Safe Haskell	None
Language	Haskell2010

Data.Ten

Contents

Typeclasses
Standard Functor10s

Description

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

Synopsis

module Data.Ten.Functor
module Data.Ten.Functor.WithIndex
module Data.Ten.Foldable
module Data.Ten.Foldable.WithIndex
module Data.Ten.Traversable
module Data.Ten.Traversable.WithIndex
module Data.Ten.Applicative
module Data.Ten.Representable
module Data.Ten.Update
module Data.Ten.Entails
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) = Comp1 {
- unComp1 :: f (g p)
}
data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) = (f p) :*: (g p)
data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k)
- = L1 (f p)
- | R1 (g p)

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 `Functor10`s

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

Instances details

(Applicative f, Constrained10 c g) => Constrained10 (c :: k -> Constraint) (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Field Methods constrained10 :: (f :.: g) (Dict1 c) Source #
Functor f => Generic1 (f :.: g :: k -> Type)	Since: base-4.9.0.0
Instance details 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)
Instance details Defined in Control.DeepSeq Methods grnf :: RnfArgs One a -> (f :.: g) a -> ()
(Foldable f, Foldable10 g) => Foldable10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Foldable Methods foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :.: g) m -> w Source #
(Functor f, Functor10 g) => Functor10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Functor Methods fmap10 :: (forall (a :: k0). m a -> n a) -> (f :.: g) m -> (f :.: g) n Source #
(Functor g, Functor10WithIndex f) => Functor10WithIndex (g :.: f :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Foldable g, Foldable10WithIndex f) => Foldable10WithIndex (g :.: f :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Foldable.WithIndex Methods ifoldMap10 :: Monoid w => (forall (a :: k0). Index10 (g :.: f) a -> m a -> w) -> (g :.: f) m -> w Source #
(Applicative f, Applicative10 g) => Applicative10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Applicative Methods pure10 :: (forall (a :: k0). m a) -> (f :.: g) m Source # (<*>!) :: forall (m :: k0 -> Type) (n :: k0 -> Type). (f :.: g) (m :->: n) -> (f :.: g) m -> (f :.: g) n Source # liftA210 :: (forall (a :: k0). m a -> n a -> o a) -> (f :.: g) m -> (f :.: g) n -> (f :.: g) o Source #
(Traversable f, Traversable10 g) => Traversable10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Traversable g, Traversable10WithIndex f) => Traversable10WithIndex (g :.: f :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Functor f, FieldPaths f, GFieldPaths10 g) => GFieldPaths10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Field Methods gfieldPaths10 :: (forall (a :: k0). [PathComponent] -> r a) -> (f :.: g) r Source #
(Representable f, GTabulate10 g) => GTabulate10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Representable Methods gtabulate10 :: (forall (a :: k0). Field10 (f :.: g) a -> r a) -> (f :.: g) r Source #
(Update f, GUpdate10 g) => GUpdate10 (f :.: g :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Functor f, Functor g) => Functor (f :.: g)	Since: base-4.9.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details 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)
Instance details 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)
Instance details 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
Instance details 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)
Instance details Defined in Data.Functor.Rep Methods gindex' :: (f :.: g) a -> GRep' (f :.: g) -> a
(Representable f, GTabulate g) => GTabulate (f :.: g)
Instance details Defined in Data.Functor.Rep Methods gtabulate' :: (GRep' (f :.: g) -> a) -> (f :.: g) a
(GTabulate f, GTabulate g) => GTabulate (f :.: g) Source #
Instance details Defined in Data.Functor.Field Methods gtabulate :: (Field (f :.: g) -> r) -> (f :.: g) r Source #
(GFieldPaths f, GFieldPaths g) => GFieldPaths (f :.: g) Source #
Instance details Defined in Data.Functor.Field Methods gfieldPaths :: ([PathComponent] -> r) -> (f :.: g) r Source #
(GUpdate f, GUpdate g) => GUpdate (f :.: g) Source #
Instance details Defined in Data.Functor.Update Methods gsetters :: ((forall a. (a -> a) -> (f :.: g) a -> (f :.: g) a) -> r) -> (f :.: g) r Source #
Eq (f (g p)) => Eq ((f :.: g) p)	Since: base-4.7.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details 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) Source #
Instance details Defined in Data.Ten.Functor.WithIndex type Index10 (g :.: f :: (k -> Type) -> Type) = Index10 f
type Rep (f :.: g)
Instance details Defined in Data.Functor.Rep type Rep (f :.: g) = (Rep f, Rep g)
type GRep' (f :.: g)
Instance details Defined in Data.Functor.Rep type GRep' (f :.: g) = (WrappedRep f, GRep' g)
type Rep ((f :.: g) p)
Instance details 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

Instances details

(Constrained10 c f, Constrained10 c g) => Constrained10 (c :: k -> Constraint) (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Field Methods constrained10 :: (f :*: g) (Dict1 c) Source #
Generic1 (f :*: g :: k -> Type)	Since: base-4.9.0.0
Instance details 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)
Instance details 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)
Instance details 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)
Instance details Defined in Data.Wrapped Methods gmempty :: forall (x :: k0). (f :*: g) x #
(GNFData arity a, GNFData arity b) => GNFData arity (a :*: b)
Instance details Defined in Control.DeepSeq Methods grnf :: RnfArgs arity a0 -> (a :*: b) a0 -> ()
(Foldable10 f, Foldable10 g) => Foldable10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Foldable Methods foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :*: g) m -> w Source #
(Functor10 f, Functor10 g) => Functor10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Functor Methods fmap10 :: (forall (a :: k0). m a -> n a) -> (f :: g) m -> (f :: g) n Source #
(Applicative10 f, Applicative10 g) => Applicative10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Applicative Methods pure10 :: (forall (a :: k0). m a) -> (f :: g) m Source # (<>!) :: forall (m :: k0 -> Type) (n :: k0 -> Type). (f :: g) (m :->: n) -> (f :: g) m -> (f :: g) n Source # liftA210 :: (forall (a :: k0). m a -> n a -> o a) -> (f :: g) m -> (f :: g) n -> (f :: g) o Source #
(Traversable10 f, Traversable10 g) => Traversable10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(GFieldPaths10 f, GFieldPaths10 g) => GFieldPaths10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Field Methods gfieldPaths10 :: (forall (a :: k0). [PathComponent] -> r a) -> (f :*: g) r Source #
(GTabulate10 f, GTabulate10 g) => GTabulate10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Representable Methods gtabulate10 :: (forall (a :: k0). Field10 (f :: g) a -> r a) -> (f :: g) r Source #
(GUpdate10 f, GUpdate10 g) => GUpdate10 (f :*: g :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Monad f, Monad g) => Monad (f :*: g)	Since: base-4.9.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details 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)
Instance details 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)
Instance details 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
Instance details 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
Instance details 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)
Instance details Defined in Data.Default.Class Methods gdef :: (a :*: b) a0
(GDiffCtor f, GDiffCtor g) => GDiffCtor (f :*: g)
Instance details Defined in Data.Portray.Diff Methods gdiffCtor :: (f :: g) x -> (f :: g) x -> (Any, DList Portrayal)
(GDiffRecord f, GDiffRecord g) => GDiffRecord (f :*: g)
Instance details Defined in Data.Portray.Diff Methods gdiffRecord :: (f :: g) x -> (f :: g) x -> DList (FactorPortrayal Portrayal)
(GIndex f, GIndex g) => GIndex (f :*: g)
Instance details Defined in Data.Functor.Rep Methods gindex' :: (f :: g) a -> GRep' (f :: g) -> a
(GTabulate f, GTabulate g) => GTabulate (f :*: g)
Instance details Defined in Data.Functor.Rep Methods gtabulate' :: (GRep' (f :: g) -> a) -> (f :: g) a
(GTabulate f, GTabulate g) => GTabulate (f :*: g) Source #
Instance details Defined in Data.Functor.Field Methods gtabulate :: (Field (f :: g) -> r) -> (f :: g) r Source #
(GFieldPaths f, GFieldPaths g) => GFieldPaths (f :*: g) Source #
Instance details Defined in Data.Functor.Field Methods gfieldPaths :: ([PathComponent] -> r) -> (f :*: g) r Source #
(GUpdate f, GUpdate g) => GUpdate (f :*: g) Source #
Instance details Defined in Data.Functor.Update Methods gsetters :: ((forall a. (a -> a) -> (f :: g) a -> (f :: g) a) -> r) -> (f :*: g) r Source #
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)	Since: base-4.7.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details 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)
Instance details Defined in Data.Functor.Rep type Rep (f :*: g) = Either (Rep f) (Rep g)
type GRep' (f :*: g)
Instance details Defined in Data.Functor.Rep type GRep' (f :*: g) = Either (GRep' f) (GRep' g)
type Rep ((f :*: g) p)
Instance details 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

Instances details

Generic1 (f :+: g :: k -> Type)	Since: base-4.9.0.0
Instance details 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)
Instance details Defined in Data.Portray Methods gportray :: forall (a :: k0). (f :+: g) a -> Portrayal #
(GNFData arity a, GNFData arity b) => GNFData arity (a :+: b)
Instance details Defined in Control.DeepSeq Methods grnf :: RnfArgs arity a0 -> (a :+: b) a0 -> ()
(Portray a, GDiff a f, GDiff a g) => GDiff a (f :+: g)
Instance details 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)
Instance details 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) Source #
Instance details Defined in Data.Ten.Foldable Methods foldMap10 :: Monoid w => (forall (a :: k0). m a -> w) -> (f :+: g) m -> w Source #
(Functor10 f, Functor10 g) => Functor10 (f :+: g :: (k -> Type) -> Type) Source #
Instance details Defined in Data.Ten.Functor Methods fmap10 :: (forall (a :: k0). m a -> n a) -> (f :+: g) m -> (f :+: g) n Source #
(Traversable10 f, Traversable10 g) => Traversable10 (f :+: g :: (k -> Type) -> Type) Source #
Instance details 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 Source #
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Contravariant f, Contravariant g) => Contravariant (f :+: g)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> (f :+: g) b -> (f :+: g) a # (>$) :: b -> (f :+: g) b -> (f :+: g) a #
(SumSize a, SumSize b) => SumSize (a :+: b)
Instance details Defined in Data.Hashable.Generic.Instances Methods sumSize :: Tagged (a :+: b)
(GSumGet a, GSumGet b) => GSumGet (a :+: b)
Instance details 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)
Instance details Defined in Data.Binary.Generic Methods sumSize :: Tagged (a :+: b) Word64
(GSumPut a, GSumPut b) => GSumPut (a :+: b)
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details 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)
Instance details 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))))

Typeclasses

Functor10

Foldable10

Traversable10

Applicative10

Representable10

Update10

Entails

Standard Functor10s

Instances

Instances

Instances

Standard `Functor10`s