    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Generics.Aliases
    -- 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/>. The present module provides
    -- a number of declarations for typical generic function types,
    -- corresponding type case, and others.
    --
    -----------------------------------------------------------------------------

    module Data.Generics.Aliases (

            -- * Combinators to \"make\" generic functions via cast
            mkT, mkQ, mkM, mkMp, mkR,
            ext0, extT, extQ, extM, extMp, extB, extR,

            -- * Type synonyms for generic function types
            GenericT,
            GenericQ,
            GenericM,
            GenericB,
            GenericR,
            Generic,
            Generic'(..),
            GenericT'(..),
            GenericQ'(..),
            GenericM'(..),

            -- * Inredients of generic functions
            orElse,

            -- * Function combinators on generic functions
            recoverMp,
            recoverQ,
            choiceMp,
            choiceQ,

            -- * Type extension for unary type constructors
            ext1T,
            ext1M,
            ext1Q,
            ext1R

      ) where

    #ifdef __HADDOCK__
    import Prelude
    #endif
    import Control.Monad
    import Data.Generics.Basics

    ------------------------------------------------------------------------------
    --
    --      Combinators to "make" generic functions
    --      We use type-safe cast in a number of ways to make generic functions.
    --
    ------------------------------------------------------------------------------

    -- | Make a generic transformation;
    --   start from a type-specific case;
    --   preserve the term otherwise
    --
    mkT :: ( Typeable a
           , Typeable b
           )
        => (b -> b)
        -> a
        -> a
    mkT = extT id

    -- | Make a generic query;
    --   start from a type-specific case;
    --   return a constant otherwise
    --
    mkQ :: ( Typeable a
           , Typeable b
           )
        => r
        -> (b -> r)
        -> a
        -> r
    (r `mkQ` br) a = case cast a of
                            Just b  -> br b
                            Nothing -> r

    -- | Make a generic monadic transformation;
    --   start from a type-specific case;
    --   resort to return otherwise
    --
    mkM :: ( Monad m
           , Typeable a
           , Typeable b
           )
        => (b -> m b)
        -> a
        -> m a
    mkM = extM return

    {-

    For the remaining definitions, we stick to a more concise style, i.e.,
    we fold maybies with "maybe" instead of case ... of ..., and we also
    use a point-free style whenever possible.

    -}

    -- | Make a generic monadic transformation for MonadPlus;
    --   use \"const mzero\" (i.e., failure) instead of return as default.
    --
    mkMp :: ( MonadPlus m
            , Typeable a
            , Typeable b
            )
         => (b -> m b)
         -> a
         -> m a
    mkMp = extM (const mzero)

    -- | Make a generic builder;
    --   start from a type-specific ase;
    --   resort to no build (i.e., mzero) otherwise
    --
    mkR :: ( MonadPlus m
           , Typeable a
           , Typeable b
           )
        => m b -> m a
    mkR f = mzero `extR` f

    -- | Flexible type extension
    ext0 :: (Typeable a, Typeable b) => c a -> c b -> c a
    ext0 def ext = maybe def id (gcast ext)

    -- | Extend a generic transformation by a type-specific case
    extT :: ( Typeable a
            , Typeable b
            )
         => (a -> a)
         -> (b -> b)
         -> a
         -> a
    extT def ext = unT ((T def) `ext0` (T ext))

    -- | Extend a generic query by a type-specific case
    extQ :: ( Typeable a
            , Typeable b
            )
         => (a -> q)
         -> (b -> q)
         -> a
         -> q
    extQ f g a = maybe (f a) g (cast a)

    -- | Extend a generic monadic transformation by a type-specific case
    extM :: ( Monad m
            , Typeable a
            , Typeable b
            )
         => (a -> m a) -> (b -> m b) -> a -> m a
    extM def ext = unM ((M def) `ext0` (M ext))

    -- | Extend a generic MonadPlus transformation by a type-specific case
    extMp :: ( MonadPlus m
             , Typeable a
             , Typeable b
             )
          => (a -> m a) -> (b -> m b) -> a -> m a
    extMp = extM

    -- | Extend a generic builder
    extB :: ( Typeable a
            , Typeable b
            )
         => a -> b -> a
    extB a = maybe a id . cast

    -- | Extend a generic reader
    extR :: ( Monad m
            , Typeable a
            , Typeable b
            )
         => m a -> m b -> m a
    extR def ext = unR ((R def) `ext0` (R ext))

    ------------------------------------------------------------------------------
    --
    --      Type synonyms for generic function types
    --
    ------------------------------------------------------------------------------

    -- | Generic transformations,
    --   i.e., take an \"a\" and return an \"a\"
    --
    type GenericT = forall a. Data a => a -> a

    -- | Generic queries of type \"r\",
    --   i.e., take any \"a\" and return an \"r\"
    --
    type GenericQ r = forall a. Data a => a -> r

    -- | Generic monadic transformations,
    --   i.e., take an \"a\" and compute an \"a\"
    --
    type GenericM m = forall a. Data a => a -> m a

    -- | Generic builders
    --   i.e., produce an \"a\".
    --
    type GenericB = forall a. Data a => a

    -- | Generic readers, say monadic builders,
    --   i.e., produce an \"a\" with the help of a monad \"m\".
    --
    type GenericR m = forall a. Data a => m a

    -- | The general scheme underlying generic functions
    --   assumed by gfoldl; there are isomorphisms such as
    --   GenericT = Generic T.
    --
    type Generic c = forall a. Data a => a -> c a

    -- | Wrapped generic functions;
    --   recall: [Generic c] would be legal but [Generic' c] not.
    --
    data Generic' c = Generic' { unGeneric' :: Generic c }

    -- | Other first-class polymorphic wrappers
    newtype GenericT'   = GT { unGT :: Data a => a -> a }
    newtype GenericQ' r = GQ { unGQ :: GenericQ r }
    newtype GenericM' m = GM { unGM :: Data a => a -> m a }

    -- | Left-biased choice on maybies
    orElse :: Maybe a -> Maybe a -> Maybe a
    x `orElse` y = case x of
                     Just _  -> x
                     Nothing -> y

    {-

    The following variations take "orElse" to the function
    level. Furthermore, we generalise from "Maybe" to any
    "MonadPlus". This makes sense for monadic transformations and
    queries. We say that the resulting combinators modell choice. We also
    provide a prime example of choice, that is, recovery from failure. In
    the case of transformations, we recover via return whereas for
    queries a given constant is returned.

    -}

    -- | Choice for monadic transformations
    choiceMp :: MonadPlus m => GenericM m -> GenericM m -> GenericM m
    choiceMp f g x = f x `mplus` g x

    -- | Choice for monadic queries
    choiceQ :: MonadPlus m => GenericQ (m r) -> GenericQ (m r) -> GenericQ (m r)
    choiceQ f g x = f x `mplus` g x

    -- | Recover from the failure of monadic transformation by identity
    recoverMp :: MonadPlus m => GenericM m -> GenericM m
    recoverMp f = f `choiceMp` return

    -- | Recover from the failure of monadic query by a constant
    recoverQ :: MonadPlus m => r -> GenericQ (m r) -> GenericQ (m r)
    recoverQ r f = f `choiceQ` const (return r)

    ------------------------------------------------------------------------------
    --
    --      Type extension for unary type constructors
    --
    ------------------------------------------------------------------------------

    -- | Flexible type extension
    ext1 :: (Data a, Typeable1 t)
         => c a
         -> (forall a. Data a => c (t a))
         -> c a
    ext1 def ext = maybe def id (dataCast1 ext)

    -- | Type extension of transformations for unary type constructors
    ext1T :: (Data d, Typeable1 t)
          => (forall d. Data d => d -> d)
          -> (forall d. Data d => t d -> t d)
          -> d -> d
    ext1T def ext = unT ((T def) `ext1` (T ext))

    -- | Type extension of monadic transformations for type constructors
    ext1M :: (Monad m, Data d, Typeable1 t)
          => (forall d. Data d => d -> m d)
          -> (forall d. Data d => t d -> m (t d))
          -> d -> m d
    ext1M def ext = unM ((M def) `ext1` (M ext))

    -- | Type extension of queries for type constructors
    ext1Q :: (Data d, Typeable1 t)
          => (d -> q)
          -> (forall d. Data d => t d -> q)
          -> d -> q
    ext1Q def ext = unQ ((Q def) `ext1` (Q ext))

    -- | Type extension of readers for type constructors
    ext1R :: (Monad m, Data d, Typeable1 t)
          => m d
          -> (forall d. Data d => m (t d))
          -> m d
    ext1R def ext = unR ((R def) `ext1` (R ext))

    ------------------------------------------------------------------------------
    --
    --      Type constructors for type-level lambdas
    --
    ------------------------------------------------------------------------------

    -- | The type constructor for transformations
    newtype T x = T { unT :: x -> x }

    -- | The type constructor for transformations
    newtype M m x = M { unM :: x -> m x }

    -- | The type constructor for queries
    newtype Q q x = Q { unQ :: x -> q }

    -- | The type constructor for readers
    newtype R m x = R { unR :: m x }