Data.SOP.BasicFunctors

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.

Basic functors

newtype K (a :: Type) (b :: k)

The constant type functor.

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

Constructors

K a

Instances

Eq2 (K :: Type -> Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> K a c -> K b d -> Bool

Ord2 (K :: Type -> Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> K a c -> K b d -> Ordering

Read2 (K :: Type -> Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

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]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (K a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [K a b]

Show2 (K :: Type -> Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

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

NFData2 (K :: Type -> Type -> Type)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> K a b -> ()

Functor (K a :: Type -> Type)

Defined in Data.SOP.BasicFunctors

Methods

fmap :: (a0 -> b) -> K a a0 -> K a b

(<$) :: a0 -> K a b -> K a a0

Monoid a => Applicative (K a :: Type -> Type)

Defined in Data.SOP.BasicFunctors

Methods

pure :: a0 -> K a a0

(<*>) :: K a (a0 -> b) -> K a a0 -> K a b

liftA2 :: (a0 -> b -> c) -> K a a0 -> K a b -> K a c

(*>) :: K a a0 -> K a b -> K a b

(<*) :: K a a0 -> K a b -> K a a0

Foldable (K a :: Type -> Type)

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => K a m -> m

foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> K a a0 -> m

foldr :: (a0 -> b -> b) -> b -> K a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b

foldl :: (b -> a0 -> b) -> b -> K a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0

toList :: K a a0 -> [a0]

null :: K a a0 -> Bool

length :: K a a0 -> Int

elem :: Eq a0 => a0 -> K a a0 -> Bool

maximum :: Ord a0 => K a a0 -> a0

minimum :: Ord a0 => K a a0 -> a0

sum :: Num a0 => K a a0 -> a0

product :: Num a0 => K a a0 -> a0

Traversable (K a :: Type -> Type)

Defined in Data.SOP.BasicFunctors

Methods

traverse :: Applicative f => (a0 -> f b) -> K a a0 -> f (K a b)

sequenceA :: Applicative f => K a (f a0) -> f (K a a0)

mapM :: Monad m => (a0 -> m b) -> K a a0 -> m (K a b)

sequence :: Monad m => K a (m a0) -> m (K a a0)

Eq a => Eq1 (K a :: Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftEq :: (a0 -> b -> Bool) -> K a a0 -> K a b -> Bool

Ord a => Ord1 (K a :: Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftCompare :: (a0 -> b -> Ordering) -> K a a0 -> K a b -> Ordering

Read a => Read1 (K a :: Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (K a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [K a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (K a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [K a a0]

Show a => Show1 (K a :: Type -> Type)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> K a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [K a a0] -> ShowS

NFData a => NFData1 (K a :: Type -> Type)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

liftRnf :: (a0 -> ()) -> K a a0 -> ()

Eq a => Eq (K a b)

Defined in Data.SOP.BasicFunctors

Methods

(==) :: K a b -> K a b -> Bool

(/=) :: K a b -> K a b -> Bool

Ord a => Ord (K a b)

Defined in Data.SOP.BasicFunctors

Methods

compare :: K a b -> K a b -> Ordering

(<) :: K a b -> K a b -> Bool

(<=) :: K a b -> K a b -> Bool

(>) :: K a b -> K a b -> Bool

(>=) :: K a b -> K a b -> Bool

max :: K a b -> K a b -> K a b

min :: K a b -> K a b -> K a b

Read a => Read (K a b)

Defined in Data.SOP.BasicFunctors

Methods

readsPrec :: Int -> ReadS (K a b)

readList :: ReadS [K a b]

readPrec :: ReadPrec (K a b)

readListPrec :: ReadPrec [K a b]

Show a => Show (K a b)

Defined in Data.SOP.BasicFunctors

Methods

showsPrec :: Int -> K a b -> ShowS

show :: K a b -> String

showList :: [K a b] -> ShowS

Generic (K a b)

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep (K a b) :: Type -> Type

Methods

from :: K a b -> Rep (K a b) x

to :: Rep (K a b) x -> K a b

Semigroup a => Semigroup (K a b)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

(<>) :: K a b -> K a b -> K a b

sconcat :: NonEmpty (K a b) -> K a b

stimes :: Integral b0 => b0 -> K a b -> K a b

Monoid a => Monoid (K a b)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

mempty :: K a b

mappend :: K a b -> K a b -> K a b

mconcat :: [K a b] -> K a b

NFData a => NFData (K a b)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

rnf :: K a b -> ()

type Rep (K a b)

Defined in Data.SOP.BasicFunctors

type Rep (K a b) = D1 ('MetaData "K" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "K" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unK :: K a b -> a

Extract the contents of a K value.

newtype I (a :: Type)

The identity type functor.

Like Identity, but with a shorter name.

Constructors

I a

Instances

Monad I

Defined in Data.SOP.BasicFunctors

Methods

(>>=) :: I a -> (a -> I b) -> I b

(>>) :: I a -> I b -> I b

return :: a -> I a

Functor I

Defined in Data.SOP.BasicFunctors

Methods

fmap :: (a -> b) -> I a -> I b

(<$) :: a -> I b -> I a

Applicative I

Defined in Data.SOP.BasicFunctors

Methods

pure :: a -> I a

(<*>) :: I (a -> b) -> I a -> I b

liftA2 :: (a -> b -> c) -> I a -> I b -> I c

(*>) :: I a -> I b -> I b

(<*) :: I a -> I b -> I a

Foldable I

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => I m -> m

foldMap :: Monoid m => (a -> m) -> I a -> 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

Defined in Data.SOP.BasicFunctors

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

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftEq :: (a -> b -> Bool) -> I a -> I b -> Bool

Ord1 I

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftCompare :: (a -> b -> Ordering) -> I a -> I b -> Ordering

Read1 I

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (I a)

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

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (I a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [I a]

Show1 I

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> I a -> ShowS

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

NFData1 I

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

liftRnf :: (a -> ()) -> I a -> ()

Eq a => Eq (I a)

Defined in Data.SOP.BasicFunctors

Methods

(==) :: I a -> I a -> Bool

(/=) :: I a -> I a -> Bool

Ord a => Ord (I a)

Defined in Data.SOP.BasicFunctors

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)

Defined in Data.SOP.BasicFunctors

Methods

readsPrec :: Int -> ReadS (I a)

readList :: ReadS [I a]

readPrec :: ReadPrec (I a)

readListPrec :: ReadPrec [I a]

Show a => Show (I a)

Defined in Data.SOP.BasicFunctors

Methods

showsPrec :: Int -> I a -> ShowS

show :: I a -> String

showList :: [I a] -> ShowS

Generic (I a)

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep (I a) :: Type -> Type

Methods

from :: I a -> Rep (I a) x

to :: Rep (I a) x -> I a

Semigroup a => Semigroup (I a)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

(<>) :: I a -> I a -> I a

sconcat :: NonEmpty (I a) -> I a

stimes :: Integral b => b -> I a -> I a

Monoid a => Monoid (I a)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

mempty :: I a

mappend :: I a -> I a -> I a

mconcat :: [I a] -> I a

NFData a => NFData (I a)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

rnf :: I a -> ()

type Rep (I a)

Defined in Data.SOP.BasicFunctors

type Rep (I a) = D1 ('MetaData "I" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "I" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

unI :: I a -> a

Extract the contents of an I value.

newtype ((f :: l -> Type) :.: (g :: k -> l)) (p :: k) infixr 7

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)

Defined in Data.SOP.BasicFunctors

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b

(<$) :: a -> (f :.: g) b -> (f :.: g) a

(Applicative f, Applicative g) => Applicative (f :.: g)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

pure :: a -> (f :.: g) a

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b

liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c

(*>) :: (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)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

fold :: Monoid m => (f :.: g) m -> m

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> 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)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b)

sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((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)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftEq :: (a -> b -> Bool) -> (f :.: g) a -> (f :.: g) b -> Bool

(Ord1 f, Ord1 g) => Ord1 (f :.: g)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

liftCompare :: (a -> b -> Ordering) -> (f :.: g) a -> (f :.: g) b -> Ordering

(Read1 f, Read1 g) => Read1 (f :.: g)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

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

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

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ((f :.: g) a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [(f :.: g) a]

(Show1 f, Show1 g) => Show1 (f :.: g)

Since: 0.2.4.0

Defined in Data.SOP.BasicFunctors

Methods

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

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

(NFData1 f, NFData1 g) => NFData1 (f :.: g)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

liftRnf :: (a -> ()) -> (f :.: g) a -> ()

(Eq1 f, Eq1 g, Eq a) => Eq ((f :.: g) a)

Defined in Data.SOP.BasicFunctors

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)

Defined in Data.SOP.BasicFunctors

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)

Defined in Data.SOP.BasicFunctors

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)

Defined in Data.SOP.BasicFunctors

Methods

showsPrec :: Int -> (f :.: g) a -> ShowS

show :: (f :.: g) a -> String

showList :: [(f :.: g) a] -> ShowS

Generic ((f :.: g) p)

Defined in Data.SOP.BasicFunctors

Associated Types

type Rep ((f :.: g) p) :: Type -> Type

Methods

from :: (f :.: g) p -> Rep ((f :.: g) p) x

to :: Rep ((f :.: g) p) x -> (f :.: g) p

Semigroup (f (g x)) => Semigroup ((f :.: g) x)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

(<>) :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x

sconcat :: NonEmpty ((f :.: g) x) -> (f :.: g) x

stimes :: Integral b => b -> (f :.: g) x -> (f :.: g) x

Monoid (f (g x)) => Monoid ((f :.: g) x)

Since: 0.4.0.0

Defined in Data.SOP.BasicFunctors

Methods

mempty :: (f :.: g) x

mappend :: (f :.: g) x -> (f :.: g) x -> (f :.: g) x

mconcat :: [(f :.: g) x] -> (f :.: g) x

NFData (f (g a)) => NFData ((f :.: g) a)

Since: 0.2.5.0

Defined in Data.SOP.BasicFunctors

Methods

rnf :: (f :.: g) a -> ()

type Rep ((f :.: g) p)

Defined in Data.SOP.BasicFunctors

type Rep ((f :.: g) p) = D1 ('MetaData ":.:" "Data.SOP.BasicFunctors" "sop-core-0.5.0.0-8Z2mcN5MN4PKIxdMlK1cP6" 'True) (C1 ('MetaCons "Comp" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g p)))))

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

Extract the contents of a Comp value.

Mapping functions

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0

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

Lift the given function.

Since: 0.2.5.0