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.
However, standalone deriving differs from a deriving clause in a number
of important ways:
The standalone deriving declaration does not need to be in the same module as the data type declaration. (But be aware of the dangers of orphan instances (Section 4.7.13, “Orphan modules and instance declarations”).
You must supply an explicit context (in the example the context is (Eq a)),
exactly as you would in an ordinary instance declaration.
(In contrast, in a deriving clause
attached to a data type declaration, the context is inferred.)
Unlike a deriving
declaration attached to a data declaration, the instance can be more specific
than the data type (assuming you also use
-XFlexibleInstances, Section 7.6.3.3, “Relaxed rules for instance contexts”). Consider
for example
data Foo a = Bar a | Baz String deriving instance Eq a => Eq (Foo [a]) deriving instance Eq a => Eq (Foo (Maybe a))
This will generate a derived instance for (Foo [a]) and (Foo (Maybe a)),
but other types such as (Foo (Int,Bool)) will not be an instance of Eq.
Unlike a deriving
declaration attached to a data declaration,
GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
boilerplate code for the specified class, and typechecks it. If there is a type error, it is
your problem. (GHC will show you the offending code if it has a type error.)
The merit of this is that you can derive instances for GADTs and other exotic data types, providing only that the boilerplate code does indeed typecheck. For example:
data T a where
T1 :: T Int
T2 :: T Bool
deriving instance Show (T a)
In this example, you cannot say ... deriving( Show ) on the
data type declaration for T,
because T is a GADT, but you can generate
the instance declaration using stand-alone deriving.
The down-side is that,
if the boilerplate code fails to typecheck, you will get an error message about that
code, which you did not write. Whereas, with a deriving clause
the side-conditions are necessarily more conservative, but any error message
may be more comprehensible.
In other ways, however, a standalone deriving obeys the same rules as ordinary deriving:
A deriving instance declaration
must obey the same rules concerning form and termination as ordinary instance declarations,
controlled by the same flags; see Section 7.6.3, “Instance declarations”.
The stand-alone syntax is generalised for newtypes in exactly the same
way that ordinary deriving clauses are generalised (Section 7.5.5, “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 several more classes that may be automatically derived:
With -XDeriveGeneric, you can derive
instances of the classes Generic and
Generic1, defined in GHC.Generics.
You can use these to define generic functions,
as described in Section 7.26, “Generic programming”.
With -XDeriveFunctor, you can derive instances of
the class Functor,
defined in GHC.Base.
With -XDeriveDataTypeable, you can derive instances of
the class Data,
defined in Data.Data. See Section 7.5.4, “Deriving Typeable instances” for
deriving Typeable.
With -XDeriveFoldable, you can derive instances of
the class Foldable,
defined in Data.Foldable.
With -XDeriveTraversable, you can derive instances of
the class Traversable,
defined in Data.Traversable. Since the Traversable
instance dictates the instances of Functor and
Foldable, you'll probably want to derive them too, so
-XDeriveTraversable implies
-XDeriveFunctor and -XDeriveFoldable.
You can also use a standalone deriving declaration instead (see Section 7.5.2, “Stand-alone deriving declarations”).
In each case the appropriate class must be in scope before it
can be mentioned in the deriving clause.
The class Typeable is very special:
Typeable is kind-polymorphic (see
Section 7.8, “Kind polymorphism”).
GHC has a custom solver for discharging constraints that involve
class Typeable, and handwritten instances are forbidden.
This ensures that the programmer cannot subert the type system by
writing bogus instances.
Derived instances of Typeable are ignored,
and may be reported as an error in a later version of the compiler.
The rules for solving `Typeable` constraints are as follows:
A concrete type constructor applied to some types.
instance (Typeable t1, .., Typeable t_n) => Typeable (T t1 .. t_n)
This rule works for any concrete type constructor, including type constructors with polymorhic kinds. The only restriction is that if the type constructor has a polymorhic kind, then it has to be applied to all of its kinds parameters, and these kinds need to be concrete (i.e., they cannot mention kind variables).
A type variable applied to some types. instance (Typeable f, Typeable t1, .., Typeable t_n) => Typeable (f t1 .. t_n)
A concrete type literal. instance Typeable 0 -- Type natural literals instance Typeable "Hello" -- Type-level symbols
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.
A derived instance is derived only for declarations of these forms (after expansion of any type synonyms)
newtype T v1..vn = MkT (t vk+1..vn) deriving (C t1..tj) newtype instance T s1..sk vk+1..vn = MkT (t vk+1..vn) deriving (C t1..tj)
where
v1..vn are type variables, and t,
s1..sk, t1..tj are types.
The (C t1..tj) is a partial applications of the class C,
where the arity of C
is exactly j+1. That is, C lacks exactly one type argument.
k is chosen so that C t1..tj (T v1...vk) is well-kinded.
(Or, in the case of a data instance, so that C t1..tj (T s1..sk) is
well kinded.)
The type t is an arbitrary type.
The type variables vk+1...vn do not occur in the types t,
s1..sk, or t1..tj.
C is not 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.
It is safe to coerce each of the methods of C. That is,
the missing last argument to C is not used
at a nominal role in any of the C's methods.
(See Section 7.27, “Roles
”.)
Then the derived instance is of form declaration is:
instance C t1..tj t => C t1..tj (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.)
With -XDeriveAnyClass you can derive any other class. The
compiler will simply generate an empty instance. The instance context will be
generated according to the same rules used when deriving Eq.
This is mostly useful in classes whose minimal
set is empty, and especially when writing
generic functions.
In case you try to derive some class on a newtype, and
-XGeneralizedNewtypeDeriving is also on,
-XDeriveAnyClass takes precedence.