6.6.5. Generalised derived instances for newtypes¶

GeneralisedNewtypeDeriving
¶ 
GeneralizedNewtypeDeriving
¶ Since: 6.8.1. British spelling since 8.6.1. Enable GHC’s cunning generalised deriving mechanism for
newtype
s
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
runtime, this instance declaration defines a dictionary which is
wholly equivalent to the Int
dictionary, only slower!
DerivingVia
(see Deriving via) is a generalization of
this idea.
6.6.5.1. Generalising the deriving clause¶
GHC now permits such instances to be derived instead, using the extension
GeneralizedNewtypeDeriving
, so one can write
newtype Dollars = Dollars { getDollars :: Int } deriving (Eq,Show,Num)
and the implementation uses the same Num
dictionary for
Dollars
as for Int
. In other words, GHC will generate something that
resembles the following code
instance Num Int => Num Dollars
and then attempt to simplify the Num Int
context as much as possible.
GHC knows that there is a Num Int
instance in scope, so it is able to
discharge the Num Int
constraint, leaving the code that GHC actually
generates
instance Num Dollars
One can think of this instance being implemented with the same code as the
Num Int
instance, but with Dollars
and getDollars
added wherever
necessary in order to make it typecheck. (In practice, GHC uses a somewhat
different approach to code generation. See the A more precise specification
section below for more details.)
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 newtype, not the entire left hand side. We
can imagine that the type declaration is “etaconverted” to generate the
context of the instance declaration.
We can even derive instances of multiparameter 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
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.
Note
It is sometimes necessary to enable additional language extensions when
deriving instances via GeneralizedNewtypeDeriving
. For instance,
consider a simple class and instance using UnboxedTuples
syntax:
{# LANGUAGE UnboxedTuples #}
module Lib where
class AClass a where
aMethod :: a > (# Int, a #)
instance AClass Int where
aMethod x = (# x, x #)
The following will fail with an “Illegal unboxed tuple” error, since the derived instance produced by the compiler makes use of unboxed tuple syntax,
{# LANGUAGE GeneralizedNewtypeDeriving #}
import Lib
newtype Int' = Int' Int
deriving (AClass)
However, enabling the UnboxedTuples
extension allows the module
to compile. Similar errors may occur with a variety of extensions,
including:
6.6.5.2. A more precise specification¶
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, andt
,s1..sk
,t1..tj
are types. The
(C t1..tj)
is a partial applications of the classC
, where the arity ofC
is exactlyj+1
. That is,C
lacks exactly one type argument. k
is chosen so thatC t1..tj (T v1...vk)
is wellkinded. (Or, in the case of adata instance
, so thatC 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 typest
,s1..sk
, ort1..tj
. C
is notRead
,Show
,Typeable
, orData
. 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. Confer with Default deriving strategy. It is safe to coerce each of the methods of
C
. That is, the missing last argument toC
is not used at a nominal role in any of theC
’s methods. (See Roles.) C
is allowed to have associated type families, provided they meet the requirements laid out in the section on GND and associated types.
Then the derived instance declaration is of the form
instance C t1..tj t => C t1..tj (T v1...vk)
Note that if C
does not contain any class methods, the instance context
is wholly unnecessary, and as such GHC will instead generate:
instance 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 “etaconverted” 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 multiparameter 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 stock derivation
applies (section 4.3.3. of the Haskell Report). (For the standard
classes Eq
, Ord
, Ix
, and Bounded
it is immaterial
whether the stock method is used or the one described here.)
6.6.5.3. Associated type families¶
GeneralizedNewtypeDeriving
also works for some type classes with
associated type families. Here is an example:
class HasRing a where
type Ring a
newtype L1Norm a = L1Norm a
deriving HasRing
The derived HasRing
instance would look like
instance HasRing (L1Norm a) where
type Ring (L1Norm a) = Ring a
To be precise, if the class being derived is of the form
class C c_1 c_2 ... c_m where
type T1 t1_1 t1_2 ... t1_n
...
type Tk tk_1 tk_2 ... tk_p
and the newtype is of the form
newtype N n_1 n_2 ... n_q = MkN <reptype>
then you can derive a C c_1 c_2 ... c_(m1)
instance for
N n_1 n_2 ... n_q
, provided that:
The type parameter
c_m
occurs once in each of the type variables ofT1
throughTk
. Imagine a class where this condition didn’t hold. For example:class Bad a b where type B a instance Bad Int a where type B Int = Char newtype Foo a = Foo a deriving (Bad Int)
For the derived
Bad Int
instance, GHC would need to generate something like this:instance Bad Int (Foo a) where type B Int = B ???
Now we’re stuck, since we have no way to refer to
a
on the righthand side of theB
family instance, so this instance doesn’t really make sense in aGeneralizedNewtypeDeriving
setting.C
does not have any associated data families (only type families). To see why data families are forbidden, imagine the following scenario:class Ex a where data D a instance Ex Int where data D Int = DInt Bool newtype Age = MkAge Int deriving Ex
For the derived
Ex
instance, GHC would need to generate something like this:instance Ex Age where data D Age = ???
But it is not clear what GHC would fill in for
???
, as each data family instance must generate fresh data constructors.
If both of these conditions are met, GHC will generate this instance:
instance C c_1 c_2 ... c_(m1) <reptype> =>
C c_1 c_2 ... c_(m1) (N n_1 n_2 ... n_q) where
type T1 t1_1 t1_2 ... (N n_1 n_2 ... n_q) ... t1_n
= T1 t1_1 t1_2 ... <reptype> ... t1_n
...
type Tk tk_1 tk_2 ... (N n_1 n_2 ... n_q) ... tk_p
= Tk tk_1 tk_2 ... <reptype> ... tk_p
Again, if C
contains no class methods, the instance context will be
redundant, so GHC will instead generate
instance C c_1 c_2 ... c_(m1) (N n_1 n_2 ... n_q)
.
Beware that in some cases, you may need to enable the
UndecidableInstances
extension in order to use this feature.
Here’s a pathological case that illustrates why this might happen:
class C a where
type T a
newtype Loop = MkLoop Loop
deriving C
This will generate the derived instance:
instance C Loop where
type T Loop = T Loop
Here, it is evident that attempting to use the type T Loop
will throw the
typechecker into an infinite loop, as its definition recurses endlessly. In
other cases, you might need to enable UndecidableInstances
even
if the generated code won’t put the typechecker into a loop. For example:
instance C Int where
type C Int = Int
newtype MyInt = MyInt Int
deriving C
This will generate the derived instance:
instance C MyInt where
type T MyInt = T Int
Although typechecking T MyInt
will terminate, GHC’s termination checker
isn’t sophisticated enough to determine this, so you’ll need to enable
UndecidableInstances
in order to use this derived instance. If
you do go down this route, make sure you can convince yourself that all of
the type family instances you’re deriving will eventually terminate if used!
Note that DerivingVia
(see Deriving via) uses essentially
the same specification to derive instances of associated type families as well
(except that it uses the via
type instead of the underlying reptype
of a newtype).