The Haskell Report is vague about exactly when a deriving clause is
legal. For example:
data T0 f a = MkT0 a deriving( Eq ) data T1 f a = MkT1 (f a) deriving( Eq ) data T2 f a = MkT2 (f (f a)) deriving( Eq )
The natural generated Eq code would result in these instance declarations:
instance Eq a => Eq (T0 f a) where ... instance Eq (f a) => Eq (T1 f a) where ... instance Eq (f (f a)) => Eq (T2 f a) where ...
The first of these is obviously fine. The second is still fine, although less obviously. The third is not Haskell 98, and risks losing termination of instances.
GHC takes a conservative position: it accepts the first two, but not the third. The rule is this: each constraint in the inferred instance context must consist only of type variables, with no repetitions.
This rule is applied regardless of flags. If you want a more exotic context, you can write it yourself, using the standalone deriving mechanism.
GHC now allows stand-alone deriving declarations, enabled by -XStandaloneDeriving:
data Foo a = Bar a | Baz String deriving instance Eq a => Eq (Foo a)
The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
deriving, and (b) the absence of the where part.
You must supply a context (in the example the context is (Eq a)),
exactly as you would in an ordinary instance declaration.
(In contrast the context is inferred in a deriving clause
attached to a data type declaration.) These deriving instance
rules obey the same rules concerning form and termination as ordinary instance declarations,
controlled by the same flags; see ???.
The stand-alone syntax is generalised for newtypes in exactly the same
way that ordinary deriving clauses are generalised (Section 8.5.4, “Generalised derived instances for newtypes”).
For example:
newtype Foo a = MkFoo (State Int a) deriving instance MonadState Int Foo
GHC always treats the last parameter of the instance
(Foo in this example) as the type whose instance is being derived.
Haskell 98 allows the programmer to add "deriving( Eq, Ord )" to a data type
declaration, to generate a standard instance declaration for classes specified in the deriving clause.
In Haskell 98, the only classes that may appear in the deriving clause are the standard
classes Eq, Ord,
Enum, Ix, Bounded, Read, and Show.
GHC extends this list with two more classes that may be automatically derived
(provided the -XDeriveDataTypeable flag is specified):
Typeable, and Data. These classes are defined in the library
modules Data.Typeable and Data.Generics respectively, and the
appropriate class must be in scope before it can be mentioned in the deriving clause.
An instance of Typeable can only be derived if the
data type has seven or fewer type parameters, all of kind *.
The reason for this is that the Typeable class is derived using the scheme
described in
Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
.
(Section 7.4 of the paper describes the multiple Typeable classes that
are used, and only Typeable1 up to
Typeable7 are provided in the library.)
In other cases, there is nothing to stop the programmer writing a TypableX
class, whose kind suits that of the data type constructor, and
then writing the data type instance by hand.
When you define an abstract type using newtype, you may want
the new type to inherit some instances from its representation. In
Haskell 98, you can inherit instances of Eq, Ord,
Enum and Bounded by deriving them, but for any
other classes you have to write an explicit instance declaration. For
example, if you define
newtype Dollars = Dollars Int
and you want to use arithmetic on Dollars, you have to
explicitly define an instance of Num:
instance Num Dollars where
Dollars a + Dollars b = Dollars (a+b)
...
All the instance does is apply and remove the newtype
constructor. It is particularly galling that, since the constructor
doesn't appear at run-time, this instance declaration defines a
dictionary which is wholly equivalent to the Int
dictionary, only slower!
GHC now permits such instances to be derived instead,
using the flag -XGeneralizedNewtypeDeriving,
so one can write
newtype Dollars = Dollars Int deriving (Eq,Show,Num)
and the implementation uses the same Num dictionary
for Dollars as for Int. Notionally, the compiler
derives an instance declaration of the form
instance Num Int => Num Dollars
which just adds or removes the newtype constructor according to the type.
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
instance Monad m => Monad (State s m) instance Monad m => Monad (Failure m)
In Haskell 98, we can define a parsing monad by
type Parser tok m a = State [tok] (Failure m) a
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 Monad, via
newtype Parser tok m a = Parser (State [tok] (Failure m) a)
deriving Monad
In this case the derived instance declaration is of the form
instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
Notice that, since Monad is a constructor class, the
instance is a partial application 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.
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 deriving
clause. For example, given the class
class StateMonad s m | m -> s where ... instance Monad m => StateMonad s (State s m) where ...
then we can derive an instance of StateMonad for Parsers by
newtype Parser tok m a = Parser (State [tok] (Failure m) a)
deriving (Monad, StateMonad [tok])
The derived instance is obtained by completing the application of the class to the new type:
instance StateMonad [tok] (State [tok] (Failure m)) =>
StateMonad [tok] (Parser tok m)
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), except
Show and Read, which really behave differently for
the newtype and its representation.
Derived instance declarations are constructed as follows. Consider the declaration (after expansion of any type synonyms)
newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
where
The ci are partial applications of
classes of the form C t1'...tj', where the arity of C
is exactly j+1. That is, C lacks exactly one type argument.
The k is chosen so that ci (T v1...vk) is well-kinded.
The type t is an arbitrary type.
The type variables vk+1...vn do not occur in t,
nor in the ci, and
None of the ci is Read, Show,
Typeable, or Data. 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.
Then, for each ci, the derived instance
declaration is:
instance ci t => ci (T v1...vk)
As an example which does not work, consider
newtype NonMonad m s = NonMonad (State s m s) deriving Monad
Here we cannot derive the instance
instance Monad (State s m) => Monad (NonMonad m)
because the type variable s occurs in State s m,
and so cannot be "eta-converted" away. It is a good thing that this
deriving clause is rejected, because NonMonad m is
not, in fact, a monad --- for the same reason. Try defining
>>= with the correct type: you won't be able to.
Notice also that the order of class parameters becomes
important, since we can only derive instances for the last one. If the
StateMonad class above were instead defined as
class StateMonad m s | m -> s where ...
then we would not have been able to derive an instance for the
Parser type above. We hypothesise that multi-parameter
classes usually have one "main" parameter for which deriving new
instances is most interesting.
Lastly, all of this applies only for classes other than
Read, Show, Typeable,
and Data, for which the built-in derivation applies (section
4.3.3. of the Haskell Report).
(For the standard classes Eq, Ord,
Ix, and Bounded it is immaterial whether
the standard method is used or the one described here.)