Difference between revisions of "GHC.Generics"
(→Example: serialization: Fix broken link to generic programming comparison report) 

(33 intermediate revisions by 8 users not shown)  
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−  GHC 7.2 includes support for ''datatypegeneric programming'' 
+  GHC 7.2 includes improved support for ''datatypegeneric programming'' through two features, enabled with two flags: <tt>DeriveGeneric</tt> and <tt>DefaultSignatures</tt>. We show how this all works in this page, starting with a detailed example. 
== Example: serialization == 
== Example: serialization == 

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He will have to specify an <hask>instance Serialize (UserTree a) where ...</hask> himself. This, however, is tedious, especially because most instances will probably be rather trivial, and should be derived automatically. 
He will have to specify an <hask>instance Serialize (UserTree a) where ...</hask> himself. This, however, is tedious, especially because most instances will probably be rather trivial, and should be derived automatically. 

−  It is here that generic programming can help you. If you are familiar with [http://www.cs.uu.nl/ 
+  It is here that generic programming can help you. If you are familiar with [http://www.cs.uu.nl/research/techreps/repo/CS2008/2008010.pdf Scrap your boilerplate (SYB)] you could use it at this stage, but now we'll see how to do this with the GHC Generic features. 
=== Generic serialization === 
=== Generic serialization === 

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<haskell> 
<haskell> 

class GSerialize f where 
class GSerialize f where 

−  gput :: f a > [ 
+  gput :: f a > [Bit] 
</haskell> 
</haskell> 

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</haskell> 
</haskell> 

−  The 
+  The serialization of multiple arguments is simply the concatenation of each of the individual serializations: 
<haskell> 
<haskell> 

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<haskell> 
<haskell> 

−  instance (Serialize a) => GSerialize (K1 i 
+  instance (Serialize a) => GSerialize (K1 i a) where 
gput (K1 x) = put x 
gput (K1 x) = put x 

</haskell> 
</haskell> 

−  So, if a user datatype 
+  So, if a user datatype has a parameter which is instantiated to <hask>Int</hask>, at this stage we will use the library instance for <hask>Serialize Int</hask>. 
==== Default implementations ==== 
==== Default implementations ==== 

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<haskell> 
<haskell> 

−  class 
+  class Generic a where 
 Encode the representation of a user datatype 
 Encode the representation of a user datatype 

−  type 
+  type Rep a :: * > * 
 Convert from the datatype to its representation 
 Convert from the datatype to its representation 

−  +  from :: a > (Rep a) x 

 Convert from the representation to the datatype 
 Convert from the representation to the datatype 

−  +  to :: (Rep a) x > a 

</haskell> 
</haskell> 

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<haskell> 
<haskell> 

−  instance 
+  instance Generic (UserTree a) where 
−  type 
+  type Rep (UserTree a) = RepUserTree a 
−  +  from Leaf = L1 U1 

−  +  from (Node a l r) = R1 (a :*: l :*: r) 

−  +  to (L1 U1) = Leaf 

−  +  to (R1 (a :*: l :*: r)) = Node a l r 

</haskell> 
</haskell> 

(Note that we are using the simpler representation <hask>RepUserTree</hask> instead of the real representation <hask>RealRepUserTree</hask>, just for simplicity.) 
(Note that we are using the simpler representation <hask>RepUserTree</hask> instead of the real representation <hask>RealRepUserTree</hask>, just for simplicity.) 

−  Equipped with a <hask> 
+  Equipped with a <hask>Generic</hask> instance, we are ready to tell the compiler how it can serialize any representable type: 
<haskell> 
<haskell> 

−  putDefault :: ( 
+  putDefault :: (Generic a, GSerialize (Rep a)) => a > [Bit] 
−  putDefault a = gput ( 
+  putDefault a = gput (from a) 
</haskell> 
</haskell> 

−  The type of <hask>putDefault</hask> says that we can serialize any <tt>a</tt> into a list of bits, as long as that <tt>a</tt> is <hask> 
+  The type of <hask>putDefault</hask> says that we can serialize any <tt>a</tt> into a list of bits, as long as that <tt>a</tt> is <hask>Generic</hask>, and its representation <hask>Rep a</hask> has a <hask>GSerialize</hask> instance. The implementation is very simple: first convert the value to its representation using <hask>from</hask>, and then call <hask>gput</hask> on that representation. 
However, we still have to write a <hask>Serialize</hask> instance for the user dataype: 
However, we still have to write a <hask>Serialize</hask> instance for the user dataype: 

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==== Deriving representations ==== 
==== Deriving representations ==== 

−  The <hask> 
+  The <hask>Generic</hask> class, and all the representation types, come with GHC in the <tt>GHC.Generics</tt> module. GHC can also derive <hask>Generic</hask> for user types, so all the user has to do is: 
<haskell> 
<haskell> 

−  {# LANGUAGE 
+  {# LANGUAGE DeriveGeneric #} 
data UserTree a = Node a (UserTree a) (UserTree a)  Leaf 
data UserTree a = Node a (UserTree a) (UserTree a)  Leaf 

−  deriving 
+  deriving Generic 
</haskell> 
</haskell> 

−  ( 
+  (Standalone deriving also works fine, and you can use it for types you have not defined yourself, but are imported from somewhere else.) You will need the new <tt>DeriveGeneric</tt> language pragma. 
==== More general default methods ==== 
==== More general default methods ==== 

−  We don't want the user to have to write the <hask>instance Serialize (UserTree a)</hask> himself, since most of the times it will just be <hask>putDefault</hask>. However, we cannot make <hask>putDefault</hask> the default implementation of the <hask>put</hask> method, because that would require adding the <hask>( 
+  We don't want the user to have to write the <hask>instance Serialize (UserTree a)</hask> himself, since most of the times it will just be <hask>putDefault</hask>. However, we cannot make <hask>putDefault</hask> the default implementation of the <hask>put</hask> method, because that would require adding the <hask>(Generic a, GSerialize (Rep a))</hask> constraint to the class head. This would restrict the ability to give adhoc instances for types that are not representable, for instance. 
We solved this by allowing the user to give a different signature for default methods: 
We solved this by allowing the user to give a different signature for default methods: 

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put :: a > [Bit] 
put :: a > [Bit] 

−  default put :: ( 
+  default put :: (Generic a, GSerialize (Rep a)) => a > [Bit] 
−  put a = gput ( 
+  put a = gput (from a) 
</haskell> 
</haskell> 

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</haskell> 
</haskell> 

−  GHC fills out the implementation for <hask>put</hask> using the default method. It will typecheck correctly because we have a <hask> 
+  GHC fills out the implementation for <hask>put</hask> using the default method. It will typecheck correctly because we have a <hask>Generic</hask> instance for <hask>UserTree</hask>, and <hask>GSerialize</hask> instances for all the representation types. 
+  
+  === Complete working example === 

+  
+  <haskell> 

+  {# LANGUAGE DefaultSignatures, DeriveGeneric, TypeOperators, FlexibleContexts #} 

+  
+  import GHC.Generics 

+  import Data.Bits 

+  
+  
+  data Bit = O  I deriving Show 

+  
+  class Serialize a where 

+  put :: a > [Bit] 

+  
+  default put :: (Generic a, GSerialize (Rep a)) => a > [Bit] 

+  put a = gput (from a) 

+  
+  get :: [Bit] > (a, [Bit]) 

+  
+  default get :: (Generic a, GSerialize (Rep a)) => [Bit] > (a, [Bit]) 

+  get xs = (to x, xs') 

+  where (x, xs') = gget xs 

+  
+  class GSerialize f where 

+  gput :: f a > [Bit] 

+  gget :: [Bit] > (f a, [Bit]) 

+  
+    Unit: used for constructors without arguments 

+  instance GSerialize U1 where 

+  gput U1 = [] 

+  gget xs = (U1, xs) 

+  
+    Products: encode multiple arguments to constructors 

+  instance (GSerialize a, GSerialize b) => GSerialize (a :*: b) where 

+  gput (a :*: b) = gput a ++ gput b 

+  gget xs = (a :*: b, xs'') 

+  where (a, xs') = gget xs 

+  (b, xs'') = gget xs' 

+  
+    Sums: encode choice between constructors 

+  instance (GSerialize a, GSerialize b) => GSerialize (a :+: b) where 

+  gput (L1 x) = O : gput x 

+  gput (R1 x) = I : gput x 

+  gget (O:xs) = (L1 x, xs') 

+  where (x, xs') = gget xs 

+  gget (I:xs) = (R1 x, xs') 

+  where (x, xs') = gget xs 

+  
+    Metainformation (constructor names, etc.) 

+  instance (GSerialize a) => GSerialize (M1 i c a) where 

+  gput (M1 x) = gput x 

+  gget xs = (M1 x, xs') 

+  where (x, xs') = gget xs 

+  
+    Constants, additional parameters and recursion of kind * 

+  instance (Serialize a) => GSerialize (K1 i a) where 

+  gput (K1 x) = put x 

+  gget xs = (K1 x, xs') 

+  where (x, xs') = get xs 

+  
+  instance Serialize Bool where 

+  put True = [I] 

+  put False = [O] 

+  get (I:xs) = (True, xs) 

+  get (O:xs) = (False, xs) 

+  
+   

+   Try it out. (Normally this would be in a separate module.) 

+   

+  
+  data UserTree a = Node a (UserTree a) (UserTree a)  Leaf 

+  deriving (Generic, Show) 

+  
+  instance (Serialize a) => Serialize (UserTree a) 

+  
+  main = do 

+  let xs = put True 

+  print (fst . get $ xs :: Bool) 

+  let ys = put (Leaf :: UserTree Bool) 

+  print (fst . get $ ys :: UserTree Bool) 

+  let zs = put (Node False Leaf Leaf :: UserTree Bool) 

+  print (fst . get $ zs :: UserTree Bool) 

+  </haskell> 

== Different perspectives == 
== Different perspectives == 

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=== The generic programmer === 
=== The generic programmer === 

−  If you are a library author and are eager to make your classes easy to instantiate by your users, then you should invest some time in defining instances for each of the representation types of <tt>GHC.Generics</tt> and defining a generic default method. See the example for <tt>Serialize</tt> above, and the [http://dreixel.net/research/pdf/gdmh.pdf original paper] for many other examples (but make sure to check the [[ 
+  If you are a library author and are eager to make your classes easy to instantiate by your users, then you should invest some time in defining instances for each of the representation types of <tt>GHC.Generics</tt> and defining a generic default method. See the example for <tt>Serialize</tt> above, and the [http://dreixel.net/research/pdf/gdmh.pdf original paper] for many other examples (but make sure to check the [[#Changes from the paperchanges from the paper]]). 
=== The GHC hacker === 
=== The GHC hacker === 

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* <tt>Representable0</tt> and <tt>Representable1</tt> have become <tt>Generic</tt> and <tt>Generic1</tt>, respectively. <tt>from0</tt>, <tt>to0</tt>, and <tt>Rep0</tt> also lost the <tt>0</tt> at the end of their names. 
* <tt>Representable0</tt> and <tt>Representable1</tt> have become <tt>Generic</tt> and <tt>Generic1</tt>, respectively. <tt>from0</tt>, <tt>to0</tt>, and <tt>Rep0</tt> also lost the <tt>0</tt> at the end of their names. 

−  * We are using type families, so the <tt>Generic</tt> and <tt>Generic1</tt> type classes have only one type argument. So, in GHC the classes look like what we describe in "Avoiding extensions" part of Section 2.3 of the paper. This change affects only a generic function writer, and not a generic function user. 
+  * We are using type families, so the <tt>Generic</tt> and <tt>Generic1</tt> type classes have only one type argument. So, in GHC the classes look like what we describe in the "Avoiding extensions" part of Section 2.3 of the paper. This change affects only a generic function writer, and not a generic function user. 
−  * Default definitions (Section 3.3) work differently. In GHC we don't use a 
+  * Default definitions (Section 3.3) work differently. In GHC we don't use a <tt>DERIVABLE</tt> pragma; instead, a type class can declare a ''generic default method'', which is akin to a standard default method, but includes a default type signature. This removes the need for a separate default definition and a pragma. For example, the <tt>Encode</tt> class of Section 3.1 is now: 
<haskell> 
<haskell> 

class Encode a where 
class Encode a where 

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</haskell> 
</haskell> 

−  * To derive generic functionality to a user type, the user no longer uses 
+  * To derive generic functionality to a user type, the user no longer uses <hask>deriving instance</hask> (Section 4.6.1). Instead, the user gives an instance without defining the method; GHC then uses the generic default. For instance: 
<haskell> 
<haskell> 

instance Encode [a]  works if there is an instance Generic [a] 
instance Encode [a]  works if there is an instance Generic [a] 

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== Limitations == 
== Limitations == 

−  * We do not yet allow <hask>deriving Generic1</hask> clauses. This means that functions like <tt>fmap</tt> cannot yet be easily expressed generically in GHC. 

⚫  
⚫  
⚫  
⚫  
+  
⚫  
+  [[Category:GHC]] 

⚫  
+  [[Category:Language extensions]] 

⚫  
⚫ 
Latest revision as of 20:24, 19 October 2020
GHC 7.2 includes improved support for datatypegeneric programming through two features, enabled with two flags: DeriveGeneric and DefaultSignatures. We show how this all works in this page, starting with a detailed example.
Example: serialization
Suppose you are writing a class for serialization of data. You have a type Bit
representing bits, and a class Serialize
:
data Bit = O  I
class Serialize a where
put :: a > [Bit]
You might have written some instances already:
instance Serialize Int where
put i = serializeInt i
instance Serialize a => Serialize [a] where
put [] = []
put (h:t) = put h ++ put t
A user of your library, however, will have his own datatypes, like:
data UserTree a = Node a (UserTree a) (UserTree a)  Leaf
He will have to specify an instance Serialize (UserTree a) where ...
himself. This, however, is tedious, especially because most instances will probably be rather trivial, and should be derived automatically.
It is here that generic programming can help you. If you are familiar with Scrap your boilerplate (SYB) you could use it at this stage, but now we'll see how to do this with the GHC Generic features.
Generic serialization
First you have to tell the compiler how to serialize any datatype, in general. Since Haskell datatypes have a regular structure, this means you can just explain how to serialize a few basic datatypes.
Representation types
We can represent most Haskell datatypes using only the following primitive types:
  Unit: used for constructors without arguments
data U1 p = U1
  Constants, additional parameters and recursion of kind *
newtype K1 i c p = K1 { unK1 :: c }
  Metainformation (constructor names, etc.)
newtype M1 i c f p = M1 { unM1 :: f p }
  Sums: encode choice between constructors
infixr 5 :+:
data (:+:) f g p = L1 (f p)  R1 (g p)
  Products: encode multiple arguments to constructors
infixr 6 :*:
data (:*:) f g p = f p :*: g p
For starters, try to ignore the p parameter in all types; it's there just for future compatibility. The easiest way to understand how you can use these types to represent others is to see an example. Let's represent the UserTree
type shown before:
type RepUserTree a =
 A UserTree is either a Leaf, which has no arguments
U1
 ... or it is a Node, which has three arguments that we put in a product
:+: a :*: UserTree a :*: UserTree a
Simple, right? Different constructors become alternatives of a sum, and multiple arguments become products. In fact, we want to have some more information in the representation, like datatype and constructor names, and to know if a product argument is a parameter or a type. We use the other primitives for this, and the representation looks more like:
type RealRepUserTree a =
 Information about the datatype
M1 D Data_UserTree (
 Leaf, with information about the constructor
M1 C Con_Leaf U1
 Node, with information about the constructor
:+: M1 C Con_Node (
 Constructor argument, which could have information
 about a record selector label
M1 S NoSelector (
 Argument, tagged with P because it is a parameter
K1 P a)
 Another argument, tagged with R because it is
 a recursive occurrence of a type
:*: M1 S NoSelector (K1 R (UserTree a))
 Idem
:*: M1 S NoSelector (K1 R (UserTree a))
))
A bit more complicated, but essentially the same. Datatypes like Data_UserTree
are empty datatypes used only for providing metainformation in the representation; you don't have to worry much about them for now. Also, GHC generates these representations for you automatically, so you should never have to define them yourself! All of this is explained in much more detail in Section 2.1. of the original paper describing the new generic deriving mechanism.
A generic function
Since GHC can represent user types using only those primitive types, all you have to do is to tell GHC how to serialize each of the individual primitive types. The best way to do that is to create a new type class:
class GSerialize f where
gput :: f a > [Bit]
This class looks very much like the original Serialize
class, just that the type argument is of kind * > *
, since our generic representation types have this p parameter lying around. Now we need to give instances for each of the basic types. For units there's nothing to serialize:
instance GSerialize U1 where
gput U1 = []
The serialization of multiple arguments is simply the concatenation of each of the individual serializations:
instance (GSerialize a, GSerialize b) => GSerialize (a :*: b) where
gput (a :*: b) = gput a ++ gput b
The case for sums is the most interesting, as we have to record which alternative we are in. We will use a 0 for left injections and a 1 for right injections:
instance (GSerialize a, GSerialize b) => GSerialize (a :+: b) where
gput (L1 x) = O : gput x
gput (R1 x) = I : gput x
We don't need to encode the metainformation, so we just go over it recursively :
instance (GSerialize a) => GSerialize (M1 i c a) where
gput (M1 x) = gput x
Finally, we're only left with the arguments. For these we will just use our first class, Serialize
, again:
instance (Serialize a) => GSerialize (K1 i a) where
gput (K1 x) = put x
So, if a user datatype has a parameter which is instantiated to Int
, at this stage we will use the library instance for Serialize Int
.
Default implementations
We've seen how to represent user types generically, and how to define functions on representation types. However, we still have to tie these two together, explaining how to convert user types to their representation and then applying the generic function.
The representation RepUserTree
we have seen earlier is only one component of the representation; we also need functions to convert to and from the user datatype into the representation. For that we use another type class:
class Generic a where
 Encode the representation of a user datatype
type Rep a :: * > *
 Convert from the datatype to its representation
from :: a > (Rep a) x
 Convert from the representation to the datatype
to :: (Rep a) x > a
So, for the UserTree
datatype shown before, GHC generates the following instance:
instance Generic (UserTree a) where
type Rep (UserTree a) = RepUserTree a
from Leaf = L1 U1
from (Node a l r) = R1 (a :*: l :*: r)
to (L1 U1) = Leaf
to (R1 (a :*: l :*: r)) = Node a l r
(Note that we are using the simpler representation RepUserTree
instead of the real representation RealRepUserTree
, just for simplicity.)
Equipped with a Generic
instance, we are ready to tell the compiler how it can serialize any representable type:
putDefault :: (Generic a, GSerialize (Rep a)) => a > [Bit]
putDefault a = gput (from a)
The type of putDefault
says that we can serialize any a into a list of bits, as long as that a is Generic
, and its representation Rep a
has a GSerialize
instance. The implementation is very simple: first convert the value to its representation using from
, and then call gput
on that representation.
However, we still have to write a Serialize
instance for the user dataype:
instance (Serialize a) => Serialize (UserTree a) where
put = putDefault
Using GHC's new features
What we have seen so far could all already be done, at the cost of writing a lot of boilerplate code yourself (or spending hours writing Template Haskell code to do it for you). Now we'll see how the new features of GHC can help you.
Deriving representations
The Generic
class, and all the representation types, come with GHC in the GHC.Generics module. GHC can also derive Generic
for user types, so all the user has to do is:
{# LANGUAGE DeriveGeneric #}
data UserTree a = Node a (UserTree a) (UserTree a)  Leaf
deriving Generic
(Standalone deriving also works fine, and you can use it for types you have not defined yourself, but are imported from somewhere else.) You will need the new DeriveGeneric language pragma.
More general default methods
We don't want the user to have to write the instance Serialize (UserTree a)
himself, since most of the times it will just be putDefault
. However, we cannot make putDefault
the default implementation of the put
method, because that would require adding the (Generic a, GSerialize (Rep a))
constraint to the class head. This would restrict the ability to give adhoc instances for types that are not representable, for instance.
We solved this by allowing the user to give a different signature for default methods:
{# LANGUAGE DefaultSignatures #}
class Serialize a where
put :: a > [Bit]
default put :: (Generic a, GSerialize (Rep a)) => a > [Bit]
put a = gput (from a)
With the new language pragma DefaultSignatures, GHC allows you to put the keyword default
before a (new) type signature for a method inside a class declaration. If you give such a default type signature, then you have to provide a default method implementation, which will be typechecked using the default signature, and not the original one.
Now the user can simply write:
instance (Serialize a) => Serialize (UserTree a)
GHC fills out the implementation for put
using the default method. It will typecheck correctly because we have a Generic
instance for UserTree
, and GSerialize
instances for all the representation types.
Complete working example
{# LANGUAGE DefaultSignatures, DeriveGeneric, TypeOperators, FlexibleContexts #}
import GHC.Generics
import Data.Bits
data Bit = O  I deriving Show
class Serialize a where
put :: a > [Bit]
default put :: (Generic a, GSerialize (Rep a)) => a > [Bit]
put a = gput (from a)
get :: [Bit] > (a, [Bit])
default get :: (Generic a, GSerialize (Rep a)) => [Bit] > (a, [Bit])
get xs = (to x, xs')
where (x, xs') = gget xs
class GSerialize f where
gput :: f a > [Bit]
gget :: [Bit] > (f a, [Bit])
  Unit: used for constructors without arguments
instance GSerialize U1 where
gput U1 = []
gget xs = (U1, xs)
  Products: encode multiple arguments to constructors
instance (GSerialize a, GSerialize b) => GSerialize (a :*: b) where
gput (a :*: b) = gput a ++ gput b
gget xs = (a :*: b, xs'')
where (a, xs') = gget xs
(b, xs'') = gget xs'
  Sums: encode choice between constructors
instance (GSerialize a, GSerialize b) => GSerialize (a :+: b) where
gput (L1 x) = O : gput x
gput (R1 x) = I : gput x
gget (O:xs) = (L1 x, xs')
where (x, xs') = gget xs
gget (I:xs) = (R1 x, xs')
where (x, xs') = gget xs
  Metainformation (constructor names, etc.)
instance (GSerialize a) => GSerialize (M1 i c a) where
gput (M1 x) = gput x
gget xs = (M1 x, xs')
where (x, xs') = gget xs
  Constants, additional parameters and recursion of kind *
instance (Serialize a) => GSerialize (K1 i a) where
gput (K1 x) = put x
gget xs = (K1 x, xs')
where (x, xs') = get xs
instance Serialize Bool where
put True = [I]
put False = [O]
get (I:xs) = (True, xs)
get (O:xs) = (False, xs)

 Try it out. (Normally this would be in a separate module.)

data UserTree a = Node a (UserTree a) (UserTree a)  Leaf
deriving (Generic, Show)
instance (Serialize a) => Serialize (UserTree a)
main = do
let xs = put True
print (fst . get $ xs :: Bool)
let ys = put (Leaf :: UserTree Bool)
print (fst . get $ ys :: UserTree Bool)
let zs = put (Node False Leaf Leaf :: UserTree Bool)
print (fst . get $ zs :: UserTree Bool)
Different perspectives
We outline the changes introduced in 7.2 regarding support for generic programming from the perspective of three different types of users: the enduser, the generic programmer, and the GHC hacker.
The enduser
If you know nothing about generic programming and would like to keep it that way, then you will be pleased to know that using generics in GHC 7.2 is easier than ever. As soon as you encounter a class with a default signature (like Serialize above), you will be able to give empty instances for your datatypes, like this:
instance (Serialize a) => Serialize (UserTree a)
You will need to add a deriving Generic
clause to each datatype that you want to have generic implementations for. You might have datatypes that use other datatypes, and you might need Generic instances for those too. In that case, you can import the module where the datatype is defined and give a standalone deriving Generic instance. In either case, you will need the XDeriveGeneric flag.
The generic programmer
If you are a library author and are eager to make your classes easy to instantiate by your users, then you should invest some time in defining instances for each of the representation types of GHC.Generics and defining a generic default method. See the example for Serialize above, and the original paper for many other examples (but make sure to check the changes from the paper).
The GHC hacker
If you are working on the GHC source code, you might find it useful to know what kind of changes were made. There is a Trac wiki page with a lowerlevel overview of things and also keeping track of what still needs to be done.
Changes from the paper
In the paper we describe the implementation in UHC. The implementation in GHC is slightly different:
 Representable0 and Representable1 have become Generic and Generic1, respectively. from0, to0, and Rep0 also lost the 0 at the end of their names.
 We are using type families, so the Generic and Generic1 type classes have only one type argument. So, in GHC the classes look like what we describe in the "Avoiding extensions" part of Section 2.3 of the paper. This change affects only a generic function writer, and not a generic function user.
 Default definitions (Section 3.3) work differently. In GHC we don't use a DERIVABLE pragma; instead, a type class can declare a generic default method, which is akin to a standard default method, but includes a default type signature. This removes the need for a separate default definition and a pragma. For example, the Encode class of Section 3.1 is now:
class Encode a where
encode :: a > [Bit]
default encode :: (Generic a, Encode1 (Rep a)) => a > [Bit]
encode = encode1 . from
 To derive generic functionality to a user type, the user no longer uses
deriving instance
(Section 4.6.1). Instead, the user gives an instance without defining the method; GHC then uses the generic default. For instance:
instance Encode [a]  works if there is an instance Generic [a]
Limitations
We cannot derive Generic instances for:
 Datatypes with a context;
 Existentiallyquantified datatypes;
 GADTs.