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.

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

Constructs an algebraic datatype

Constructs the Int type

Constructs the Float type

Constructs the Char type

Constructs a non-representation for a non-representable type

Gets the type constructor including the module

Public representation of datatypes

Gets the public presentation of a datatype

Look up a constructor by its representation

Test for an algebraic type

Gets the constructors of an algebraic datatype

Gets the constructor for an index (algebraic datatypes only)

Gets the maximum constructor index of an algebraic datatype

Test for a non-representable type

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.

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

Fixity of constructors

Constructs a constructor

Makes a constructor for Char.

Gets the datatype of a constructor

Public representation of constructors

Gets the public presentation of constructors

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.

Gets the fixity of a constructor

Gets the index of a constructor (algebraic datatypes only)

Gets the string for a constructor

Lookup a constructor via a string

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

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

Build a term skeleton

Build a term and use a generic function for subterms

Monadic variation on fromConstrB