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.
Note the following points:

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.)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”.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 7.6.3.2, “Relaxed rules for instance contexts”). Consider for exampledata 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 stand-alone syntax is generalised for newtypes in exactly the same way that ordinary

`deriving`

clauses are generalised (Section 7.5.4, “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 several more classes that may be automatically derived:

With

`-XDeriveDataTypeable`

, you can derive instances of the classes`Typeable`

, and`Data`

, defined in the library modules`Data.Typeable`

and`Data.Generics`

respectively.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.With

`-XDeriveFunctor`

, you can derive instances of the class`Functor`

, defined in`GHC.Base`

.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`

.

In each case the appropriate class must be in scope before it
can be mentioned in the `deriving`

clause.

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 `Parser`

s 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`

, andNone 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.)