Data.Ten

Typeclass hierarchy of functors from k -> Type to Type.

The naming convention Functor10 comes from the fact that it's a functor from the category of objects with one type parameter to the category of objects with zero type parameters. See http://hackage.haskell.org/package/hakaru-0.4.0/docs/src/Language.Hakaru.Syntax.IClasses.html for precedent for this naming convention.

In this, the argument morphisms are of the form forall a. m a -> n a, and the result morphisms are of the form f m -> f n.

The main parts of this are:

• Functor10 and the other similarly-named typeclasses, which are essentially just translations of Functor et al. to kind (k -> Type) -> Type. These are essentially Functors with additional "tag" types available at each occurrence of the argument. Applying them to Identity, you get essentially normal records, but other type parameters give other interesting objects.
• (:**) and Exists (two stock Functor10 types) plus appropriate instances for products, sums, and compositions of functors as provided by GHC.Generics: (:*:), (:+:), and (:.:).
• Entails, which uses a GADT-like value to retrieve instances for its type parameter. This adds a lot of power to the otherwise-pretty-weak Functor10 class hierarchy, since without access to corresponding instances, all the input morphisms are unable to do anything whatsoever with the "tag" types. With Entails, though, one can use the fact that every occurrence of m a in f m satisfies c a to make instances of c available while mappingfoldingtraversing/etc. an f m.

The provided GHC.Generics-based deriving functionality is meant to be used with the DerivingVia extension. To get the full suite of classes on a generic-record type, make sure every field is either an Ap10, another nested generic-record, or an instance of Update applied to one of the above. Then, just add the deriving clauses:

    data MyType f = MyType { _mrInt :: Ap10 Int f, _mrBool :: Ap10 Bool f }
      deriving Generic1
      deriving
        ( Functor10, Foldable10, Traversable10
        , Applicative10, Representable10, Update10, Constrained10 c
        ) via Wrapped1 Generic1 MyType
      deriving
        ( Functor10WithIndex, Foldable10WithIndex, Traversable10WithIndex
        ) via Wrapped1 Representable10 MyType

    type instance Index10 MyType = Rep10 MyType

Typeclasses

Functor10

module Data.Ten.Functor

module Data.Ten.Functor.WithIndex

Foldable10

module Data.Ten.Foldable

module Data.Ten.Foldable.WithIndex

Traversable10

module Data.Ten.Traversable

module Data.Ten.Traversable.WithIndex

Applicative10

module Data.Ten.Applicative

Representable10

module Data.Ten.Representable

Update10

module Data.Ten.Update

Entails

module Data.Ten.Entails

Standard Functor10s

module Data.Ten.Ap

module Data.Ten.Exists

module Data.Ten.Field

module Data.Ten.Sigma

newtype ((f :: k2 -> Type) :.: (g :: k1 -> k2)) (p :: k1) infixr 7

Composition of functors

Constructors

Comp1

Fields

• unComp1 :: f (g p)

Instances

(Applicative f, Constrained10 c g) => Constrained10 (c :: k -> Constraint) (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Field

Methods

constrained10 :: (f :.: g) (Dict1 c)

Functor f => Generic1 (f :.: g :: k -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Associated Types

type Rep1 (f :.: g) :: k -> Type

Methods

from1 :: forall (a :: k0). (f :.: g) a -> Rep1 (f :.: g) a

to1 :: forall (a :: k0). Rep1 (f :.: g) a -> (f :.: g) a

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

Defined in Control.DeepSeq

Methods

grnf :: RnfArgs One a -> (f :.: g) a -> ()

(Foldable f, Foldable10 g) => Foldable10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Foldable

Methods

foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :.: g) m -> w

(Functor f, Functor10 g) => Functor10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Functor

Methods

fmap10 :: (forall (a :: k0). m a -> n a) -> (f :.: g) m -> (f :.: g) n

(Functor g, Functor10WithIndex f) => Functor10WithIndex (g :.: f :: (k -> Type) -> Type)

Defined in Data.Ten.Functor.WithIndex

Methods

imap10 :: (forall (a :: k0). Index10 (g :.: f) a -> m a -> n a) -> (g :.: f) m -> (g :.: f) n

(Foldable g, Foldable10WithIndex f) => Foldable10WithIndex (g :.: f :: (k -> Type) -> Type)

Defined in Data.Ten.Foldable.WithIndex

Methods

ifoldMap10 :: Monoid w => (forall (a :: k0). Index10 (g :.: f) a -> m a -> w) -> (g :.: f) m -> w

(Applicative f, Applicative10 g) => Applicative10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Applicative

Methods

pure10 :: (forall (a :: k0). m a) -> (f :.: g) m

(<*>!) :: forall (m :: k0 -> Type) (n :: k0 -> Type). (f :.: g) (m :->: n) -> (f :.: g) m -> (f :.: g) n

liftA210 :: (forall (a :: k0). m a -> n a -> o a) -> (f :.: g) m -> (f :.: g) n -> (f :.: g) o

(Traversable f, Traversable10 g) => Traversable10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Traversable

Methods

mapTraverse10 :: forall f0 m n r. Applicative f0 => ((f :.: g) n -> r) -> (forall (a :: k0). m a -> f0 (n a)) -> (f :.: g) m -> f0 r

(Traversable g, Traversable10WithIndex f) => Traversable10WithIndex (g :.: f :: (k -> Type) -> Type)

Defined in Data.Ten.Traversable.WithIndex

Methods

imapTraverse10 :: Applicative g0 => ((g :.: f) n -> r) -> (forall (a :: k0). Index10 (g :.: f) a -> m a -> g0 (n a)) -> (g :.: f) m -> g0 r

(Functor f, FieldPaths f, GFieldPaths10 g) => GFieldPaths10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Field

Methods

gfieldPaths10 :: (forall (a :: k0). [PathComponent] -> r a) -> (f :.: g) r

(Representable f, GTabulate10 g) => GTabulate10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Representable

Methods

gtabulate10 :: (forall (a :: k0). Field10 (f :.: g) a -> r a) -> (f :.: g) r

(Update f, GUpdate10 g) => GUpdate10 (f :.: g :: (k -> Type) -> Type)

Defined in Data.Ten.Update

Methods

gsetters10 :: (forall (a :: k0). (forall (m :: k0 -> Type). (m a -> m a) -> (f :.: g) m -> (f :.: g) m) -> r a) -> (f :.: g) r

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

Since: base-4.9.0.0

Defined in GHC.Generics

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: base-4.9.0.0

Defined in GHC.Generics

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: base-4.9.0.0

Defined in Data.Foldable

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: base-4.9.0.0

Defined in Data.Traversable

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)

(Distributive a, Distributive b) => Distributive (a :.: b)

Defined in Data.Distributive

Methods

distribute :: Functor f => f ((a :.: b) a0) -> (a :.: b) (f a0)

collect :: Functor f => (a0 -> (a :.: b) b0) -> f a0 -> (a :.: b) (f b0)

distributeM :: Monad m => m ((a :.: b) a0) -> (a :.: b) (m a0)

collectM :: Monad m => (a0 -> (a :.: b) b0) -> m a0 -> (a :.: b) (m b0)

(Functor f, Contravariant g) => Contravariant (f :.: g)

Defined in Data.Functor.Contravariant

Methods

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

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

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

Defined in Data.Functor.Rep

Associated Types

type Rep (f :.: g)

Methods

tabulate :: (Rep (f :.: g) -> a) -> (f :.: g) a

index :: (f :.: g) a -> Rep (f :.: g) -> a

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

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :.: g) a

(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a

some :: (f :.: g) a -> (f :.: g) [a]

many :: (f :.: g) a -> (f :.: g) [a]

(Representable f, GIndex g) => GIndex (f :.: g)

Defined in Data.Functor.Rep

Methods

gindex' :: (f :.: g) a -> GRep' (f :.: g) -> a

(Representable f, GTabulate g) => GTabulate (f :.: g)

Defined in Data.Functor.Rep

Methods

gtabulate' :: (GRep' (f :.: g) -> a) -> (f :.: g) a

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

Defined in Data.Functor.Field

Methods

gtabulate :: (Field (f :.: g) -> r) -> (f :.: g) r

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

Defined in Data.Functor.Field

Methods

gfieldPaths :: ([PathComponent] -> r) -> (f :.: g) r

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

Defined in Data.Functor.Update

Methods

gsetters :: ((forall a. (a -> a) -> (f :.: g) a -> (f :.: g) a) -> r) -> (f :.: g) r

Eq (f (g p)) => Eq ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool

Ord (f (g p)) => Ord ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

compare :: (f :.: g) p -> (f :.: g) p -> Ordering

(<) :: (f :.: g) p -> (f :.: g) p -> Bool

(<=) :: (f :.: g) p -> (f :.: g) p -> Bool

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

(>=) :: (f :.: g) p -> (f :.: g) p -> Bool

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

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

Read (f (g p)) => Read ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :.: g) p)

readList :: ReadS [(f :.: g) p]

readPrec :: ReadPrec ((f :.: g) p)

readListPrec :: ReadPrec [(f :.: g) p]

Show (f (g p)) => Show ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

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

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

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

Generic ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

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

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

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

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

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

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

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: (f :.: g) p

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

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

type Rep1 (f :.: g :: k -> Type)

Defined in GHC.Generics

type Rep1 (f :.: g :: k -> Type) = D1 ('MetaData ":.:" "GHC.Generics" "base" 'True) (C1 ('MetaCons "Comp1" 'PrefixI 'True) (S1 ('MetaSel ('Just "unComp1") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (f :.: Rec1 g)))

type Index10 (g :.: f :: (k -> Type) -> Type)

Defined in Data.Ten.Functor.WithIndex

type Index10 (g :.: f :: (k -> Type) -> Type) = Index10 f

type Rep (f :.: g)

Defined in Data.Functor.Rep

type Rep (f :.: g) = (Rep f, Rep g)

type GRep' (f :.: g)

Defined in Data.Functor.Rep

type GRep' (f :.: g) = (WrappedRep f, GRep' g)

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

Defined in GHC.Generics

type Rep ((f :.: g) p) = D1 ('MetaData ":.:" "GHC.Generics" "base" 'True) (C1 ('MetaCons "Comp1" 'PrefixI 'True) (S1 ('MetaSel ('Just "unComp1") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g p)))))

data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) infixr 6

Products: encode multiple arguments to constructors

Constructors

(f p) :*: (g p) infixr 6

Instances

(Constrained10 c f, Constrained10 c g) => Constrained10 (c :: k -> Constraint) (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Field

Methods

constrained10 :: (f :*: g) (Dict1 c)

Generic1 (f :*: g :: k -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Associated Types

type Rep1 (f :*: g) :: k -> Type

Methods

from1 :: forall (a :: k0). (f :*: g) a -> Rep1 (f :*: g) a

to1 :: forall (a :: k0). Rep1 (f :*: g) a -> (f :*: g) a

(GPortrayProduct f, GPortrayProduct g) => GPortrayProduct (f :*: g :: k -> Type)

Defined in Data.Portray

Methods

gportrayProduct :: forall (a :: k0). (f :*: g) a -> [FactorPortrayal Portrayal] -> [FactorPortrayal Portrayal]

(GSemigroup f, GSemigroup g) => GSemigroup (f :*: g :: k -> Type)

Defined in Data.Wrapped

Methods

gsop :: forall (x :: k0). (f :*: g) x -> (f :*: g) x -> (f :*: g) x

(GMonoid f, GMonoid g) => GMonoid (f :*: g :: k -> Type)

Defined in Data.Wrapped

Methods

gmempty :: forall (x :: k0). (f :*: g) x

(GNFData arity a, GNFData arity b) => GNFData arity (a :*: b)

Defined in Control.DeepSeq

Methods

grnf :: RnfArgs arity a0 -> (a :*: b) a0 -> ()

(Foldable10 f, Foldable10 g) => Foldable10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Foldable

Methods

foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :*: g) m -> w

(Functor10 f, Functor10 g) => Functor10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Functor

Methods

fmap10 :: (forall (a :: k0). m a -> n a) -> (f :*: g) m -> (f :*: g) n

(Applicative10 f, Applicative10 g) => Applicative10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Applicative

Methods

pure10 :: (forall (a :: k0). m a) -> (f :*: g) m

(<*>!) :: forall (m :: k0 -> Type) (n :: k0 -> Type). (f :*: g) (m :->: n) -> (f :*: g) m -> (f :*: g) n

liftA210 :: (forall (a :: k0). m a -> n a -> o a) -> (f :*: g) m -> (f :*: g) n -> (f :*: g) o

(Traversable10 f, Traversable10 g) => Traversable10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Traversable

Methods

mapTraverse10 :: forall f0 m n r. Applicative f0 => ((f :*: g) n -> r) -> (forall (a :: k0). m a -> f0 (n a)) -> (f :*: g) m -> f0 r

(GFieldPaths10 f, GFieldPaths10 g) => GFieldPaths10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Field

Methods

gfieldPaths10 :: (forall (a :: k0). [PathComponent] -> r a) -> (f :*: g) r

(GTabulate10 f, GTabulate10 g) => GTabulate10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Representable

Methods

gtabulate10 :: (forall (a :: k0). Field10 (f :*: g) a -> r a) -> (f :*: g) r

(GUpdate10 f, GUpdate10 g) => GUpdate10 (f :*: g :: (k -> Type) -> Type)

Defined in Data.Ten.Update

Methods

gsetters10 :: (forall (a :: k0). (forall (m :: k0 -> Type). (m a -> m a) -> (f :*: g) m -> (f :*: g) m) -> r a) -> (f :*: g) r

(Monad f, Monad g) => Monad (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b

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

return :: a -> (f :*: g) a

(Functor f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

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: base-4.9.0.0

Defined in GHC.Generics

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: base-4.9.0.0

Defined in Data.Foldable

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: base-4.9.0.0

Defined in Data.Traversable

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)

(Distributive a, Distributive b) => Distributive (a :*: b)

Defined in Data.Distributive

Methods

distribute :: Functor f => f ((a :*: b) a0) -> (a :*: b) (f a0)

collect :: Functor f => (a0 -> (a :*: b) b0) -> f a0 -> (a :*: b) (f b0)

distributeM :: Monad m => m ((a :*: b) a0) -> (a :*: b) (m a0)

collectM :: Monad m => (a0 -> (a :*: b) b0) -> m a0 -> (a :*: b) (m b0)

(Contravariant f, Contravariant g) => Contravariant (f :*: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a -> b) -> (f :*: g) b -> (f :*: g) a

(>$) :: b -> (f :*: g) b -> (f :*: g) a

(Representable f, Representable g) => Representable (f :*: g)

Defined in Data.Functor.Rep

Associated Types

type Rep (f :*: g)

Methods

tabulate :: (Rep (f :*: g) -> a) -> (f :*: g) a

index :: (f :*: g) a -> Rep (f :*: g) -> a

(Alternative f, Alternative g) => Alternative (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

empty :: (f :*: g) a

(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

some :: (f :*: g) a -> (f :*: g) [a]

many :: (f :*: g) a -> (f :*: g) [a]

(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: (f :*: g) a

mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

(GDefault a, GDefault b) => GDefault (a :*: b)

Defined in Data.Default.Class

Methods

gdef :: (a :*: b) a0

(GDiffCtor f, GDiffCtor g) => GDiffCtor (f :*: g)

Defined in Data.Portray.Diff

Methods

gdiffCtor :: (f :*: g) x -> (f :*: g) x -> (Any, DList Portrayal)

(GDiffRecord f, GDiffRecord g) => GDiffRecord (f :*: g)

Defined in Data.Portray.Diff

Methods

gdiffRecord :: (f :*: g) x -> (f :*: g) x -> DList (FactorPortrayal Portrayal)

(GIndex f, GIndex g) => GIndex (f :*: g)

Defined in Data.Functor.Rep

Methods

gindex' :: (f :*: g) a -> GRep' (f :*: g) -> a

(GTabulate f, GTabulate g) => GTabulate (f :*: g)

Defined in Data.Functor.Rep

Methods

gtabulate' :: (GRep' (f :*: g) -> a) -> (f :*: g) a

(GTabulate f, GTabulate g) => GTabulate (f :*: g)

Defined in Data.Functor.Field

Methods

gtabulate :: (Field (f :*: g) -> r) -> (f :*: g) r

(GFieldPaths f, GFieldPaths g) => GFieldPaths (f :*: g)

Defined in Data.Functor.Field

Methods

gfieldPaths :: ([PathComponent] -> r) -> (f :*: g) r

(GUpdate f, GUpdate g) => GUpdate (f :*: g)

Defined in Data.Functor.Update

Methods

gsetters :: ((forall a. (a -> a) -> (f :*: g) a -> (f :*: g) a) -> r) -> (f :*: g) r

(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool

(Ord (f p), Ord (g p)) => Ord ((f :*: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

compare :: (f :*: g) p -> (f :*: g) p -> Ordering

(<) :: (f :*: g) p -> (f :*: g) p -> Bool

(<=) :: (f :*: g) p -> (f :*: g) p -> Bool

(>) :: (f :*: g) p -> (f :*: g) p -> Bool

(>=) :: (f :*: g) p -> (f :*: g) p -> Bool

max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

(Read (f p), Read (g p)) => Read ((f :*: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :*: g) p)

readList :: ReadS [(f :*: g) p]

readPrec :: ReadPrec ((f :*: g) p)

readListPrec :: ReadPrec [(f :*: g) p]

(Show (f p), Show (g p)) => Show ((f :*: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS

show :: (f :*: g) p -> String

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

Generic ((f :*: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

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 p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: (f :*: g) p

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

mconcat :: [(f :*: g) p] -> (f :*: g) p

type Rep1 (f :*: g :: k -> Type)

Defined in GHC.Generics

type Rep1 (f :*: g :: k -> Type) = D1 ('MetaData ":*:" "GHC.Generics" "base" 'False) (C1 ('MetaCons ":*:" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))

type Rep (f :*: g)

Defined in Data.Functor.Rep

type Rep (f :*: g) = Either (Rep f) (Rep g)

type GRep' (f :*: g)

Defined in Data.Functor.Rep

type GRep' (f :*: g) = Either (GRep' f) (GRep' g)

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

Defined in GHC.Generics

type Rep ((f :*: g) p) = D1 ('MetaData ":*:" "GHC.Generics" "base" 'False) (C1 ('MetaCons ":*:" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f p)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g p))))

data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k) infixr 5

Sums: encode choice between constructors

Constructors

L1 (f p)

R1 (g p)

Instances

Generic1 (f :+: g :: k -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Associated Types

type Rep1 (f :+: g) :: k -> Type

Methods

from1 :: forall (a :: k0). (f :+: g) a -> Rep1 (f :+: g) a

to1 :: forall (a :: k0). Rep1 (f :+: g) a -> (f :+: g) a

(GPortray f, GPortray g) => GPortray (f :+: g :: k -> Type)

Defined in Data.Portray

Methods

gportray :: forall (a :: k0). (f :+: g) a -> Portrayal

(GNFData arity a, GNFData arity b) => GNFData arity (a :+: b)

Defined in Control.DeepSeq

Methods

grnf :: RnfArgs arity a0 -> (a :+: b) a0 -> ()

(Portray a, GDiff a f, GDiff a g) => GDiff a (f :+: g)

Defined in Data.Portray.Diff

Methods

gdiff :: a -> a -> (f :+: g) x -> (f :+: g) x -> Maybe Portrayal

(GSum arity a, GSum arity b) => GSum arity (a :+: b)

Defined in Data.Hashable.Generic.Instances

Methods

hashSum :: HashArgs arity a0 -> Int -> Int -> (a :+: b) a0 -> Int

(Foldable10 f, Foldable10 g) => Foldable10 (f :+: g :: (k -> Type) -> Type)

Defined in Data.Ten.Foldable

Methods

foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :+: g) m -> w

(Functor10 f, Functor10 g) => Functor10 (f :+: g :: (k -> Type) -> Type)

Defined in Data.Ten.Functor

Methods

fmap10 :: (forall (a :: k0). m a -> n a) -> (f :+: g) m -> (f :+: g) n

(Traversable10 f, Traversable10 g) => Traversable10 (f :+: g :: (k -> Type) -> Type)

Defined in Data.Ten.Traversable

Methods

mapTraverse10 :: forall f0 m n r. Applicative f0 => ((f :+: g) n -> r) -> (forall (a :: k0). m a -> f0 (n a)) -> (f :+: g) m -> f0 r

(Functor f, Functor g) => Functor (f :+: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

(Foldable f, Foldable g) => Foldable (f :+: g)

Since: base-4.9.0.0

Defined in Data.Foldable

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: base-4.9.0.0

Defined in Data.Traversable

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)

(Contravariant f, Contravariant g) => Contravariant (f :+: g)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a

(>$) :: b -> (f :+: g) b -> (f :+: g) a

(SumSize a, SumSize b) => SumSize (a :+: b)

Defined in Data.Hashable.Generic.Instances

Methods

sumSize :: Tagged (a :+: b)

(GSumGet a, GSumGet b) => GSumGet (a :+: b)

Defined in Data.Binary.Generic

Methods

getSum :: (Ord word, Num word, Bits word) => word -> word -> Get ((a :+: b) a0)

(SumSize a, SumSize b) => SumSize (a :+: b)

Defined in Data.Binary.Generic

Methods

sumSize :: Tagged (a :+: b) Word64

(GSumPut a, GSumPut b) => GSumPut (a :+: b)

Defined in Data.Binary.Generic

Methods

putSum :: (Num w, Bits w, Binary w) => w -> w -> (a :+: b) a0 -> Put

(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool

(Ord (f p), Ord (g p)) => Ord ((f :+: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

compare :: (f :+: g) p -> (f :+: g) p -> Ordering

(<) :: (f :+: g) p -> (f :+: g) p -> Bool

(<=) :: (f :+: g) p -> (f :+: g) p -> Bool

(>) :: (f :+: g) p -> (f :+: g) p -> Bool

(>=) :: (f :+: g) p -> (f :+: g) p -> Bool

max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p

min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p

(Read (f p), Read (g p)) => Read ((f :+: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

readsPrec :: Int -> ReadS ((f :+: g) p)

readList :: ReadS [(f :+: g) p]

readPrec :: ReadPrec ((f :+: g) p)

readListPrec :: ReadPrec [(f :+: g) p]

(Show (f p), Show (g p)) => Show ((f :+: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS

show :: (f :+: g) p -> String

showList :: [(f :+: g) p] -> ShowS

Generic ((f :+: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

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

type Rep1 (f :+: g :: k -> Type)

Defined in GHC.Generics

type Rep1 (f :+: g :: k -> Type) = D1 ('MetaData ":+:" "GHC.Generics" "base" 'False) (C1 ('MetaCons "L1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)) :+: C1 ('MetaCons "R1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))

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

Defined in GHC.Generics

type Rep ((f :+: g) p) = D1 ('MetaData ":+:" "GHC.Generics" "base" 'False) (C1 ('MetaCons "L1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f p))) :+: C1 ('MetaCons "R1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g p))))