice to give a type signature for a function. On some occasions,
+it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
+John Hughes had to define the data type:
+<Screen>
+ data Set cxt a = Set [a]
+ | Unused (cxt a -> ())
+</Screen>
+The only use for the <literal>Unused</literal> constructor was to force the correct
+kind for the type variable <literal>cxt</literal>.
</para>
<para>
-After expanding type synonyms, GHC does validity checking on types, looking for
-the following mal-formedness which isn't detected simply by kind checking:
+GHC now instead allows you to specify the kind of a type variable directly, wherever
+a type variable is explicitly bound. Namely:
<itemizedlist>
-<listitem><para>
-Type constructor applied to a type involving for-alls.
-</para></listitem>
-<listitem><para>
-Unboxed tuple on left of an arrow.
-</para></listitem>
-<listitem><para>
-Partially-applied type synonym.
-</para></listitem>
+<listitem><para><literal>data</literal> declarations:
+<Screen>
+ data Set (cxt :: * -> *) a = Set [a]
+</Screen></para></listitem>
+<listitem><para><literal>type</literal> declarations:
+<Screen>
+ type T (f :: * -> *) = f Int
+</Screen></para></listitem>
+<listitem><para><literal>class</literal> declarations:
+<Screen>
+ class (Eq a) => C (f :: * -> *) a where ...
+</Screen></para></listitem>
+<listitem><para><literal>forall</literal>'s in type signatures:
+<Screen>
+ f :: forall (cxt :: * -> *). Set cxt Int
+</Screen></para></listitem>
</itemizedlist>
-So, for example,
-this will be rejected:
-<programlisting>
- type Pr = (# Int, Int #)
+</para>
- h :: Pr -> Int
- h x = ...
-</programlisting>
-because GHC does not allow unboxed tuples on the left of a function arrow.
+<para>
+The parentheses are required. Some of the spaces are required too, to
+separate the lexemes. If you write <literal>(f::*->*)</literal> you
+will get a parse error, because "<literal>::*->*</literal>" is a
+single lexeme in Haskell.
</para>
-</sect2>
-<sect2 id="hoist">
-<title>For-all hoisting</title>
<para>
-It is often convenient to use generalised type synonyms at the right hand
-end of an arrow, thus:
-<programlisting>
- type Discard a = forall b. a -> b -> a
+As part of the same extension, you can put kind annotations in types
+as well. Thus:
+<Screen>
+ f :: (Int :: *) -> Int
+ g :: forall a. a -> (a :: *)
+</Screen>
+The syntax is
+<Screen>
+ atype ::= '(' ctype '::' kind ')
+</Screen>
+The parentheses are required.
+</para>
+</sect2>
- g :: Int -> Discard Int
- g x y z = x+y
-</programlisting>
-Simply expanding the type synonym would give
-<programlisting>
- g :: Int -> (forall b. Int -> b -> Int)
-</programlisting>
-but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
-<programlisting>
- g :: forall b. Int -> Int -> b -> Int
-</programlisting>
-In general, the rule is this: <emphasis>to determine the type specified by any explicit
-user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
-performs the transformation:</emphasis>
-<programlisting>
- <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
-==>
- forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
-</programlisting>
-(In fact, GHC tries to retain as much synonym information as possible for use in
-error messages, but that is a usability issue.) This rule applies, of course, whether
-or not the <literal>forall</literal> comes from a synonym. For example, here is another
-valid way to write <literal>g</literal>'s type signature:
-<programlisting>
- g :: Int -> Int -> forall b. b -> Int
-</programlisting>
+
+<sect2 id="universal-quantification">
+<title>Arbitrary-rank polymorphism
+</title>
+
+<para>
+Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
+allows us to say exactly what this means. For example:
</para>
<para>
-When doing this hoisting operation, GHC eliminates duplicate constraints. For
-example:
<programlisting>
- type Foo a = (?x::Int) => Bool -> a
- g :: Foo (Foo Int)
+ g :: b -> b
</programlisting>
-means
+means this:
<programlisting>
- g :: (?x::Int) => Bool -> Bool -> Int
+ g :: forall b. (b -> b)
</programlisting>
+The two are treated identically.
</para>
-</sect2>
+<para>
+However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
+explicit universal quantification in
+types.
+For example, all the following types are legal:
+<programlisting>
+ f1 :: forall a b. a -> b -> a
+ g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
-<sect2 id="existential-quantification">
-<title>Existentially quantified data constructors
-</title>
+ f2 :: (forall a. a->a) -> Int -> Int
+ g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
+ f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
+</programlisting>
+Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
+can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
+The <literal>forall</literal> makes explicit the universal quantification that
+is implicitly added by Haskell.
+</para>
<para>
-The 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:
+The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
+the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
+shows, the polymorphic type on the left of the function arrow can be overloaded.
</para>
-
<para>
-
+The function <literal>f3</literal> has a rank-3 type;
+it has rank-2 types on the left of a function arrow.
+</para>
+<para>
+GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
+arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
+that restriction has now been lifted.)
+In particular, a forall-type (also called a "type scheme"),
+including an operational type class context, is legal:
+<itemizedlist>
+<listitem> <para> On the left of a function arrow </para> </listitem>
+<listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
+<listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
+example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
+field type signatures.</para> </listitem>
+<listitem> <para> As the type of an implicit parameter </para> </listitem>
+<listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
+</itemizedlist>
+There is one place you cannot put a <literal>forall</literal>:
+you cannot instantiate a type variable with a forall-type. So you cannot
+make a forall-type the argument of a type constructor. So these types are illegal:
<programlisting>
- data Foo = forall a. MkFoo a (a -> Bool)
- | Nil
+ x1 :: [forall a. a->a]
+ x2 :: (forall a. a->a, Int)
+ x3 :: Maybe (forall a. a->a)
</programlisting>
-
-</para>
-
-<para>
-The data type <literal>Foo</literal> has two constructors with types:
+Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
+a type variable any more!
</para>
-<para>
-
-<programlisting>
- MkFoo :: forall a. a -> (a -> Bool) -> Foo
- Nil :: Foo
-</programlisting>
-</para>
+<sect3 id="univ">
+<title>Examples
+</title>
<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:
+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>
<programlisting>
- [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
-</programlisting>
+data T a = T1 (forall b. b -> b -> b) a
-</para>
+data MonadT m = MkMonad { return :: forall a. a -> m a,
+ bind :: forall a b. m a -> (a -> m b) -> m b
+ }
+
+newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
+</programlisting>
-<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>?
+The constructors have rank-2 types:
</para>
<para>
<programlisting>
- f (MkFoo val fn) = ???
+T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
+MkMonad :: forall m. (forall a. a -> m a)
+ -> (forall a b. m a -> (a -> m b) -> m b)
+ -> MonadT m
+MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
</programlisting>
</para>
<para>
-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:
+Notice that you don't need to use a <literal>forall</literal> if there's an
+explicit context. For example in the first argument of the
+constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
+prefixed to the argument type. The implicit <literal>forall</literal>
+quantifies all type variables that are not already in scope, and are
+mentioned in the type quantified over.
</para>
<para>
+As for type signatures, implicit quantification happens for non-overloaded
+types too. So if you write this:
<programlisting>
- f :: Foo -> Bool
- f (MkFoo val fn) = fn val
+ data T a = MkT (Either a b) (b -> b)
</programlisting>
-</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>
-
-<sect3 id="existential">
-<title>Why existential?
-</title>
-
-<para>
-What has this to do with <emphasis>existential</emphasis> quantification?
-Simply that <function>MkFoo</function> has the (nearly) isomorphic type
-</para>
-
-<para>
+it's just as if you had written this:
<programlisting>
- MkFoo :: (exists a . (a, a -> Bool)) -> Foo
+ data T a = MkT (forall b. Either a b) (forall b. b -> b)
</programlisting>
+That is, since the type variable <literal>b</literal> isn't in scope, it's
+implicitly universally quantified. (Arguably, it would be better
+to <emphasis>require</emphasis> explicit quantification on constructor arguments
+where that is what is wanted. Feedback welcomed.)
</para>
<para>
-But Haskell programmers can safely think of the ordinary
-<emphasis>universally</emphasis> quantified type given above, thereby avoiding
-adding a new existential quantification construct.
-</para>
-
-</sect3>
-
-<sect3>
-<title>Type classes</title>
-
-<para>
-An easy extension (implemented in <Command>hbc</Command>) is to allow
-arbitrary contexts before the constructor. For example:
+You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
+the constructor to suitable values, just as usual. For example,
</para>
<para>
<programlisting>
-data Baz = forall a. Eq a => Baz1 a a
- | forall b. Show b => Baz2 b (b -> b)
-</programlisting>
+ a1 :: T Int
+ a1 = T1 (\xy->x) 3
+
+ a2, a3 :: Swizzle
+ a2 = MkSwizzle sort
+ a3 = MkSwizzle reverse
+
+ a4 :: MonadT Maybe
+ a4 = let r x = Just x
+ b m k = case m of
+ Just y -> k y
+ Nothing -> Nothing
+ in
+ MkMonad r b
-</para>
+ mkTs :: (forall b. b -> b -> b) -> a -> [T a]
+ mkTs f x y = [T1 f x, T1 f y]
+</programlisting>
-<para>
-The two constructors have the types you'd expect:
</para>
<para>
-
-<programlisting>
-Baz1 :: forall a. Eq a => a -> a -> Baz
-Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
-</programlisting>
-
+The type of the argument can, as usual, be more general than the type
+required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
+does not need the <literal>Ord</literal> constraint.)
</para>
<para>
-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:
+When you use pattern matching, the bound variables may now have
+polymorphic types. For example:
</para>
<para>
<programlisting>
- f :: Baz -> String
- f (Baz1 p q) | p == q = "Yes"
- | otherwise = "No"
- f (Baz2 v fn) = show (fn v)
-</programlisting>
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
-</para>
+ g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
+ g (MkSwizzle s) xs f = s (map f (s xs))
+
+ h :: MonadT m -> [m a] -> m [a]
+ h m [] = return m []
+ h m (x:xs) = bind m x $ \y ->
+ bind m (h m xs) $ \ys ->
+ return m (y:ys)
+</programlisting>
-<para>
-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
-extract it on pattern matching.
</para>
<para>
-Notice the way that the syntax fits smoothly with that used for
-universal quantification earlier.
+In the function <function>h</function> we use the record selectors <literal>return</literal>
+and <literal>bind</literal> to extract the polymorphic bind and return functions
+from the <literal>MonadT</literal> data structure, rather than using pattern
+matching.
</para>
-
</sect3>
<sect3>
-<title>Restrictions</title>
+<title>Type inference</title>
<para>
-There are several restrictions on the ways in which existentially-quantified
-constructors can be use.
+In general, type inference for arbitrary-rank types is undecideable.
+GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
+to get a decidable algorithm by requiring some help from the programmer.
+We do not yet have a formal specification of "some help" but the rule is this:
</para>
-
<para>
-
-<itemizedlist>
-<listitem>
-
+<emphasis>For a lambda-bound or case-bound variable, x, either the programmer
+provides an explicit polymorphic type for x, or GHC's type inference will assume
+that x's type has no foralls in it</emphasis>.
+</para>
<para>
- 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>
-f1 (MkFoo a f) = a
-</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:
-
-
+What does it mean to "provide" an explicit type for x? You can do that by
+giving a type signature for x directly, using a pattern type signature
+(<xref linkend="scoped-type-variables">), thus:
<programlisting>
- f1 :: Foo -> a -- Weird!
+ \ f :: (forall a. a->a) -> (f True, f 'c')
</programlisting>
-
-
-What is this "<literal>a</literal>" in the result type? Clearly we don't mean
-this:
-
-
+Alternatively, you can give a type signature to the enclosing
+context, which GHC can "push down" to find the type for the variable:
<programlisting>
- f1 :: forall a. Foo -> a -- Wrong!
+ (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
</programlisting>
-
-
-The original program is just plain wrong. Here's another sort of error
-
-
+Here the type signature on the expression can be pushed inwards
+to give a type signature for f. Similarly, and more commonly,
+one can give a type signature for the function itself:
<programlisting>
- f2 (Baz1 a b) (Baz1 p q) = a==q
+ h :: (forall a. a->a) -> (Bool,Char)
+ h f = (f True, f 'c')
</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.
-
-
-</para>
-</listitem>
-<listitem>
-
-<para>
-You can't pattern-match on an existentially quantified
-constructor in a <literal>let</literal> or <literal>where</literal> group of
-bindings. So this is illegal:
-
-
+You don't need to give a type signature if the lambda bound variable
+is a constructor argument. Here is an example we saw earlier:
<programlisting>
- f3 x = a==b where { Baz1 a b = x }
+ f :: T a -> a -> (a, Char)
+ f (T1 w k) x = (w k x, w 'c' 'd')
</programlisting>
+Here we do not need to give a type signature to <literal>w</literal>, because
+it is an argument of constructor <literal>T1</literal> and that tells GHC all
+it needs to know.
+</para>
+</sect3>
-You can only pattern-match
-on an existentially-quantified constructor in a <literal>case</literal> expression or
-in the patterns of a function definition.
-
-The reason for this restriction is really an implementation one.
-Type-checking binding groups is already a nightmare without
-existentials complicating the picture. Also an existential pattern
-binding at the top level of a module doesn't make sense, because it's
-not clear how to prevent the existentially-quantified type "escaping".
-So for now, there's a simple-to-state restriction. We'll see how
-annoying it is.
-</para>
-</listitem>
-<listitem>
+<sect3 id="implicit-quant">
+<title>Implicit quantification</title>
<para>
-You can't use existential quantification for <literal>newtype</literal>
-declarations. So this is illegal:
-
-
+GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
+user-written types, if and only if there is no explicit <literal>forall</literal>,
+GHC finds all the type variables mentioned in the type that are not already
+in scope, and universally quantifies them.</emphasis> For example, the following pairs are
+equivalent:
<programlisting>
- newtype T = forall a. Ord a => MkT a
-</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
-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
-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,
-but single-field existentially quantified constructors aren't much
-use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
-stands, unless there are convincing reasons to change it.
-
+ f :: a -> a
+ f :: forall a. a -> a
+ g (x::a) = let
+ h :: a -> b -> b
+ h x y = y
+ in ...
+ g (x::a) = let
+ h :: forall b. a -> b -> b
+ h x y = y
+ in ...
+</programlisting>
</para>
-</listitem>
-<listitem>
-
<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:#
-
+Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
+point. For example:
<programlisting>
-data T = forall a. MkT [a] deriving( Eq )
-</programlisting>
+ f :: (a -> a) -> Int
+ -- MEANS
+ f :: forall a. (a -> a) -> Int
+ -- NOT
+ f :: (forall a. a -> a) -> Int
-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>
-instance Eq T where
- (MkT a) == (MkT b) = ???
+ g :: (Ord a => a -> a) -> Int
+ -- MEANS the illegal type
+ g :: forall a. (Ord a => a -> a) -> Int
+ -- NOT
+ g :: (forall a. Ord a => a -> a) -> Int
</programlisting>
-
-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!
+The latter produces an illegal type, which you might think is silly,
+but at least the rule is simple. If you want the latter type, you
+can write your for-alls explicitly. Indeed, doing so is strongly advised
+for rank-2 types.
</para>
-</listitem>
-
-</itemizedlist>
+</sect3>
+</sect2>
-</para>
-</sect3>
-</sect2>
<sect2 id="scoped-type-variables">
<title>Scoped type variables
</sect3>
<sect3>
-<title>Result type signatures</title>
+<title>Where a pattern type signature can occur</title>
<para>
-
+A pattern type signature can occur in any pattern. For example:
<itemizedlist>
+
+<listitem>
+<para>
+A pattern type signature can be on an arbitrary sub-pattern, not
+ust on a variable:
+
+
+<programlisting>
+ f ((x,y)::(a,b)) = (y,x) :: (b,a)
+</programlisting>
+
+
+</para>
+</listitem>
+<listitem>
+
+<para>
+ Pattern type signatures, including the result part, can be used
+in lambda abstractions:
+
+<programlisting>
+ (\ (x::a, y) :: a -> x)
+</programlisting>
+</para>
+</listitem>
+<listitem>
+
+<para>
+ Pattern type signatures, including the result part, can be used
+in <literal>case</literal> expressions:
+
+
+<programlisting>
+ case e of { (x::a, y) :: a -> x }
+</programlisting>
+
+</para>
+</listitem>
+
+<listitem>
+<para>
+To avoid ambiguity, the type after the “<literal>::</literal>” in a result
+pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
+token or a parenthesised type of some sort). To see why,
+consider how one would parse this:
+
+
+<programlisting>
+ \ x :: a -> b -> x
+</programlisting>
+
+
+</para>
+</listitem>
+
+<listitem>
+
+<para>
+ Pattern type signatures can bind existential type variables.
+For example:
+
+
+<programlisting>
+ data T = forall a. MkT [a]
+
+ f :: T -> T
+ f (MkT [t::a]) = MkT t3
+ where
+ t3::[a] = [t,t,t]
+</programlisting>
+
+
+</para>
+</listitem>
+
+
<listitem>
<para>
- The result type of a function can be given a signature,
-thus:
+Pattern type signatures
+can be used in pattern bindings:
+
+<programlisting>
+ f x = let (y, z::a) = x in ...
+ f1 x = let (y, z::Int) = x in ...
+ f2 (x::(Int,a)) = let (y, z::a) = x in ...
+ f3 :: (b->b) = \x -> x
+</programlisting>
+
+In all such cases, the binding is not generalised over the pattern-bound
+type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
+has type <literal>b -> b</literal> for some type <literal>b</literal>,
+and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
+In contrast, the binding
+<programlisting>
+ f4 :: b->b
+ f4 = \x -> x
+</programlisting>
+makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
+in <literal>f4</literal>'s scope.
+
+</para>
+</listitem>
+</itemizedlist>
+</para>
+
+</sect3>
+
+<sect3>
+<title>Result type signatures</title>
+
+<para>
+The result type of a function can be given a signature, thus:
<programlisting>
in \xs -> map g (reverse xs `zip` xs)
</programlisting>
-
</para>
-</listitem>
-
-</itemizedlist>
+<para>
+The type variables bound in a result type signature scope over the right hand side
+of the definition. However, consider this corner-case:
+<programlisting>
+ rev1 :: [a] -> [a] = \xs -> reverse xs
+ foo ys = rev (ys::[a])
+</programlisting>
+The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
+type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
+itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
+In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
+is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
+</para>
+<para>
+As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
+For example, the following program would be rejected, because it claims that <literal>rev1</literal>
+is polymorphic:
+<programlisting>
+ rev1 :: [b] -> [b]
+ rev1 :: [a] -> [a] = \xs -> reverse xs
+</programlisting>
</para>
<para>
</sect3>
-<sect3>
-<title>Where a pattern type signature can occur</title>
+</sect2>
+
+<sect2 id="deriving-typeable">
+<title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
<para>
-A pattern type signature can occur in any pattern. For example:
-<itemizedlist>
+Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
+declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
+In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
+classes <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
+</para>
+<para>
+GHC extends this list with two more classes that may be automatically derived
+(provided the <option>-fglasgow-exts</option> flag is specified):
+<literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
+modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
+appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
+</para>
+</sect2>
+
+<sect2 id="newtype-deriving">
+<title>Generalised derived instances for newtypes</title>
-<listitem>
<para>
-A pattern type signature can be on an arbitrary sub-pattern, not
-ust on a variable:
+When you define an abstract type using <literal>newtype</literal>, you may want
+the new type to inherit some instances from its representation. In
+Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
+<literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
+other classes you have to write an explicit instance declaration. For
+example, if you define
+
+<programlisting>
+ newtype Dollars = Dollars Int
+</programlisting>
+
+and you want to use arithmetic on <literal>Dollars</literal>, you have to
+explicitly define an instance of <literal>Num</literal>:
+
+<programlisting>
+ instance Num Dollars where
+ Dollars a + Dollars b = Dollars (a+b)
+ ...
+</programlisting>
+All the instance does is apply and remove the <literal>newtype</literal>
+constructor. It is particularly galling that, since the constructor
+doesn't appear at run-time, this instance declaration defines a
+dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
+dictionary, only slower!
+</para>
-<programlisting>
- f ((x,y)::(a,b)) = (y,x) :: (b,a)
-</programlisting>
+<sect3> <title> Generalising the deriving clause </title>
+<para>
+GHC now permits such instances to be derived instead, so one can write
+<programlisting>
+ newtype Dollars = Dollars Int deriving (Eq,Show,Num)
+</programlisting>
+
+and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
+for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
+derives an instance declaration of the form
+<programlisting>
+ instance Num Int => Num Dollars
+</programlisting>
+which just adds or removes the <literal>newtype</literal> constructor according to the type.
</para>
-</listitem>
-<listitem>
-
<para>
- Pattern type signatures, including the result part, can be used
-in lambda abstractions:
-<programlisting>
- (\ (x::a, y) :: a -> x)
-</programlisting>
-</para>
-</listitem>
-<listitem>
+We can also derive instances of constructor classes in a similar
+way. For example, suppose we have implemented state and failure monad
+transformers, such that
-<para>
- Pattern type signatures, including the result part, can be used
-in <literal>case</literal> expressions:
+<programlisting>
+ instance Monad m => Monad (State s m)
+ instance Monad m => Monad (Failure m)
+</programlisting>
+In Haskell 98, we can define a parsing monad by
+<programlisting>
+ type Parser tok m a = State [tok] (Failure m) a
+</programlisting>
+which is automatically a monad thanks to the instance declarations
+above. With the extension, we can make the parser type abstract,
+without needing to write an instance of class <literal>Monad</literal>, via
-<programlisting>
- case e of { (x::a, y) :: a -> x }
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving Monad
</programlisting>
+In this case the derived instance declaration is of the form
+<programlisting>
+ instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
+</programlisting>
+Notice that, since <literal>Monad</literal> is a constructor class, the
+instance is a <emphasis>partial application</emphasis> of the new type, not the
+entire left hand side. We can imagine that the type declaration is
+``eta-converted'' to generate the context of the instance
+declaration.
</para>
-</listitem>
-
-<listitem>
<para>
-To avoid ambiguity, the type after the “<literal>::</literal>” in a result
-pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
-token or a parenthesised type of some sort). To see why,
-consider how one would parse this:
+We can even derive instances of multi-parameter classes, provided the
+newtype is the last class parameter. In this case, a ``partial
+application'' of the class appears in the <literal>deriving</literal>
+clause. For example, given the class
-<programlisting>
- \ x :: a -> b -> x
+<programlisting>
+ class StateMonad s m | m -> s where ...
+ instance Monad m => StateMonad s (State s m) where ...
+</programlisting>
+then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
+<programlisting>
+ newtype Parser tok m a = Parser (State [tok] (Failure m) a)
+ deriving (Monad, StateMonad [tok])
</programlisting>
+The derived instance is obtained by completing the application of the
+class to the new type:
+<programlisting>
+ instance StateMonad [tok] (State [tok] (Failure m)) =>
+ StateMonad [tok] (Parser tok m)
+</programlisting>
</para>
-</listitem>
+<para>
-<listitem>
+As a result of this extension, all derived instances in newtype
+declarations are treated uniformly (and implemented just by reusing
+the dictionary for the representation type), <emphasis>except</emphasis>
+<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
+the newtype and its representation.
+</para>
+</sect3>
+<sect3> <title> A more precise specification </title>
<para>
- Pattern type signatures can bind existential type variables.
-For example:
-
+Derived instance declarations are constructed as follows. Consider the
+declaration (after expansion of any type synonyms)
-<programlisting>
- data T = forall a. MkT [a]
+<programlisting>
+ newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
+</programlisting>
- f :: T -> T
- f (MkT [t::a]) = MkT t3
- where
- t3::[a] = [t,t,t]
+where
+ <itemizedlist>
+<listitem><para>
+ <literal>S</literal> is a type constructor,
+</para></listitem>
+<listitem><para>
+ The <literal>t1...tk</literal> are types,
+</para></listitem>
+<listitem><para>
+ The <literal>vk+1...vn</literal> are type variables which do not occur in any of
+ the <literal>ti</literal>, and
+</para></listitem>
+<listitem><para>
+ The <literal>ci</literal> are partial applications of
+ classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
+ is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
+</para></listitem>
+<listitem><para>
+ None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
+ <literal>Typeable</literal>, or <literal>Data</literal>. These classes
+ should not "look through" the type or its constructor. You can still
+ derive these classes for a newtype, but it happens in the usual way, not
+ via this new mechanism.
+</para></listitem>
+</itemizedlist>
+Then, for each <literal>ci</literal>, the derived instance
+declaration is:
+<programlisting>
+ instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
</programlisting>
-
-
+where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
+right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
</para>
-</listitem>
-
+<para>
-<listitem>
+As an example which does <emphasis>not</emphasis> work, consider
+<programlisting>
+ newtype NonMonad m s = NonMonad (State s m s) deriving Monad
+</programlisting>
+Here we cannot derive the instance
+<programlisting>
+ instance Monad (State s m) => Monad (NonMonad m)
+</programlisting>
+because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
+and so cannot be "eta-converted" away. It is a good thing that this
+<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
+not, in fact, a monad --- for the same reason. Try defining
+<literal>>>=</literal> with the correct type: you won't be able to.
+</para>
<para>
-Pattern type signatures
-can be used in pattern bindings:
-<programlisting>
- f x = let (y, z::a) = x in ...
- f1 x = let (y, z::Int) = x in ...
- f2 (x::(Int,a)) = let (y, z::a) = x in ...
- f3 :: (b->b) = \x -> x
-</programlisting>
+Notice also that the <emphasis>order</emphasis> of class parameters becomes
+important, since we can only derive instances for the last one. If the
+<literal>StateMonad</literal> class above were instead defined as
-In all such cases, the binding is not generalised over the pattern-bound
-type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
-has type <literal>b -> b</literal> for some type <literal>b</literal>,
-and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
-In contrast, the binding
-<programlisting>
- f4 :: b->b
- f4 = \x -> x
+<programlisting>
+ class StateMonad m s | m -> s where ...
</programlisting>
-makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
-in <literal>f4</literal>'s scope.
+then we would not have been able to derive an instance for the
+<literal>Parser</literal> type above. We hypothesise that multi-parameter
+classes usually have one "main" parameter for which deriving new
+instances is most interesting.
</para>
-</listitem>
-</itemizedlist>
-</para>
-
</sect3>
+
</sect2>
</sect1>
<!-- ==================== End of type system extensions ================= -->
+<!-- ====================== TEMPLATE HASKELL ======================= -->
-<!-- ==================== ASSERTIONS ================= -->
-
-<sect1 id="sec-assertions">
-<title>Assertions
-<indexterm><primary>Assertions</primary></indexterm>
-</title>
-
-<para>
-If you want to make use of assertions in your standard Haskell code, you
-could define a function like the following:
-</para>
-
-<para>
-
-<programlisting>
-assert :: Bool -> a -> a
-assert False x = error "assertion failed!"
-assert _ x = x
-</programlisting>
+<sect1 id="template-haskell">
+<title>Template Haskell</title>
+<para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
+Template Haskell at <ulink url="http://www.haskell.org/th/">
+http://www.haskell.org/th/</ulink>, while
+the background to
+the main technical innovations is discussed in "<ulink
+url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
+Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
+The details of the Template Haskell design are still in flux. Make sure you
+consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
+(search for the type ExpQ).
+[Temporary: many changes to the original design are described in
+ <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
+Not all of these changes are in GHC 6.2.]
</para>
-<para>
-which works, but gives you back a less than useful error message --
-an assertion failed, but which and where?
+<para> The first example from that paper is set out below as a worked example to help get you started.
</para>
<para>
-One way out is to define an extended <function>assert</function> function which also
-takes a descriptive string to include in the error message and
-perhaps combine this with the use of a pre-processor which inserts
-the source location where <function>assert</function> was used.
+The documentation here describes the realisation in GHC. (It's rather sketchy just now;
+Tim Sheard is going to expand it.)
</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>
+ <sect2>
+ <title>Syntax</title>
+
+ <para> Template Haskell has the following new syntactic
+ constructions. You need to use the flag
+ <option>-fth</option><indexterm><primary><option>-fth</option></primary>
+ </indexterm>to switch these syntactic extensions on
+ (<option>-fth</option> is currently implied by
+ <option>-fglasgow-exts</option>, but you are encouraged to
+ specify it explicitly).</para>
+
+ <itemizedlist>
+ <listitem><para>
+ A splice is written <literal>$x</literal>, where <literal>x</literal> is an
+ identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
+ There must be no space between the "$" and the identifier or parenthesis. This use
+ of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
+ of "." as an infix operator. If you want the infix operator, put spaces around it.
+ </para>
+ <para> A splice can occur in place of
+ <itemizedlist>
+ <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
+ <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
+ <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
+ </itemizedlist>
+ (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
+ the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
+ as in the paper.)
+ </para></listitem>
+
+
+ <listitem><para>
+ A expression quotation is written in Oxford brackets, thus:
+ <itemizedlist>
+ <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
+ the quotation has type <literal>Expr</literal>.</para></listitem>
+ <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
+ the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
+ <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
+ the quotation has type <literal>Type</literal>.</para></listitem>
+ </itemizedlist></para></listitem>
+
+ <listitem><para>
+ Reification is written thus:
+ <itemizedlist>
+ <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
+ has type <literal>Dec</literal>. </para></listitem>
+ <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
+ <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
+ <listitem><para> Still to come: fixities </para></listitem>
+
+ </itemizedlist></para>
+ </listitem>
+
+
+ </itemizedlist>
+</sect2>
+<sect2> <title> Using Template Haskell </title>
<para>
-
-<programlisting>
-kelvinToC :: Double -> Double
-kelvinToC k = assert (k >= 0.0) (k+273.15)
-</programlisting>
-
+<itemizedlist>
+ <listitem><para>
+ The data types and monadic constructor functions for Template Haskell are in the library
+ <literal>Language.Haskell.THSyntax</literal>.
+ </para></listitem>
+
+ <listitem><para>
+ You can only run a function at compile time if it is imported from another module. That is,
+ you can't define a function in a module, and call it from within a splice in the same module.
+ (It would make sense to do so, but it's hard to implement.)
+ </para></listitem>
+
+ <listitem><para>
+ The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
+ </para></listitem>
+ <listitem><para>
+ If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
+ run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
+ compiles and runs a program, and then looks at the result. So it's important that
+ the program it compiles produces results whose representations are identical to
+ those of the compiler itself.
+ </para></listitem>
+</itemizedlist>
</para>
-
-<para>
-Ghc will rewrite this to also include the source location where the
-assertion was made,
+<para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
+ or file-at-a-time). There used to be a restriction to the former two, but that restriction
+ has been lifted.
</para>
-
-<para>
+</sect2>
+
+<sect2> <title> A Template Haskell Worked Example </title>
+<para>To help you get over the confidence barrier, try out this skeletal worked example.
+ First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
<programlisting>
-assert pred val ==> assertError "Main.hs|15" pred val
-</programlisting>
-
-</para>
-
-<para>
-The rewrite is only performed by the compiler when it spots
-applications of <function>Control.Exception.assert</function>, so you
-can still define and use your own versions of
-<function>assert</function>, should you so wish. If not, import
-<literal>Control.Exception</literal> to make use
-<function>assert</function> in your code.
-</para>
-
-<para>
-To have the compiler ignore uses of assert, use the compiler option
-<option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
-option</primary></indexterm> That is, expressions of the form
-<literal>assert pred e</literal> will be rewritten to
-<literal>e</literal>.
-</para>
-
-<para>
-Assertion failures can be caught, see the documentation for the
-<literal>Control.Exception</literal> library for the details.
-</para>
-
-</sect1>
+{- Main.hs -}
+module Main where
-<sect1 id="syntax-extns">
-<title>Syntactic extensions</title>
+-- Import our template "pr"
+import Printf ( pr )
-<!-- ====================== HIERARCHICAL MODULES ======================= -->
+-- The splice operator $ takes the Haskell source code
+-- generated at compile time by "pr" and splices it into
+-- the argument of "putStrLn".
+main = putStrLn ( $(pr "Hello") )
- <sect2 id="hierarchical-modules">
- <title>Hierarchical Modules</title>
- <para>GHC supports a small extension to the syntax of module
- names: a module name is allowed to contain a dot
- <literal>‘.’</literal>. This is also known as the
- “hierarchical module namespace” extension, because
- it extends the normally flat Haskell module namespace into a
- more flexible hierarchy of modules.</para>
+{- Printf.hs -}
+module Printf where
- <para>This extension has very little impact on the language
- itself; modules names are <emphasis>always</emphasis> fully
- qualified, so you can just think of the fully qualified module
- name as <quote>the module name</quote>. In particular, this
- means that the full module name must be given after the
- <literal>module</literal> keyword at the beginning of the
- module; for example, the module <literal>A.B.C</literal> must
- begin</para>
+-- Skeletal printf from the paper.
+-- It needs to be in a separate module to the one where
+-- you intend to use it.
-<programlisting>module A.B.C</programlisting>
+-- Import some Template Haskell syntax
+import Language.Haskell.THSyntax
+-- Describe a format string
+data Format = D | S | L String
- <para>It is a common strategy to use the <literal>as</literal>
- keyword to save some typing when using qualified names with
- hierarchical modules. For example:</para>
+-- Parse a format string. This is left largely to you
+-- as we are here interested in building our first ever
+-- Template Haskell program and not in building printf.
+parse :: String -> [Format]
+parse s = [ L s ]
+-- Generate Haskell source code from a parsed representation
+-- of the format string. This code will be spliced into
+-- the module which calls "pr", at compile time.
+gen :: [Format] -> ExpQ
+gen [D] = [| \n -> show n |]
+gen [S] = [| \s -> s |]
+gen [L s] = stringE s
+
+-- Here we generate the Haskell code for the splice
+-- from an input format string.
+pr :: String -> ExpQ
+pr s = gen (parse s)
+</programlisting>
+
+<para>Now run the compiler (here we are a Cygwin prompt on Windows):
+</para>
<programlisting>
-import qualified Control.Monad.ST.Strict as ST
+$ ghc --make -fth main.hs -o main.exe
</programlisting>
- <para>Hierarchical modules have an impact on the way that GHC
- searches for files. For a description, see <xref
- linkend="finding-hierarchical-modules">.</para>
+<para>Run "main.exe" and here is your output:</para>
- <para>GHC comes with a large collection of libraries arranged
- hierarchically; see the accompanying library documentation.
- There is an ongoing project to create and maintain a stable set
- of <quote>core</quote> libraries used by several Haskell
- compilers, and the libraries that GHC comes with represent the
- current status of that project. For more details, see <ulink
- url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
- Libraries</ulink>.</para>
+<programlisting>
+$ ./main
+Hello
+</programlisting>
- </sect2>
+</sect2>
+
+</sect1>
-<!-- ====================== PATTERN GUARDS ======================= -->
+<!-- ===================== Arrow notation =================== -->
-<sect2 id="pattern-guards">
-<title>Pattern guards</title>
+<sect1 id="arrow-notation">
+<title>Arrow notation
+</title>
+
+<para>Arrows are a generalization of monads introduced by John Hughes.
+For more details, see
+<itemizedlist>
+<listitem>
<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.)
+“Generalising Monads to Arrows”,
+John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
+pp67–111, May 2000.
</para>
+</listitem>
+<listitem>
<para>
-Suppose we have an abstract data type of finite maps, with a
-lookup operation:
-
-<programlisting>
-lookup :: FiniteMap -> Int -> Maybe Int
-</programlisting>
+“<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
+Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
+</para>
+</listitem>
-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:
+<listitem>
+<para>
+“<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
+Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
+Palgrave, 2003.
</para>
+</listitem>
-<programlisting>
-clunky env var1 var2 | ok1 && ok2 = val1 + val2
-| otherwise = var1 + var2
-where
- m1 = lookup env var1
- m2 = lookup env var2
- ok1 = maybeToBool m1
- ok2 = maybeToBool m2
- val1 = expectJust m1
- val2 = expectJust m2
-</programlisting>
+</itemizedlist>
+and the arrows web page at
+<ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
+With the <option>-farrows</option> flag, GHC supports the arrow
+notation described in the second of these papers.
+What follows is a brief introduction to the notation;
+it won't make much sense unless you've read Hughes's paper.
+This notation is translated to ordinary Haskell,
+using combinators from the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module.
+</para>
+
+<para>The extension adds a new kind of expression for defining arrows,
+of the form <literal>proc pat -> cmd</literal>,
+where <literal>proc</literal> is a new keyword.
+The variables of the pattern are bound in the body of the
+<literal>proc</literal>-expression,
+which is a new sort of thing called a <firstterm>command</firstterm>.
+The syntax of commands is as follows:
+<screen>
+cmd ::= exp1 -< exp2
+ | exp1 -<< exp2
+ | do { cstmt1 .. cstmtn ; cmd }
+ | let decls in cmd
+ | if exp then cmd1 else cmd2
+ | case exp of { calts }
+ | cmd1 qop cmd2
+ | (| aexp cmd1 .. cmdn |)
+ | \ pat1 .. patn -> cmd
+ | cmd aexp
+ | ( cmd )
+
+cstmt ::= let decls
+ | pat <- cmd
+ | rec { cstmt1 .. cstmtn }
+ | cmd
+</screen>
+Commands produce values, but (like monadic computations)
+may yield more than one value,
+or none, and may do other things as well.
+For the most part, familiarity with monadic notation is a good guide to
+using commands.
+However the values of expressions, even monadic ones,
+are determined by the values of the variables they contain;
+this is not necessarily the case for commands.
+</para>
<para>
-The auxiliary functions are
+A simple example of the new notation is the expression
+<screen>
+proc x -> f -< x+1
+</screen>
+We call this a <firstterm>procedure</firstterm> or
+<firstterm>arrow abstraction</firstterm>.
+As with a lambda expression, the variable <literal>x</literal>
+is a new variable bound within the <literal>proc</literal>-expression.
+It refers to the input to the arrow.
+In the above example, <literal>-<</literal> is not an identifier but an
+new reserved symbol used for building commands from an expression of arrow
+type and an expression to be fed as input to that arrow.
+(The weird look will make more sense later.)
+It may be read as analogue of application for arrows.
+The above example is equivalent to the Haskell expression
+<screen>
+arr (\ x -> x+1) >>> f
+</screen>
+That would make no sense if the expression to the left of
+<literal>-<</literal> involves the bound variable <literal>x</literal>.
+More generally, the expression to the left of <literal>-<</literal>
+may not involve any <firstterm>local variable</firstterm>,
+i.e. a variable bound in the current arrow abstraction.
+For such a situation there is a variant <literal>-<<</literal>, as in
+<screen>
+proc x -> f x -<< x+1
+</screen>
+which is equivalent to
+<screen>
+arr (\ x -> (f, x+1)) >>> app
+</screen>
+so in this case the arrow must belong to the <literal>ArrowApply</literal>
+class.
+Such an arrow is equivalent to a monad, so if you're using this form
+you may find a monadic formulation more convenient.
</para>
-<programlisting>
-maybeToBool :: Maybe a -> Bool
-maybeToBool (Just x) = True
-maybeToBool Nothing = False
+<sect2>
+<title>do-notation for commands</title>
-expectJust :: Maybe a -> a
-expectJust (Just x) = x
-expectJust Nothing = error "Unexpected Nothing"
-</programlisting>
+<para>
+Another form of command is a form of <literal>do</literal>-notation.
+For example, you can write
+<screen>
+proc x -> do
+ y <- f -< x+1
+ g -< 2*y
+ let z = x+y
+ t <- h -< x*z
+ returnA -< t+z
+</screen>
+You can read this much like ordinary <literal>do</literal>-notation,
+but with commands in place of monadic expressions.
+The first line sends the value of <literal>x+1</literal> as an input to
+the arrow <literal>f</literal>, and matches its output against
+<literal>y</literal>.
+In the next line, the output is discarded.
+The arrow <literal>returnA</literal> is defined in the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module as <literal>arr id</literal>.
+The above example is treated as an abbreviation for
+<screen>
+arr (\ x -> (x, x)) >>>
+ first (arr (\ x -> x+1) >>> f) >>>
+ arr (\ (y, x) -> (y, (x, y))) >>>
+ first (arr (\ y -> 2*y) >>> g) >>>
+ arr snd >>>
+ arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
+ first (arr (\ (x, z) -> x*z) >>> h) >>>
+ arr (\ (t, z) -> t+z) >>>
+ returnA
+</screen>
+Note that variables not used later in the composition are projected out.
+After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
+defined in the
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
+module, this reduces to
+<screen>
+arr (\ x -> (x+1, x)) >>>
+ first f >>>
+ arr (\ (y, x) -> (2*y, (x, y))) >>>
+ first g >>>
+ arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
+ first h >>>
+ arr (\ (t, z) -> t+z)
+</screen>
+which is what you might have written by hand.
+With arrow notation, GHC keeps track of all those tuples of variables for you.
+</para>
<para>
-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.
+Note that although the above translation suggests that
+<literal>let</literal>-bound variables like <literal>z</literal> must be
+monomorphic, the actual translation produces Core,
+so polymorphic variables are allowed.
</para>
<para>
-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:
+It's also possible to have mutually recursive bindings,
+using the new <literal>rec</literal> keyword, as in the following example:
+<screen>
+counter :: ArrowCircuit a => a Bool Int
+counter = proc reset -> do
+ rec output <- returnA -< if reset then 0 else next
+ next <- delay 0 -< output+1
+ returnA -< output
+</screen>
+The translation of such forms uses the <literal>loop</literal> combinator,
+so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
</para>
-<programlisting>
-clunky env var1 var1 = case lookup env var1 of
- Nothing -> fail
- Just val1 -> case lookup env var2 of
- Nothing -> fail
- Just val2 -> val1 + val2
-where
- fail = val1 + val2
-</programlisting>
+</sect2>
+
+<sect2>
+<title>Conditional commands</title>
<para>
-This is a bit shorter, but hardly better. Of course, we can rewrite any set
-of pattern-matching, guarded equations as case expressions; that is
-precisely what the compiler does when compiling equations! The reason that
-Haskell provides guarded equations is because they allow us to write down
-the cases we want to consider, one at a time, independently of each other.
-This structure is hidden in the case version. Two of the right-hand sides
-are really the same (<function>fail</function>), and the whole expression
-tends to become more and more indented.
+In the previous example, we used a conditional expression to construct the
+input for an arrow.
+Sometimes we want to conditionally execute different commands, as in
+<screen>
+proc (x,y) ->
+ if f x y
+ then g -< x+1
+ else h -< y+2
+</screen>
+which is translated to
+<screen>
+arr (\ (x,y) -> if f x y then Left x else Right y) >>>
+ (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
+</screen>
+Since the translation uses <literal>|||</literal>,
+the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
</para>
<para>
-Here is how I would write clunky:
+There are also <literal>case</literal> commands, like
+<screen>
+case input of
+ [] -> f -< ()
+ [x] -> g -< x+1
+ x1:x2:xs -> do
+ y <- h -< (x1, x2)
+ ys <- k -< xs
+ returnA -< y:ys
+</screen>
+The syntax is the same as for <literal>case</literal> expressions,
+except that the bodies of the alternatives are commands rather than expressions.
+The translation is similar to that of <literal>if</literal> commands.
+</para>
+
+</sect2>
+
+<sect2>
+<title>Defining your own control structures</title>
+
+<para>
+As we're seen, arrow notation provides constructs,
+modelled on those for expressions,
+for sequencing, value recursion and conditionals.
+But suitable combinators,
+which you can define in ordinary Haskell,
+may also be used to build new commands out of existing ones.
+The basic idea is that a command defines an arrow from environments to values.
+These environments assign values to the free local variables of the command.
+Thus combinators that produce arrows from arrows
+may also be used to build commands from commands.
+For example, the <literal>ArrowChoice</literal> class includes a combinator
+<programlisting>
+ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
+</programlisting>
+so we can use it to build commands:
+<programlisting>
+expr' = proc x ->
+ returnA -< x
+ <+> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y
+ <+> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y
+</programlisting>
+This is equivalent to
+<programlisting>
+expr' = (proc x -> returnA -< x)
+ <+> (proc x -> do
+ symbol Plus -< ()
+ y <- term -< ()
+ expr' -< x + y)
+ <+> (proc x -> do
+ symbol Minus -< ()
+ y <- term -< ()
+ expr' -< x - y)
+</programlisting>
+It is essential that this operator be polymorphic in <literal>e</literal>
+(representing the environment input to the command
+and thence to its subcommands)
+and satisfy the corresponding naturality property
+<screen>
+arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
+</screen>
+at least for strict <literal>k</literal>.
+(This should be automatic if you're not using <literal>seq</literal>.)
+This ensures that environments seen by the subcommands are environments
+of the whole command,
+and also allows the translation to safely trim these environments.
+The operator must also not use any variable defined within the current
+arrow abstraction.
</para>
+<para>
+We could define our own operator
<programlisting>
-clunky env var1 var1
- | Just val1 <- lookup env var1
- , Just val2 <- lookup env var2
- = val1 + val2
-...other equations for clunky...
+untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
+untilA body cond = proc x ->
+ if cond x then returnA -< ()
+ else do
+ body -< x
+ untilA body cond -< x
</programlisting>
+and use it in the same way.
+Of course this infix syntax only makes sense for binary operators;
+there is also a more general syntax involving special brackets:
+<screen>
+proc x -> do
+ y <- f -< x+1
+ (|untilA (increment -< x+y) (within 0.5 -< x)|)
+</screen>
+</para>
+
+</sect2>
+
+<sect2>
+<title>Primitive constructs</title>
<para>
-The semantics should be clear enough. The qualifers are matched in order.
-For a <literal><-</literal> qualifier, which I call a pattern guard, the
-right hand side is evaluated and matched against the pattern on the left.
-If the match fails then the whole guard fails and the next equation is
-tried. If it succeeds, then the appropriate binding takes place, and the
-next qualifier is matched, in the augmented environment. Unlike list
-comprehensions, however, the type of the expression to the right of the
-<literal><-</literal> is the same as the type of the pattern to its
-left. The bindings introduced by pattern guards scope over all the
-remaining guard qualifiers, and over the right hand side of the equation.
+Some operators will need to pass additional inputs to their subcommands.
+For example, in an arrow type supporting exceptions,
+the operator that attaches an exception handler will wish to pass the
+exception that occurred to the handler.
+Such an operator might have a type
+<screen>
+handleA :: ... => a e c -> a (e,Ex) c -> a e c
+</screen>
+where <literal>Ex</literal> is the type of exceptions handled.
+You could then use this with arrow notation by writing a command
+<screen>
+body `handleA` \ ex -> handler
+</screen>
+so that if an exception is raised in the command <literal>body</literal>,
+the variable <literal>ex</literal> is bound to the value of the exception
+and the command <literal>handler</literal>,
+which typically refers to <literal>ex</literal>, is entered.
+Though the syntax here looks like a functional lambda,
+we are talking about commands, and something different is going on.
+The input to the arrow represented by a command consists of values for
+the free local variables in the command, plus a stack of anonymous values.
+In all the prior examples, this stack was empty.
+In the second argument to <literal>handleA</literal>,
+this stack consists of one value, the value of the exception.
+The command form of lambda merely gives this value a name.
+</para>
+
+<para>
+More concretely,
+the values on the stack are paired to the right of the environment.
+So when designing operators like <literal>handleA</literal> that pass
+extra inputs to their subcommands,
+More precisely, the type of each argument of the operator (and its result)
+should have the form
+<screen>
+a (...(e,t1), ... tn) t
+</screen>
+where <replaceable>e</replaceable> is a polymorphic variable
+(representing the environment)
+and <replaceable>ti</replaceable> are the types of the values on the stack,
+with <replaceable>t1</replaceable> being the <quote>top</quote>.
+The polymorphic variable <replaceable>e</replaceable> must not occur in
+<replaceable>a</replaceable>, <replaceable>ti</replaceable> or
+<replaceable>t</replaceable>.
+However the arrows involved need not be the same.
+Here are some more examples of suitable operators:
+<screen>
+bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
+runReader :: ... => a e c -> a' (e,State) c
+runState :: ... => a e c -> a' (e,State) (c,State)
+</screen>
+We can supply the extra input required by commands built with the last two
+by applying them to ordinary expressions, as in
+<screen>
+proc x -> do
+ s <- ...
+ (|runReader (do { ... })|) s
+</screen>
+which adds <literal>s</literal> to the stack of inputs to the command
+built using <literal>runReader</literal>.
</para>
<para>
-Just as with list comprehensions, boolean expressions can be freely mixed
-with among the pattern guards. For example:
-</para>
+The command versions of lambda abstraction and application are analogous to
+the expression versions.
+In particular, the beta and eta rules describe equivalences of commands.
+These three features (operators, lambda abstraction and application)
+are the core of the notation; everything else can be built using them,
+though the results would be somewhat clumsy.
+For example, we could simulate <literal>do</literal>-notation by defining
+<programlisting>
+bind :: Arrow a => a e b -> a (e,b) c -> a e c
+u `bind` f = returnA &&& u >>> f
+bind_ :: Arrow a => a e b -> a e c -> a e c
+u `bind_` f = u `bind` (arr fst >>> f)
+</programlisting>
+We could simulate <literal>do</literal> by defining
<programlisting>
-f x | [y] <- x
- , y > 3
- , Just z <- h y
- = ...
+cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
+cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
</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.
+</sect2>
+
+<sect2>
+<title>Differences with the paper</title>
+
+<itemizedlist>
+
+<listitem>
+<para>Instead of a single form of arrow application (arrow tail) with two
+translations, the implementation provides two forms
+<quote><literal>-<</literal></quote> (first-order)
+and <quote><literal>-<<</literal></quote> (higher-order).
+</para>
+</listitem>
+
+<listitem>
+<para>User-defined operators are flagged with banana brackets instead of
+a new <literal>form</literal> keyword.
</para>
+</listitem>
+
+</itemizedlist>
+
</sect2>
-<!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
+<sect2>
+<title>Portability</title>
+
+<para>
+Although only GHC implements arrow notation directly,
+there is also a preprocessor
+(available from the
+<ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
+that translates arrow notation into Haskell 98
+for use with other Haskell systems.
+You would still want to check arrow programs with GHC;
+tracing type errors in the preprocessor output is not easy.
+Modules intended for both GHC and the preprocessor must observe some
+additional restrictions:
+<itemizedlist>
- <sect2 id="parallel-list-comprehensions">
- <title>Parallel List Comprehensions</title>
- <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
- </indexterm>
- <indexterm><primary>parallel list comprehensions</primary>
- </indexterm>
+<listitem>
+<para>
+The module must import
+<ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
+</para>
+</listitem>
- <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>
+<listitem>
+<para>
+The preprocessor cannot cope with other Haskell extensions.
+These would have to go in separate modules.
+</para>
+</listitem>
- <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>
+<listitem>
+<para>
+Because the preprocessor targets Haskell (rather than Core),
+<literal>let</literal>-bound variables are monomorphic.
+</para>
+</listitem>
-<programlisting>
- [ (x, y) | x <- xs | y <- ys ]
-</programlisting>
+</itemizedlist>
+</para>
- <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>
+</sect2>
- <para>We can define parallel list comprehensions by translation to
- regular comprehensions. Here's the basic idea:</para>
+</sect1>
- <para>Given a parallel comprehension of the form: </para>
+<!-- ==================== ASSERTIONS ================= -->
+
+<sect1 id="sec-assertions">
+<title>Assertions
+<indexterm><primary>Assertions</primary></indexterm>
+</title>
+
+<para>
+If you want to make use of assertions in your standard Haskell code, you
+could define a function like the following:
+</para>
+
+<para>
<programlisting>
- [ e | p1 <- e11, p2 <- e12, ...
- | q1 <- e21, q2 <- e22, ...
- ...
- ]
+assert :: Bool -> a -> a
+assert False x = error "assertion failed!"
+assert _ x = x
</programlisting>
- <para>This will be translated to: </para>
+</para>
-<programlisting>
- [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
- [(q1,q2) | q1 <- e21, q2 <- e22, ...]
- ...
- ]
-</programlisting>
+<para>
+which works, but gives you back a less than useful error message --
+an assertion failed, but which and where?
+</para>
- <para>where `zipN' is the appropriate zip for the given number of
- branches.</para>
+<para>
+One way out is to define an extended <function>assert</function> function which also
+takes a descriptive string to include in the error message and
+perhaps combine this with the use of a pre-processor which inserts
+the source location where <function>assert</function> was used.
+</para>
- </sect2>
+<para>
+Ghc offers a helping hand here, doing all of this for you. For every
+use of <function>assert</function> in the user's source:
+</para>
-<sect2 id="rebindable-syntax">
-<title>Rebindable syntax</title>
+<para>
+<programlisting>
+kelvinToC :: Double -> Double
+kelvinToC k = assert (k >= 0.0) (k+273.15)
+</programlisting>
- <para>GHC allows most kinds of built-in syntax to be rebound by
- the user, to facilitate replacing the <literal>Prelude</literal>
- with a home-grown version, for example.</para>
+</para>
- <para>You may want to define your own numeric class
- hierarchy. It completely defeats that purpose if the
- literal "1" means "<literal>Prelude.fromInteger
- 1</literal>", which is what the Haskell Report specifies.
- So the <option>-fno-implicit-prelude</option> flag causes
- the following pieces of built-in syntax to refer to
- <emphasis>whatever is in scope</emphasis>, not the Prelude
- versions:</para>
+<para>
+Ghc will rewrite this to also include the source location where the
+assertion was made,
+</para>
- <itemizedlist>
- <listitem>
- <para>Integer and fractional literals mean
- "<literal>fromInteger 1</literal>" and
- "<literal>fromRational 3.2</literal>", not the
- Prelude-qualified versions; both in expressions and in
- patterns. </para>
- <para>However, the standard Prelude <literal>Eq</literal> class
- is still used for the equality test necessary for literal patterns.</para>
- </listitem>
+<para>
- <listitem>
- <para>Negation (e.g. "<literal>- (f x)</literal>")
- means "<literal>negate (f x)</literal>" (not
- <literal>Prelude.negate</literal>).</para>
- </listitem>
+<programlisting>
+assert pred val ==> assertError "Main.hs|15" pred val
+</programlisting>
- <listitem>
- <para>In an n+k pattern, the standard Prelude
- <literal>Ord</literal> class is still used for comparison,
- but the necessary subtraction uses whatever
- "<literal>(-)</literal>" is in scope (not
- "<literal>Prelude.(-)</literal>").</para>
- </listitem>
+</para>
- <listitem>
- <para>"Do" notation is translated using whatever
- functions <literal>(>>=)</literal>,
- <literal>(>>)</literal>, <literal>fail</literal>, and
- <literal>return</literal>, are in scope (not the Prelude
- versions). List comprehensions, and parallel array
- comprehensions, are unaffected. </para></listitem>
- </itemizedlist>
+<para>
+The rewrite is only performed by the compiler when it spots
+applications of <function>Control.Exception.assert</function>, so you
+can still define and use your own versions of
+<function>assert</function>, should you so wish. If not, import
+<literal>Control.Exception</literal> to make use
+<function>assert</function> in your code.
+</para>
- <para>Be warned: this is an experimental facility, with fewer checks than
- usual. In particular, it is essential that the functions GHC finds in scope
- must have the appropriate types, namely:
- <screen>
- fromInteger :: forall a. (...) => Integer -> a
- fromRational :: forall a. (...) => Rational -> a
- negate :: forall a. (...) => a -> a
- (-) :: forall a. (...) => a -> a -> a
- (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
- (>>) :: forall m a. (...) => m a -> m b -> m b
- return :: forall m a. (...) => a -> m a
- fail :: forall m a. (...) => String -> m a
- </screen>
- (The (...) part can be any context including the empty context; that part
- is up to you.)
- If the functions don't have the right type, very peculiar things may
- happen. Use <literal>-dcore-lint</literal> to
- typecheck the desugared program. If Core Lint is happy you should be all right.</para>
+<para>
+To have the compiler ignore uses of assert, use the compiler option
+<option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
+option</primary></indexterm> That is, expressions of the form
+<literal>assert pred e</literal> will be rewritten to
+<literal>e</literal>.
+</para>
+
+<para>
+Assertion failures can be caught, see the documentation for the
+<literal>Control.Exception</literal> library for the details.
+</para>
-</sect2>
</sect1>
+
<!-- =============================== PRAGMAS =========================== -->
<sect1 id="pragmas">
unrecognised <replaceable>word</replaceable> is (silently)
ignored.</para>
-<sect2 id="inline-pragma">
-<title>INLINE pragma
+ <sect2 id="deprecated-pragma">
+ <title>DEPRECATED pragma</title>
+ <indexterm><primary>DEPRECATED</primary>
+ </indexterm>
-<indexterm><primary>INLINE pragma</primary></indexterm>
-<indexterm><primary>pragma, INLINE</primary></indexterm></title>
+ <para>The DEPRECATED pragma lets you specify that a particular
+ function, class, or type, is deprecated. There are two
+ forms.
-<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>
+ <itemizedlist>
+ <listitem>
+ <para>You can deprecate an entire module thus:</para>
+<programlisting>
+ module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
+ ...
+</programlisting>
+ <para>When you compile any module that import
+ <literal>Wibble</literal>, GHC will print the specified
+ message.</para>
+ </listitem>
-<para>
-You will probably see these unfoldings (in Core syntax) in your
-interface files.
-</para>
+ <listitem>
+ <para>You can deprecate a function, class, or type, with the
+ following top-level declaration:</para>
+<programlisting>
+ {-# DEPRECATED f, C, T "Don't use these" #-}
+</programlisting>
+ <para>When you compile any module that imports and uses any
+ of the specifed entities, GHC will print the specified
+ message.</para>
+ </listitem>
+ </itemizedlist>
+ Any use of the deprecated item, or of anything from a deprecated
+ module, will be flagged with an appropriate message. However,
+ deprecations are not reported for
+ (a) uses of a deprecated function within its defining module, and
+ (b) uses of a deprecated function in an export list.
+ The latter reduces spurious complaints within a library
+ in which one module gathers together and re-exports
+ the exports of several others.
+ </para>
+ <para>You can suppress the warnings with the flag
+ <option>-fno-warn-deprecations</option>.</para>
+ </sect2>
-<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>
+ <sect2 id="inline-noinline-pragma">
+ <title>INLINE and NOINLINE pragmas</title>
-<para>
-The sledgehammer you can bring to bear is the
-<literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
+ <para>These pragmas control the inlining of function
+ definitions.</para>
+
+ <sect3 id="inline-pragma">
+ <title>INLINE pragma</title>
+ <indexterm><primary>INLINE</primary></indexterm>
+
+ <para>GHC (with <option>-O</option>, as always) tries to
+ inline (or “unfold”) functions/values that are
+ “small enough,” thus avoiding the call overhead
+ and possibly exposing other more-wonderful optimisations.
+ Normally, if GHC decides a function is “too
+ expensive” to inline, it will not do so, nor will it
+ export that unfolding for other modules to use.</para>
+
+ <para>The sledgehammer you can bring to bear is the
+ <literal>INLINE</literal><indexterm><primary>INLINE
+ pragma</primary></indexterm> pragma, used thusly:</para>
<programlisting>
key_function :: Int -> String -> (Bool, Double)
#endif
</programlisting>
-(You don't need to do the C pre-processor carry-on unless you're going
-to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
-</para>
+ <para>(You don't need to do the C pre-processor carry-on
+ unless you're going to stick the code through HBC—it
+ doesn't like <literal>INLINE</literal> pragmas.)</para>
-<para>
-The major effect of an <literal>INLINE</literal> pragma is to declare a function's
-“cost” to be very low. The normal unfolding machinery will then be
-very keen to inline it.
-</para>
+ <para>The major effect of an <literal>INLINE</literal> pragma
+ is to declare a function's “cost” to be very low.
+ The normal unfolding machinery will then be very keen to
+ inline it.</para>
-<para>
-An <literal>INLINE</literal> pragma for a function can be put anywhere its type
-signature could be put.
-</para>
+ <para>Syntactially, an <literal>INLINE</literal> pragma for a
+ function can be put anywhere its type signature could be
+ put.</para>
-<para>
-<literal>INLINE</literal> pragmas are a particularly good idea for the
-<literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
-For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
+ <para><literal>INLINE</literal> pragmas are a particularly
+ good idea for the
+ <literal>then</literal>/<literal>return</literal> (or
+ <literal>bind</literal>/<literal>unit</literal>) functions in
+ a monad. For example, in GHC's own
+ <literal>UniqueSupply</literal> monad code, we have:</para>
<programlisting>
#ifdef __GLASGOW_HASKELL__
#endif
</programlisting>
-</para>
+ <para>See also the <literal>NOINLINE</literal> pragma (<xref
+ linkend="noinline-pragma">).</para>
+ </sect3>
+
+ <sect3 id="noinline-pragma">
+ <title>NOINLINE pragma</title>
+
+ <indexterm><primary>NOINLINE</primary></indexterm>
+ <indexterm><primary>NOTINLINE</primary></indexterm>
+
+ <para>The <literal>NOINLINE</literal> pragma does exactly what
+ you'd expect: it stops the named function from being inlined
+ by the compiler. You shouldn't ever need to do this, unless
+ you're very cautious about code size.</para>
+
+ <para><literal>NOTINLINE</literal> is a synonym for
+ <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
+ specified by Haskell 98 as the standard way to disable
+ inlining, so it should be used if you want your code to be
+ portable).</para>
+ </sect3>
+
+ <sect3 id="phase-control">
+ <title>Phase control</title>
+
+ <para> Sometimes you want to control exactly when in GHC's
+ pipeline the INLINE pragma is switched on. Inlining happens
+ only during runs of the <emphasis>simplifier</emphasis>. Each
+ run of the simplifier has a different <emphasis>phase
+ number</emphasis>; the phase number decreases towards zero.
+ If you use <option>-dverbose-core2core</option> you'll see the
+ sequence of phase numbers for successive runs of the
+ simpifier. In an INLINE pragma you can optionally specify a
+ phase number, thus:</para>
+
+ <itemizedlist>
+ <listitem>
+ <para>You can say "inline <literal>f</literal> in Phase 2
+ and all subsequent phases":
+<programlisting>
+ {-# INLINE [2] f #-}
+</programlisting>
+ </para>
+ </listitem>
-</sect2>
+ <listitem>
+ <para>You can say "inline <literal>g</literal> in all
+ phases up to, but not including, Phase 3":
+<programlisting>
+ {-# INLINE [~3] g #-}
+</programlisting>
+ </para>
+ </listitem>
-<sect2 id="noinline-pragma">
-<title>NOINLINE pragma
-</title>
+ <listitem>
+ <para>If you omit the phase indicator, you mean "inline in
+ all phases".</para>
+ </listitem>
+ </itemizedlist>
-<indexterm><primary>NOINLINE pragma</primary></indexterm>
-<indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
-<indexterm><primary>NOTINLINE pragma</primary></indexterm>
-<indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
+ <para>You can use a phase number on a NOINLINE pragma too:</para>
-<para>
-The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
-it stops the named function from being inlined by the compiler. You
-shouldn't ever need to do this, unless you're very cautious about code
-size.
-</para>
+ <itemizedlist>
+ <listitem>
+ <para>You can say "do not inline <literal>f</literal>
+ until Phase 2; in Phase 2 and subsequently behave as if
+ there was no pragma at all":
+<programlisting>
+ {-# NOINLINE [2] f #-}
+</programlisting>
+ </para>
+ </listitem>
-<para><literal>NOTINLINE</literal> is a synonym for
-<literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
-by Haskell 98 as the standard way to disable inlining, so it should be
-used if you want your code to be portable).</para>
+ <listitem>
+ <para>You can say "do not inline <literal>g</literal> in
+ Phase 3 or any subsequent phase; before that, behave as if
+ there was no pragma":
+<programlisting>
+ {-# NOINLINE [~3] g #-}
+</programlisting>
+ </para>
+ </listitem>
-</sect2>
+ <listitem>
+ <para>If you omit the phase indicator, you mean "never
+ inline this function".</para>
+ </listitem>
+ </itemizedlist>
+
+ <para>The same phase-numbering control is available for RULES
+ (<xref LinkEnd="rewrite-rules">).</para>
+ </sect3>
+ </sect2>
+
+ <sect2 id="line-pragma">
+ <title>LINE pragma</title>
+
+ <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
+ <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
+ <para>This pragma is similar to C's <literal>#line</literal>
+ pragma, and is mainly for use in automatically generated Haskell
+ code. It lets you specify the line number and filename of the
+ original code; for example</para>
+
+<programlisting>
+{-# LINE 42 "Foo.vhs" #-}
+</programlisting>
+
+ <para>if you'd generated the current file from something called
+ <filename>Foo.vhs</filename> and this line corresponds to line
+ 42 in the original. GHC will adjust its error messages to refer
+ to the line/file named in the <literal>LINE</literal>
+ pragma.</para>
+ </sect2>
+
+ <sect2 id="options-pragma">
+ <title>OPTIONS pragma</title>
+ <indexterm><primary>OPTIONS</primary>
+ </indexterm>
+ <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
+ </indexterm>
+
+ <para>The <literal>OPTIONS</literal> pragma is used to specify
+ additional options that are given to the compiler when compiling
+ this source file. See <xref linkend="source-file-options"> for
+ details.</para>
+ </sect2>
+
+ <sect2 id="rules">
+ <title>RULES pragma</title>
+
+ <para>The RULES pragma lets you specify rewrite rules. It is
+ described in <xref LinkEnd="rewrite-rules">.</para>
+ </sect2>
<sect2 id="specialize-pragma">
<title>SPECIALIZE pragma</title>
{-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
</programlisting>
- <para>To get very fancy, you can also specify a named function
- to use for the specialised value, as in:</para>
-
-<programlisting>
-{-# RULES hammeredLookup = 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>
-
- <para>Note we use the <literal>RULE</literal> pragma here to
- indicate that <literal>hammeredLookup</literal> applied at a
- certain type should be replaced by <literal>blah</literal>. See
- <xref linkend="rules"> for more information on
- <literal>RULES</literal>.</para>
-
- <para>An example in which using <literal>RULES</literal> for
- specialisation will Win Big:
-
-<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>
-
<para>A <literal>SPECIALIZE</literal> pragma for a function can
be put anywhere its type signature could be put.</para>
- </sect2>
-
-<sect2 id="specialize-instance-pragma">
-<title>SPECIALIZE instance pragma
-</title>
-
-<para>
-<indexterm><primary>SPECIALIZE pragma</primary></indexterm>
-<indexterm><primary>overloading, death to</primary></indexterm>
-Same idea, except for instance declarations. For example:
-
+<para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
+version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
+rewrites a call to the un-specialised function into a call to the specialised
+one. You can, instead, provide your own specialised function and your own rewrite rule.
+For example, suppose that:
<programlisting>
-instance (Eq a) => Eq (Foo a) where {
- {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
- ... usual stuff ...
- }
+ genericLookup :: Ord a => Table a b -> a -> b
+ intLookup :: Table Int b -> Int -> b
</programlisting>
-The pragma must occur inside the <literal>where</literal> part
-of the instance declaration.
-</para>
-<para>
-Compatible with HBC, by the way, except perhaps in the placement
-of the pragma.
-</para>
-
-</sect2>
-
-<sect2 id="line-pragma">
-<title>LINE pragma
-</title>
-
-<para>
-<indexterm><primary>LINE pragma</primary></indexterm>
-<indexterm><primary>pragma, LINE</primary></indexterm>
-</para>
-
-<para>
-This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
-automatically generated Haskell code. It lets you specify the line
-number and filename of the original code; for example
-</para>
-
-<para>
-
+where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
+that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
<programlisting>
-{-# LINE 42 "Foo.vhs" #-}
+ {-# RULES "intLookup" genericLookup = intLookup #-}
</programlisting>
+(see <xref linkend="rule-spec">). It is <emphasis>Your
+ Responsibility</emphasis> to make sure that
+ <function>intLookup</function> really behaves as a specialised
+ version of <function>genericLookup</function>!!!</para>
-</para>
-
-<para>
-if you'd generated the current file from something called <filename>Foo.vhs</filename>
-and this line corresponds to line 42 in the original. GHC will adjust
-its error messages to refer to the line/file named in the <literal>LINE</literal>
-pragma.
-</para>
+ <para>An example in which using <literal>RULES</literal> for
+ specialisation will Win Big:
-</sect2>
+<programlisting>
+ toDouble :: Real a => a -> Double
+ toDouble = fromRational . toRational
-<sect2 id="rules">
-<title>RULES pragma</title>
+ {-# RULES "toDouble/Int" toDouble = i2d #-}
+ i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
+</programlisting>
-<para>
-The RULES pragma lets you specify rewrite rules. It is described in
-<xref LinkEnd="rewrite-rules">.
-</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>
-</sect2>
+ </sect2>
-<sect2 id="deprecated-pragma">
-<title>DEPRECATED pragma</title>
+<sect2 id="specialize-instance-pragma">
+<title>SPECIALIZE instance pragma
+</title>
<para>
-The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
-There are two forms.
-</para>
-<itemizedlist>
-<listitem><para>
-You can deprecate an entire module thus:</para>
-<programlisting>
- module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
- ...
-</programlisting>
-<para>
-When you compile any module that import <literal>Wibble</literal>, GHC will print
-the specified message.</para>
-</listitem>
+<indexterm><primary>SPECIALIZE pragma</primary></indexterm>
+<indexterm><primary>overloading, death to</primary></indexterm>
+Same idea, except for instance declarations. For example:
-<listitem>
-<para>
-You can deprecate a function, class, or type, with the following top-level declaration:
-</para>
<programlisting>
- {-# DEPRECATED f, C, T "Don't use these" #-}
+instance (Eq a) => Eq (Foo a) where {
+ {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
+ ... usual stuff ...
+ }
</programlisting>
+The pragma must occur inside the <literal>where</literal> part
+of the instance declaration.
+</para>
<para>
-When you compile any module that imports and uses any of the specifed entities,
-GHC will print the specified message.
+Compatible with HBC, by the way, except perhaps in the placement
+of the pragma.
</para>
-</listitem>
-</itemizedlist>
-<para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
</sect2>
+ <sect2 id="unpack-pragma">
+ <title>UNPACK pragma</title>
+
+ <indexterm><primary>UNPACK</primary></indexterm>
+
+ <para>The <literal>UNPACK</literal> indicates to the compiler
+ that it should unpack the contents of a constructor field into
+ the constructor itself, removing a level of indirection. For
+ example:</para>
+
+<ProgramListing>
+data T = T {-# UNPACK #-} !Float
+ {-# UNPACK #-} !Float
+</ProgramListing>
+
+ <para>will create a constructor <literal>T</literal> containing
+ two unboxed floats. This may not always be an optimisation: if
+ the <Function>T</Function> constructor is scrutinised and the
+ floats passed to a non-strict function for example, they will
+ have to be reboxed (this is done automatically by the
+ compiler).</para>
+
+ <para>Unpacking constructor fields should only be used in
+ conjunction with <option>-O</option>, in order to expose
+ unfoldings to the compiler so the reboxing can be removed as
+ often as possible. For example:</para>
+
+<ProgramListing>
+f :: T -> Float
+f (T f1 f2) = f1 + f2
+</ProgramListing>
+
+ <para>The compiler will avoid reboxing <Function>f1</Function>
+ and <Function>f2</Function> by inlining <Function>+</Function>
+ on floats, but only when <option>-O</option> is on.</para>
+
+ <para>Any single-constructor data is eligible for unpacking; for
+ example</para>
+
+<ProgramListing>
+data T = T {-# UNPACK #-} !(Int,Int)
+</ProgramListing>
+
+ <para>will store the two <literal>Int</literal>s directly in the
+ <Function>T</Function> constructor, by flattening the pair.
+ Multi-level unpacking is also supported:</para>
+
+<ProgramListing>
+data T = T {-# UNPACK #-} !S
+data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
+</ProgramListing>
+
+ <para>will store two unboxed <literal>Int#</literal>s
+ directly in the <Function>T</Function> constructor. The
+ unpacker can see through newtypes, too.</para>
+
+ <para>If a field cannot be unpacked, you will not get a warning,
+ so it might be an idea to check the generated code with
+ <option>-ddump-simpl</option>.</para>
+
+ <para>See also the <option>-funbox-strict-fields</option> flag,
+ which essentially has the effect of adding
+ <literal>{-# UNPACK #-}</literal> to every strict
+ constructor field.</para>
+ </sect2>
+
</sect1>
<!-- ======================= REWRITE RULES ======================== -->
<para>
The programmer can specify rewrite rules as part of the source program
-(in a pragma). GHC applies these rewrite rules wherever it can.
+(in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
+the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
+and (b) the <option>-frules-off</option> flag
+(<xref LinkEnd="options-f">) is not specified.
</para>
<para>
<listitem>
<para>
+ There may be zero or more rules in a <literal>RULES</literal> pragma.
+</para>
+</listitem>
+
+<listitem>
+
+<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>
+<listitem>
<para>
- There may be zero or more rules in a <literal>RULES</literal> pragma.
+A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
+immediately after the name of the rule. Thus:
+<programlisting>
+ {-# RULES
+ "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
+ #-}
+</programlisting>
+The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
+notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
+Phase 2.
</para>
</listitem>
+
+
<listitem>
<para>
enclosing definitions.
</para>
</listitem>
+
<listitem>
<para>
</para>
-<para>
+ <para>
So, for example, the following should generate no intermediate lists:
<programlisting>
<listitem>
<para>
- The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
+ The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
<programlisting>
build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
<listitem>
<para>
- In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
+ In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
see how to write rules that will do fusion and yet give an efficient
-program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
+program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
</para>
</listitem>
</sect2>
+<sect2 id="core-pragma">
+ <title>CORE pragma</title>
+
+ <indexterm><primary>CORE pragma</primary></indexterm>
+ <indexterm><primary>pragma, CORE</primary></indexterm>
+ <indexterm><primary>core, annotation</primary></indexterm>
+
+<para>
+ The external core format supports <quote>Note</quote> annotations;
+ the <literal>CORE</literal> pragma gives a way to specify what these
+ should be in your Haskell source code. Syntactically, core
+ annotations are attached to expressions and take a Haskell string
+ literal as an argument. The following function definition shows an
+ example:
+
+<programlisting>
+f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
+</programlisting>
+
+ Sematically, this is equivalent to:
+
+<programlisting>
+g x = show x
+</programlisting>
+</para>
+
+<para>
+ However, when external for is generated (via
+ <option>-fext-core</option>), there will be Notes attached to the
+ expressions <function>show</function> and <VarName>x</VarName>.
+ The core function declaration for <function>f</function> is:
+</para>
+
+<programlisting>
+ f :: %forall a . GHCziShow.ZCTShow a ->
+ a -> GHCziBase.ZMZN GHCziBase.Char =
+ \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
+ (%note "foo"
+ %case zddShow %of (tpl::GHCziShow.ZCTShow a)
+ {GHCziShow.ZCDShow
+ (tpl1::GHCziBase.Int ->
+ a ->
+ GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
+r)
+ (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
+ (tpl3::GHCziBase.ZMZN a ->
+ GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
+r) ->
+ tpl2})
+ (%note "foo"
+ eta);
+</programlisting>
+
+<para>
+ Here, we can see that the function <function>show</function> (which
+ has been expanded out to a case expression over the Show dictionary)
+ has a <literal>%note</literal> attached to it, as does the
+ expression <VarName>eta</VarName> (which used to be called
+ <VarName>x</VarName>).
+</para>
+
+</sect2>
+
</sect1>
<sect1 id="generic-classes">
instance (Bin a, Bin b) => Bin (a,b)
instance Bin a => Bin [a]
</programlisting>
-That is, just leave off the "where" clasuse. Of course, you can put in the
+That is, just leave off the "where" clause. Of course, you can put in the
where clause and over-ride whichever methods you please.
</para>
</sect2>
</sect1>
-<sect1 id="newtype-deriving">
-<title>Generalised derived instances for newtypes</title>
-
-<para>
-When you define an abstract type using <literal>newtype</literal>, you may want
-the new type to inherit some instances from its representation. In
-Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
-<literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
-other classes you have to write an explicit instance declaration. For
-example, if you define
-
-<programlisting>
- newtype Dollars = Dollars Int
-</programlisting>
-
-and you want to use arithmetic on <literal>Dollars</literal>, you have to
-explicitly define an instance of <literal>Num</literal>:
-
-<programlisting>
- instance Num Dollars where
- Dollars a + Dollars b = Dollars (a+b)
- ...
-</programlisting>
-All the instance does is apply and remove the <literal>newtype</literal>
-constructor. It is particularly galling that, since the constructor
-doesn't appear at run-time, this instance declaration defines a
-dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
-dictionary, only slower!
-</para>
-
-<sect2> <title> Generalising the deriving clause </title>
-<para>
-GHC now permits such instances to be derived instead, so one can write
-<programlisting>
- newtype Dollars = Dollars Int deriving (Eq,Show,Num)
-</programlisting>
-
-and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
-for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
-derives an instance declaration of the form
-
-<programlisting>
- instance Num Int => Num Dollars
-</programlisting>
-
-which just adds or removes the <literal>newtype</literal> constructor according to the type.
-</para>
-<para>
-
-We can also derive instances of constructor classes in a similar
-way. For example, suppose we have implemented state and failure monad
-transformers, such that
-
-<programlisting>
- instance Monad m => Monad (State s m)
- instance Monad m => Monad (Failure m)
-</programlisting>
-In Haskell 98, we can define a parsing monad by
-<programlisting>
- type Parser tok m a = State [tok] (Failure m) a
-</programlisting>
-
-which is automatically a monad thanks to the instance declarations
-above. With the extension, we can make the parser type abstract,
-without needing to write an instance of class <literal>Monad</literal>, via
-
-<programlisting>
- newtype Parser tok m a = Parser (State [tok] (Failure m) a)
- deriving Monad
-</programlisting>
-In this case the derived instance declaration is of the form
-<programlisting>
- instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
-</programlisting>
-
-Notice that, since <literal>Monad</literal> is a constructor class, the
-instance is a <emphasis>partial application</emphasis> of the new type, not the
-entire left hand side. We can imagine that the type declaration is
-``eta-converted'' to generate the context of the instance
-declaration.
-</para>
-<para>
-
-We can even derive instances of multi-parameter classes, provided the
-newtype is the last class parameter. In this case, a ``partial
-application'' of the class appears in the <literal>deriving</literal>
-clause. For example, given the class
-
-<programlisting>
- class StateMonad s m | m -> s where ...
- instance Monad m => StateMonad s (State s m) where ...
-</programlisting>
-then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
-<programlisting>
- newtype Parser tok m a = Parser (State [tok] (Failure m) a)
- deriving (Monad, StateMonad [tok])
-</programlisting>
-
-The derived instance is obtained by completing the application of the
-class to the new type:
-
-<programlisting>
- instance StateMonad [tok] (State [tok] (Failure m)) =>
- StateMonad [tok] (Parser tok m)
-</programlisting>
-</para>
-<para>
-
-As a result of this extension, all derived instances in newtype
-declarations are treated uniformly (and implemented just by reusing
-the dictionary for the representation type), <emphasis>except</emphasis>
-<literal>Show</literal> and <literal>Read</literal>, which really behave differently for
-the newtype and its representation.
-</para>
-</sect2>
-
-<sect2> <title> A more precise specification </title>
-<para>
-Derived instance declarations are constructed as follows. Consider the
-declaration (after expansion of any type synonyms)
-
-<programlisting>
- newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
-</programlisting>
-
-where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
-types,
-<literal>vk+1...vn</literal> are type variables which do not occur in any of
-the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
-classes of the form <literal>C t1'...tj'</literal>. The derived instance
-declarations are, for each <literal>ci</literal>,
-
-<programlisting>
- instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
-</programlisting>
-where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
-right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
-</para>
-<para>
-
-As an example which does <emphasis>not</emphasis> work, consider
-<programlisting>
- newtype NonMonad m s = NonMonad (State s m s) deriving Monad
-</programlisting>
-Here we cannot derive the instance
-<programlisting>
- instance Monad (State s m) => Monad (NonMonad m)
-</programlisting>
-
-because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
-and so cannot be "eta-converted" away. It is a good thing that this
-<literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
-not, in fact, a monad --- for the same reason. Try defining
-<literal>>>=</literal> with the correct type: you won't be able to.
-</para>
-<para>
-
-Notice also that the <emphasis>order</emphasis> of class parameters becomes
-important, since we can only derive instances for the last one. If the
-<literal>StateMonad</literal> class above were instead defined as
-
-<programlisting>
- class StateMonad m s | m -> s where ...
-</programlisting>
-
-then we would not have been able to derive an instance for the
-<literal>Parser</literal> type above. We hypothesise that multi-parameter
-classes usually have one "main" parameter for which deriving new
-instances is most interesting.
-</para>
-</sect2>
-</sect1>
-
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