Copyright	(c) Ross Paterson 2013
License	BSD-style (see the file LICENSE)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Functor.Classes

Contents

Liftings of Prelude classes
- For unary constructors
- For binary constructors
Helper functions
- Obsolete helpers

Description

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

Synopsis

Liftings of Prelude classes

For unary constructors

class Eq1 f where #

Lifting of the Eq class to unary type constructors.

Minimal complete definition

liftEq

Methods

liftEq :: (a -> b -> Bool) -> f a -> f b -> Bool #

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.

Instances

Eq1 [] #
Methods liftEq :: (a -> b -> Bool) -> [a] -> [b] -> Bool #
Eq1 Maybe #
Methods liftEq :: (a -> b -> Bool) -> Maybe a -> Maybe b -> Bool #
Eq1 Identity #
Methods liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool #
Eq a => Eq1 (Either a) #
Methods liftEq :: (a -> b -> Bool) -> Either a a -> Either a b -> Bool #
Eq a => Eq1 ((,) a) #
Methods liftEq :: (a -> b -> Bool) -> (a, a) -> (a, b) -> Bool #
Eq1 (Proxy *) #	Since: 4.9.0.0
Methods liftEq :: (a -> b -> Bool) -> Proxy * a -> Proxy * b -> Bool #
Eq a => Eq1 (Const * a) #
Methods liftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool #
(Eq1 f, Eq1 g) => Eq1 (Product * f g) #
Methods liftEq :: (a -> b -> Bool) -> Product * f g a -> Product * f g b -> Bool #
(Eq1 f, Eq1 g) => Eq1 (Sum * f g) #
Methods liftEq :: (a -> b -> Bool) -> Sum * f g a -> Sum * f g b -> Bool #
(Eq1 f, Eq1 g) => Eq1 (Compose * * f g) #
Methods liftEq :: (a -> b -> Bool) -> Compose * * f g a -> Compose * * f g b -> Bool #

eq1 :: (Eq1 f, Eq a) => f a -> f a -> Bool #

Lift the standard (==) function through the type constructor.

class Eq1 f => Ord1 f where #

Lifting of the Ord class to unary type constructors.

Minimal complete definition

liftCompare

Methods

liftCompare :: (a -> b -> Ordering) -> f a -> f b -> Ordering #

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.

Instances

Ord1 [] #
Methods liftCompare :: (a -> b -> Ordering) -> [a] -> [b] -> Ordering #
Ord1 Maybe #
Methods liftCompare :: (a -> b -> Ordering) -> Maybe a -> Maybe b -> Ordering #
Ord1 Identity #
Methods liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering #
Ord a => Ord1 (Either a) #
Methods liftCompare :: (a -> b -> Ordering) -> Either a a -> Either a b -> Ordering #
Ord a => Ord1 ((,) a) #
Methods liftCompare :: (a -> b -> Ordering) -> (a, a) -> (a, b) -> Ordering #
Ord1 (Proxy *) #	Since: 4.9.0.0
Methods liftCompare :: (a -> b -> Ordering) -> Proxy * a -> Proxy * b -> Ordering #
Ord a => Ord1 (Const * a) #
Methods liftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering #
(Ord1 f, Ord1 g) => Ord1 (Product * f g) #
Methods liftCompare :: (a -> b -> Ordering) -> Product * f g a -> Product * f g b -> Ordering #
(Ord1 f, Ord1 g) => Ord1 (Sum * f g) #
Methods liftCompare :: (a -> b -> Ordering) -> Sum * f g a -> Sum * f g b -> Ordering #
(Ord1 f, Ord1 g) => Ord1 (Compose * * f g) #
Methods liftCompare :: (a -> b -> Ordering) -> Compose * * f g a -> Compose * * f g b -> Ordering #

compare1 :: (Ord1 f, Ord a) => f a -> f a -> Ordering #

Lift the standard compare function through the type constructor.

class Read1 f where #

Lifting of the Read class to unary type constructors.

Minimal complete definition

liftReadsPrec

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a) #

readsPrec function for an application of the type constructor based on readsPrec and readList functions for the argument type.

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> 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.

Instances

Read1 [] #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS [a] # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [[a]] #
Read1 Maybe #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] #
Read1 Identity #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a] #
Read a => Read1 (Either a) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Either a a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Either a a] #
Read a => Read1 ((,) a) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (a, a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [(a, a)] #
Read1 (Proxy *) #	Since: 4.9.0.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Proxy * a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Proxy * a] #
Read a => Read1 (Const * a) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Const * a a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Const * a a] #
(Read1 f, Read1 g) => Read1 (Product * f g) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Product * f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Product * f g a] #
(Read1 f, Read1 g) => Read1 (Sum * f g) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Sum * f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Sum * f g a] #
(Read1 f, Read1 g) => Read1 (Compose * * f g) #
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose * * f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose * * f g a] #

readsPrec1 :: (Read1 f, Read a) => Int -> ReadS (f a) #

Lift the standard readsPrec and readList functions through the type constructor.

class Show1 f where #

Lifting of the Show class to unary type constructors.

Minimal complete definition

liftShowsPrec

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS #

showsPrec function for an application of the type constructor based on showsPrec and showList functions for the argument type.

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [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.

Instances

Show1 [] #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> [a] -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [[a]] -> ShowS #
Show1 Maybe #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Maybe a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Maybe a] -> ShowS #
Show1 Identity #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS #
Show a => Show1 (Either a) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Either a a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Either a a] -> ShowS #
Show a => Show1 ((,) a) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> (a, a) -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [(a, a)] -> ShowS #
Show1 (Proxy *) #	Since: 4.9.0.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Proxy * a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Proxy * a] -> ShowS #
Show a => Show1 (Const * a) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Const * a a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Const * a a] -> ShowS #
(Show1 f, Show1 g) => Show1 (Product * f g) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Product * f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Product * f g a] -> ShowS #
(Show1 f, Show1 g) => Show1 (Sum * f g) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Sum * f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Sum * f g a] -> ShowS #
(Show1 f, Show1 g) => Show1 (Compose * * f g) #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose * * f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose * * f g a] -> ShowS #

showsPrec1 :: (Show1 f, Show a) => Int -> f a -> ShowS #

Lift the standard showsPrec and showList functions through the type constructor.

For binary constructors

class Eq2 f where #

Lifting of the Eq class to binary type constructors.

Minimal complete definition

liftEq2

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool #

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.

Instances

Eq2 Either #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Either a c -> Either b d -> Bool #
Eq2 (,) #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> (a, c) -> (b, d) -> Bool #
Eq2 (Const *) #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool #

eq2 :: (Eq2 f, Eq a, Eq b) => f a b -> f a b -> Bool #

Lift the standard (==) function through the type constructor.

class Eq2 f => Ord2 f where #

Lifting of the Ord class to binary type constructors.

Minimal complete definition

liftCompare2

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> f a c -> f b d -> Ordering #

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.

Instances

Ord2 Either #
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Either a c -> Either b d -> Ordering #
Ord2 (,) #
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> (a, c) -> (b, d) -> Ordering #
Ord2 (Const *) #
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering #

compare2 :: (Ord2 f, Ord a, Ord b) => f a b -> f a b -> Ordering #

Lift the standard compare function through the type constructor.

class Read2 f where #

Lifting of the Read class to binary type constructors.

Minimal complete definition

liftReadsPrec2

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (f a b) #

readsPrec function for an application of the type constructor based on readsPrec and readList functions for the argument types.

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> 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.

Instances

Read2 Either #
Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] #
Read2 (,) #
Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (a, b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [(a, b)] #
Read2 (Const *) #
Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const * a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const * a b] #

readsPrec2 :: (Read2 f, Read a, Read b) => Int -> ReadS (f a b) #

Lift the standard readsPrec function through the type constructor.

class Show2 f where #

Lifting of the Show class to binary type constructors.

Minimal complete definition

liftShowsPrec2

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> f a b -> ShowS #

showsPrec function for an application of the type constructor based on showsPrec and showList functions for the argument types.

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [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.

Instances

Show2 Either #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Either a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Either a b] -> ShowS #
Show2 (,) #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> (a, b) -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [(a, b)] -> ShowS #
Show2 (Const *) #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const * a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const * a b] -> ShowS #

showsPrec2 :: (Show2 f, Show a, Show b) => Int -> f a b -> ShowS #

Lift the standard showsPrec function through the type constructor.

Helper functions

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

readsData :: (String -> ReadS a) -> Int -> ReadS a #

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.

readsUnaryWith :: (Int -> ReadS a) -> String -> (a -> t) -> String -> ReadS t #

readsUnaryWith rp n c n' matches the name of a unary data constructor and then parses its argument using rp.

readsBinaryWith :: (Int -> ReadS a) -> (Int -> ReadS b) -> String -> (a -> b -> t) -> String -> ReadS t #

readsBinaryWith rp1 rp2 n c n' matches the name of a binary data constructor and then parses its arguments using rp1 and rp2 respectively.

showsUnaryWith :: (Int -> a -> ShowS) -> String -> Int -> a -> ShowS #

showsUnaryWith sp n d x produces the string representation of a unary data constructor with name n and argument x, in precedence context d.

showsBinaryWith :: (Int -> a -> ShowS) -> (Int -> b -> ShowS) -> String -> Int -> a -> b -> ShowS #

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.

Obsolete helpers

readsUnary :: Read a => String -> (a -> t) -> String -> ReadS t #

Deprecated: Use readsUnaryWith to define liftReadsPrec

readsUnary n c n' matches the name of a unary data constructor and then parses its argument using readsPrec.

readsUnary1 :: (Read1 f, Read a) => String -> (f a -> t) -> String -> ReadS t #

Deprecated: Use readsUnaryWith to define liftReadsPrec

readsUnary1 n c n' matches the name of a unary data constructor and then parses its argument using readsPrec1.

readsBinary1 :: (Read1 f, Read1 g, Read a) => String -> (f a -> g a -> t) -> String -> ReadS t #

Deprecated: Use readsBinaryWith to define liftReadsPrec

readsBinary1 n c n' matches the name of a binary data constructor and then parses its arguments using readsPrec1.

showsUnary :: Show a => String -> Int -> a -> ShowS #

Deprecated: Use showsUnaryWith to define liftShowsPrec

showsUnary n d x produces the string representation of a unary data constructor with name n and argument x, in precedence context d.

showsUnary1 :: (Show1 f, Show a) => String -> Int -> f a -> ShowS #

Deprecated: Use showsUnaryWith to define liftShowsPrec

showsUnary1 n d x produces the string representation of a unary data constructor with name n and argument x, in precedence context d.

showsBinary1 :: (Show1 f, Show1 g, Show a) => String -> Int -> f a -> g a -> ShowS #

Deprecated: Use showsBinaryWith to define liftShowsPrec

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.