Generics.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 b

The constant type functor.

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

Constructors

K a

Instances

Eq2 (K *)

Since: 0.2.4.0

Methods

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

Ord2 (K *)

Since: 0.2.4.0

Methods

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

Read2 (K *)

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 *)

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)

Methods

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

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

Monoid a => Applicative (K * a)

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)

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)

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)

Since: 0.2.4.0

Methods

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

Ord a => Ord1 (K * a)

Since: 0.2.4.0

Methods

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

Read a => Read1 (K * a)

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)

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)

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)

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)

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)

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)

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)

Since: 0.2.5.0

Methods

rnf :: K k a b -> ()

type Rep (K k a b)

type Rep (K k a b) = D1 (MetaData "K" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-4uFPMMqbRNMCAcLGs4abxX" True) (C1 (MetaCons "K" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Code (K * a0 b0)

type Code (K * a0 b0) = (:) [*] ((:) * a0 ([] *)) ([] [*])

unK :: K a b -> a

Extract the contents of a K value.

newtype I a

The identity type functor.

Like Identity, but with a shorter name.

Constructors

I a

Instances

Monad I

Methods

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

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

return :: a -> I a

fail :: String -> I a

Functor I

Methods

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

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

Applicative I

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

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

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

Methods

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

Ord1 I

Since: 0.2.4.0

Methods

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

Read1 I

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

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)

Methods

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

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

Ord a => Ord (I a)

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)

Methods

readsPrec :: Int -> ReadS (I a)

readList :: ReadS [I a]

readPrec :: ReadPrec (I a)

readListPrec :: ReadPrec [I a]

Show a => Show (I a)

Methods

showsPrec :: Int -> I a -> ShowS

show :: I a -> String

showList :: [I a] -> ShowS

Generic (I a)

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)

Since: 0.2.5.0

Methods

rnf :: I a -> ()

type Rep (I a)

type Rep (I a) = D1 (MetaData "I" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-4uFPMMqbRNMCAcLGs4abxX" True) (C1 (MetaCons "I" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Code (I a0)

type Code (I a0) = (:) [*] ((:) * a0 ([] *)) ([] [*])

unI :: I a -> a

Extract the contents of an I value.

newtype (f :.: g) p 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)

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

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)

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)

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)

Since: 0.2.4.0

Methods

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

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

Since: 0.2.4.0

Methods

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

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

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)

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)

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)

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)

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)

Methods

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

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

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

Generic ((:.:) k l f g p)

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)

Since: 0.2.5.0

Methods

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

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

type Rep ((:.:) k l f g p) = D1 (MetaData ":.:" "Generics.SOP.BasicFunctors" "generics-sop-0.2.5.0-4uFPMMqbRNMCAcLGs4abxX" True) (C1 (MetaCons "Comp" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (g p)))))

type Code ((:.:) * * f0 g0 p0)

type Code ((:.:) * * f0 g0 p0) = (:) [*] ((:) * (f0 (g0 p0)) ([] *)) ([] [*])

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