base-4.3.1.0: Basic libraries

Portability | non-portable (local universal quantification)
Stability | experimental
Maintainer | libraries@haskell.org

Data.Data

Contents

- Module Data.Typeable re-exported for convenience
- The Data class for processing constructor applications
- Datatype representations
  - Constructors
  - Observers
  - Convenience functions
- Data constructor representations
  - Constructors
  - Observers
  - Convenience function: algebraic data types
  - From strings to constructors and vice versa: all data types
- Convenience functions: take type constructors apart
- Generic operations defined in terms of `gunfold`

Description

"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.

Synopsis

- module Data.Typeable
- class Typeable a => Data a where
  - gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a
  - gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a
  - toConstr :: a -> Constr
  - dataTypeOf :: a -> DataType
  - dataCast1 :: Typeable1 t => (forall d. Data d => c (t d)) -> Maybe (c a)
  - dataCast2 :: Typeable2 t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)
  - gmapT :: (forall b. Data b => b -> b) -> a -> a
  - gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
  - gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
  - gmapQ :: (forall d. Data d => d -> u) -> a -> [u]
  - gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> a -> u
  - gmapM :: forall m. Monad m => (forall d. Data d => d -> m d) -> a -> m a
  - gmapMp :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
  - gmapMo :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
- data DataType
- mkDataType :: String -> [Constr] -> DataType
- mkIntType :: String -> DataType
- mkFloatType :: String -> DataType
- mkStringType :: String -> DataType
- mkCharType :: String -> DataType
- mkNoRepType :: String -> DataType
- mkNorepType :: String -> DataType
- dataTypeName :: DataType -> String
- data DataRep
  - = AlgRep [Constr]
  - | IntRep
  - | FloatRep
  - | CharRep
  - | NoRep
- dataTypeRep :: DataType -> DataRep
- repConstr :: DataType -> ConstrRep -> Constr
- isAlgType :: DataType -> Bool
- dataTypeConstrs :: DataType -> [Constr]
- indexConstr :: DataType -> ConIndex -> Constr
- maxConstrIndex :: DataType -> ConIndex
- isNorepType :: DataType -> Bool
- data Constr
- type ConIndex = Int
- data Fixity
  - = Prefix
  - | Infix
- mkConstr :: DataType -> String -> [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
- constrType :: Constr -> DataType
- data ConstrRep
  - = AlgConstr ConIndex
  - | IntConstr Integer
  - | FloatConstr Rational
  - | CharConstr Char
- constrRep :: Constr -> ConstrRep
- constrFields :: Constr -> [String]
- constrFixity :: Constr -> Fixity
- constrIndex :: Constr -> ConIndex
- showConstr :: Constr -> String
- readConstr :: DataType -> String -> Maybe Constr
- tyconUQname :: String -> String
- tyconModule :: String -> String
- fromConstr :: Data a => Constr -> a
- fromConstrB :: Data a => (forall d. Data d => d) -> Constr -> a
- fromConstrM :: forall m a. (Monad m, Data a) => (forall d. Data d => m d) -> Constr -> m a

# Module Data.Typeable re-exported for convenience

module Data.Typeable

# The Data class for processing constructor applications

class Typeable a => Data a where

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.

Methods

gfoldl

Arguments

:: (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.

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 a

Unfolding constructor applications

toConstr :: a -> Constr

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 -> DataType

The outer type constructor of the type

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

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)

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 -> a

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 -> r

A generic query with a left-associative binary operator

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

A generic query with a right-associative binary operator

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

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 -> u

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 a

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 a

Transformation of at least one immediate subterm does not fail

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

Transformation of one immediate subterm with success

Instances

Data Bool |
Data Char |
Data Double |
Data Float |
Data Int |
Data Int8 |
Data Int16 |
Data Int32 |
Data Int64 |
Data Integer |
Data Ordering |
Data Word |
Data Word8 |
Data Word16 |
Data Word32 |
Data Word64 |
Data () |
Data SpecConstrAnnotation |
Data a => Data [a] |
(Data a, Integral a) => Data (Ratio a) |
Typeable a => Data (Ptr a) |
Data a => Data (Maybe a) |
Typeable a => Data (ForeignPtr a) |
(Data a, RealFloat a) => Data (Complex a) |
Typeable a => Data (Fixed a) |
(Data a, Data b) => Data (Either a b) |
(Data a, Data b) => Data (a, b) |
(Typeable a, Data b, Ix a) => Data (Array a b) |
(Data a, Data b, Data c) => Data (a, b, c) |
(Data a, Data b, Data c, Data d) => Data (a, b, c, d) |
(Data a, Data b, Data c, Data d, Data e) => Data (a, b, c, d, e) |
(Data a, Data b, Data c, Data d, Data e, Data f) => Data (a, b, c, d, e, f) |
(Data a, Data b, Data c, Data d, Data e, Data f, Data g) => Data (a, b, c, d, e, f, g) |

# Datatype representations

data DataType

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

Instances

Show DataType |

## Constructors

mkDataType :: String -> [Constr] -> DataType

Constructs an algebraic datatype

mkIntType :: String -> DataType

Constructs the `Int` type

mkFloatType :: String -> DataType

Constructs the `Float` type

mkStringType :: String -> DataType

This function is now deprecated. Please use `mkCharType` instead.

mkCharType :: String -> DataType

Constructs the `Char` type

mkNoRepType :: String -> DataType

Constructs a non-representation for a non-presentable type

mkNorepType :: String -> DataType

Deprecated version (misnamed)

## Observers

dataTypeName :: DataType -> String

Gets the type constructor including the module

data DataRep

Public representation of datatypes

Constructors

AlgRep [Constr] |
IntRep |
FloatRep |
CharRep |
NoRep |

Instances

Eq DataRep |
Show DataRep |

dataTypeRep :: DataType -> DataRep

Gets the public presentation of a datatype

## Convenience functions

repConstr :: DataType -> ConstrRep -> Constr

Look up a constructor by its representation

isAlgType :: DataType -> Bool

Test for an algebraic type

dataTypeConstrs :: DataType -> [Constr]

Gets the constructors of an algebraic datatype

indexConstr :: DataType -> ConIndex -> Constr

Gets the constructor for an index (algebraic datatypes only)

maxConstrIndex :: DataType -> ConIndex

Gets the maximum constructor index of an algebraic datatype

isNorepType :: DataType -> Bool

Test for a non-representable type

# Data constructor representations

data Constr

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.

Instances

Eq Constr | Equality of constructors
Show Constr |

type ConIndex = Int

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

data Fixity

Fixity of constructors

Constructors

Prefix |
Infix |

Instances

Eq Fixity |
Show Fixity |

## Constructors

mkConstr :: DataType -> String -> [String] -> Fixity -> Constr

Constructs a constructor

mkIntConstr :: DataType -> Integer -> Constr

This function is now deprecated. Please use `mkIntegralConstr` instead.

mkFloatConstr :: DataType -> Double -> Constr

This function is now deprecated. Please use `mkRealConstr` instead.

mkIntegralConstr :: Integral a => DataType -> a -> Constr

mkRealConstr :: Real a => DataType -> a -> Constr

mkStringConstr :: DataType -> String -> Constr

This function is now deprecated. Please use `mkCharConstr` instead.

mkCharConstr :: DataType -> Char -> Constr

Makes a constructor for `Char`.

## Observers

constrType :: Constr -> DataType

Gets the datatype of a constructor

data ConstrRep

Public representation of constructors

Constructors

AlgConstr ConIndex |
IntConstr Integer |
FloatConstr Rational |
CharConstr Char |

Instances

Eq ConstrRep |
Show ConstrRep |

constrRep :: Constr -> ConstrRep

Gets the public presentation of constructors

constrFields :: Constr -> [String]

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.

constrFixity :: Constr -> Fixity

Gets the fixity of a constructor

## Convenience function: algebraic data types

constrIndex :: Constr -> ConIndex

Gets the index of a constructor (algebraic datatypes only)

## From strings to constructors and vice versa: all data types

showConstr :: Constr -> String

Gets the string for a constructor

readConstr :: DataType -> String -> Maybe Constr

Lookup a constructor via a string

# Convenience functions: take type constructors apart

tyconUQname :: String -> String

Gets the unqualified type constructor: drop *.*.*... before name

tyconModule :: String -> String

Gets the module of a type constructor: take *.*.*... before name

# Generic operations defined in terms of `gunfold`

fromConstr :: Data a => Constr -> a

Build a term skeleton

fromConstrB :: Data a => (forall d. Data d => d) -> Constr -> a

Build a term and use a generic function for subterms

fromConstrM :: forall m a. (Monad m, Data a) => (forall d. Data d => m d) -> Constr -> m a

Monadic variation on `fromConstrB`