6.8.4. Default method signatures¶

DefaultSignatures
¶ Since: 7.2.1 Allows the definition of default method signatures in class definitions.
Haskell 98 allows you to define a default implementation when declaring a class:
class Enum a where
enum :: [a]
enum = []
The type of the enum
method is [a]
, and this is also the type of
the default method. You can change the type of the default method by
requiring a different context using the extension
DefaultSignatures
. For instance, if you have written a
generic implementation of enumeration in a class GEnum
with method
genum
, you can specify a default method that uses that generic
implementation. But your default implementation can only be used if the
constraints are satisfied, therefore you need to change the type of the
default method
class Enum a where
enum :: [a]
default enum :: (Generic a, GEnum (Rep a)) => [a]
enum = map to genum
We reuse the keyword default
to signal that a signature applies to
the default method only; when defining instances of the Enum
class,
the original type [a]
of enum
still applies. When giving an
empty instance, however, the default implementation (map to genum)
is
filledin, and typechecked with the type
(Generic a, GEnum (Rep a)) => [a]
.
The type signature for a default method of a type class must take on the same
form as the corresponding main method’s type signature. Otherwise, the
typechecker will reject that class’s definition. By “take on the same form”, we
mean that the default type signature should differ from the main type signature
only in their outermost contexts. Therefore, if you have a method bar
:
class Foo a where
bar :: forall b. C => a > b > b
Then a default method for bar
must take on the form:
default bar :: forall b. C' => a > b > b
bar = ...
C
is allowed to be different from C'
, but the righthand sides of the
type signatures must coincide. We require this because when you declare an
empty instance for a class that uses DefaultSignatures
, GHC
implicitly fills in the default implementation like this:
instance Foo Int where
bar = default_bar
Where default_bar
is a toplevel function based on the default type
signature and implementation for bar
:
default_bar :: forall a b. (Foo a, C') => a > b > b
default_bar = ...
In order for this approach to work, the default type signature for bar
should be the same as the nondefault signature, modulo the outermost context
(with some caveats—see
Detailed requirements for default type signatures). There is no obligation
for C
and C'
to be the same, and indeed, the Enum
example above
relies on enum
’s default type signature having a more specific context than
the original type signature.
We use default signatures to simplify generic programming in GHC (Generic programming).
6.8.5. Detailed requirements for default type signatures¶
The rest of this section gives further details about what constitutes valid default type signatures.
Ignoring outermost contexts, a default type signature must match the original type signature according to GHC’s subsumption rules. As a result, the order of type variables in the default signature is important. Recall the
Foo
example from the previous section:class Foo a where bar :: forall b. C => a > b > b default bar :: forall b. C' => a > b > b bar = ...
This is legal because if you remove the outermost contexts
C
andC'
, then the two type signatures are the same. It is not necessarily the case that the default signature has to be exactly the same, however. For instance, this would also be an acceptable default type signature, as it is alphaequivalent to the original type signature:default bar :: forall x. C' => a > x > x
On the other hand, this is not an acceptable default type signature, since the type variable
a
is in the wrong place:default bar :: forall b. C' => b > a > b
The only place where a default type signature is allowed to more precise than the original type signature is in the outermost context. For example, this would not be an acceptable default type signature, since we can’t match the type variable
b
with the concrete typeInt
:default bar :: C' => a > Int > Int
You can, however, use type equalities to achieve the same result:
default bar :: forall b. (C', b ~ Int) => a > b > b
Because of GHC’s subsumption rules rules, there are relatively tight restrictions concerning nested or higherrank
forall
s (see Arbitraryrank polymorphism). Consider this class:class C x where m :: x > forall a b. a > b
GHC would not permit the following default type signature for
m
:default m :: x > forall b a. a > b
This is because the default signature quantifies the nested
forall
s in a different order than the original type signature. In order for this to typecheck, the default signature must preserve the original order:default m :: x > forall a b. a > b
Note that unlike nested or higherrank
forall
s, outermostforall
s have more flexibility in how they are ordered. As a result, GHC will permit the following:class C' x where m' :: forall a b. x > a > b default m' :: forall b a. x > a > b m' = ...
Just as the order of nested or higherrank
forall
s is restricted, a similar restriction applies to the order in which nested or higherrank contexts appear. As a result, GHC will not permit the following:class D a where n :: a > forall b. (Eq b, Show b) => b > String default n :: a > forall b. (Show b, Eq b) => b > String n = ...
GHC will permit reordering constraints within an outermost context, however, as demonstrated by the fact that GHC accepts the following:
class D' a where n' :: (Eq b, Show b) => a > b > String default n' :: (Show b, Eq b) => a > b > String n' = ...
Because a default signature is only ever allowed to differ from its original type signature in the outermost context, not in nested or higherrank contexts, there are certain defaults that cannot be written without reordering
forall
s. Consider this example:class E a where p :: Int > forall b. b > String
Suppose one wishes to write a default signature for
p
where the context must mention botha
andb
. While the natural thing to do would be to write this default:default p :: Int > forall b. DefaultClass a b => b > String
This will not typecheck, since the default type signature now differs from the original type signature in its use of nested contexts. The only way to make such a default signature work is to change the order in which
b
is quantified:default p :: forall b. DefaultClass a b => Int > b > String
This works, but at the expense of changing
p
’s behavior with respect to Visible type application.