Data.Functor.Classes

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

Liftings of Prelude classes

For unary constructors

class Eq1 f where

Lifting of the Eq class to unary type constructors.

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 []

Eq1 Identity

Eq1 Maybe

Eq a => Eq1 (Either a)

Eq a => Eq1 ((,) a)

Eq a => Eq1 (Const a)

Eq1 f => Eq1 (Lift f)

Eq1 m => Eq1 (ListT m)

Eq1 m => Eq1 (MaybeT m)

Eq a => Eq1 (Constant * a)

(Eq e, Eq1 m) => Eq1 (ExceptT e m)

(Eq e, Eq1 m) => Eq1 (ErrorT e m)

Eq1 f => Eq1 (IdentityT * f)

(Eq w, Eq1 m) => Eq1 (WriterT w m)

(Eq w, Eq1 m) => Eq1 (WriterT w m)

Eq1 f => Eq1 (Backwards * f)

Eq1 f => Eq1 (Reverse * f)

(Eq1 f, Eq1 g) => Eq1 (Product * f g)

(Eq1 f, Eq1 g) => Eq1 (Sum * f g)

(Eq1 f, Eq1 g) => Eq1 (Compose * * f g)

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.

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 []

Ord1 Identity

Ord1 Maybe

Ord a => Ord1 (Either a)

Ord a => Ord1 ((,) a)

Ord a => Ord1 (Const a)

Ord1 f => Ord1 (Lift f)

Ord1 m => Ord1 (ListT m)

Ord1 m => Ord1 (MaybeT m)

Ord a => Ord1 (Constant * a)

(Ord e, Ord1 m) => Ord1 (ExceptT e m)

(Ord e, Ord1 m) => Ord1 (ErrorT e m)

Ord1 f => Ord1 (IdentityT * f)

(Ord w, Ord1 m) => Ord1 (WriterT w m)

(Ord w, Ord1 m) => Ord1 (WriterT w m)

Ord1 f => Ord1 (Backwards * f)

Ord1 f => Ord1 (Reverse * f)

(Ord1 f, Ord1 g) => Ord1 (Product * f g)

(Ord1 f, Ord1 g) => Ord1 (Sum * f g)

(Ord1 f, Ord1 g) => Ord1 (Compose * * f g)

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 []

Read1 Identity

Read1 Maybe

Read a => Read1 (Either a)

Read a => Read1 ((,) a)

Read a => Read1 (Const a)

Read1 f => Read1 (Lift f)

Read1 m => Read1 (ListT m)

Read1 m => Read1 (MaybeT m)

Read a => Read1 (Constant * a)

(Read e, Read1 m) => Read1 (ExceptT e m)

(Read e, Read1 m) => Read1 (ErrorT e m)

Read1 f => Read1 (IdentityT * f)

(Read w, Read1 m) => Read1 (WriterT w m)

(Read w, Read1 m) => Read1 (WriterT w m)

Read1 f => Read1 (Backwards * f)

Read1 f => Read1 (Reverse * f)

(Read1 f, Read1 g) => Read1 (Product * f g)

(Read1 f, Read1 g) => Read1 (Sum * f g)

(Read1 f, Read1 g) => Read1 (Compose * * f g)

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 []

Show1 Identity

Show1 Maybe

Show a => Show1 (Either a)

Show a => Show1 ((,) a)

Show a => Show1 (Const a)

Show1 f => Show1 (Lift f)

Show1 m => Show1 (ListT m)

Show1 m => Show1 (MaybeT m)

Show a => Show1 (Constant * a)

(Show e, Show1 m) => Show1 (ExceptT e m)

(Show e, Show1 m) => Show1 (ErrorT e m)

Show1 f => Show1 (IdentityT * f)

(Show w, Show1 m) => Show1 (WriterT w m)

(Show w, Show1 m) => Show1 (WriterT w m)

Show1 f => Show1 (Backwards * f)

Show1 f => Show1 (Reverse * f)

(Show1 f, Show1 g) => Show1 (Product * f g)

(Show1 f, Show1 g) => Show1 (Sum * f g)

(Show1 f, Show1 g) => Show1 (Compose * * f g)

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.

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

Eq2 (,)

Eq2 Const

Eq2 (Constant *)

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.

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

Ord2 (,)

Ord2 Const

Ord2 (Constant *)

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

Read2 (,)

Read2 Const

Read2 (Constant *)

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

Show2 (,)

Show2 Const

Show2 (Constant *)

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.