7.5. Extensions to the "deriving" mechanism
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## 7.5. Extensions to the "deriving" mechanism

### 7.5.1. Inferred context for deriving clauses

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.

### 7.5.2. Stand-alone deriving declarations

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.) 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 7.6.3.1, “Relaxed rules for instance declarations”). 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`.

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.

### 7.5.3. Deriving clause for classes `Typeable` and `Data`

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.

### 7.5.4. Generalised derived instances for newtypes

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!

#### 7.5.4.1. Generalising the deriving clause

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.

#### 7.5.4.2. A more precise specification

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.)

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