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><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="CLASS-EXTENSIONS"
>6.2. Type class extensions</A
></H1
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="FLEXIBLE-CONTEXTS"
>6.2.1. More flexible contexts</A
></H2
><P
>In Haskell 98, contexts consist of class constraints
on type variables applied to zero or more types, as in
<PRE
CLASS="PROGRAMLISTING"
>f :: (Functor f, Num (f Int)) => f String -> f Int -> f Int</PRE
>
In class and instance declarations only type variables may be constrained.
With the <CODE
CLASS="OPTION"
>-98</CODE
> option,
any type may be constrained by a class, as in
<PRE
CLASS="PROGRAMLISTING"
>g :: (C [a], D (a -> b)) => [a] -> b</PRE
>
Classes are not limited to a single argument either
(see <A
HREF="class-extensions.html#MULTI-PARAM"
>Section 6.2.4</A
>).</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="FLEXIBLE-INSTANCES"
>6.2.2. More flexible instance declarations</A
></H2
><P
>In Haskell 98, instances may only be declared for
a <TT
CLASS="LITERAL"
>data</TT
> or <TT
CLASS="LITERAL"
>newtype</TT
> type constructor
applied to type variables.
With the <CODE
CLASS="OPTION"
>-98</CODE
> option, any type may be made an instance:
<PRE
CLASS="PROGRAMLISTING"
>instance Monoid (a -> a) where ...
instance Show (Tree Int) where ...
instance MyClass a where ...
instance C String where</PRE
>
This relaxation, together with the relaxation of contexts mentioned above,
makes the checking of constraints undecidable in general
(because you can now code arbitrary Prolog programs using instances).
To ensure that type checking terminates,
Hugs imposes a limit on the depth of constraints it will check,
and type checking fails if this limit is reached.
You can raise the limit with the
<A
HREF="options.html#OPTION-CONSTRAINT-CUTOFF"
><CODE
CLASS="OPTION"
>-c</CODE
></A
> option,
but such a failure usually indicates that the type checker wasn't going to
terminate for the particular constraint problem you set it.</P
><P
>Note that GHC implements a different solution, placing syntactic
restrictions on instances to ensure termination, though you can also
turn these off, in which case a depth limit like that in Hugs is used.</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="OVERLAPPING-INSTANCES"
>6.2.3. Overlapping instances</A
></H2
><P
>With the relaxation on the form of instances discussed in the previous
section, it seems we could write
<PRE
CLASS="PROGRAMLISTING"
>class C a where c :: a
instance C (Bool,a) where ...
instance C (a,Char) where ...</PRE
>
but then in the expression <TT
CLASS="LITERAL"
>c :: (Bool,Char)</TT
>,
either instance could be chosen.
For this reason, overlapping instances are forbidden:
<PRE
CLASS="SCREEN"
>ERROR "Test.hs":4 - Overlapping instances for class "C"
*** This instance : C (a,Char)
*** Overlaps with : C (Bool,a)
*** Common instance : C (Bool,Char)</PRE
>
However if the
<A
HREF="options.html#OPTION-OVERLAPPING"
><CODE
CLASS="OPTION"
>+o</CODE
></A
> option is set,
they are permitted when one of the types is a substitution instance of
the other (but not equivalent to it), as in
<PRE
CLASS="PROGRAMLISTING"
>class C a where toString :: a -> String
instance C [Char] where ...
instance C a => C [a] where ...</PRE
>
Now for the type <TT
CLASS="LITERAL"
>[Char]</TT
>, the first instance is used;
for any type <TT
CLASS="LITERAL"
>[<TT
CLASS="REPLACEABLE"
><I
>t</I
></TT
>]</TT
>,
where <TT
CLASS="REPLACEABLE"
><I
>t</I
></TT
> is a type distinct from
<TT
CLASS="LITERAL"
>Char</TT
>, the second instance is used.
Note that the context plays no part in the acceptability of the instances,
or in the choice of which to use.</P
><P
>The above analysis omitted one case, where the type <TT
CLASS="LITERAL"
>t</TT
> is
a type variable, as in
<PRE
CLASS="PROGRAMLISTING"
>f :: C a => [a] -> String
f xs = toString xs</PRE
>
We cannot decide which instance to choose, so Hugs rejects this definition.
However if the
<A
HREF="options.html#OPTION-OVERLAPPING"
><CODE
CLASS="OPTION"
>+O</CODE
></A
> option is set,
this declaration is accepted, and the more general instance is selected,
even though this will be the wrong choice if <TT
CLASS="LITERAL"
>f</TT
> is later
applied to a list of <TT
CLASS="LITERAL"
>Char</TT
>.</P
><P
>Hugs used to have a <CODE
CLASS="OPTION"
>+m</CODE
> option
(for multi-instance resolution,
if Hugs was compiled with <TT
CLASS="LITERAL"
>MULTI_INST</TT
> set),
which accepted more overlapping instances by deferring the choice between them,
but it is currently broken.</P
><P
>Sometimes one can avoid overlapping instances.
The particular example discussed above is similar to the situation described
by the <TT
CLASS="LITERAL"
>Show</TT
> class in the <TT
CLASS="LITERAL"
>Prelude</TT
>.
However there overlapping instances are avoided by adding the method
<CODE
CLASS="FUNCTION"
>showList</CODE
> to the class.</P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="MULTI-PARAM"
>6.2.4. Multiple parameter type classes</A
></H2
><P
>In Haskell 98, type classes have a single parameter;
they may be thought of as sets of types.
In Hugs, they may have one or more parameters,
corresponding to relations between types, e.g.
<PRE
CLASS="PROGRAMLISTING"
>class Isomorphic a b where
from :: a -> b
to :: b -> a</PRE
></P
></DIV
><DIV
CLASS="SECT2"
><H2
CLASS="SECT2"
><A
NAME="FUNCTIONAL-DEPENDENCIES"
>6.2.5. Functional dependencies</A
></H2
><P
>Multiple parameter type classes often lead to ambiguity.
Functional dependencies (inspired by relational databases)
provide a partial solution,
and were introduced in
<I
CLASS="CITETITLE"
>Type Classes with Functional Dependencies</I
>,
Mark P. Jones, In
<I
CLASS="CITETITLE"
>Proceedings of the 9th European Symposium on Programming</I
>, LNCS vol. 1782, Springer 2000.</P
><P
>Functional dependencies are introduced by a vertical bar:
<PRE
CLASS="PROGRAMLISTING"
>class MyClass a b c | a -> b where</PRE
>
This says that the <TT
CLASS="LITERAL"
>b</TT
> parameter is determined by the
<TT
CLASS="LITERAL"
>a</TT
> parameter;
there cannot be two instances of <TT
CLASS="LITERAL"
>MyClass</TT
> with the same
first parameter and different second parameters.
The type inference system then uses this information to resolve many
ambiguities.
You can have several dependencies:
<PRE
CLASS="PROGRAMLISTING"
>class MyClass a b c | a -> b, a -> c where</PRE
>
This example could also be written
<PRE
CLASS="PROGRAMLISTING"
>class MyClass a b c | a -> b c where</PRE
>
Similarly more than one type parameter may appear to the left of the arrow:
<PRE
CLASS="PROGRAMLISTING"
>class MyClass a b c | a b -> c where</PRE
>
This says that the <TT
CLASS="LITERAL"
>c</TT
> parameter is determined by the
<TT
CLASS="LITERAL"
>a</TT
> and <TT
CLASS="LITERAL"
>b</TT
> parameters together;
there cannot be two instances of <TT
CLASS="LITERAL"
>MyClass</TT
> with the same
first and second parameters, but different third parameters.</P
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