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-{-# LANGUAGE CPP #-}
-#if __GLASGOW_HASKELL__ >= 702
-{-# LANGUAGE Safe #-}
-#endif
-#if __GLASGOW_HASKELL__ >= 708
-{-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE StandaloneDeriving #-}
-#endif
------------------------------------------------------------------------------
--- |
--- Module      :  Data.Functor.Classes
--- Copyright   :  (c) Ross Paterson 2013
--- License     :  BSD-style (see the file LICENSE)
---
--- Maintainer  :  R.Paterson@city.ac.uk
--- Stability   :  experimental
--- Portability :  portable
---
--- Liftings of the Prelude classes 'Eq', 'Ord', 'Read' and 'Show' to
--- unary and binary type constructors.
---
--- These classes are needed to express the constraints on arguments of
--- transformers in portable Haskell.  Thus for a new transformer @T@,
--- one might write instances like
---
--- > instance (Eq1 f) => Eq1 (T f) where ...
--- > instance (Ord1 f) => Ord1 (T f) where ...
--- > instance (Read1 f) => Read1 (T f) where ...
--- > instance (Show1 f) => Show1 (T f) where ...
---
--- If these instances can be defined, defining instances of the base
--- classes is mechanical:
---
--- > instance (Eq1 f, Eq a) => Eq (T f a) where (==) = eq1
--- > instance (Ord1 f, Ord a) => Ord (T f a) where compare = compare1
--- > instance (Read1 f, Read a) => Read (T f a) where readsPrec = readsPrec1
--- > instance (Show1 f, Show a) => Show (T f a) where showsPrec = showsPrec1
---
------------------------------------------------------------------------------
-
-module Data.Functor.Classes (
-    -- * Liftings of Prelude classes
-    -- ** For unary constructors
-    Eq1(..), eq1,
-    Ord1(..), compare1,
-    Read1(..), readsPrec1,
-    Show1(..), showsPrec1,
-    -- ** For binary constructors
-    Eq2(..), eq2,
-    Ord2(..), compare2,
-    Read2(..), readsPrec2,
-    Show2(..), showsPrec2,
-    -- * Helper functions
-    -- $example
-    readsData,
-    readsUnaryWith,
-    readsBinaryWith,
-    showsUnaryWith,
-    showsBinaryWith,
-    -- ** Obsolete helpers
-    readsUnary,
-    readsUnary1,
-    readsBinary1,
-    showsUnary,
-    showsUnary1,
-    showsBinary1,
-  ) where
-
-import Control.Applicative (Const(Const))
-import Data.Functor.Identity (Identity(Identity))
-import Data.Monoid (mappend)
-#if MIN_VERSION_base(4,7,0)
-import Data.Proxy (Proxy(Proxy))
-#endif
-#if __GLASGOW_HASKELL__ >= 708
-import Data.Typeable
-#endif
-import Text.Show (showListWith)
-
--- | Lifting of the 'Eq' class to unary type constructors.
-class Eq1 f where
-    -- | Lift an equality test through the type constructor.
-    --
-    -- The function will usually be applied to an equality function,
-    -- but the more general type ensures that the implementation uses
-    -- it to compare elements of the first container with elements of
-    -- the second.
-    liftEq :: (a -> b -> Bool) -> f a -> f b -> Bool
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Eq1
-#endif
-
--- | Lift the standard @('==')@ function through the type constructor.
-eq1 :: (Eq1 f, Eq a) => f a -> f a -> Bool
-eq1 = liftEq (==)
-
--- | Lifting of the 'Ord' class to unary type constructors.
-class (Eq1 f) => Ord1 f where
-    -- | Lift a 'compare' function through the type constructor.
-    --
-    -- The function will usually be applied to a comparison function,
-    -- but the more general type ensures that the implementation uses
-    -- it to compare elements of the first container with elements of
-    -- the second.
-    liftCompare :: (a -> b -> Ordering) -> f a -> f b -> Ordering
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Ord1
-#endif
-
--- | Lift the standard 'compare' function through the type constructor.
-compare1 :: (Ord1 f, Ord a) => f a -> f a -> Ordering
-compare1 = liftCompare compare
-
--- | Lifting of the 'Read' class to unary type constructors.
-class Read1 f where
-    -- | 'readsPrec' function for an application of the type constructor
-    -- based on 'readsPrec' and 'readList' functions for the argument type.
-    liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
-
-    -- | 'readList' function for an application of the type constructor
-    -- based on 'readsPrec' and 'readList' functions for the argument type.
-    -- The default implementation using standard list syntax is correct
-    -- for most types.
-    liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [f a]
-    liftReadList rp rl = readListWith (liftReadsPrec rp rl 0)
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Read1
-#endif
-
--- | Read a list (using square brackets and commas), given a function
--- for reading elements.
-readListWith :: ReadS a -> ReadS [a]
-readListWith rp =
-    readParen False (\r -> [pr | ("[",s) <- lex r, pr <- readl s])
-  where
-    readl s = [([],t) | ("]",t) <- lex s] ++
-        [(x:xs,u) | (x,t) <- rp s, (xs,u) <- readl' t]
-    readl' s = [([],t) | ("]",t) <- lex s] ++
-        [(x:xs,v) | (",",t) <- lex s, (x,u) <- rp t, (xs,v) <- readl' u]
-
--- | Lift the standard 'readsPrec' and 'readList' functions through the
--- type constructor.
-readsPrec1 :: (Read1 f, Read a) => Int -> ReadS (f a)
-readsPrec1 = liftReadsPrec readsPrec readList
-
--- | Lifting of the 'Show' class to unary type constructors.
-class Show1 f where
-    -- | 'showsPrec' function for an application of the type constructor
-    -- based on 'showsPrec' and 'showList' functions for the argument type.
-    liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) ->
-        Int -> f a -> ShowS
-
-    -- | 'showList' function for an application of the type constructor
-    -- based on 'showsPrec' and 'showList' functions for the argument type.
-    -- The default implementation using standard list syntax is correct
-    -- for most types.
-    liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) ->
-        [f a] -> ShowS
-    liftShowList sp sl = showListWith (liftShowsPrec sp sl 0)
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Show1
-#endif
-
--- | Lift the standard 'showsPrec' and 'showList' functions through the
--- type constructor.
-showsPrec1 :: (Show1 f, Show a) => Int -> f a -> ShowS
-showsPrec1 = liftShowsPrec showsPrec showList
-
--- | Lifting of the 'Eq' class to binary type constructors.
-class Eq2 f where
-    -- | Lift equality tests through the type constructor.
-    --
-    -- The function will usually be applied to equality functions,
-    -- but the more general type ensures that the implementation uses
-    -- them to compare elements of the first container with elements of
-    -- the second.
-    liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Eq2
-#endif
-
--- | Lift the standard @('==')@ function through the type constructor.
-eq2 :: (Eq2 f, Eq a, Eq b) => f a b -> f a b -> Bool
-eq2 = liftEq2 (==) (==)
-
--- | Lifting of the 'Ord' class to binary type constructors.
-class (Eq2 f) => Ord2 f where
-    -- | Lift 'compare' functions through the type constructor.
-    --
-    -- The function will usually be applied to comparison functions,
-    -- but the more general type ensures that the implementation uses
-    -- them to compare elements of the first container with elements of
-    -- the second.
-    liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) ->
-        f a c -> f b d -> Ordering
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Ord2
-#endif
-
--- | Lift the standard 'compare' function through the type constructor.
-compare2 :: (Ord2 f, Ord a, Ord b) => f a b -> f a b -> Ordering
-compare2 = liftCompare2 compare compare
-
--- | Lifting of the 'Read' class to binary type constructors.
-class Read2 f where
-    -- | 'readsPrec' function for an application of the type constructor
-    -- based on 'readsPrec' and 'readList' functions for the argument types.
-    liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] ->
-        (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (f a b)
-
-    -- | 'readList' function for an application of the type constructor
-    -- based on 'readsPrec' and 'readList' functions for the argument types.
-    -- The default implementation using standard list syntax is correct
-    -- for most types.
-    liftReadList2 :: (Int -> ReadS a) -> ReadS [a] ->
-        (Int -> ReadS b) -> ReadS [b] -> ReadS [f a b]
-    liftReadList2 rp1 rl1 rp2 rl2 =
-        readListWith (liftReadsPrec2 rp1 rl1 rp2 rl2 0)
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Read2
-#endif
-
--- | Lift the standard 'readsPrec' function through the type constructor.
-readsPrec2 :: (Read2 f, Read a, Read b) => Int -> ReadS (f a b)
-readsPrec2 = liftReadsPrec2 readsPrec readList readsPrec readList
-
--- | Lifting of the 'Show' class to binary type constructors.
-class Show2 f where
-    -- | 'showsPrec' function for an application of the type constructor
-    -- based on 'showsPrec' and 'showList' functions for the argument types.
-    liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) ->
-        (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> f a b -> ShowS
-
-    -- | 'showList' function for an application of the type constructor
-    -- based on 'showsPrec' and 'showList' functions for the argument types.
-    -- The default implementation using standard list syntax is correct
-    -- for most types.
-    liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) ->
-        (Int -> b -> ShowS) -> ([b] -> ShowS) -> [f a b] -> ShowS
-    liftShowList2 sp1 sl1 sp2 sl2 =
-        showListWith (liftShowsPrec2 sp1 sl1 sp2 sl2 0)
-
-#if __GLASGOW_HASKELL__ >= 708
-deriving instance Typeable Show2
-#endif
-
--- | Lift the standard 'showsPrec' function through the type constructor.
-showsPrec2 :: (Show2 f, Show a, Show b) => Int -> f a b -> ShowS
-showsPrec2 = liftShowsPrec2 showsPrec showList showsPrec showList
-
--- Instances for Prelude type constructors
-
-instance Eq1 Maybe where
-    liftEq _ Nothing Nothing = True
-    liftEq _ Nothing (Just _) = False
-    liftEq _ (Just _) Nothing = False
-    liftEq eq (Just x) (Just y) = eq x y
-
-instance Ord1 Maybe where
-    liftCompare _ Nothing Nothing = EQ
-    liftCompare _ Nothing (Just _) = LT
-    liftCompare _ (Just _) Nothing = GT
-    liftCompare comp (Just x) (Just y) = comp x y
-
-instance Read1 Maybe where
-    liftReadsPrec rp _ d =
-         readParen False (\ r -> [(Nothing,s) | ("Nothing",s) <- lex r])
-         `mappend`
-         readsData (readsUnaryWith rp "Just" Just) d
-
-instance Show1 Maybe where
-    liftShowsPrec _ _ _ Nothing = showString "Nothing"
-    liftShowsPrec sp _ d (Just x) = showsUnaryWith sp "Just" d x
-
-instance Eq1 [] where
-    liftEq _ [] [] = True
-    liftEq _ [] (_:_) = False
-    liftEq _ (_:_) [] = False
-    liftEq eq (x:xs) (y:ys) = eq x y && liftEq eq xs ys
-
-instance Ord1 [] where
-    liftCompare _ [] [] = EQ
-    liftCompare _ [] (_:_) = LT
-    liftCompare _ (_:_) [] = GT
-    liftCompare comp (x:xs) (y:ys) = comp x y `mappend` liftCompare comp xs ys
-
-instance Read1 [] where
-    liftReadsPrec _ rl _ = rl
-
-instance Show1 [] where
-    liftShowsPrec _ sl _ = sl
-
-instance Eq2 (,) where
-    liftEq2 e1 e2 (x1, y1) (x2, y2) = e1 x1 x2 && e2 y1 y2
-
-instance Ord2 (,) where
-    liftCompare2 comp1 comp2 (x1, y1) (x2, y2) =
-        comp1 x1 x2 `mappend` comp2 y1 y2
-
-instance Read2 (,) where
-    liftReadsPrec2 rp1 _ rp2 _ _ = readParen False $ \ r ->
-        [((x,y), w) | ("(",s) <- lex r,
-                      (x,t)   <- rp1 0 s,
-                      (",",u) <- lex t,
-                      (y,v)   <- rp2 0 u,
-                      (")",w) <- lex v]
-
-instance Show2 (,) where
-    liftShowsPrec2 sp1 _ sp2 _ _ (x, y) =
-        showChar '(' . sp1 0 x . showChar ',' . sp2 0 y . showChar ')'
-
-instance (Eq a) => Eq1 ((,) a) where
-    liftEq = liftEq2 (==)
-
-instance (Ord a) => Ord1 ((,) a) where
-    liftCompare = liftCompare2 compare
-
-instance (Read a) => Read1 ((,) a) where
-    liftReadsPrec = liftReadsPrec2 readsPrec readList
-
-instance (Show a) => Show1 ((,) a) where
-    liftShowsPrec = liftShowsPrec2 showsPrec showList
-
-instance Eq2 Either where
-    liftEq2 e1 _ (Left x) (Left y) = e1 x y
-    liftEq2 _ _ (Left _) (Right _) = False
-    liftEq2 _ _ (Right _) (Left _) = False
-    liftEq2 _ e2 (Right x) (Right y) = e2 x y
-
-instance Ord2 Either where
-    liftCompare2 comp1 _ (Left x) (Left y) = comp1 x y
-    liftCompare2 _ _ (Left _) (Right _) = LT
-    liftCompare2 _ _ (Right _) (Left _) = GT
-    liftCompare2 _ comp2 (Right x) (Right y) = comp2 x y
-
-instance Read2 Either where
-    liftReadsPrec2 rp1 _ rp2 _ = readsData $
-         readsUnaryWith rp1 "Left" Left `mappend`
-         readsUnaryWith rp2 "Right" Right
-
-instance Show2 Either where
-    liftShowsPrec2 sp1 _ _ _ d (Left x) = showsUnaryWith sp1 "Left" d x
-    liftShowsPrec2 _ _ sp2 _ d (Right x) = showsUnaryWith sp2 "Right" d x
-
-instance (Eq a) => Eq1 (Either a) where
-    liftEq = liftEq2 (==)
-
-instance (Ord a) => Ord1 (Either a) where
-    liftCompare = liftCompare2 compare
-
-instance (Read a) => Read1 (Either a) where
-    liftReadsPrec = liftReadsPrec2 readsPrec readList
-
-instance (Show a) => Show1 (Either a) where
-    liftShowsPrec = liftShowsPrec2 showsPrec showList
-
-#if MIN_VERSION_base(4,7,0)
-instance Eq1 Proxy where
-    liftEq _ _ _ = True
-
-instance Ord1 Proxy where
-    liftCompare _ _ _ = EQ
-
-instance Show1 Proxy where
-    liftShowsPrec _ _ _ _ = showString "Proxy"
-
-instance Read1 Proxy where
-    liftReadsPrec _ _ d =
-        readParen (d > 10) (\r -> [(Proxy, s) | ("Proxy",s) <- lex r ])
-#endif
-
--- Instances for other functors defined in the base package
-
-instance Eq1 Identity where
-    liftEq eq (Identity x) (Identity y) = eq x y
-
-instance Ord1 Identity where
-    liftCompare comp (Identity x) (Identity y) = comp x y
-
-instance Read1 Identity where
-    liftReadsPrec rp _ = readsData $
-         readsUnaryWith rp "Identity" Identity
-
-instance Show1 Identity where
-    liftShowsPrec sp _ d (Identity x) = showsUnaryWith sp "Identity" d x
-
-instance Eq2 Const where
-    liftEq2 eq _ (Const x) (Const y) = eq x y
-
-instance Ord2 Const where
-    liftCompare2 comp _ (Const x) (Const y) = comp x y
-
-instance Read2 Const where
-    liftReadsPrec2 rp _ _ _ = readsData $
-         readsUnaryWith rp "Const" Const
-
-instance Show2 Const where
-    liftShowsPrec2 sp _ _ _ d (Const x) = showsUnaryWith sp "Const" d x
-
-instance (Eq a) => Eq1 (Const a) where
-    liftEq = liftEq2 (==)
-instance (Ord a) => Ord1 (Const a) where
-    liftCompare = liftCompare2 compare
-instance (Read a) => Read1 (Const a) where
-    liftReadsPrec = liftReadsPrec2 readsPrec readList
-instance (Show a) => Show1 (Const a) where
-    liftShowsPrec = liftShowsPrec2 showsPrec showList
-
--- Building blocks
-
--- | @'readsData' p d@ is a parser for datatypes where each alternative
--- begins with a data constructor.  It parses the constructor and
--- passes it to @p@.  Parsers for various constructors can be constructed
--- with 'readsUnary', 'readsUnary1' and 'readsBinary1', and combined with
--- @mappend@ from the @Monoid@ class.
-readsData :: (String -> ReadS a) -> Int -> ReadS a
-readsData reader d =
-    readParen (d > 10) $ \ r -> [res | (kw,s) <- lex r, res <- reader kw s]
-
--- | @'readsUnaryWith' rp n c n'@ matches the name of a unary data constructor
--- and then parses its argument using @rp@.
-readsUnaryWith :: (Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t
-readsUnaryWith rp name cons kw s =
-    [(cons x,t) | kw == name, (x,t) <- rp 11 s]
-
--- | @'readsBinaryWith' rp1 rp2 n c n'@ matches the name of a binary
--- data constructor and then parses its arguments using @rp1@ and @rp2@
--- respectively.
-readsBinaryWith :: (Int -> ReadS a) -> (Int -> ReadS b) ->
-    String -> (a -> b -> t) -> String -> ReadS t
-readsBinaryWith rp1 rp2 name cons kw s =
-    [(cons x y,u) | kw == name, (x,t) <- rp1 11 s, (y,u) <- rp2 11 t]
-
--- | @'showsUnaryWith' sp n d x@ produces the string representation of a
--- unary data constructor with name @n@ and argument @x@, in precedence
--- context @d@.
-showsUnaryWith :: (Int -> a -> ShowS) -> String -> Int -> a -> ShowS
-showsUnaryWith sp name d x = showParen (d > 10) $
-    showString name . showChar ' ' . sp 11 x
-
--- | @'showsBinaryWith' sp1 sp2 n d x y@ produces the string
--- representation of a binary data constructor with name @n@ and arguments
--- @x@ and @y@, in precedence context @d@.
-showsBinaryWith :: (Int -> a -> ShowS) -> (Int -> b -> ShowS) ->
-    String -> Int -> a -> b -> ShowS
-showsBinaryWith sp1 sp2 name d x y = showParen (d > 10) $
-    showString name . showChar ' ' . sp1 11 x . showChar ' ' . sp2 11 y
-
--- Obsolete building blocks
-
--- | @'readsUnary' n c n'@ matches the name of a unary data constructor
--- and then parses its argument using 'readsPrec'.
-{-# DEPRECATED readsUnary "Use readsUnaryWith to define liftReadsPrec" #-}
-readsUnary :: (Read a) => String -> (a -> t) -> String -> ReadS t
-readsUnary name cons kw s =
-    [(cons x,t) | kw == name, (x,t) <- readsPrec 11 s]
-
--- | @'readsUnary1' n c n'@ matches the name of a unary data constructor
--- and then parses its argument using 'readsPrec1'.
-{-# DEPRECATED readsUnary1 "Use readsUnaryWith to define liftReadsPrec" #-}
-readsUnary1 :: (Read1 f, Read a) => String -> (f a -> t) -> String -> ReadS t
-readsUnary1 name cons kw s =
-    [(cons x,t) | kw == name, (x,t) <- readsPrec1 11 s]
-
--- | @'readsBinary1' n c n'@ matches the name of a binary data constructor
--- and then parses its arguments using 'readsPrec1'.
-{-# DEPRECATED readsBinary1 "Use readsBinaryWith to define liftReadsPrec" #-}
-readsBinary1 :: (Read1 f, Read1 g, Read a) =>
-    String -> (f a -> g a -> t) -> String -> ReadS t
-readsBinary1 name cons kw s =
-    [(cons x y,u) | kw == name,
-        (x,t) <- readsPrec1 11 s, (y,u) <- readsPrec1 11 t]
-
--- | @'showsUnary' n d x@ produces the string representation of a unary data
--- constructor with name @n@ and argument @x@, in precedence context @d@.
-{-# DEPRECATED showsUnary "Use showsUnaryWith to define liftShowsPrec" #-}
-showsUnary :: (Show a) => String -> Int -> a -> ShowS
-showsUnary name d x = showParen (d > 10) $
-    showString name . showChar ' ' . showsPrec 11 x
-
--- | @'showsUnary1' n d x@ produces the string representation of a unary data
--- constructor with name @n@ and argument @x@, in precedence context @d@.
-{-# DEPRECATED showsUnary1 "Use showsUnaryWith to define liftShowsPrec" #-}
-showsUnary1 :: (Show1 f, Show a) => String -> Int -> f a -> ShowS
-showsUnary1 name d x = showParen (d > 10) $
-    showString name . showChar ' ' . showsPrec1 11 x
-
--- | @'showsBinary1' n d x y@ produces the string representation of a binary
--- data constructor with name @n@ and arguments @x@ and @y@, in precedence
--- context @d@.
-{-# DEPRECATED showsBinary1 "Use showsBinaryWith to define liftShowsPrec" #-}
-showsBinary1 :: (Show1 f, Show1 g, Show a) =>
-    String -> Int -> f a -> g a -> ShowS
-showsBinary1 name d x y = showParen (d > 10) $
-    showString name . showChar ' ' . showsPrec1 11 x .
-        showChar ' ' . showsPrec1 11 y
-
-{- $example
-These functions can be used to assemble 'Read' and 'Show' instances for
-new algebraic types.  For example, given the definition
-
-> data T f a = Zero a | One (f a) | Two a (f a)
-
-a standard 'Read1' instance may be defined as
-
-> instance (Read1 f) => Read1 (T f) where
->     liftReadsPrec rp rl = readsData $
->         readsUnaryWith rp "Zero" Zero `mappend`
->         readsUnaryWith (liftReadsPrec rp rl) "One" One `mappend`
->         readsBinaryWith rp (liftReadsPrec rp rl) "Two" Two
-
-and the corresponding 'Show1' instance as
-
-> instance (Show1 f) => Show1 (T f) where
->     liftShowsPrec sp _ d (Zero x) =
->         showsUnaryWith sp "Zero" d x
->     liftShowsPrec sp sl d (One x) =
->         showsUnaryWith (liftShowsPrec sp sl) "One" d x
->     liftShowsPrec sp sl d (Two x y) =
->         showsBinaryWith sp (liftShowsPrec sp sl) "Two" d x y
-
--}