GHC/Generics.hs

    {-# LANGUAGE Trustworthy            #-}
    {-# LANGUAGE CPP                    #-}
    {-# LANGUAGE NoImplicitPrelude      #-}
    {-# LANGUAGE TypeSynonymInstances   #-}
    {-# LANGUAGE TypeOperators          #-}
    {-# LANGUAGE KindSignatures         #-}
    {-# LANGUAGE TypeFamilies           #-}
    {-# LANGUAGE StandaloneDeriving     #-}
    {-# LANGUAGE DeriveGeneric          #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  GHC.Generics
    -- Copyright   :  (c) Universiteit Utrecht 2010-2011, University of Oxford 2012-2013
    -- License     :  see libraries/base/LICENSE
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  internal
    -- Portability :  non-portable
    --
    -- @since 4.6.0.0
    --
    -- If you're using @GHC.Generics@, you should consider using the
    -- <http://hackage.haskell.org/package/generic-deriving> package, which
    -- contains many useful generic functions.

    module GHC.Generics  (
    -- * Introduction
    --
    -- |
    --
    -- Datatype-generic functions are are based on the idea of converting values of
    -- a datatype @T@ into corresponding values of a (nearly) isomorphic type @'Rep' T@.
    -- The type @'Rep' T@ is
    -- built from a limited set of type constructors, all provided by this module. A
    -- datatype-generic function is then an overloaded function with instances
    -- for most of these type constructors, together with a wrapper that performs
    -- the mapping between @T@ and @'Rep' T@. By using this technique, we merely need
    -- a few generic instances in order to implement functionality that works for any
    -- representable type.
    --
    -- Representable types are collected in the 'Generic' class, which defines the
    -- associated type 'Rep' as well as conversion functions 'from' and 'to'.
    -- Typically, you will not define 'Generic' instances by hand, but have the compiler
    -- derive them for you.

    -- ** Representing datatypes
    --
    -- |
    --
    -- The key to defining your own datatype-generic functions is to understand how to
    -- represent datatypes using the given set of type constructors.
    --
    -- Let us look at an example first:
    --
    -- @
    -- data Tree a = Leaf a | Node (Tree a) (Tree a)
    --   deriving 'Generic'
    -- @
    --
    -- The above declaration (which requires the language pragma @DeriveGeneric@)
    -- causes the following representation to be generated:
    --
    -- @
    -- instance 'Generic' (Tree a) where
    --   type 'Rep' (Tree a) =
    --     'D1' D1Tree
    --       ('C1' C1_0Tree
    --          ('S1' 'NoSelector' ('Par0' a))
    --        ':+:'
    --        'C1' C1_1Tree
    --          ('S1' 'NoSelector' ('Rec0' (Tree a))
    --           ':*:'
    --           'S1' 'NoSelector' ('Rec0' (Tree a))))
    --   ...
    -- @
    --
    -- /Hint:/ You can obtain information about the code being generated from GHC by passing
    -- the @-ddump-deriv@ flag. In GHCi, you can expand a type family such as 'Rep' using
    -- the @:kind!@ command.
    --
    #if 0
    -- /TODO:/ Newer GHC versions abandon the distinction between 'Par0' and 'Rec0' and will
    -- use 'Rec0' everywhere.
    --
    #endif
    -- This is a lot of information! However, most of it is actually merely meta-information
    -- that makes names of datatypes and constructors and more available on the type level.
    --
    -- Here is a reduced representation for 'Tree' with nearly all meta-information removed,
    -- for now keeping only the most essential aspects:
    --
    -- @
    -- instance 'Generic' (Tree a) where
    --   type 'Rep' (Tree a) =
    --     'Par0' a
    --     ':+:'
    --     ('Rec0' (Tree a) ':*:' 'Rec0' (Tree a))
    -- @
    --
    -- The @Tree@ datatype has two constructors. The representation of individual constructors
    -- is combined using the binary type constructor ':+:'.
    --
    -- The first constructor consists of a single field, which is the parameter @a@. This is
    -- represented as @'Par0' a@.
    --
    -- The second constructor consists of two fields. Each is a recursive field of type @Tree a@,
    -- represented as @'Rec0' (Tree a)@. Representations of individual fields are combined using
    -- the binary type constructor ':*:'.
    --
    -- Now let us explain the additional tags being used in the complete representation:
    --
    --    * The @'S1' 'NoSelector'@ indicates that there is no record field selector associated with
    --      this field of the constructor.
    --
    --    * The @'C1' C1_0Tree@ and @'C1' C1_1Tree@ invocations indicate that the enclosed part is
    --      the representation of the first and second constructor of datatype @Tree@, respectively.
    --      Here, @C1_0Tree@ and @C1_1Tree@ are datatypes generated by the compiler as part of
    --      @deriving 'Generic'@. These datatypes are proxy types with no values. They are useful
    --      because they are instances of the type class 'Constructor'. This type class can be used
    --      to obtain information about the constructor in question, such as its name
    --      or infix priority.
    --
    --    * The @'D1' D1Tree@ tag indicates that the enclosed part is the representation of the
    --      datatype @Tree@. Again, @D1Tree@ is a datatype generated by the compiler. It is a
    --      proxy type, and is useful by being an instance of class 'Datatype', which
    --      can be used to obtain the name of a datatype, the module it has been defined in, and
    --      whether it has been defined using @data@ or @newtype@.

    -- ** Derived and fundamental representation types
    --
    -- |
    --
    -- There are many datatype-generic functions that do not distinguish between positions that
    -- are parameters or positions that are recursive calls. There are also many datatype-generic
    -- functions that do not care about the names of datatypes and constructors at all. To keep
    -- the number of cases to consider in generic functions in such a situation to a minimum,
    -- it turns out that many of the type constructors introduced above are actually synonyms,
    -- defining them to be variants of a smaller set of constructors.

    -- *** Individual fields of constructors: 'K1'
    --
    -- |
    --
    -- The type constructors 'Par0' and 'Rec0' are variants of 'K1':
    --
    -- @
    -- type 'Par0' = 'K1' 'P'
    -- type 'Rec0' = 'K1' 'R'
    -- @
    --
    -- Here, 'P' and 'R' are type-level proxies again that do not have any associated values.

    -- *** Meta information: 'M1'
    --
    -- |
    --
    -- The type constructors 'S1', 'C1' and 'D1' are all variants of 'M1':
    --
    -- @
    -- type 'S1' = 'M1' 'S'
    -- type 'C1' = 'M1' 'C'
    -- type 'D1' = 'M1' 'D'
    -- @
    --
    -- The types 'S', 'C' and 'D' are once again type-level proxies, just used to create
    -- several variants of 'M1'.

    -- *** Additional generic representation type constructors
    --
    -- |
    --
    -- Next to 'K1', 'M1', ':+:' and ':*:' there are a few more type constructors that occur
    -- in the representations of other datatypes.

    -- **** Empty datatypes: 'V1'
    --
    -- |
    --
    -- For empty datatypes, 'V1' is used as a representation. For example,
    --
    -- @
    -- data Empty deriving 'Generic'
    -- @
    --
    -- yields
    --
    -- @
    -- instance 'Generic' Empty where
    --   type 'Rep' Empty = 'D1' D1Empty 'V1'
    -- @

    -- **** Constructors without fields: 'U1'
    --
    -- |
    --
    -- If a constructor has no arguments, then 'U1' is used as its representation. For example
    -- the representation of 'Bool' is
    --
    -- @
    -- instance 'Generic' Bool where
    --   type 'Rep' Bool =
    --     'D1' D1Bool
    --       ('C1' C1_0Bool 'U1' ':+:' 'C1' C1_1Bool 'U1')
    -- @

    -- *** Representation of types with many constructors or many fields
    --
    -- |
    --
    -- As ':+:' and ':*:' are just binary operators, one might ask what happens if the
    -- datatype has more than two constructors, or a constructor with more than two
    -- fields. The answer is simple: the operators are used several times, to combine
    -- all the constructors and fields as needed. However, users /should not rely on
    -- a specific nesting strategy/ for ':+:' and ':*:' being used. The compiler is
    -- free to choose any nesting it prefers. (In practice, the current implementation
    -- tries to produce a more or less balanced nesting, so that the traversal of the
    -- structure of the datatype from the root to a particular component can be performed
    -- in logarithmic rather than linear time.)

    -- ** Defining datatype-generic functions
    --
    -- |
    --
    -- A datatype-generic function comprises two parts:
    --
    --    1. /Generic instances/ for the function, implementing it for most of the representation
    --       type constructors introduced above.
    --
    --    2. A /wrapper/ that for any datatype that is in `Generic`, performs the conversion
    --       between the original value and its `Rep`-based representation and then invokes the
    --       generic instances.
    --
    -- As an example, let us look at a function 'encode' that produces a naive, but lossless
    -- bit encoding of values of various datatypes. So we are aiming to define a function
    --
    -- @
    -- encode :: 'Generic' a => a -> [Bool]
    -- @
    --
    -- where we use 'Bool' as our datatype for bits.
    --
    -- For part 1, we define a class @Encode'@. Perhaps surprisingly, this class is parameterized
    -- over a type constructor @f@ of kind @* -> *@. This is a technicality: all the representation
    -- type constructors operate with kind @* -> *@ as base kind. But the type argument is never
    -- being used. This may be changed at some point in the future. The class has a single method,
    -- and we use the type we want our final function to have, but we replace the occurrences of
    -- the generic type argument @a@ with @f p@ (where the @p@ is any argument; it will not be used).
    --
    -- > class Encode' f where
    -- >   encode' :: f p -> [Bool]
    --
    -- With the goal in mind to make @encode@ work on @Tree@ and other datatypes, we now define
    -- instances for the representation type constructors 'V1', 'U1', ':+:', ':*:', 'K1', and 'M1'.

    -- *** Definition of the generic representation types
    --
    -- |
    --
    -- In order to be able to do this, we need to know the actual definitions of these types:
    --
    -- @
    -- data    'V1'        p                       -- lifted version of Empty
    -- data    'U1'        p = 'U1'                  -- lifted version of ()
    -- data    (':+:') f g p = 'L1' (f p) | 'R1' (g p) -- lifted version of 'Either'
    -- data    (':*:') f g p = (f p) ':*:' (g p)     -- lifted version of (,)
    -- newtype 'K1'    i c p = 'K1' { 'unK1' :: c }    -- a container for a c
    -- newtype 'M1'  i t f p = 'M1' { 'unM1' :: f p }  -- a wrapper
    -- @
    --
    -- So, 'U1' is just the unit type, ':+:' is just a binary choice like 'Either',
    -- ':*:' is a binary pair like the pair constructor @(,)@, and 'K1' is a value
    -- of a specific type @c@, and 'M1' wraps a value of the generic type argument,
    -- which in the lifted world is an @f p@ (where we do not care about @p@).

    -- *** Generic instances
    --
    -- |
    --
    -- The instance for 'V1' is slightly awkward (but also rarely used):
    --
    -- @
    -- instance Encode' 'V1' where
    --   encode' x = undefined
    -- @
    --
    -- There are no values of type @V1 p@ to pass (except undefined), so this is
    -- actually impossible. One can ask why it is useful to define an instance for
    -- 'V1' at all in this case? Well, an empty type can be used as an argument to
    -- a non-empty type, and you might still want to encode the resulting type.
    -- As a somewhat contrived example, consider @[Empty]@, which is not an empty
    -- type, but contains just the empty list. The 'V1' instance ensures that we
    -- can call the generic function on such types.
    --
    -- There is exactly one value of type 'U1', so encoding it requires no
    -- knowledge, and we can use zero bits:
    --
    -- @
    -- instance Encode' 'U1' where
    --   encode' 'U1' = []
    -- @
    --
    -- In the case for ':+:', we produce 'False' or 'True' depending on whether
    -- the constructor of the value provided is located on the left or on the right:
    --
    -- @
    -- instance (Encode' f, Encode' g) => Encode' (f ':+:' g) where
    --   encode' ('L1' x) = False : encode' x
    --   encode' ('R1' x) = True  : encode' x
    -- @
    --
    -- In the case for ':*:', we append the encodings of the two subcomponents:
    --
    -- @
    -- instance (Encode' f, Encode' g) => Encode' (f ':*:' g) where
    --   encode' (x ':*:' y) = encode' x ++ encode' y
    -- @
    --
    -- The case for 'K1' is rather interesting. Here, we call the final function
    -- 'encode' that we yet have to define, recursively. We will use another type
    -- class 'Encode' for that function:
    --
    -- @
    -- instance (Encode c) => Encode' ('K1' i c) where
    --   encode' ('K1' x) = encode x
    -- @
    --
    -- Note how 'Par0' and 'Rec0' both being mapped to 'K1' allows us to define
    -- a uniform instance here.
    --
    -- Similarly, we can define a uniform instance for 'M1', because we completely
    -- disregard all meta-information:
    --
    -- @
    -- instance (Encode' f) => Encode' ('M1' i t f) where
    --   encode' ('M1' x) = encode' x
    -- @
    --
    -- Unlike in 'K1', the instance for 'M1' refers to 'encode'', not 'encode'.

    -- *** The wrapper and generic default
    --
    -- |
    --
    -- We now define class 'Encode' for the actual 'encode' function:
    --
    -- @
    -- class Encode a where
    --   encode :: a -> [Bool]
    --   default encode :: ('Generic' a) => a -> [Bool]
    --   encode x = encode' ('from' x)
    -- @
    --
    -- The incoming 'x' is converted using 'from', then we dispatch to the
    -- generic instances using 'encode''. We use this as a default definition
    -- for 'encode'. We need the 'default encode' signature because ordinary
    -- Haskell default methods must not introduce additional class constraints,
    -- but our generic default does.
    --
    -- Defining a particular instance is now as simple as saying
    --
    -- @
    -- instance (Encode a) => Encode (Tree a)
    -- @
    --
    #if 0
    -- /TODO:/ Add usage example?
    --
    #endif
    -- The generic default is being used. In the future, it will hopefully be
    -- possible to use @deriving Encode@ as well, but GHC does not yet support
    -- that syntax for this situation.
    --
    -- Having 'Encode' as a class has the advantage that we can define
    -- non-generic special cases, which is particularly useful for abstract
    -- datatypes that have no structural representation. For example, given
    -- a suitable integer encoding function 'encodeInt', we can define
    --
    -- @
    -- instance Encode Int where
    --   encode = encodeInt
    -- @

    -- *** Omitting generic instances
    --
    -- |
    --
    -- It is not always required to provide instances for all the generic
    -- representation types, but omitting instances restricts the set of
    -- datatypes the functions will work for:
    --
    --    * If no ':+:' instance is given, the function may still work for
    --      empty datatypes or datatypes that have a single constructor,
    --      but will fail on datatypes with more than one constructor.
    --
    --    * If no ':*:' instance is given, the function may still work for
    --      datatypes where each constructor has just zero or one field,
    --      in particular for enumeration types.
    --
    --    * If no 'K1' instance is given, the function may still work for
    --      enumeration types, where no constructor has any fields.
    --
    --    * If no 'V1' instance is given, the function may still work for
    --      any datatype that is not empty.
    --
    --    * If no 'U1' instance is given, the function may still work for
    --      any datatype where each constructor has at least one field.
    --
    -- An 'M1' instance is always required (but it can just ignore the
    -- meta-information, as is the case for 'encode' above).
    #if 0
    -- *** Using meta-information
    --
    -- |
    --
    -- TODO
    #endif
    -- ** Generic constructor classes
    --
    -- |
    --
    -- Datatype-generic functions as defined above work for a large class
    -- of datatypes, including parameterized datatypes. (We have used 'Tree'
    -- as our example above, which is of kind @* -> *@.) However, the
    -- 'Generic' class ranges over types of kind @*@, and therefore, the
    -- resulting generic functions (such as 'encode') must be parameterized
    -- by a generic type argument of kind @*@.
    --
    -- What if we want to define generic classes that range over type
    -- constructors (such as 'Functor', 'Traversable', or 'Foldable')?

    -- *** The 'Generic1' class
    --
    -- |
    --
    -- Like 'Generic', there is a class 'Generic1' that defines a
    -- representation 'Rep1' and conversion functions 'from1' and 'to1',
    -- only that 'Generic1' ranges over types of kind @* -> *@.
    -- The 'Generic1' class is also derivable.
    --
    -- The representation 'Rep1' is ever so slightly different from 'Rep'.
    -- Let us look at 'Tree' as an example again:
    --
    -- @
    -- data Tree a = Leaf a | Node (Tree a) (Tree a)
    --   deriving 'Generic1'
    -- @
    --
    -- The above declaration causes the following representation to be generated:
    --
    -- instance 'Generic1' Tree where
    --   type 'Rep1' Tree =
    --     'D1' D1Tree
    --       ('C1' C1_0Tree
    --          ('S1' 'NoSelector' 'Par1')
    --        ':+:'
    --        'C1' C1_1Tree
    --          ('S1' 'NoSelector' ('Rec1' Tree)
    --           ':*:'
    --           'S1' 'NoSelector' ('Rec1' Tree)))
    --   ...
    --
    -- The representation reuses 'D1', 'C1', 'S1' (and thereby 'M1') as well
    -- as ':+:' and ':*:' from 'Rep'. (This reusability is the reason that we
    -- carry around the dummy type argument for kind-@*@-types, but there are
    -- already enough different names involved without duplicating each of
    -- these.)
    --
    -- What's different is that we now use 'Par1' to refer to the parameter
    -- (and that parameter, which used to be @a@), is not mentioned explicitly
    -- by name anywhere; and we use 'Rec1' to refer to a recursive use of @Tree a@.

    -- *** Representation of @* -> *@ types
    --
    -- |
    --
    -- Unlike 'Par0' and 'Rec0', the 'Par1' and 'Rec1' type constructors do not
    -- map to 'K1'. They are defined directly, as follows:
    --
    -- @
    -- newtype 'Par1'   p = 'Par1' { 'unPar1' ::   p } -- gives access to parameter p
    -- newtype 'Rec1' f p = 'Rec1' { 'unRec1' :: f p } -- a wrapper
    -- @
    --
    -- In 'Par1', the parameter @p@ is used for the first time, whereas 'Rec1' simply
    -- wraps an application of @f@ to @p@.
    --
    -- Note that 'K1' (in the guise of 'Rec0') can still occur in a 'Rep1' representation,
    -- namely when the datatype has a field that does not mention the parameter.
    --
    -- The declaration
    --
    -- @
    -- data WithInt a = WithInt Int a
    --   deriving 'Generic1'
    -- @
    --
    -- yields
    --
    -- @
    -- class 'Rep1' WithInt where
    --   type 'Rep1' WithInt =
    --     'D1' D1WithInt
    --       ('C1' C1_0WithInt
    --         ('S1' 'NoSelector' ('Rec0' Int)
    --          ':*:'
    --          'S1' 'NoSelector' 'Par1'))
    -- @
    --
    -- If the parameter @a@ appears underneath a composition of other type constructors,
    -- then the representation involves composition, too:
    --
    -- @
    -- data Rose a = Fork a [Rose a]
    -- @
    --
    -- yields
    --
    -- @
    -- class 'Rep1' Rose where
    --   type 'Rep1' Rose =
    --     'D1' D1Rose
    --       ('C1' C1_0Rose
    --         ('S1' 'NoSelector' 'Par1'
    --          ':*:'
    --          'S1' 'NoSelector' ([] ':.:' 'Rec1' Rose)
    -- @
    --
    -- where
    --
    -- @
    -- newtype (':.:') f g p = 'Comp1' { 'unComp1' :: f (g p) }
    -- @
    #if 0
    -- *** Limitations
    --
    -- |
    --
    -- /TODO/
    --
    -- /TODO:/ Also clear up confusion about 'Rec0' and 'Rec1' not really indicating recursion.
    --
    #endif
    -----------------------------------------------------------------------------

      -- * Generic representation types
        V1, U1(..), Par1(..), Rec1(..), K1(..), M1(..)
      , (:+:)(..), (:*:)(..), (:.:)(..)

      -- ** Synonyms for convenience
      , Rec0, Par0, R, P
      , D1, C1, S1, D, C, S

      -- * Meta-information
      , Datatype(..), Constructor(..), Selector(..), NoSelector
      , Fixity(..), Associativity(..), Arity(..), prec

      -- * Generic type classes
      , Generic(..), Generic1(..)

      ) where

    -- We use some base types
    import GHC.Types
    import Data.Maybe ( Maybe(..) )
    import Data.Either ( Either(..) )

    -- Needed for instances
    import GHC.Classes ( Eq, Ord )
    import GHC.Read ( Read )
    import GHC.Show ( Show )
    import Data.Proxy

    --------------------------------------------------------------------------------
    -- Representation types
    --------------------------------------------------------------------------------

    -- | Void: used for datatypes without constructors
    data V1 p

    -- | Unit: used for constructors without arguments
    data U1 p = U1
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Used for marking occurrences of the parameter
    newtype Par1 p = Par1 { unPar1 :: p }
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Recursive calls of kind * -> *
    newtype Rec1 f p = Rec1 { unRec1 :: f p }
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Constants, additional parameters and recursion of kind *
    newtype K1 i c p = K1 { unK1 :: c }
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Meta-information (constructor names, etc.)
    newtype M1 i c f p = M1 { unM1 :: f p }
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Sums: encode choice between constructors
    infixr 5 :+:
    data (:+:) f g p = L1 (f p) | R1 (g p)
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Products: encode multiple arguments to constructors
    infixr 6 :*:
    data (:*:) f g p = f p :*: g p
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Composition of functors
    infixr 7 :.:
    newtype (:.:) f g p = Comp1 { unComp1 :: f (g p) }
      deriving (Eq, Ord, Read, Show, Generic)

    -- | Tag for K1: recursion (of kind *)
    data R
    -- | Tag for K1: parameters (other than the last)
    data P

    -- | Type synonym for encoding recursion (of kind *)
    type Rec0  = K1 R
    -- | Type synonym for encoding parameters (other than the last)
    type Par0  = K1 P
    {-# DEPRECATED Par0 "'Par0' is no longer used; use 'Rec0' instead" #-} -- deprecated in 7.6
    {-# DEPRECATED P "'P' is no longer used; use 'R' instead" #-} -- deprecated in 7.6

    -- | Tag for M1: datatype
    data D
    -- | Tag for M1: constructor
    data C
    -- | Tag for M1: record selector
    data S

    -- | Type synonym for encoding meta-information for datatypes
    type D1 = M1 D

    -- | Type synonym for encoding meta-information for constructors
    type C1 = M1 C

    -- | Type synonym for encoding meta-information for record selectors
    type S1 = M1 S

    -- | Class for datatypes that represent datatypes
    class Datatype d where
      -- | The name of the datatype (unqualified)
      datatypeName :: t d (f :: * -> *) a -> [Char]
      -- | The fully-qualified name of the module where the type is declared
      moduleName   :: t d (f :: * -> *) a -> [Char]
      -- | Marks if the datatype is actually a newtype
      isNewtype    :: t d (f :: * -> *) a -> Bool
      isNewtype _ = False

    -- | Class for datatypes that represent records
    class Selector s where
      -- | The name of the selector
      selName :: t s (f :: * -> *) a -> [Char]

    -- | Used for constructor fields without a name
    data NoSelector

    instance Selector NoSelector where selName _ = ""

    -- | Class for datatypes that represent data constructors
    class Constructor c where
      -- | The name of the constructor
      conName :: t c (f :: * -> *) a -> [Char]

      -- | The fixity of the constructor
      conFixity :: t c (f :: * -> *) a -> Fixity
      conFixity _ = Prefix

      -- | Marks if this constructor is a record
      conIsRecord :: t c (f :: * -> *) a -> Bool
      conIsRecord _ = False

    -- | Datatype to represent the arity of a tuple.
    data Arity = NoArity | Arity Int
      deriving (Eq, Show, Ord, Read, Generic)

    -- | Datatype to represent the fixity of a constructor. An infix
    -- | declaration directly corresponds to an application of 'Infix'.
    data Fixity = Prefix | Infix Associativity Int
      deriving (Eq, Show, Ord, Read, Generic)

    -- | Get the precedence of a fixity value.
    prec :: Fixity -> Int
    prec Prefix      = 10
    prec (Infix _ n) = n

    -- | Datatype to represent the associativity of a constructor
    data Associativity = LeftAssociative
                       | RightAssociative
                       | NotAssociative
      deriving (Eq, Show, Ord, Read, Generic)

    -- | Representable types of kind *.
    -- This class is derivable in GHC with the DeriveGeneric flag on.
    class Generic a where
      -- | Generic representation type
      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

    -- | Representable types of kind * -> *.
    -- This class is derivable in GHC with the DeriveGeneric flag on.
    class Generic1 f where
      -- | Generic representation type
      type Rep1 f :: * -> *
      -- | Convert from the datatype to its representation
      from1  :: f a -> (Rep1 f) a
      -- | Convert from the representation to the datatype
      to1    :: (Rep1 f) a -> f a

    --------------------------------------------------------------------------------
    -- Derived instances
    --------------------------------------------------------------------------------
    deriving instance Generic [a]
    deriving instance Generic (Maybe a)
    deriving instance Generic (Either a b)
    deriving instance Generic Bool
    deriving instance Generic Ordering
    deriving instance Generic ()
    deriving instance Generic ((,) a b)
    deriving instance Generic ((,,) a b c)
    deriving instance Generic ((,,,) a b c d)
    deriving instance Generic ((,,,,) a b c d e)
    deriving instance Generic ((,,,,,) a b c d e f)
    deriving instance Generic ((,,,,,,) a b c d e f g)

    deriving instance Generic1 []
    deriving instance Generic1 Maybe
    deriving instance Generic1 (Either a)
    deriving instance Generic1 ((,) a)
    deriving instance Generic1 ((,,) a b)
    deriving instance Generic1 ((,,,) a b c)
    deriving instance Generic1 ((,,,,) a b c d)
    deriving instance Generic1 ((,,,,,) a b c d e)
    deriving instance Generic1 ((,,,,,,) a b c d e f)

    --------------------------------------------------------------------------------
    -- Primitive representations
    --------------------------------------------------------------------------------

    -- Int
    data D_Int
    data C_Int

    instance Datatype D_Int where
      datatypeName _ = "Int"
      moduleName   _ = "GHC.Int"

    instance Constructor C_Int where
      conName _ = "" -- JPM: I'm not sure this is the right implementation...

    instance Generic Int where
      type Rep Int = D1 D_Int (C1 C_Int (S1 NoSelector (Rec0 Int)))
      from x = M1 (M1 (M1 (K1 x)))
      to (M1 (M1 (M1 (K1 x)))) = x

    -- Float
    data D_Float
    data C_Float

    instance Datatype D_Float where
      datatypeName _ = "Float"
      moduleName   _ = "GHC.Float"

    instance Constructor C_Float where
      conName _ = "" -- JPM: I'm not sure this is the right implementation...

    instance Generic Float where
      type Rep Float = D1 D_Float (C1 C_Float (S1 NoSelector (Rec0 Float)))
      from x = M1 (M1 (M1 (K1 x)))
      to (M1 (M1 (M1 (K1 x)))) = x

    -- Double
    data D_Double
    data C_Double

    instance Datatype D_Double where
      datatypeName _ = "Double"
      moduleName   _ = "GHC.Float"

    instance Constructor C_Double where
      conName _ = "" -- JPM: I'm not sure this is the right implementation...

    instance Generic Double where
      type Rep Double = D1 D_Double (C1 C_Double (S1 NoSelector (Rec0 Double)))
      from x = M1 (M1 (M1 (K1 x)))
      to (M1 (M1 (M1 (K1 x)))) = x

    -- Char
    data D_Char
    data C_Char

    instance Datatype D_Char where
      datatypeName _ = "Char"
      moduleName   _ = "GHC.Base"

    instance Constructor C_Char where
      conName _ = "" -- JPM: I'm not sure this is the right implementation...

    instance Generic Char where
      type Rep Char = D1 D_Char (C1 C_Char (S1 NoSelector (Rec0 Char)))
      from x = M1 (M1 (M1 (K1 x)))
      to (M1 (M1 (M1 (K1 x)))) = x

    deriving instance Generic (Proxy t)