Data/Data.hs

{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE CPP, Rank2Types, ScopedTypeVariables #-}

-----------------------------------------------------------------------------
-- |
-- 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.cs.vu.nl/boilerplate/>. 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, -- :: ... -> a -> c a
 gunfold, -- :: ... -> Constr -> c a
 toConstr, -- :: a -> Constr
 dataTypeOf, -- :: a -> DataType
 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, instance of: Show
 -- ** Constructors
 mkDataType, -- :: String -> [Constr] -> DataType
 mkIntType, -- :: String -> DataType
 mkFloatType, -- :: String -> DataType
 mkStringType, -- :: String -> DataType
 mkCharType, -- :: String -> DataType
 mkNoRepType, -- :: String -> DataType
 mkNorepType, -- :: String -> DataType
 -- ** Observers
 dataTypeName, -- :: DataType -> String
 DataRep(..), -- instance of: Eq, Show
 dataTypeRep, -- :: DataType -> DataRep
 -- ** Convenience functions
 repConstr, -- :: DataType -> ConstrRep -> Constr
 isAlgType, -- :: DataType -> Bool
 dataTypeConstrs,-- :: DataType -> [Constr]
 indexConstr, -- :: DataType -> ConIndex -> Constr
 maxConstrIndex, -- :: DataType -> ConIndex
 isNorepType, -- :: DataType -> Bool

 -- * Data constructor representations
 Constr, -- abstract, instance of: Eq, Show
 ConIndex, -- alias for Int, start at 1
 Fixity(..), -- instance of: Eq, Show
 -- ** Constructors
 mkConstr, -- :: DataType -> String -> Fixity -> Constr
 mkIntConstr, -- :: DataType -> Integer -> Constr
 mkFloatConstr, -- :: DataType -> Double -> Constr
 mkIntegralConstr,-- :: (Integral a) => DataType -> a -> Constr
 mkRealConstr, -- :: (Real a) => DataType -> a -> Constr
 mkStringConstr, -- :: DataType -> String -> Constr
 mkCharConstr, -- :: DataType -> Char -> Constr
 -- ** Observers
 constrType, -- :: Constr -> DataType
 ConstrRep(..), -- instance of: Eq, Show
 constrRep, -- :: Constr -> ConstrRep
 constrFields, -- :: Constr -> [String]
 constrFixity, -- :: Constr -> Fixity
 -- ** Convenience function: algebraic data types
 constrIndex, -- :: Constr -> ConIndex
 -- ** From strings to constructors and vice versa: all data types
 showConstr, -- :: Constr -> String
 readConstr, -- :: DataType -> String -> Maybe Constr

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

 -- * Generic operations defined in terms of 'gunfold'
 fromConstr, -- :: Constr -> a
 fromConstrB, -- :: ... -> Constr -> a
 fromConstrM -- :: Monad m => ... -> Constr -> m a

 ) where


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

import Prelude -- necessary to get dependencies right

import Data.Typeable
import Data.Maybe
import Control.Monad

-- Imports for the instances
import Data.Int -- So we can give Data instance for Int8, ...
import Data.Word -- So we can give Data instance for Word8, ...
#ifdef __GLASGOW_HASKELL__
import GHC.Real( Ratio(..) ) -- 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 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
#else
# ifdef __HUGS__
import Hugs.Prelude( Ratio(..) )
# endif
import Foreign.Ptr
import Foreign.ForeignPtr
import Data.Array
#endif

#include "Typeable.h"



------------------------------------------------------------------------------
--
-- 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 @T a@, 'dataCast1' should be defined
 -- as 'gcast1'.
 --
 -- The default definition is @'const' 'Nothing'@, which is appropriate
 -- for non-unary type constructors.
 dataCast1 :: Typeable1 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 @T a b@, 'dataCast2' should be
 -- defined as 'gcast2'.
 --
 -- The default definition is @'const' 'Nothing'@, which is appropriate
 -- for non-binary type constructors.
 dataCast2 :: Typeable2 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 an identity datatype constructor ID (see below)
 -- to instantiate the type constructor c in the type of gfoldl,
 -- and perform injections ID and projections unID accordingly.
 --
 gmapT f x0 = unID (gfoldl k ID x0)
 where
 k :: Data d => ID (d->b) -> d -> ID b
 k (ID c) x = ID (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 = unCONST . gfoldl k z
 where
 k :: Data d => CONST r (d->b) -> d -> CONST r b
 k c x = CONST $ (unCONST 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 declaratoin 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)
 )


-- | The identity type constructor needed for the definition of gmapT
newtype ID x = ID { unID :: x }


-- | The constant type constructor needed for the definition of gmapQl
newtype CONST c a = CONST { unCONST :: c }


-- | 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 (error "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 = unID . gunfold k z
 where
 k :: forall b r. Data b => ID (b -> r) -> ID r
 k c = ID (unID c f)
 
 z :: forall r. r -> ID r
 z = ID


-- | 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

-- | 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
 }

instance Show Constr where
 show = constring


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


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

 deriving (Eq,Show)
-- 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,Show)


-- | 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,Show)


------------------------------------------------------------------------------
--
-- 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) -> mkIntConstr dt i
 (FloatRep, FloatConstr f) -> mkRealConstr dt f
 (CharRep, CharConstr c) -> mkCharConstr dt c
 _ -> error "Data.Data.repConstr"



------------------------------------------------------------------------------
--
-- 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
 _ -> error "Data.Data.dataTypeConstrs"


-- | 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 funtions: 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)
 _ -> error "Data.Data.indexConstr"


-- | Gets the index of a constructor (algebraic datatypes only)
constrIndex :: Constr -> ConIndex
constrIndex con = case constrRep con of
 (AlgConstr idx) -> idx
 _ -> error "Data.Data.constrIndex"


-- | Gets the maximum constructor index of an algebraic datatype
maxConstrIndex :: DataType -> ConIndex
maxConstrIndex dt = case dataTypeRep dt of
 AlgRep cs -> length cs
 _ -> error "Data.Data.maxConstrIndex"



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


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


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


-- | This function is now deprecated. Please use 'mkCharType' instead.
{-# DEPRECATED mkStringType "Use mkCharType instead" #-}
mkStringType :: String -> DataType
mkStringType = mkCharType

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


-- | Helper for 'mkIntType', 'mkFloatType', 'mkStringType'
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 = error "Data.Data.confields"
 , confixity = error "Data.Data.confixity"
 }

-- | This function is now deprecated. Please use 'mkIntegralConstr' instead.
{-# DEPRECATED mkIntConstr "Use mkIntegralConstr instead" #-}
mkIntConstr :: DataType -> Integer -> Constr
mkIntConstr = mkIntegralConstr

mkIntegralConstr :: (Integral a, Show a) => DataType -> a -> Constr
mkIntegralConstr dt i = case datarep dt of
 IntRep -> mkPrimCon dt (show i) (IntConstr (toInteger i))
 _ -> error "Data.Data.mkIntegralConstr"

-- | This function is now deprecated. Please use 'mkRealConstr' instead.
{-# DEPRECATED mkFloatConstr "Use mkRealConstr instead" #-}
mkFloatConstr :: DataType -> Double -> Constr
mkFloatConstr dt = mkRealConstr dt . toRational

mkRealConstr :: (Real a, Show a) => DataType -> a -> Constr
mkRealConstr dt f = case datarep dt of
 FloatRep -> mkPrimCon dt (show f) (FloatConstr (toRational f))
 _ -> error "Data.Data.mkRealConstr"

-- | This function is now deprecated. Please use 'mkCharConstr' instead.
{-# DEPRECATED mkStringConstr "Use mkCharConstr instead" #-}
mkStringConstr :: DataType -> String -> Constr
mkStringConstr dt str =
 case datarep dt of
 CharRep -> case str of
 [c] -> mkPrimCon dt (show c) (CharConstr c)
 _ -> error "Data.Data.mkStringConstr: input String must contain a single character"
 _ -> error "Data.Data.mkStringConstr"

-- | Makes a constructor for 'Char'.
mkCharConstr :: DataType -> Char -> Constr
mkCharConstr dt c = case datarep dt of
 CharRep -> mkPrimCon dt (show c) (CharConstr c)
 _ -> error "Data.Data.mkCharConstr"


------------------------------------------------------------------------------
--
-- Non-representations for non-presentable types
--
------------------------------------------------------------------------------


-- | Deprecated version (misnamed)
{-# DEPRECATED mkNorepType "Use mkNoRepType instead" #-}
mkNorepType :: String -> DataType
mkNorepType str = DataType
 { tycon = str
 , datarep = NoRep
 }

-- | Constructs a non-representation for a non-presentable 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.
--
------------------------------------------------------------------------------


falseConstr :: Constr
falseConstr = mkConstr boolDataType "False" [] Prefix
trueConstr :: Constr
trueConstr = mkConstr boolDataType "True" [] Prefix

boolDataType :: DataType
boolDataType = mkDataType "Prelude.Bool" [falseConstr,trueConstr]

instance Data Bool where
 toConstr False = falseConstr
 toConstr True = trueConstr
 gunfold _ z c = case constrIndex c of
 1 -> z False
 2 -> z True
 _ -> error "Data.Data.gunfold(Bool)"
 dataTypeOf _ = boolDataType


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

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

instance Data Char where
 toConstr x = mkCharConstr charType x
 gunfold _ z c = case constrRep c of
 (CharConstr x) -> z x
 _ -> error "Data.Data.gunfold(Char)"
 dataTypeOf _ = charType


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

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

instance Data Float where
 toConstr = mkRealConstr floatType
 gunfold _ z c = case constrRep c of
 (FloatConstr x) -> z (realToFrac x)
 _ -> error "Data.Data.gunfold(Float)"
 dataTypeOf _ = floatType


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

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

instance Data Double where
 toConstr = mkRealConstr doubleType
 gunfold _ z c = case constrRep c of
 (FloatConstr x) -> z (realToFrac x)
 _ -> error "Data.Data.gunfold(Double)"
 dataTypeOf _ = doubleType


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

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

instance Data Int where
 toConstr x = mkIntConstr intType (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Int)"
 dataTypeOf _ = intType


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

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

instance Data Integer where
 toConstr = mkIntConstr integerType
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z x
 _ -> error "Data.Data.gunfold(Integer)"
 dataTypeOf _ = integerType


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

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

instance Data Int8 where
 toConstr x = mkIntConstr int8Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Int8)"
 dataTypeOf _ = int8Type


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

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

instance Data Int16 where
 toConstr x = mkIntConstr int16Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Int16)"
 dataTypeOf _ = int16Type


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

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

instance Data Int32 where
 toConstr x = mkIntConstr int32Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Int32)"
 dataTypeOf _ = int32Type


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

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

instance Data Int64 where
 toConstr x = mkIntConstr int64Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Int64)"
 dataTypeOf _ = int64Type


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

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

instance Data Word where
 toConstr x = mkIntConstr wordType (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Word)"
 dataTypeOf _ = wordType


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

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

instance Data Word8 where
 toConstr x = mkIntConstr word8Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Word8)"
 dataTypeOf _ = word8Type


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

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

instance Data Word16 where
 toConstr x = mkIntConstr word16Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Word16)"
 dataTypeOf _ = word16Type


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

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

instance Data Word32 where
 toConstr x = mkIntConstr word32Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Word32)"
 dataTypeOf _ = word32Type


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

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

instance Data Word64 where
 toConstr x = mkIntConstr word64Type (fromIntegral x)
 gunfold _ z c = case constrRep c of
 (IntConstr x) -> z (fromIntegral x)
 _ -> error "Data.Data.gunfold(Word64)"
 dataTypeOf _ = word64Type


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

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

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

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 _ _ _ = error "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]

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 (:)))
 _ -> error "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')


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

nothingConstr :: Constr
nothingConstr = mkConstr maybeDataType "Nothing" [] Prefix
justConstr :: Constr
justConstr = mkConstr maybeDataType "Just" [] Prefix

maybeDataType :: DataType
maybeDataType = mkDataType "Prelude.Maybe" [nothingConstr,justConstr]

instance Data a => Data (Maybe a) where
 gfoldl _ z Nothing = z Nothing
 gfoldl f z (Just x) = z Just `f` x
 toConstr Nothing = nothingConstr
 toConstr (Just _) = justConstr
 gunfold k z c = case constrIndex c of
 1 -> z Nothing
 2 -> k (z Just)
 _ -> error "Data.Data.gunfold(Maybe)"
 dataTypeOf _ = maybeDataType
 dataCast1 f = gcast1 f


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

ltConstr :: Constr
ltConstr = mkConstr orderingDataType "LT" [] Prefix
eqConstr :: Constr
eqConstr = mkConstr orderingDataType "EQ" [] Prefix
gtConstr :: Constr
gtConstr = mkConstr orderingDataType "GT" [] Prefix

orderingDataType :: DataType
orderingDataType = mkDataType "Prelude.Ordering" [ltConstr,eqConstr,gtConstr]

instance Data Ordering where
 gfoldl _ z LT = z LT
 gfoldl _ z EQ = z EQ
 gfoldl _ z GT = z GT
 toConstr LT = ltConstr
 toConstr EQ = eqConstr
 toConstr GT = gtConstr
 gunfold _ z c = case constrIndex c of
 1 -> z LT
 2 -> z EQ
 3 -> z GT
 _ -> error "Data.Data.gunfold(Ordering)"
 dataTypeOf _ = orderingDataType


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

leftConstr :: Constr
leftConstr = mkConstr eitherDataType "Left" [] Prefix

rightConstr :: Constr
rightConstr = mkConstr eitherDataType "Right" [] Prefix

eitherDataType :: DataType
eitherDataType = mkDataType "Prelude.Either" [leftConstr,rightConstr]

instance (Data a, Data b) => Data (Either a b) where
 gfoldl f z (Left a) = z Left `f` a
 gfoldl f z (Right a) = z Right `f` a
 toConstr (Left _) = leftConstr
 toConstr (Right _) = rightConstr
 gunfold k z c = case constrIndex c of
 1 -> k (z Left)
 2 -> k (z Right)
 _ -> error "Data.Data.gunfold(Either)"
 dataTypeOf _ = eitherDataType
 dataCast2 f = gcast2 f


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

tuple0Constr :: Constr
tuple0Constr = mkConstr tuple0DataType "()" [] Prefix

tuple0DataType :: DataType
tuple0DataType = mkDataType "Prelude.()" [tuple0Constr]

instance Data () where
 toConstr () = tuple0Constr
 gunfold _ z c | constrIndex c == 1 = z ()
 gunfold _ _ _ = error "Data.Data.gunfold(unit)"
 dataTypeOf _ = tuple0DataType


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

tuple2Constr :: Constr
tuple2Constr = mkConstr tuple2DataType "(,)" [] Infix

tuple2DataType :: DataType
tuple2DataType = mkDataType "Prelude.(,)" [tuple2Constr]

instance (Data a, Data b) => Data (a,b) where
 gfoldl f z (a,b) = z (,) `f` a `f` b
 toConstr (_,_) = tuple2Constr
 gunfold k z c | constrIndex c == 1 = k (k (z (,)))
 gunfold _ _ _ = error "Data.Data.gunfold(tup2)"
 dataTypeOf _ = tuple2DataType
 dataCast2 f = gcast2 f


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

tuple3Constr :: Constr
tuple3Constr = mkConstr tuple3DataType "(,,)" [] Infix

tuple3DataType :: DataType
tuple3DataType = mkDataType "Prelude.(,,)" [tuple3Constr]

instance (Data a, Data b, Data c) => Data (a,b,c) where
 gfoldl f z (a,b,c) = z (,,) `f` a `f` b `f` c
 toConstr (_,_,_) = tuple3Constr
 gunfold k z c | constrIndex c == 1 = k (k (k (z (,,))))
 gunfold _ _ _ = error "Data.Data.gunfold(tup3)"
 dataTypeOf _ = tuple3DataType


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

tuple4Constr :: Constr
tuple4Constr = mkConstr tuple4DataType "(,,,)" [] Infix

tuple4DataType :: DataType
tuple4DataType = mkDataType "Prelude.(,,,)" [tuple4Constr]

instance (Data a, Data b, Data c, Data d)
 => Data (a,b,c,d) where
 gfoldl f z (a,b,c,d) = z (,,,) `f` a `f` b `f` c `f` d
 toConstr (_,_,_,_) = tuple4Constr
 gunfold k z c = case constrIndex c of
 1 -> k (k (k (k (z (,,,)))))
 _ -> error "Data.Data.gunfold(tup4)"
 dataTypeOf _ = tuple4DataType


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

tuple5Constr :: Constr
tuple5Constr = mkConstr tuple5DataType "(,,,,)" [] Infix

tuple5DataType :: DataType
tuple5DataType = mkDataType "Prelude.(,,,,)" [tuple5Constr]

instance (Data a, Data b, Data c, Data d, Data e)
 => Data (a,b,c,d,e) where
 gfoldl f z (a,b,c,d,e) = z (,,,,) `f` a `f` b `f` c `f` d `f` e
 toConstr (_,_,_,_,_) = tuple5Constr
 gunfold k z c = case constrIndex c of
 1 -> k (k (k (k (k (z (,,,,))))))
 _ -> error "Data.Data.gunfold(tup5)"
 dataTypeOf _ = tuple5DataType


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

tuple6Constr :: Constr
tuple6Constr = mkConstr tuple6DataType "(,,,,,)" [] Infix

tuple6DataType :: DataType
tuple6DataType = mkDataType "Prelude.(,,,,,)" [tuple6Constr]

instance (Data a, Data b, Data c, Data d, Data e, Data f)
 => Data (a,b,c,d,e,f) where
 gfoldl f z (a,b,c,d,e,f') = z (,,,,,) `f` a `f` b `f` c `f` d `f` e `f` f'
 toConstr (_,_,_,_,_,_) = tuple6Constr
 gunfold k z c = case constrIndex c of
 1 -> k (k (k (k (k (k (z (,,,,,)))))))
 _ -> error "Data.Data.gunfold(tup6)"
 dataTypeOf _ = tuple6DataType


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

tuple7Constr :: Constr
tuple7Constr = mkConstr tuple7DataType "(,,,,,,)" [] Infix

tuple7DataType :: DataType
tuple7DataType = mkDataType "Prelude.(,,,,,,)" [tuple7Constr]

instance (Data a, Data b, Data c, Data d, Data e, Data f, Data g)
 => Data (a,b,c,d,e,f,g) where
 gfoldl f z (a,b,c,d,e,f',g) =
 z (,,,,,,) `f` a `f` b `f` c `f` d `f` e `f` f' `f` g
 toConstr (_,_,_,_,_,_,_) = tuple7Constr
 gunfold k z c = case constrIndex c of
 1 -> k (k (k (k (k (k (k (z (,,,,,,))))))))
 _ -> error "Data.Data.gunfold(tup7)"
 dataTypeOf _ = tuple7DataType


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

instance Typeable a => Data (Ptr a) where
 toConstr _ = error "Data.Data.toConstr(Ptr)"
 gunfold _ _ = error "Data.Data.gunfold(Ptr)"
 dataTypeOf _ = mkNoRepType "GHC.Ptr.Ptr"


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

instance Typeable a => Data (ForeignPtr a) where
 toConstr _ = error "Data.Data.toConstr(ForeignPtr)"
 gunfold _ _ = error "Data.Data.gunfold(ForeignPtr)"
 dataTypeOf _ = mkNoRepType "GHC.ForeignPtr.ForeignPtr"


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