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Language	Haskell2010

Generics.SOP.BasicFunctors

Contents

Basic functors
Mapping functions

Description

Basic functors.

Definitions of the type-level equivalents of const, id, and (.), and a definition of the lifted function space.

These datatypes are generally useful, but in this library, they're primarily used as parameters for the NP, NS, POP, and SOP types.

We define own variants of Const, Identity and Compose for various reasons.

Const and Compose become kind polymorphic only in base-4.9.0.0 (transformers-0.5.0.0).
Shorter names are convenient, and pattern synonyms aren't (yet) powerful enough, particularly exhaustiveness check doesn't work properly. See https://ghc.haskell.org/trac/ghc/ticket/8779.

Synopsis

Basic functors

newtype K a b Source #

The constant type functor.

Like Constant, but kind-polymorphic in its second argument and with a shorter name.

Constructors

K a

Instances

Eq2 (K *) Source #	Since: 0.2.4.0
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> K * a c -> K * b d -> Bool #
Ord2 (K *) Source #	Since: 0.2.4.0
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> K * a c -> K * b d -> Ordering #
Read2 (K *) Source #	Since: 0.2.4.0
Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (K * a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [K * a b] #
Show2 (K *) Source #	Since: 0.2.4.0
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> K * a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [K * a b] -> ShowS #
Functor (K * a) Source #
Methods fmap :: (a -> b) -> K * a a -> K * a b # (<$) :: a -> K * a b -> K * a a #
Monoid a => Applicative (K * a) Source #
Methods pure :: a -> K * a a # (<>) :: K a (a -> b) -> K * a a -> K * a b # (>) :: K a a -> K * a b -> K * a b # (<) :: K a a -> K * a b -> K * a a #
Foldable (K * a) Source #
Methods fold :: Monoid m => K * a m -> m # foldMap :: Monoid m => (a -> m) -> K * a a -> m # foldr :: (a -> b -> b) -> b -> K * a a -> b # foldr' :: (a -> b -> b) -> b -> K * a a -> b # foldl :: (b -> a -> b) -> b -> K * a a -> b # foldl' :: (b -> a -> b) -> b -> K * a a -> b # foldr1 :: (a -> a -> a) -> K * a a -> a # foldl1 :: (a -> a -> a) -> K * a a -> a # toList :: K * a a -> [a] # null :: K * a a -> Bool # length :: K * a a -> Int # elem :: Eq a => a -> K * a a -> Bool # maximum :: Ord a => K * a a -> a # minimum :: Ord a => K * a a -> a # sum :: Num a => K * a a -> a # product :: Num a => K * a a -> a #
Traversable (K * a) Source #
Methods traverse :: Applicative f => (a -> f b) -> K * a a -> f (K * a b) # sequenceA :: Applicative f => K * a (f a) -> f (K * a a) # mapM :: Monad m => (a -> m b) -> K * a a -> m (K * a b) # sequence :: Monad m => K * a (m a) -> m (K * a a) #
Eq a => Eq1 (K * a) Source #	Since: 0.2.4.0
Methods liftEq :: (a -> b -> Bool) -> K * a a -> K * a b -> Bool #
Ord a => Ord1 (K * a) Source #	Since: 0.2.4.0
Methods liftCompare :: (a -> b -> Ordering) -> K * a a -> K * a b -> Ordering #
Read a => Read1 (K * a) Source #	Since: 0.2.4.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (K * a a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [K * a a] #
Show a => Show1 (K * a) Source #	Since: 0.2.4.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> K * a a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [K * a a] -> ShowS #
Eq a => Eq (K k a b) Source #
Methods (==) :: K k a b -> K k a b -> Bool # (/=) :: K k a b -> K k a b -> Bool #
Ord a => Ord (K k a b) Source #
Methods compare :: K k a b -> K k a b -> Ordering # (<) :: K k a b -> K k a b -> Bool # (<=) :: K k a b -> K k a b -> Bool # (>) :: K k a b -> K k a b -> Bool # (>=) :: K k a b -> K k a b -> Bool # max :: K k a b -> K k a b -> K k a b # min :: K k a b -> K k a b -> K k a b #
Read a => Read (K k a b) Source #
Methods readsPrec :: Int -> ReadS (K k a b) # readList :: ReadS [K k a b] # readPrec :: ReadPrec (K k a b) # readListPrec :: ReadPrec [K k a b] #
Show a => Show (K k a b) Source #
Methods showsPrec :: Int -> K k a b -> ShowS # show :: K k a b -> String # showList :: [K k a b] -> ShowS #
Generic (K k a b) Source #
Associated Types type Rep (K k a b) :: * -> * # Methods from :: K k a b -> Rep (K k a b) x # to :: Rep (K k a b) x -> K k a b #
NFData a => NFData (K k a b) Source #	Since: 0.2.5.0
Methods rnf :: K k a b -> () #
type Rep (K k a b) Source #
type Rep (K k a b) = D1 (MetaData "K" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-12lxo1SLuajA6W53awQMOK" True) (C1 (MetaCons "K" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Code (K * a0 b0) Source #
type Code (K * a0 b0) = (:) [] ((:) a0 ([] )) ([] [])

unK :: K a b -> a Source #

Extract the contents of a K value.

newtype I a Source #

The identity type functor.

Like Identity, but with a shorter name.

Constructors

I a

Instances

Monad I Source #
Methods (>>=) :: I a -> (a -> I b) -> I b # (>>) :: I a -> I b -> I b # return :: a -> I a # fail :: String -> I a #
Functor I Source #
Methods fmap :: (a -> b) -> I a -> I b # (<$) :: a -> I b -> I a #
Applicative I Source #
Methods pure :: a -> I a # (<>) :: I (a -> b) -> I a -> I b # (>) :: I a -> I b -> I b # (<*) :: I a -> I b -> I a #
Foldable I Source #
Methods fold :: Monoid m => I m -> m # foldMap :: Monoid m => (a -> m) -> I a -> m # foldr :: (a -> b -> b) -> b -> I a -> b # foldr' :: (a -> b -> b) -> b -> I a -> b # foldl :: (b -> a -> b) -> b -> I a -> b # foldl' :: (b -> a -> b) -> b -> I a -> b # foldr1 :: (a -> a -> a) -> I a -> a # foldl1 :: (a -> a -> a) -> I a -> a # toList :: I a -> [a] # null :: I a -> Bool # length :: I a -> Int # elem :: Eq a => a -> I a -> Bool # maximum :: Ord a => I a -> a # minimum :: Ord a => I a -> a # sum :: Num a => I a -> a # product :: Num a => I a -> a #
Traversable I Source #
Methods traverse :: Applicative f => (a -> f b) -> I a -> f (I b) # sequenceA :: Applicative f => I (f a) -> f (I a) # mapM :: Monad m => (a -> m b) -> I a -> m (I b) # sequence :: Monad m => I (m a) -> m (I a) #
Eq1 I Source #	Since: 0.2.4.0
Methods liftEq :: (a -> b -> Bool) -> I a -> I b -> Bool #
Ord1 I Source #	Since: 0.2.4.0
Methods liftCompare :: (a -> b -> Ordering) -> I a -> I b -> Ordering #
Read1 I Source #	Since: 0.2.4.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (I a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [I a] #
Show1 I Source #	Since: 0.2.4.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> I a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [I a] -> ShowS #
Eq a => Eq (I a) Source #
Methods (==) :: I a -> I a -> Bool # (/=) :: I a -> I a -> Bool #
Ord a => Ord (I a) Source #
Methods compare :: I a -> I a -> Ordering # (<) :: I a -> I a -> Bool # (<=) :: I a -> I a -> Bool # (>) :: I a -> I a -> Bool # (>=) :: I a -> I a -> Bool # max :: I a -> I a -> I a # min :: I a -> I a -> I a #
Read a => Read (I a) Source #
Methods readsPrec :: Int -> ReadS (I a) # readList :: ReadS [I a] # readPrec :: ReadPrec (I a) # readListPrec :: ReadPrec [I a] #
Show a => Show (I a) Source #
Methods showsPrec :: Int -> I a -> ShowS # show :: I a -> String # showList :: [I a] -> ShowS #
Generic (I a) Source #
Associated Types type Rep (I a) :: * -> * # Methods from :: I a -> Rep (I a) x # to :: Rep (I a) x -> I a #
NFData a => NFData (I a) Source #	Since: 0.2.5.0
Methods rnf :: I a -> () #
type Rep (I a) Source #
type Rep (I a) = D1 (MetaData "I" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-12lxo1SLuajA6W53awQMOK" True) (C1 (MetaCons "I" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Code (I a0) Source #
type Code (I a0) = (:) [] ((:) a0 ([] )) ([] [])

unI :: I a -> a Source #

Extract the contents of an I value.

newtype (f :.: g) p infixr 7 Source #

Composition of functors.

Like Compose, but kind-polymorphic and with a shorter name.

Constructors

Comp (f (g p))

Instances

(Functor f, Functor g) => Functor ((:.:) * * f g) Source #
Methods fmap :: (a -> b) -> (* :.: ) f g a -> ( :.: ) f g b # (<$) :: a -> ( :.: ) f g b -> ( :.: *) f g a #
(Applicative f, Applicative g) => Applicative ((:.:) * * f g) Source #	Since: 0.2.5.0
Methods pure :: a -> (* :.: ) f g a # (<>) :: (* :.: ) f g (a -> b) -> ( :.: ) f g a -> ( :.: ) f g b # (>) :: (* :.: ) f g a -> ( :.: ) f g b -> ( :.: ) f g b # (<) :: (* :.: ) f g a -> ( :.: ) f g b -> ( :.: *) f g a #
(Foldable f, Foldable g) => Foldable ((:.:) * * f g) Source #	Since: 0.2.5.0
Methods fold :: Monoid m => (* :.: ) f g m -> m # foldMap :: Monoid m => (a -> m) -> ( :.: ) f g a -> m # foldr :: (a -> b -> b) -> b -> ( :.: ) f g a -> b # foldr' :: (a -> b -> b) -> b -> ( :.: ) f g a -> b # foldl :: (b -> a -> b) -> b -> ( :.: ) f g a -> b # foldl' :: (b -> a -> b) -> b -> ( :.: ) f g a -> b # foldr1 :: (a -> a -> a) -> ( :.: ) f g a -> a # foldl1 :: (a -> a -> a) -> ( :.: ) f g a -> a # toList :: ( :.: ) f g a -> [a] # null :: ( :.: ) f g a -> Bool # length :: ( :.: ) f g a -> Int # elem :: Eq a => a -> ( :.: ) f g a -> Bool # maximum :: Ord a => ( :.: ) f g a -> a # minimum :: Ord a => ( :.: ) f g a -> a # sum :: Num a => ( :.: ) f g a -> a # product :: Num a => ( :.: *) f g a -> a #
(Traversable f, Traversable g) => Traversable ((:.:) * * f g) Source #	Since: 0.2.5.0
Methods traverse :: Applicative f => (a -> f b) -> (* :.: ) f g a -> f (( :.: ) f g b) # sequenceA :: Applicative f => ( :.: ) f g (f a) -> f (( :.: ) f g a) # mapM :: Monad m => (a -> m b) -> ( :.: ) f g a -> m (( :.: ) f g b) # sequence :: Monad m => ( :.: ) f g (m a) -> m (( :.: *) f g a) #
(Eq1 f, Eq1 g) => Eq1 ((:.:) * * f g) Source #	Since: 0.2.4.0
Methods liftEq :: (a -> b -> Bool) -> (* :.: ) f g a -> ( :.: *) f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 ((:.:) * * f g) Source #	Since: 0.2.4.0
Methods liftCompare :: (a -> b -> Ordering) -> (* :.: ) f g a -> ( :.: *) f g b -> Ordering #
(Read1 f, Read1 g) => Read1 ((:.:) * * f g) Source #	Since: 0.2.4.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ((* :.: ) f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [( :.: *) f g a] #
(Show1 f, Show1 g) => Show1 ((:.:) * * f g) Source #	Since: 0.2.4.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> (* :.: ) f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [( :.: *) f g a] -> ShowS #
(Eq1 f, Eq1 g, Eq a) => Eq ((:.:) * * f g a) Source #
Methods (==) :: (* :.: ) f g a -> ( :.: ) f g a -> Bool # (/=) :: ( :.: ) f g a -> ( :.: *) f g a -> Bool #
(Ord1 f, Ord1 g, Ord a) => Ord ((:.:) * * f g a) Source #
Methods compare :: (* :.: ) f g a -> ( :.: ) f g a -> Ordering # (<) :: ( :.: ) f g a -> ( :.: ) f g a -> Bool # (<=) :: ( :.: ) f g a -> ( :.: ) f g a -> Bool # (>) :: ( :.: ) f g a -> ( :.: ) f g a -> Bool # (>=) :: ( :.: ) f g a -> ( :.: ) f g a -> Bool # max :: ( :.: ) f g a -> ( :.: ) f g a -> ( :.: ) f g a # min :: ( :.: ) f g a -> ( :.: ) f g a -> ( :.: *) f g a #
(Read1 f, Read1 g, Read a) => Read ((:.:) * * f g a) Source #
Methods readsPrec :: Int -> ReadS ((* :.: ) f g a) # readList :: ReadS [( :.: ) f g a] # readPrec :: ReadPrec (( :.: ) f g a) # readListPrec :: ReadPrec [( :.: *) f g a] #
(Show1 f, Show1 g, Show a) => Show ((:.:) * * f g a) Source #
Methods showsPrec :: Int -> (* :.: ) f g a -> ShowS # show :: ( :.: ) f g a -> String # showList :: [( :.: *) f g a] -> ShowS #
Generic ((:.:) k l f g p) Source #
Associated Types type Rep ((:.:) k l f g p) :: * -> * # Methods from :: (k :.: l) f g p -> Rep ((k :.: l) f g p) x # to :: Rep ((k :.: l) f g p) x -> (k :.: l) f g p #
NFData (f (g a)) => NFData ((:.:) k l f g a) Source #	Since: 0.2.5.0
Methods rnf :: (k :.: l) f g a -> () #
type Rep ((:.:) k l f g p) Source #
type Rep ((:.:) k l f g p) = D1 (MetaData ":.:" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-12lxo1SLuajA6W53awQMOK" True) (C1 (MetaCons "Comp" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (g p)))))
type Code ((:.:) * * f0 g0 p0) Source #
type Code ((:.:) * * f0 g0 p0) = (:) [] ((:) (f0 (g0 p0)) ([] )) ([] [])

unComp :: (f :.: g) p -> f (g p) Source #

Extract the contents of a Comp value.

Mapping functions

mapII :: (a -> b) -> I a -> I b Source #

Lift the given function.

Since: 0.2.5.0

mapIK :: (a -> b) -> I a -> K b c Source #

Lift the given function.

Since: 0.2.5.0

mapKI :: (a -> b) -> K a c -> I b Source #

Lift the given function.

Since: 0.2.5.0

mapKK :: (a -> b) -> K a c -> K b d Source #

Lift the given function.

Since: 0.2.5.0

mapIII :: (a -> b -> c) -> I a -> I b -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapIIK :: (a -> b -> c) -> I a -> I b -> K c d Source #

Lift the given function.

Since: 0.2.5.0

mapIKI :: (a -> b -> c) -> I a -> K b d -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapIKK :: (a -> b -> c) -> I a -> K b d -> K c e Source #

Lift the given function.

Since: 0.2.5.0

mapKII :: (a -> b -> c) -> K a d -> I b -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapKIK :: (a -> b -> c) -> K a d -> I b -> K c e Source #

Lift the given function.

Since: 0.2.5.0

mapKKI :: (a -> b -> c) -> K a d -> K b e -> I c Source #

Lift the given function.

Since: 0.2.5.0

mapKKK :: (a -> b -> c) -> K a d -> K b e -> K c f Source #

Lift the given function.

Since: 0.2.5.0