Data/Functor/Classes.hs

    {-# LANGUAGE Safe #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.Functor.Classes
    -- Copyright   :  (c) Ross Paterson 2013
    -- License     :  BSD-style (see the file LICENSE)
    --
    -- Maintainer  :  libraries@haskell.org
    -- 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
    --
    -- @since 4.9.0.0
    -----------------------------------------------------------------------------

    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.Proxy (Proxy(Proxy))
    import Data.Monoid (mappend)
    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

    -- | 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

    -- | 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)

    -- | 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)

    -- | 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

    -- | 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

    -- | 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)

    -- | 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)

    -- | 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

    -- 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

    -- Proxy unfortunately imports this module, hence these instances are placed
    -- here,
    -- | @since 4.9.0.0
    instance Eq1 Proxy where
      liftEq _ _ _ = True

    -- | @since 4.9.0.0
    instance Ord1 Proxy where
      liftCompare _ _ _ = EQ

    -- | @since 4.9.0.0
    instance Show1 Proxy where
      liftShowsPrec _ _ _ _ = showString "Proxy"

    -- | @since 4.9.0.0
    instance Read1 Proxy where
      liftReadsPrec _ _ d =
        readParen (d > 10) (\r -> [(Proxy, s) | ("Proxy",s) <- lex r ])

    -- 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

    -}