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Add Data.Data module
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Anupam Jain
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288
src/Data/Data.purs
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288
src/Data/Data.purs
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module Data.Data where
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import Control.Alt ((<|>))
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import Control.Alternative (empty)
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import Control.Applicative (pure)
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import Control.Bind (bind, (>>=))
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import Control.Category (identity, (<<<))
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import Control.Monad (class Monad)
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import Control.MonadPlus (class MonadPlus)
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import Data.Array as A
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import Data.CommutativeRing ((+))
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import Data.Const (Const(..))
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import Data.Eq ((==))
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import Data.Foldable (foldl)
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import Data.Function (const, ($))
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import Data.Identity (Identity(..))
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import Data.Maybe (Maybe(..), fromMaybe, maybe)
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import Data.Newtype (unwrap)
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import Data.Tuple (Tuple(..))
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import Data.Typeable (class Tag1, class Typeable, cast)
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import Unsafe.Coerce (unsafeCoerce)
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mkT :: forall a b. Typeable a => Typeable b => (b -> b) -> a -> a
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mkT f = fromMaybe identity (cast f)
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mkQ :: forall a b r. Typeable a => Typeable b => r -> (b -> r) -> a -> r
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mkQ r q a = maybe r q (cast a)
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mkM :: forall a b m. Typeable a => Typeable b => Monad m => Tag1 m => (b -> m b) -> a -> m a
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mkM f = fromMaybe pure (cast f)
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-- Purescript can't have cycles in typeclasses
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-- So we manually reify the dictionary into the DataDict datatype
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-- Not using wrapped records here because Purescript can't handle constraints inside records
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newtype DataDict a = DataDict
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(forall c. (forall d b. Data d => c (d -> b) -> d -> c b)
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-- ^ defines how nonempty constructor applications are
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-- folded. It takes the folded tail of the constructor
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-- application and its head, i.e., an immediate subterm,
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-- and combines them in some way.
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-> (forall g. g -> c g)
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-- ^ defines how the empty constructor application is
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-- folded, like the neutral \/ start element for list
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-- folding.
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-> a
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-- ^ structure to be folded.
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-> c a
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-- ^ result, with a type defined in terms of @a@, but
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-- variability is achieved by means of type constructor
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-- @c@ for the construction of the actual result type.
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)
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gfoldl :: forall a c. Data a => (forall d b. Data d => c (d -> b) -> d -> c b)
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-- ^ defines how nonempty constructor applications are
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-- folded. It takes the folded tail of the constructor
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-- application and its head, i.e., an immediate subterm,
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-- and combines them in some way.
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-> (forall g. g -> c g)
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-- ^ defines how the empty constructor application is
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-- folded, like the neutral \/ start element for list
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-- folding.
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-> a
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-- ^ structure to be folded.
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-> c a
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-- ^ result, with a type defined in terms of @a@, but
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-- variability is achieved by means of type constructor
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-- @c@ for the construction of the actual result type.
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gfoldl = let DataDict f = dataDict in f
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-- ((forall b. Data b => b -> b) -> a -> a)
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-- (forall r. (forall b. Data b => b -> r) -> a -> Array r)
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-- (forall m. (Monad m => (forall b. Data b => b -> m b) -> a -> m a))
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class Typeable a <= Data a where
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dataDict :: DataDict a
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-- | A generic transformation that maps over the immediate subterms
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--
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-- The default definition instantiates the type constructor @c@ in the
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-- type of 'gfoldl' to an identity datatype constructor, using the
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-- isomorphism pair as injection and projection.
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gmapT :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a
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-- Use the Identity datatype constructor
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-- to instantiate the type constructor c in the type of gfoldl,
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-- and perform injections Identity and projections runIdentity accordingly.
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--
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gmapT f x0 = unwrap (gfoldl k Identity x0)
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where
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k :: forall d b. Data d => Identity (d->b) -> d -> Identity b
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k (Identity c) x = Identity (c (f x))
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-- | A generic query with a left-associative binary operator
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gmapQl :: forall a r r'. Data a => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
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gmapQl o r f = unwrap <<< gfoldl k z
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where
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k :: forall d b. Data d => Const r (d->b) -> d -> Const r b
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k c x = Const $ (unwrap c) `o` f x
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z :: forall g. g -> Const r g
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z _ = Const r
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-- | A generic query with a right-associative binary operator
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gmapQr :: forall a r r'. Data a => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r
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gmapQr o r0 f x0 = unQr (gfoldl k (const (Qr identity)) x0) r0
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where
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k :: forall d b. Data d => Qr r (d->b) -> d -> Qr r b
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k (Qr c) x = Qr (\r -> c (f x `o` r))
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-- | A generic query that processes the immediate subterms and returns a list
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-- of results. The list is given in the same order as originally specified
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-- in the declaration of the data constructors.
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gmapQ :: forall a u. Data a => (forall d. Data d => d -> u) -> a -> Array u
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gmapQ f = gmapQr (A.cons) [] f
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-- | A generic query that processes one child by index (zero-based)
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gmapQi :: forall u a. Data a => Int -> (forall d. Data d => d -> u) -> a -> u
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gmapQi i f x = case gfoldl k z x of Qi _ q -> case q of
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Nothing -> unsafeCoerce "UNEXPECTED NOTHING"
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Just q' -> q'
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where
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k :: forall d b. Data d => Qi u (d -> b) -> d -> Qi u b
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k (Qi i' q) a = Qi (i'+1) (if i==i' then Just (f a) else q)
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z :: forall g q. g -> Qi q g
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z _ = Qi 0 Nothing
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-- | A generic monadic transformation that maps over the immediate subterms
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--
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-- The default definition instantiates the type constructor @c@ in
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-- the type of 'gfoldl' to the monad datatype constructor, defining
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-- injection and projection using 'return' and '>>='.
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gmapM :: forall m a. Data a => Monad m => (forall d. Data d => d -> m d) -> a -> m a
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-- Use immediately the monad datatype constructor
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-- to instantiate the type constructor c in the type of gfoldl,
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-- so injection and projection is done by return and >>=.
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--
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gmapM f = gfoldl k pure
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where
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k :: forall b d. Data d => m (d -> b) -> d -> m b
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k c x = do c' <- c
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x' <- f x
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pure (c' x')
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-- | Transformation of at least one immediate subterm does not fail
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gmapMp :: forall m a. Data a => MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
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{-
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The type constructor that we use here simply keeps track of the fact
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if we already succeeded for an immediate subterm; see Mp below. To
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this end, we couple the monadic computation with a Boolean.
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-}
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gmapMp f x = unMp (gfoldl k z x) >>= \(Tuple x' b) ->
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if b then pure x' else empty
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where
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z :: forall g. g -> Mp m g
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z g = Mp (pure (Tuple g false))
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k :: forall d b. Data d => Mp m (d -> b) -> d -> Mp m b
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k (Mp c) y
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= Mp ( c >>= \(Tuple h b) ->
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(f y >>= \y' -> pure (Tuple (h y') true))
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<|> pure (Tuple (h y) b)
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)
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-- | Transformation of one immediate subterm with success
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gmapMo :: forall m a. Data a => MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a
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{-
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We use the same pairing trick as for gmapMp,
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i.e., we use an extra Boolean component to keep track of the
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fact whether an immediate subterm was processed successfully.
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However, we cut of mapping over subterms once a first subterm
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was transformed successfully.
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-}
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gmapMo f x = unMp (gfoldl k z x) >>= \(Tuple x' b) ->
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if b then pure x' else empty
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where
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z :: forall g. g -> Mp m g
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z g = Mp (pure (Tuple g false))
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k :: forall d b. Data d => Mp m (d -> b) -> d -> Mp m b
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k (Mp c) y
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= Mp ( c >>= \(Tuple h b) -> if b
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then pure (Tuple (h y) b)
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else (f y >>= \y' -> pure (Tuple (h y') true))
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<|> pure (Tuple (h y) b)
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)
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-- | Type constructor for adding counters to queries
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data Qi q a = Qi Int (Maybe q)
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-- | The type constructor used in definition of gmapQr
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newtype Qr r a = Qr (r -> r)
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unQr :: forall r a. Qr r a -> r -> r
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unQr (Qr f) = f
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-- | The type constructor used in definition of gmapMp
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newtype Mp m x = Mp (m (Tuple x Boolean))
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unMp :: forall m x. Mp m x -> m (Tuple x Boolean)
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unMp (Mp f) = f
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{-
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gmapT :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a
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gmapT = let DataDict f _ _ = dataDict in f
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gmapQ :: forall a. Data a => forall r. (forall b. Data b => b -> r) -> a -> Array r
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gmapQ = let DataDict _ f _ = dataDict in f
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gmapM :: forall a. Data a => (forall m. Monad m => (forall b. Data b => b -> m b) -> a -> m a)
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gmapM = let DataDict _ _ f = dataDict in f
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-}
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-- | Left-associative fold operation for constructor applications.
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--
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-- The type of 'gfoldl' is a headache, but operationally it is a simple
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-- generalisation of a list fold.
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--
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-- The default definition for 'gfoldl' is @'const' 'id'@, which is
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-- suitable for abstract datatypes with no substructures.
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-- gfoldl
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{-
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-- Common instances
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-- TODO: Why do we need `Tag0` here? Instead of `Typeable`.
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instance dataArray :: (Tag0 a, Data a) => Data (Array a) where
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dataDict = DataDict gmapT' gmapQ' gmapM'
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where
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gmapT' :: (forall b. Data b => b -> b) -> Array a -> Array a
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gmapT' f arr = case A.uncons arr of
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Nothing -> []
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Just x -> A.cons (f x.head) (f x.tail)
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gmapQ' :: forall r. (forall b. Data b => b -> r) -> Array a -> Array r
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gmapQ' f arr = case A.uncons arr of
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Nothing -> []
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Just x -> [f x.head, f x.tail]
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gmapM' :: forall m. (Monad m => (forall b. Data b => b -> m b) -> Array a -> m (Array a))
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gmapM' f arr = case A.uncons arr of
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Nothing -> pure []
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Just x -> do
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x' <- f x.head
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xs' <- f x.tail
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pure (A.cons x' xs')
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instance dataBoolean :: Data Boolean where
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dataDict = DataDict gmapT' gmapQ' gmapM'
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where
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gmapT' :: (forall b. Data b => b -> b) -> Boolean -> Boolean
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gmapT' f x = x
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gmapQ' :: forall r. (forall b. Data b => b -> r) -> Boolean -> Array r
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gmapQ' f x = []
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gmapM' :: forall m. (Monad m => (forall b. Data b => b -> m b) -> Boolean -> m Boolean)
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gmapM' f x = pure x
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-}
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-- Combinators
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-- | Apply a transformation everywhere, bottom-up
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everywhere :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a
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everywhere f x = f (gmapT (everywhere f) x)
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-- | Apply a transformation everywhere, top-down
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everywhere' :: forall a. Data a => (forall b. Data b => b -> b) -> a -> a
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everywhere' f x = gmapT (everywhere' f) (f x)
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-- | Summarise all nodes in top-down, left-to-right
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everything :: forall a r. Data a => (r -> r -> r) -> (forall b. Data b => b -> r) -> a -> r
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everything k f x = foldl k (f x) (gmapQ (everything k f) x)
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-- | Apply a monadic transformation everywhere, bottom-up
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everywhereM :: forall m a. Monad m => Data a => (forall b. Data b => b -> m b) -> a -> m a
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everywhereM f x = gmapM (everywhereM f) x >>= f
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