----------------------------------------------------------------------------- -- | -- Module : Data.Generics.Basics -- 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. -- ----------------------------------------------------------------------------- module Data.Generics.Basics ( -- * 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 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 mkStringConstr, -- :: DataType -> String -> 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 ------------------------------------------------------------------------------ -- -- 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 @-fglasgow-exts@ 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 a b. Data a => c (a -> b) -> a -> 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 a. Data a => c (t a)) -> 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 a b. (Data a, Data b) => c (t a b)) -> 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 x = unID (gfoldl k ID x) where k (ID c) x = ID (c (f x)) -- | A generic query with a left-associative binary operator gmapQl :: (r -> r' -> r) -> r -> (forall a. Data a => a -> r') -> a -> r gmapQl o r f = unCONST . gfoldl k z where k c x = CONST $ (unCONST c) `o` f x z _ = CONST r -- | A generic query with a right-associative binary operator gmapQr :: (r' -> r -> r) -> r -> (forall a. Data a => a -> r') -> a -> r gmapQr o r f x = unQr (gfoldl k (const (Qr id)) x) r where 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 a. Data a => a -> u) -> a -> [u] gmapQ f = gmapQr (:) [] f -- | A generic query that processes one child by index (zero-based) gmapQi :: Int -> (forall a. Data a => a -> u) -> a -> u gmapQi i f x = case gfoldl k z x of { Qi _ q -> fromJust q } where k (Qi i' q) a = Qi (i'+1) (if i==i' then Just (f a) else q) z f = 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 :: Monad m => (forall a. Data a => a -> m a) -> 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 c x = do c' <- c x' <- f x return (c' x') -- | Transformation of at least one immediate subterm does not fail gmapMp :: MonadPlus m => (forall a. Data a => a -> m a) -> 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 (return (g,False)) k (Mp c) x = Mp ( c >>= \(h,b) -> (f x >>= \x' -> return (h x',True)) `mplus` return (h x,b) ) -- | Transformation of one immediate subterm with success gmapMo :: MonadPlus m => (forall a. Data a => a -> m a) -> 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 (return (g,False)) k (Mp c) x = Mp ( c >>= \(h,b) -> if b then return (h x,b) else (f x >>= \x' -> return (h x',True)) `mplus` return (h x,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 undefined -- | Build a term and use a generic function for subterms fromConstrB :: Data a => (forall a. Data a => a) -> Constr -> a fromConstrB f = unID . gunfold k z where k c = ID (unID c f) z = ID -- | Monadic variation on 'fromConstrB' fromConstrM :: (Monad m, Data a) => (forall a. Data a => m a) -> Constr -> m a fromConstrM f = gunfold k z where k c = do { c' <- c; b <- f; return (c' b) } 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 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 | StringRep | 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 Double | StringConstr String 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) -> mkFloatConstr dt f (StringRep, StringConstr str) -> mkStringConstr dt str _ -> error "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 "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 (\f -> (mkPrimCon dt str (FloatConstr f))) StringRep -> Just (mkStringConstr dt str) 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) ------------------------------------------------------------------------------ -- -- 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 "indexConstr" -- | Gets the index of a constructor (algebraic datatypes only) constrIndex :: Constr -> ConIndex constrIndex con = case constrRep con of (AlgConstr idx) -> idx _ -> error "constrIndex" -- | Gets the maximum constructor index of an algebraic datatype maxConstrIndex :: DataType -> ConIndex maxConstrIndex dt = case dataTypeRep dt of AlgRep cs -> length cs _ -> error "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 -- | Constructs the 'String' type mkStringType :: String -> DataType mkStringType = mkPrimType StringRep -- | 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 "constrFields" , confixity = error "constrFixity" } mkIntConstr :: DataType -> Integer -> Constr mkIntConstr dt i = case datarep dt of IntRep -> mkPrimCon dt (show i) (IntConstr i) _ -> error "mkIntConstr" mkFloatConstr :: DataType -> Double -> Constr mkFloatConstr dt f = case datarep dt of FloatRep -> mkPrimCon dt (show f) (FloatConstr f) _ -> error "mkFloatConstr" mkStringConstr :: DataType -> String -> Constr mkStringConstr dt str = case datarep dt of StringRep -> mkPrimCon dt str (StringConstr str) _ -> error "mkStringConstr" ------------------------------------------------------------------------------ -- -- Non-representations for non-presentable types -- ------------------------------------------------------------------------------ -- | 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' x = let x' = tyconModule x in if x' == "" then "" else ('.':x')