6.8.4. Default method signatures¶
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
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
the original type
enum still applies. When giving an
empty instance, however, the default implementation
(map to genum) is
filled-in, and type-checked 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
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 right-hand sides of the
type signatures must coincide. We require this because when you declare an
empty instance for a class that uses
implicitly fills in the default implementation like this:
instance Foo Int where bar = default_bar
default_bar is a top-level function based on the default type
signature and implementation for
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
should be the same as the non-default signature, modulo the outermost context
(with some caveats—see
Detailed requirements for default type signatures). There is no obligation
C' to be the same, and indeed, the
Enum example above
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
Fooexample 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', 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 alpha-equivalent 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
ais 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
bwith the concrete type
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 higher-rank
foralls (see Arbitrary-rank 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
default m :: x -> forall b a. a -> b
This is because the default signature quantifies the nested
foralls 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 higher-rank
foralls 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 higher-rank
foralls is restricted, a similar restriction applies to the order in which nested or higher-rank 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 higher-rank contexts, there are certain defaults that cannot be written without reordering
foralls. Consider this example:
class E a where p :: Int -> forall b. b -> String
Suppose one wishes to write a default signature for
pwhere the context must mention both
b. 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
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.