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Showing content from http://hackage.haskell.org/packages/archive/base/4.6.0.0/doc/html/Data-Data.html below:

Data.Data

module Data.Typeable

class Typeable a => Data a whereSource

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 gmapQx 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.

Methods

gfoldlSource

Arguments

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.

defines how the empty constructor application is folded, like the neutral / start element for list folding.

structure to be folded.

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.

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.

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c aSource

Unfolding constructor applications

toConstr :: a -> ConstrSource

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).

dataTypeOf :: a -> DataTypeSource

The outer type constructor of the type

dataCast1 :: Typeable1 t => (forall d. Data d => c (t d)) -> Maybe (c a)Source

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.

dataCast2 :: Typeable2 t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)Source

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.

gmapT :: (forall b. Data b => b -> b) -> a -> aSource

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.

gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> rSource

A generic query with a left-associative binary operator

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> rSource

A generic query with a right-associative binary operator

gmapQ :: (forall d. Data d => d -> u) -> a -> [u]Source

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.

gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> a -> uSource

A generic query that processes one child by index (zero-based)

gmapM :: forall m. Monad m => (forall d. Data d => d -> m d) -> a -> m aSource

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 >>=.

gmapMp :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m aSource

Transformation of at least one immediate subterm does not fail

gmapMo :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m aSource

Transformation of one immediate subterm with success

Instances

data DataType Source

Representation of datatypes. A package of constructor representations with names of type and module.

data Constr Source

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.

type ConIndex = IntSource

Unique index for datatype constructors, counting from 1 in the order they are given in the program text.

mkIntegralConstr :: (Integral a, Show a) => DataType -> a -> ConstrSource

mkRealConstr :: (Real a, Show a) => DataType -> a -> ConstrSource

constrFields :: Constr -> [String]Source

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.

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