Data/Data.hs

    {-# LANGUAGE BangPatterns #-}
    {-# LANGUAGE DeriveDataTypeable #-}
    {-# LANGUAGE FlexibleContexts #-}
    {-# LANGUAGE FlexibleInstances #-}
    {-# LANGUAGE GADTs #-}
    {-# LANGUAGE NoImplicitPrelude #-}
    {-# LANGUAGE DataKinds #-}
    {-# LANGUAGE PolyKinds #-}
    {-# LANGUAGE RankNTypes #-}
    {-# LANGUAGE ScopedTypeVariables #-}
    {-# LANGUAGE StandaloneDeriving #-}
    {-# LANGUAGE Trustworthy #-}
    {-# LANGUAGE TypeOperators #-}

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Data
    -- Copyright   :  (c) The University of Glasgow, CWI 2001--2004
    -- License     :  BSD-style (see the file libraries/base/LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  experimental
    -- Portability :  non-portable (local universal quantification)
    --
    -- \"Scrap your boilerplate\" --- Generic programming in Haskell.  See
    -- <http://www.haskell.org/haskellwiki/Research_papers/Generics#Scrap_your_boilerplate.21>.
    -- This module provides the 'Data' class with its primitives for
    -- generic programming, along with instances for many datatypes. It
    -- corresponds to a merge between the previous "Data.Generics.Basics"
    -- and almost all of "Data.Generics.Instances". The instances that are
    -- not present in this module were moved to the
    -- @Data.Generics.Instances@ module in the @syb@ package.
    --
    -- For more information, please visit the new
    -- SYB wiki: <http://www.cs.uu.nl/wiki/bin/view/GenericProgramming/SYB>.
    --
    -----------------------------------------------------------------------------

    module Data.Data (

            -- * Module Data.Typeable re-exported for convenience
            module Data.Typeable,

            -- * The Data class for processing constructor applications
            Data(
                    gfoldl,
                    gunfold,
                    toConstr,
                    dataTypeOf,
                    dataCast1,      -- mediate types and unary type constructors
                    dataCast2,      -- mediate types and binary type constructors
                    -- Generic maps defined in terms of gfoldl
                    gmapT,
                    gmapQ,
                    gmapQl,
                    gmapQr,
                    gmapQi,
                    gmapM,
                    gmapMp,
                    gmapMo
                ),

            -- * Datatype representations
            DataType,       -- abstract
            -- ** Constructors
            mkDataType,
            mkIntType,
            mkFloatType,
            mkCharType,
            mkNoRepType,
            -- ** Observers
            dataTypeName,
            DataRep(..),
            dataTypeRep,
            -- ** Convenience functions
            repConstr,
            isAlgType,
            dataTypeConstrs,
            indexConstr,
            maxConstrIndex,
            isNorepType,

            -- * Data constructor representations
            Constr,         -- abstract
            ConIndex,       -- alias for Int, start at 1
            Fixity(..),
            -- ** Constructors
            mkConstr,
            mkIntegralConstr,
            mkRealConstr,
            mkCharConstr,
            -- ** Observers
            constrType,
            ConstrRep(..),
            constrRep,
            constrFields,
            constrFixity,
            -- ** Convenience function: algebraic data types
            constrIndex,
            -- ** From strings to constructors and vice versa: all data types
            showConstr,
            readConstr,

            -- * Convenience functions: take type constructors apart
            tyconUQname,
            tyconModule,

            -- * Generic operations defined in terms of 'gunfold'
            fromConstr,
            fromConstrB,
            fromConstrM

      ) where

    ------------------------------------------------------------------------------

    import Data.Functor.Const
    import Data.Either
    import Data.Eq
    import Data.Maybe
    import Data.Monoid
    import Data.Ord
    import Data.Typeable
    import Data.Version( Version(..) )
    import GHC.Base hiding (Any, IntRep, FloatRep)
    import GHC.List
    import GHC.Num
    import GHC.Read
    import GHC.Show
    import Text.Read( reads )

    -- Imports for the instances
    import Data.Functor.Identity -- So we can give Data instance for Identity
    import Data.Int              -- So we can give Data instance for Int8, ...
    import Data.Type.Coercion
    import Data.Word             -- So we can give Data instance for Word8, ...
    import GHC.Real              -- So we can give Data instance for Ratio
    --import GHC.IOBase            -- So we can give Data instance for IO, Handle
    import GHC.Ptr               -- So we can give Data instance for Ptr
    import GHC.ForeignPtr        -- So we can give Data instance for ForeignPtr
    import Foreign.Ptr (IntPtr(..), WordPtr(..))
                                 -- So we can give Data instance for IntPtr and WordPtr
    --import GHC.Stable            -- So we can give Data instance for StablePtr
    --import GHC.ST                -- So we can give Data instance for ST
    --import GHC.Conc              -- So we can give Data instance for MVar & Co.
    import GHC.Arr               -- So we can give Data instance for Array
    import qualified GHC.Generics as Generics (Fixity(..))
    import GHC.Generics hiding (Fixity(..))
                                 -- So we can give Data instance for U1, V1, ...

    ------------------------------------------------------------------------------
    --
    --      The Data class
    --
    ------------------------------------------------------------------------------

    {- |
    The 'Data' class comprehends a fundamental primitive 'gfoldl' for
    folding over constructor applications, say terms. This primitive can
    be instantiated in several ways to map over the immediate subterms
    of a term; see the @gmap@ combinators later in this class.  Indeed, a
    generic programmer does not necessarily need to use the ingenious gfoldl
    primitive but rather the intuitive @gmap@ combinators.  The 'gfoldl'
    primitive is completed by means to query top-level constructors, to
    turn constructor representations into proper terms, and to list all
    possible datatype constructors.  This completion allows us to serve
    generic programming scenarios like read, show, equality, term generation.

    The combinators 'gmapT', 'gmapQ', 'gmapM', etc are all provided with
    default definitions in terms of 'gfoldl', leaving open the opportunity
    to provide datatype-specific definitions.
    (The inclusion of the @gmap@ combinators as members of class 'Data'
    allows the programmer or the compiler to derive specialised, and maybe
    more efficient code per datatype.  /Note/: 'gfoldl' is more higher-order
    than the @gmap@ combinators.  This is subject to ongoing benchmarking
    experiments.  It might turn out that the @gmap@ combinators will be
    moved out of the class 'Data'.)

    Conceptually, the definition of the @gmap@ combinators in terms of the
    primitive 'gfoldl' requires the identification of the 'gfoldl' function
    arguments.  Technically, we also need to identify the type constructor
    @c@ for the construction of the result type from the folded term type.

    In the definition of @gmapQ@/x/ combinators, we use phantom type
    constructors for the @c@ in the type of 'gfoldl' because the result type
    of a query does not involve the (polymorphic) type of the term argument.
    In the definition of 'gmapQl' we simply use the plain constant type
    constructor because 'gfoldl' is left-associative anyway and so it is
    readily suited to fold a left-associative binary operation over the
    immediate subterms.  In the definition of gmapQr, extra effort is
    needed. We use a higher-order accumulation trick to mediate between
    left-associative constructor application vs. right-associative binary
    operation (e.g., @(:)@).  When the query is meant to compute a value
    of type @r@, then the result type withing generic folding is @r -> r@.
    So the result of folding is a function to which we finally pass the
    right unit.

    With the @-XDeriveDataTypeable@ option, GHC can generate instances of the
    'Data' class automatically.  For example, given the declaration

    > data T a b = C1 a b | C2 deriving (Typeable, Data)

    GHC will generate an instance that is equivalent to

    > instance (Data a, Data b) => Data (T a b) where
    >     gfoldl k z (C1 a b) = z C1 `k` a `k` b
    >     gfoldl k z C2       = z C2
    >
    >     gunfold k z c = case constrIndex c of
    >                         1 -> k (k (z C1))
    >                         2 -> z C2
    >
    >     toConstr (C1 _ _) = con_C1
    >     toConstr C2       = con_C2
    >
    >     dataTypeOf _ = ty_T
    >
    > con_C1 = mkConstr ty_T "C1" [] Prefix
    > con_C2 = mkConstr ty_T "C2" [] Prefix
    > ty_T   = mkDataType "Module.T" [con_C1, con_C2]

    This is suitable for datatypes that are exported transparently.

    -}

    class Typeable a => Data a where

      -- | Left-associative fold operation for constructor applications.
      --
      -- The type of 'gfoldl' is a headache, but operationally it is a simple
      -- generalisation of a list fold.
      --
      -- The default definition for 'gfoldl' is @'const' 'id'@, which is
      -- suitable for abstract datatypes with no substructures.
      gfoldl  :: (forall d b. Data d => c (d -> b) -> d -> c b)
                    -- ^ defines how nonempty constructor applications are
                    -- folded.  It takes the folded tail of the constructor
                    -- application and its head, i.e., an immediate subterm,
                    -- and combines them in some way.
              -> (forall g. g -> c g)
                    -- ^ defines how the empty constructor application is
                    -- folded, like the neutral \/ start element for list
                    -- folding.
              -> a
                    -- ^ structure to be folded.
              -> c a
                    -- ^ result, with a type defined in terms of @a@, but
                    -- variability is achieved by means of type constructor
                    -- @c@ for the construction of the actual result type.

      -- See the 'Data' instances in this file for an illustration of 'gfoldl'.

      gfoldl _ z = z

      -- | Unfolding constructor applications
      gunfold :: (forall b r. Data b => c (b -> r) -> c r)
              -> (forall r. r -> c r)
              -> Constr
              -> c a

      -- | Obtaining the constructor from a given datum.
      -- For proper terms, this is meant to be the top-level constructor.
      -- Primitive datatypes are here viewed as potentially infinite sets of
      -- values (i.e., constructors).
      toConstr   :: a -> Constr

      -- | The outer type constructor of the type
      dataTypeOf  :: a -> DataType

    ------------------------------------------------------------------------------
    --
    -- Mediate types and type constructors
    --
    ------------------------------------------------------------------------------

      -- | Mediate types and unary type constructors.
      --
      -- In 'Data' instances of the form
      --
      -- @
      --     instance (Data a, ...) => Data (T a)
      -- @
      --
      -- 'dataCast1' should be defined as 'gcast1'.
      --
      -- The default definition is @'const' 'Nothing'@, which is appropriate
      -- for instances of other forms.
      dataCast1 :: Typeable t
                => (forall d. Data d => c (t d))
                -> Maybe (c a)
      dataCast1 _ = Nothing

      -- | Mediate types and binary type constructors.
      --
      -- In 'Data' instances of the form
      --
      -- @
      --     instance (Data a, Data b, ...) => Data (T a b)
      -- @
      --
      -- 'dataCast2' should be defined as 'gcast2'.
      --
      -- The default definition is @'const' 'Nothing'@, which is appropriate
      -- for instances of other forms.
      dataCast2 :: Typeable t
                => (forall d e. (Data d, Data e) => c (t d e))
                -> Maybe (c a)
      dataCast2 _ = Nothing

    ------------------------------------------------------------------------------
    --
    --      Typical generic maps defined in terms of gfoldl
    --
    ------------------------------------------------------------------------------

      -- | A generic transformation that maps over the immediate subterms
      --
      -- The default definition instantiates the type constructor @c@ in the
      -- type of 'gfoldl' to an identity datatype constructor, using the
      -- isomorphism pair as injection and projection.
      gmapT :: (forall b. Data b => b -> b) -> a -> a

      -- Use the Identity datatype constructor
      -- to instantiate the type constructor c in the type of gfoldl,
      -- and perform injections Identity and projections runIdentity accordingly.
      --
      gmapT f x0 = runIdentity (gfoldl k Identity x0)
        where
          k :: Data d => Identity (d->b) -> d -> Identity b
          k (Identity c) x = Identity (c (f x))

      -- | A generic query with a left-associative binary operator
      gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
      gmapQl o r f = getConst . gfoldl k z
        where
          k :: Data d => Const r (d->b) -> d -> Const r b
          k c x = Const $ (getConst c) `o` f x
          z :: g -> Const r g
          z _   = Const r

      -- | A generic query with a right-associative binary operator
      gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
      gmapQr o r0 f x0 = unQr (gfoldl k (const (Qr id)) x0) r0
        where
          k :: Data d => Qr r (d->b) -> d -> Qr r b
          k (Qr c) x = Qr (\r -> c (f x `o` r))

      -- | A generic query that processes the immediate subterms and returns a list
      -- of results.  The list is given in the same order as originally specified
      -- in the declaration of the data constructors.
      gmapQ :: (forall d. Data d => d -> u) -> a -> [u]
      gmapQ f = gmapQr (:) [] f

      -- | A generic query that processes one child by index (zero-based)
      gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> a -> u
      gmapQi i f x = case gfoldl k z x of { Qi _ q -> fromJust q }
        where
          k :: Data d => Qi u (d -> b) -> d -> Qi u b
          k (Qi i' q) a = Qi (i'+1) (if i==i' then Just (f a) else q)
          z :: g -> Qi q g
          z _           = Qi 0 Nothing

      -- | A generic monadic transformation that maps over the immediate subterms
      --
      -- The default definition instantiates the type constructor @c@ in
      -- the type of 'gfoldl' to the monad datatype constructor, defining
      -- injection and projection using 'return' and '>>='.
      gmapM :: forall m. Monad m => (forall d. Data d => d -> m d) -> a -> m a

      -- Use immediately the monad datatype constructor
      -- to instantiate the type constructor c in the type of gfoldl,
      -- so injection and projection is done by return and >>=.
      --
      gmapM f = gfoldl k return
        where
          k :: Data d => m (d -> b) -> d -> m b
          k c x = do c' <- c
                     x' <- f x
                     return (c' x')

      -- | Transformation of at least one immediate subterm does not fail
      gmapMp :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a

    {-

    The type constructor that we use here simply keeps track of the fact
    if we already succeeded for an immediate subterm; see Mp below. To
    this end, we couple the monadic computation with a Boolean.

    -}

      gmapMp f x = unMp (gfoldl k z x) >>= \(x',b) ->
                    if b then return x' else mzero
        where
          z :: g -> Mp m g
          z g = Mp (return (g,False))
          k :: Data d => Mp m (d -> b) -> d -> Mp m b
          k (Mp c) y
            = Mp ( c >>= \(h, b) ->
                     (f y >>= \y' -> return (h y', True))
                     `mplus` return (h y, b)
                 )

      -- | Transformation of one immediate subterm with success
      gmapMo :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a

    {-

    We use the same pairing trick as for gmapMp,
    i.e., we use an extra Bool component to keep track of the
    fact whether an immediate subterm was processed successfully.
    However, we cut of mapping over subterms once a first subterm
    was transformed successfully.

    -}

      gmapMo f x = unMp (gfoldl k z x) >>= \(x',b) ->
                    if b then return x' else mzero
        where
          z :: g -> Mp m g
          z g = Mp (return (g,False))
          k :: Data d => Mp m (d -> b) -> d -> Mp m b
          k (Mp c) y
            = Mp ( c >>= \(h,b) -> if b
                            then return (h y, b)
                            else (f y >>= \y' -> return (h y',True))
                                 `mplus` return (h y, b)
                 )

    -- | Type constructor for adding counters to queries
    data Qi q a = Qi Int (Maybe q)

    -- | The type constructor used in definition of gmapQr
    newtype Qr r a = Qr { unQr  :: r -> r }

    -- | The type constructor used in definition of gmapMp
    newtype Mp m x = Mp { unMp :: m (x, Bool) }

    ------------------------------------------------------------------------------
    --
    --      Generic unfolding
    --
    ------------------------------------------------------------------------------

    -- | Build a term skeleton
    fromConstr :: Data a => Constr -> a
    fromConstr = fromConstrB (errorWithoutStackTrace "Data.Data.fromConstr")

    -- | Build a term and use a generic function for subterms
    fromConstrB :: Data a
                => (forall d. Data d => d)
                -> Constr
                -> a
    fromConstrB f = runIdentity . gunfold k z
     where
      k :: forall b r. Data b => Identity (b -> r) -> Identity r
      k c = Identity (runIdentity c f)

      z :: forall r. r -> Identity r
      z = Identity

    -- | Monadic variation on 'fromConstrB'
    fromConstrM :: forall m a. (Monad m, Data a)
                => (forall d. Data d => m d)
                -> Constr
                -> m a
    fromConstrM f = gunfold k z
     where
      k :: forall b r. Data b => m (b -> r) -> m r
      k c = do { c' <- c; b <- f; return (c' b) }

      z :: forall r. r -> m r
      z = return

    ------------------------------------------------------------------------------
    --
    --      Datatype and constructor representations
    --
    ------------------------------------------------------------------------------

    --
    -- | Representation of datatypes.
    -- A package of constructor representations with names of type and module.
    --
    data DataType = DataType
                            { tycon   :: String
                            , datarep :: DataRep
                            }

                  deriving Show -- ^ @since 4.0.0.0

    -- | Representation of constructors. Note that equality on constructors
    -- with different types may not work -- i.e. the constructors for 'False' and
    -- 'Nothing' may compare equal.
    data Constr = Constr
                            { conrep    :: ConstrRep
                            , constring :: String
                            , confields :: [String] -- for AlgRep only
                            , confixity :: Fixity   -- for AlgRep only
                            , datatype  :: DataType
                            }

    -- | @since 4.0.0.0
    instance Show Constr where
     show = constring

    -- | Equality of constructors
    --
    -- @since 4.0.0.0
    instance Eq Constr where
      c == c' = constrRep c == constrRep c'

    -- | Public representation of datatypes
    data DataRep = AlgRep [Constr]
                 | IntRep
                 | FloatRep
                 | CharRep
                 | NoRep

                deriving ( Eq   -- ^ @since 4.0.0.0
                         , Show -- ^ @since 4.0.0.0
                         )
    -- The list of constructors could be an array, a balanced tree, or others.

    -- | Public representation of constructors
    data ConstrRep = AlgConstr    ConIndex
                   | IntConstr    Integer
                   | FloatConstr  Rational
                   | CharConstr   Char

                   deriving ( Eq   -- ^ @since 4.0.0.0
                            , Show -- ^ @since 4.0.0.0
                            )

    -- | Unique index for datatype constructors,
    -- counting from 1 in the order they are given in the program text.
    type ConIndex = Int

    -- | Fixity of constructors
    data Fixity = Prefix
                | Infix     -- Later: add associativity and precedence

                deriving ( Eq   -- ^ @since 4.0.0.0
                         , Show -- ^ @since 4.0.0.0
                         )

    ------------------------------------------------------------------------------
    --
    --      Observers for datatype representations
    --
    ------------------------------------------------------------------------------

    -- | Gets the type constructor including the module
    dataTypeName :: DataType -> String
    dataTypeName = tycon

    -- | Gets the public presentation of a datatype
    dataTypeRep :: DataType -> DataRep
    dataTypeRep = datarep

    -- | Gets the datatype of a constructor
    constrType :: Constr -> DataType
    constrType = datatype

    -- | Gets the public presentation of constructors
    constrRep :: Constr -> ConstrRep
    constrRep = conrep

    -- | Look up a constructor by its representation
    repConstr :: DataType -> ConstrRep -> Constr
    repConstr dt cr =
          case (dataTypeRep dt, cr) of
            (AlgRep cs, AlgConstr i)      -> cs !! (i-1)
            (IntRep,    IntConstr i)      -> mkIntegralConstr dt i
            (FloatRep,  FloatConstr f)    -> mkRealConstr dt f
            (CharRep,   CharConstr c)     -> mkCharConstr dt c
            _ -> errorWithoutStackTrace "Data.Data.repConstr: The given ConstrRep does not fit to the given DataType."

    ------------------------------------------------------------------------------
    --
    --      Representations of algebraic data types
    --
    ------------------------------------------------------------------------------

    -- | Constructs an algebraic datatype
    mkDataType :: String -> [Constr] -> DataType
    mkDataType str cs = DataType
                            { tycon   = str
                            , datarep = AlgRep cs
                            }

    -- | Constructs a constructor
    mkConstr :: DataType -> String -> [String] -> Fixity -> Constr
    mkConstr dt str fields fix =
            Constr
                    { conrep    = AlgConstr idx
                    , constring = str
                    , confields = fields
                    , confixity = fix
                    , datatype  = dt
                    }
      where
        idx = head [ i | (c,i) <- dataTypeConstrs dt `zip` [1..],
                         showConstr c == str ]

    -- | Gets the constructors of an algebraic datatype
    dataTypeConstrs :: DataType -> [Constr]
    dataTypeConstrs dt = case datarep dt of
                            (AlgRep cons) -> cons
                            _ -> errorWithoutStackTrace $ "Data.Data.dataTypeConstrs is not supported for "
                                        ++ dataTypeName dt ++
                                        ", as it is not an algebraic data type."

    -- | Gets the field labels of a constructor.  The list of labels
    -- is returned in the same order as they were given in the original
    -- constructor declaration.
    constrFields :: Constr -> [String]
    constrFields = confields

    -- | Gets the fixity of a constructor
    constrFixity :: Constr -> Fixity
    constrFixity = confixity

    ------------------------------------------------------------------------------
    --
    --      From strings to constr's and vice versa: all data types
    --
    ------------------------------------------------------------------------------

    -- | Gets the string for a constructor
    showConstr :: Constr -> String
    showConstr = constring

    -- | Lookup a constructor via a string
    readConstr :: DataType -> String -> Maybe Constr
    readConstr dt str =
          case dataTypeRep dt of
            AlgRep cons -> idx cons
            IntRep      -> mkReadCon (\i -> (mkPrimCon dt str (IntConstr i)))
            FloatRep    -> mkReadCon ffloat
            CharRep     -> mkReadCon (\c -> (mkPrimCon dt str (CharConstr c)))
            NoRep       -> Nothing
      where

        -- Read a value and build a constructor
        mkReadCon :: Read t => (t -> Constr) -> Maybe Constr
        mkReadCon f = case (reads str) of
                        [(t,"")] -> Just (f t)
                        _ -> Nothing

        -- Traverse list of algebraic datatype constructors
        idx :: [Constr] -> Maybe Constr
        idx cons = let fit = filter ((==) str . showConstr) cons
                    in if fit == []
                         then Nothing
                         else Just (head fit)

        ffloat :: Double -> Constr
        ffloat =  mkPrimCon dt str . FloatConstr . toRational

    ------------------------------------------------------------------------------
    --
    --      Convenience functions: algebraic data types
    --
    ------------------------------------------------------------------------------

    -- | Test for an algebraic type
    isAlgType :: DataType -> Bool
    isAlgType dt = case datarep dt of
                     (AlgRep _) -> True
                     _ -> False

    -- | Gets the constructor for an index (algebraic datatypes only)
    indexConstr :: DataType -> ConIndex -> Constr
    indexConstr dt idx = case datarep dt of
                            (AlgRep cs) -> cs !! (idx-1)
                            _           -> errorWithoutStackTrace $ "Data.Data.indexConstr is not supported for "
                                                   ++ dataTypeName dt ++
                                                   ", as it is not an algebraic data type."

    -- | Gets the index of a constructor (algebraic datatypes only)
    constrIndex :: Constr -> ConIndex
    constrIndex con = case constrRep con of
                        (AlgConstr idx) -> idx
                        _ -> errorWithoutStackTrace $ "Data.Data.constrIndex is not supported for "
                                     ++ dataTypeName (constrType con) ++
                                     ", as it is not an algebraic data type."

    -- | Gets the maximum constructor index of an algebraic datatype
    maxConstrIndex :: DataType -> ConIndex
    maxConstrIndex dt = case dataTypeRep dt of
                            AlgRep cs -> length cs
                            _            -> errorWithoutStackTrace $ "Data.Data.maxConstrIndex is not supported for "
                                                     ++ dataTypeName dt ++
                                                     ", as it is not an algebraic data type."

    ------------------------------------------------------------------------------
    --
    --      Representation of primitive types
    --
    ------------------------------------------------------------------------------

    -- | Constructs the 'Int' type
    mkIntType :: String -> DataType
    mkIntType = mkPrimType IntRep

    -- | Constructs the 'Float' type
    mkFloatType :: String -> DataType
    mkFloatType = mkPrimType FloatRep

    -- | Constructs the 'Char' type
    mkCharType :: String -> DataType
    mkCharType = mkPrimType CharRep

    -- | Helper for 'mkIntType', 'mkFloatType'
    mkPrimType :: DataRep -> String -> DataType
    mkPrimType dr str = DataType
                            { tycon   = str
                            , datarep = dr
                            }

    -- Makes a constructor for primitive types
    mkPrimCon :: DataType -> String -> ConstrRep -> Constr
    mkPrimCon dt str cr = Constr
                            { datatype  = dt
                            , conrep    = cr
                            , constring = str
                            , confields = errorWithoutStackTrace "Data.Data.confields"
                            , confixity = errorWithoutStackTrace "Data.Data.confixity"
                            }

    mkIntegralConstr :: (Integral a, Show a) => DataType -> a -> Constr
    mkIntegralConstr dt i = case datarep dt of
                      IntRep -> mkPrimCon dt (show i) (IntConstr (toInteger  i))
                      _ -> errorWithoutStackTrace $ "Data.Data.mkIntegralConstr is not supported for "
                                   ++ dataTypeName dt ++
                                   ", as it is not an Integral data type."

    mkRealConstr :: (Real a, Show a) => DataType -> a -> Constr
    mkRealConstr dt f = case datarep dt of
                        FloatRep -> mkPrimCon dt (show f) (FloatConstr (toRational f))
                        _ -> errorWithoutStackTrace $ "Data.Data.mkRealConstr is not supported for "
                                     ++ dataTypeName dt ++
                                     ", as it is not a Real data type."

    -- | Makes a constructor for 'Char'.
    mkCharConstr :: DataType -> Char -> Constr
    mkCharConstr dt c = case datarep dt of
                       CharRep -> mkPrimCon dt (show c) (CharConstr c)
                       _ -> errorWithoutStackTrace $ "Data.Data.mkCharConstr is not supported for "
                                    ++ dataTypeName dt ++
                                    ", as it is not an Char data type."

    ------------------------------------------------------------------------------
    --
    --      Non-representations for non-representable types
    --
    ------------------------------------------------------------------------------

    -- | Constructs a non-representation for a non-representable type
    mkNoRepType :: String -> DataType
    mkNoRepType str = DataType
                            { tycon   = str
                            , datarep = NoRep
                            }

    -- | Test for a non-representable type
    isNorepType :: DataType -> Bool
    isNorepType dt = case datarep dt of
                       NoRep -> True
                       _ -> False

    ------------------------------------------------------------------------------
    --
    --      Convenience for qualified type constructors
    --
    ------------------------------------------------------------------------------

    -- | Gets the unqualified type constructor:
    -- drop *.*.*... before name
    --
    tyconUQname :: String -> String
    tyconUQname x = let x' = dropWhile (not . (==) '.') x
                     in if x' == [] then x else tyconUQname (tail x')

    -- | Gets the module of a type constructor:
    -- take *.*.*... before name
    tyconModule :: String -> String
    tyconModule x = let (a,b) = break ((==) '.') x
                     in if b == ""
                          then b
                          else a ++ tyconModule' (tail b)
      where
        tyconModule' y = let y' = tyconModule y
                          in if y' == "" then "" else ('.':y')

    ------------------------------------------------------------------------------
    ------------------------------------------------------------------------------
    --
    --      Instances of the Data class for Prelude-like types.
    --      We define top-level definitions for representations.
    --
    ------------------------------------------------------------------------------

    -- | @since 4.0.0.0
    deriving instance Data Bool

    ------------------------------------------------------------------------------

    charType :: DataType
    charType = mkCharType "Prelude.Char"

    -- | @since 4.0.0.0
    instance Data Char where
      toConstr x = mkCharConstr charType x
      gunfold _ z c = case constrRep c of
                        (CharConstr x) -> z x
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Char."
      dataTypeOf _ = charType

    ------------------------------------------------------------------------------

    floatType :: DataType
    floatType = mkFloatType "Prelude.Float"

    -- | @since 4.0.0.0
    instance Data Float where
      toConstr = mkRealConstr floatType
      gunfold _ z c = case constrRep c of
                        (FloatConstr x) -> z (realToFrac x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Float."
      dataTypeOf _ = floatType

    ------------------------------------------------------------------------------

    doubleType :: DataType
    doubleType = mkFloatType "Prelude.Double"

    -- | @since 4.0.0.0
    instance Data Double where
      toConstr = mkRealConstr doubleType
      gunfold _ z c = case constrRep c of
                        (FloatConstr x) -> z (realToFrac x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Double."
      dataTypeOf _ = doubleType

    ------------------------------------------------------------------------------

    intType :: DataType
    intType = mkIntType "Prelude.Int"

    -- | @since 4.0.0.0
    instance Data Int where
      toConstr x = mkIntegralConstr intType x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Int."
      dataTypeOf _ = intType

    ------------------------------------------------------------------------------

    integerType :: DataType
    integerType = mkIntType "Prelude.Integer"

    -- | @since 4.0.0.0
    instance Data Integer where
      toConstr = mkIntegralConstr integerType
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z x
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Integer."
      dataTypeOf _ = integerType

    ------------------------------------------------------------------------------

    -- This follows the same style as the other integral 'Data' instances
    -- defined in "Data.Data"
    naturalType :: DataType
    naturalType = mkIntType "Numeric.Natural.Natural"

    -- | @since 4.8.0.0
    instance Data Natural where
      toConstr x = mkIntegralConstr naturalType x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Natural"
      dataTypeOf _ = naturalType

    ------------------------------------------------------------------------------

    int8Type :: DataType
    int8Type = mkIntType "Data.Int.Int8"

    -- | @since 4.0.0.0
    instance Data Int8 where
      toConstr x = mkIntegralConstr int8Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Int8."
      dataTypeOf _ = int8Type

    ------------------------------------------------------------------------------

    int16Type :: DataType
    int16Type = mkIntType "Data.Int.Int16"

    -- | @since 4.0.0.0
    instance Data Int16 where
      toConstr x = mkIntegralConstr int16Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Int16."
      dataTypeOf _ = int16Type

    ------------------------------------------------------------------------------

    int32Type :: DataType
    int32Type = mkIntType "Data.Int.Int32"

    -- | @since 4.0.0.0
    instance Data Int32 where
      toConstr x = mkIntegralConstr int32Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Int32."
      dataTypeOf _ = int32Type

    ------------------------------------------------------------------------------

    int64Type :: DataType
    int64Type = mkIntType "Data.Int.Int64"

    -- | @since 4.0.0.0
    instance Data Int64 where
      toConstr x = mkIntegralConstr int64Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Int64."
      dataTypeOf _ = int64Type

    ------------------------------------------------------------------------------

    wordType :: DataType
    wordType = mkIntType "Data.Word.Word"

    -- | @since 4.0.0.0
    instance Data Word where
      toConstr x = mkIntegralConstr wordType x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Word"
      dataTypeOf _ = wordType

    ------------------------------------------------------------------------------

    word8Type :: DataType
    word8Type = mkIntType "Data.Word.Word8"

    -- | @since 4.0.0.0
    instance Data Word8 where
      toConstr x = mkIntegralConstr word8Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Word8."
      dataTypeOf _ = word8Type

    ------------------------------------------------------------------------------

    word16Type :: DataType
    word16Type = mkIntType "Data.Word.Word16"

    -- | @since 4.0.0.0
    instance Data Word16 where
      toConstr x = mkIntegralConstr word16Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Word16."
      dataTypeOf _ = word16Type

    ------------------------------------------------------------------------------

    word32Type :: DataType
    word32Type = mkIntType "Data.Word.Word32"

    -- | @since 4.0.0.0
    instance Data Word32 where
      toConstr x = mkIntegralConstr word32Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Word32."
      dataTypeOf _ = word32Type

    ------------------------------------------------------------------------------

    word64Type :: DataType
    word64Type = mkIntType "Data.Word.Word64"

    -- | @since 4.0.0.0
    instance Data Word64 where
      toConstr x = mkIntegralConstr word64Type x
      gunfold _ z c = case constrRep c of
                        (IntConstr x) -> z (fromIntegral x)
                        _ -> errorWithoutStackTrace $ "Data.Data.gunfold: Constructor " ++ show c
                                     ++ " is not of type Word64."
      dataTypeOf _ = word64Type

    ------------------------------------------------------------------------------

    ratioConstr :: Constr
    ratioConstr = mkConstr ratioDataType ":%" [] Infix

    ratioDataType :: DataType
    ratioDataType = mkDataType "GHC.Real.Ratio" [ratioConstr]

    -- NB: This Data instance intentionally uses the (%) smart constructor instead
    -- of the internal (:%) constructor to preserve the invariant that a Ratio
    -- value is reduced to normal form. See Trac #10011.

    -- | @since 4.0.0.0
    instance (Data a, Integral a) => Data (Ratio a) where
      gfoldl k z (a :% b) = z (%) `k` a `k` b
      toConstr _ = ratioConstr
      gunfold k z c | constrIndex c == 1 = k (k (z (%)))
      gunfold _ _ _ = errorWithoutStackTrace "Data.Data.gunfold(Ratio)"
      dataTypeOf _  = ratioDataType

    ------------------------------------------------------------------------------

    nilConstr :: Constr
    nilConstr    = mkConstr listDataType "[]" [] Prefix
    consConstr :: Constr
    consConstr   = mkConstr listDataType "(:)" [] Infix

    listDataType :: DataType
    listDataType = mkDataType "Prelude.[]" [nilConstr,consConstr]

    -- | @since 4.0.0.0
    instance Data a => Data [a] where
      gfoldl _ z []     = z []
      gfoldl f z (x:xs) = z (:) `f` x `f` xs
      toConstr []    = nilConstr
      toConstr (_:_) = consConstr
      gunfold k z c = case constrIndex c of
                        1 -> z []
                        2 -> k (k (z (:)))
                        _ -> errorWithoutStackTrace "Data.Data.gunfold(List)"
      dataTypeOf _ = listDataType
      dataCast1 f  = gcast1 f

    --
    -- The gmaps are given as an illustration.
    -- This shows that the gmaps for lists are different from list maps.
    --
      gmapT  _   []     = []
      gmapT  f   (x:xs) = (f x:f xs)
      gmapQ  _   []     = []
      gmapQ  f   (x:xs) = [f x,f xs]
      gmapM  _   []     = return []
      gmapM  f   (x:xs) = f x >>= \x' -> f xs >>= \xs' -> return (x':xs')

    ------------------------------------------------------------------------------

    -- | @since 4.9.0.0
    deriving instance Data a => Data (NonEmpty a)

    -- | @since 4.0.0.0
    deriving instance Data a => Data (Maybe a)

    -- | @since 4.0.0.0
    deriving instance Data Ordering

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b) => Data (Either a b)

    -- | @since 4.0.0.0
    deriving instance Data ()

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b) => Data (a,b)

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b, Data c) => Data (a,b,c)

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b, Data c, Data d)
             => Data (a,b,c,d)

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b, Data c, Data d, Data e)
             => Data (a,b,c,d,e)

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b, Data c, Data d, Data e, Data f)
             => Data (a,b,c,d,e,f)

    -- | @since 4.0.0.0
    deriving instance (Data a, Data b, Data c, Data d, Data e, Data f, Data g)
             => Data (a,b,c,d,e,f,g)

    ------------------------------------------------------------------------------

    -- | @since 4.8.0.0
    instance Data a => Data (Ptr a) where
      toConstr _   = errorWithoutStackTrace "Data.Data.toConstr(Ptr)"
      gunfold _ _  = errorWithoutStackTrace "Data.Data.gunfold(Ptr)"
      dataTypeOf _ = mkNoRepType "GHC.Ptr.Ptr"
      dataCast1 x  = gcast1 x

    ------------------------------------------------------------------------------

    -- | @since 4.8.0.0
    instance Data a => Data (ForeignPtr a) where
      toConstr _   = errorWithoutStackTrace "Data.Data.toConstr(ForeignPtr)"
      gunfold _ _  = errorWithoutStackTrace "Data.Data.gunfold(ForeignPtr)"
      dataTypeOf _ = mkNoRepType "GHC.ForeignPtr.ForeignPtr"
      dataCast1 x  = gcast1 x

    -- | @since 4.11.0.0
    deriving instance Data IntPtr

    -- | @since 4.11.0.0
    deriving instance Data WordPtr

    ------------------------------------------------------------------------------
    -- The Data instance for Array preserves data abstraction at the cost of
    -- inefficiency. We omit reflection services for the sake of data abstraction.
    -- | @since 4.8.0.0
    instance (Data a, Data b, Ix a) => Data (Array a b)
     where
      gfoldl f z a = z (listArray (bounds a)) `f` (elems a)
      toConstr _   = errorWithoutStackTrace "Data.Data.toConstr(Array)"
      gunfold _ _  = errorWithoutStackTrace "Data.Data.gunfold(Array)"
      dataTypeOf _ = mkNoRepType "Data.Array.Array"
      dataCast2 x  = gcast2 x

    ----------------------------------------------------------------------------
    -- Data instance for Proxy

    -- | @since 4.7.0.0
    deriving instance (Data t) => Data (Proxy t)

    -- | @since 4.7.0.0
    deriving instance (a ~ b, Data a) => Data (a :~: b)

    -- | @since 4.10.0.0
    deriving instance (Typeable i, Typeable j, Typeable a, Typeable b,
                        (a :: i) ~~ (b :: j))
        => Data (a :~~: b)

    -- | @since 4.7.0.0
    deriving instance (Coercible a b, Data a, Data b) => Data (Coercion a b)

    -- | @since 4.9.0.0
    deriving instance Data a => Data (Identity a)

    -- | @since 4.10.0.0
    deriving instance (Typeable k, Data a, Typeable (b :: k)) => Data (Const a b)

    -- | @since 4.7.0.0
    deriving instance Data Version

    ----------------------------------------------------------------------------
    -- Data instances for Data.Monoid wrappers

    -- | @since 4.8.0.0
    deriving instance Data a => Data (Dual a)

    -- | @since 4.8.0.0
    deriving instance Data All

    -- | @since 4.8.0.0
    deriving instance Data Any

    -- | @since 4.8.0.0
    deriving instance Data a => Data (Sum a)

    -- | @since 4.8.0.0
    deriving instance Data a => Data (Product a)

    -- | @since 4.8.0.0
    deriving instance Data a => Data (First a)

    -- | @since 4.8.0.0
    deriving instance Data a => Data (Last a)

    -- | @since 4.8.0.0
    deriving instance (Data (f a), Data a, Typeable f) => Data (Alt f a)

    -- | @since 4.12.0.0
    deriving instance (Data (f a), Data a, Typeable f) => Data (Ap f a)

    ----------------------------------------------------------------------------
    -- Data instances for GHC.Generics representations

    -- | @since 4.9.0.0
    deriving instance Data p => Data (U1 p)

    -- | @since 4.9.0.0
    deriving instance Data p => Data (Par1 p)

    -- | @since 4.9.0.0
    deriving instance (Data (f p), Typeable f, Data p) => Data (Rec1 f p)

    -- | @since 4.9.0.0
    deriving instance (Typeable i, Data p, Data c) => Data (K1 i c p)

    -- | @since 4.9.0.0
    deriving instance (Data p, Data (f p), Typeable c, Typeable i, Typeable f)
        => Data (M1 i c f p)

    -- | @since 4.9.0.0
    deriving instance (Typeable f, Typeable g, Data p, Data (f p), Data (g p))
        => Data ((f :+: g) p)

    -- | @since 4.9.0.0
    deriving instance (Typeable (f :: Type -> Type), Typeable (g :: Type -> Type),
              Data p, Data (f (g p)))
        => Data ((f :.: g) p)

    -- | @since 4.9.0.0
    deriving instance Data p => Data (V1 p)

    -- | @since 4.9.0.0
    deriving instance (Typeable f, Typeable g, Data p, Data (f p), Data (g p))
        => Data ((f :*: g) p)

    -- | @since 4.9.0.0
    deriving instance Data Generics.Fixity

    -- | @since 4.9.0.0
    deriving instance Data Associativity

    -- | @since 4.9.0.0
    deriving instance Data SourceUnpackedness

    -- | @since 4.9.0.0
    deriving instance Data SourceStrictness

    -- | @since 4.9.0.0
    deriving instance Data DecidedStrictness

    ----------------------------------------------------------------------------
    -- Data instances for Data.Ord

    -- | @since 4.12.0.0
    deriving instance Data a => Data (Down a)