Pandora.Paradigm.Schemes.TU

Documentation

newtype TU ct cu t u a

Constructors

TU ((t :. u) := a)

Instances

(forall a. Chain a) => Insertable Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

insert :: a -> Binary a -> Binary a

Insertable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

insert :: a -> Stack a -> Stack a

Set Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

member :: Setoid a => a -> Stack a -> Boolean

Semigroup (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(+) :: Stack a -> Stack a -> Stack a

Monoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

zero :: Stack a

Setoid a => Setoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(==) :: Stack a -> Stack a -> Boolean

(/=) :: Stack a -> Stack a -> Boolean

Substructure (Left :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Left Binary a :: Type

Methods

substructure :: Tagged Left (Binary a) :-. Substructural Left Binary a

Substructure (Right :: Type -> Wye Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural Right Binary a :: Type

Methods

substructure :: Tagged Right (Binary a) :-. Substructural Right Binary a

Substructure (Just :: Type -> Maybe Type) Rose

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural Just Rose a :: Type

Methods

substructure :: Tagged Just (Rose a) :-. Substructural Just Rose a

(forall a. Chain a) => Focusable (Root :: Type -> Location Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Focusing Root Binary a :: Type

Methods

focusing :: Tagged Root (Binary a) :-. Focusing Root Binary a

Focusable (Root :: Type -> Location Type) Rose

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Focusing Root Rose a :: Type

Methods

focusing :: Tagged Root (Rose a) :-. Focusing Root Rose a

Focusable (Head :: Type -> Location Type) Stack

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Focusing Head Stack a :: Type

Methods

focusing :: Tagged Head (Stack a) :-. Focusing Head Stack a

Substructure (Just :: Type -> Maybe Type) (Construction Stack)

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural Just (Construction Stack) a :: Type

Methods

substructure :: Tagged Just (Construction Stack a) :-. Substructural Just (Construction Stack) a

Focusable (Root :: Type -> Location Type) (Construction Stack)

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Focusing Root (Construction Stack) a :: Type

Methods

focusing :: Tagged Root (Construction Stack a) :-. Focusing Root (Construction Stack) a

Covariant t => Hoistable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

hoist :: Covariant u => (u ~> v) -> TU Covariant Covariant t u ~> TU Covariant Covariant t v

Covariant u => Covariant (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

(<$>) :: (a -> b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

comap :: (a -> b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

(<$) :: a -> ((->) e <:.> u) b -> ((->) e <:.> u) a

($>) :: ((->) e <:.> u) a -> b -> ((->) e <:.> u) b

void :: ((->) e <:.> u) a -> ((->) e <:.> u) ()

loeb :: ((->) e <:.> u) (a <-| ((->) e <:.> u)) -> ((->) e <:.> u) a

(<&>) :: ((->) e <:.> u) a -> (a -> b) -> ((->) e <:.> u) b

(<$$>) :: Covariant u0 => (a -> b) -> ((((->) e <:.> u) :. u0) := a) -> (((->) e <:.> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((->) e <:.> u) :. (u0 :. v)) := a) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((->) e <:.> u) :. u0) := a) -> (a -> b) -> (((->) e <:.> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((->) e <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(Covariant t, Covariant u) => Covariant (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<$>) :: (a -> b) -> (u <:.> Construction t) a -> (u <:.> Construction t) b

comap :: (a -> b) -> (u <:.> Construction t) a -> (u <:.> Construction t) b

(<$) :: a -> (u <:.> Construction t) b -> (u <:.> Construction t) a

($>) :: (u <:.> Construction t) a -> b -> (u <:.> Construction t) b

void :: (u <:.> Construction t) a -> (u <:.> Construction t) ()

loeb :: (u <:.> Construction t) (a <-| (u <:.> Construction t)) -> (u <:.> Construction t) a

(<&>) :: (u <:.> Construction t) a -> (a -> b) -> (u <:.> Construction t) b

(<$$>) :: Covariant u0 => (a -> b) -> (((u <:.> Construction t) :. u0) := a) -> ((u <:.> Construction t) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((u <:.> Construction t) :. (u0 :. v)) := a) -> ((u <:.> Construction t) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((u <:.> Construction t) :. (u0 :. (v :. w))) := a) -> ((u <:.> Construction t) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((u <:.> Construction t) :. u0) := a) -> (a -> b) -> ((u <:.> Construction t) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((u <:.> Construction t) :. (u0 :. v)) := a) -> (a -> b) -> ((u <:.> Construction t) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((u <:.> Construction t) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((u <:.> Construction t) :. (u0 :. (v :. w))) := b

Covariant u => Covariant ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(<$>) :: (a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

comap :: (a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

(<$) :: a -> ((:*:) e <:.> u) b -> ((:*:) e <:.> u) a

($>) :: ((:*:) e <:.> u) a -> b -> ((:*:) e <:.> u) b

void :: ((:*:) e <:.> u) a -> ((:*:) e <:.> u) ()

loeb :: ((:*:) e <:.> u) (a <-| ((:*:) e <:.> u)) -> ((:*:) e <:.> u) a

(<&>) :: ((:*:) e <:.> u) a -> (a -> b) -> ((:*:) e <:.> u) b

(<$$>) :: Covariant u0 => (a -> b) -> ((((:*:) e <:.> u) :. u0) := a) -> (((:*:) e <:.> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((:*:) e <:.> u) :. u0) := a) -> (a -> b) -> (((:*:) e <:.> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

Covariant (Delta <:.> Stack)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(<$>) :: (a -> b) -> (Delta <:.> Stack) a -> (Delta <:.> Stack) b

comap :: (a -> b) -> (Delta <:.> Stack) a -> (Delta <:.> Stack) b

(<$) :: a -> (Delta <:.> Stack) b -> (Delta <:.> Stack) a

($>) :: (Delta <:.> Stack) a -> b -> (Delta <:.> Stack) b

void :: (Delta <:.> Stack) a -> (Delta <:.> Stack) ()

loeb :: (Delta <:.> Stack) (a <-| (Delta <:.> Stack)) -> (Delta <:.> Stack) a

(<&>) :: (Delta <:.> Stack) a -> (a -> b) -> (Delta <:.> Stack) b

(<$$>) :: Covariant u => (a -> b) -> (((Delta <:.> Stack) :. u) := a) -> ((Delta <:.> Stack) :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> (((Delta <:.> Stack) :. (u :. v)) := a) -> ((Delta <:.> Stack) :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> (((Delta <:.> Stack) :. (u :. (v :. w))) := a) -> ((Delta <:.> Stack) :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => (((Delta <:.> Stack) :. u) := a) -> (a -> b) -> ((Delta <:.> Stack) :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => (((Delta <:.> Stack) :. (u :. v)) := a) -> (a -> b) -> ((Delta <:.> Stack) :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => (((Delta <:.> Stack) :. (u :. (v :. w))) := a) -> (a -> b) -> ((Delta <:.> Stack) :. (u :. (v :. w))) := b

Bindable u => Bindable (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

(>>=) :: ((->) e <:.> u) a -> (a -> ((->) e <:.> u) b) -> ((->) e <:.> u) b

(=<<) :: (a -> ((->) e <:.> u) b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

bind :: (a -> ((->) e <:.> u) b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

join :: ((((->) e <:.> u) :. ((->) e <:.> u)) := a) -> ((->) e <:.> u) a

(>=>) :: (a -> ((->) e <:.> u) b) -> (b -> ((->) e <:.> u) c) -> a -> ((->) e <:.> u) c

(<=<) :: (b -> ((->) e <:.> u) c) -> (a -> ((->) e <:.> u) b) -> a -> ((->) e <:.> u) c

($>>=) :: Covariant u0 => (a -> ((->) e <:.> u) b) -> ((u0 :. ((->) e <:.> u)) := a) -> (u0 :. ((->) e <:.> u)) := b

(<>>=) :: (((->) e <:.> u) b -> c) -> (a -> ((->) e <:.> u) b) -> ((->) e <:.> u) a -> c

Applicative u => Applicative (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

(<*>) :: ((->) e <:.> u) (a -> b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

apply :: ((->) e <:.> u) (a -> b) -> ((->) e <:.> u) a -> ((->) e <:.> u) b

(*>) :: ((->) e <:.> u) a -> ((->) e <:.> u) b -> ((->) e <:.> u) b

(<*) :: ((->) e <:.> u) a -> ((->) e <:.> u) b -> ((->) e <:.> u) a

forever :: ((->) e <:.> u) a -> ((->) e <:.> u) b

(<**>) :: Applicative u0 => ((((->) e <:.> u) :. u0) := (a -> b)) -> ((((->) e <:.> u) :. u0) := a) -> (((->) e <:.> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((->) e <:.> u) :. (u0 :. v)) := (a -> b)) -> ((((->) e <:.> u) :. (u0 :. v)) := a) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((->) e <:.> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(Applicative t, Applicative u) => Applicative (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<*>) :: (u <:.> Construction t) (a -> b) -> (u <:.> Construction t) a -> (u <:.> Construction t) b

apply :: (u <:.> Construction t) (a -> b) -> (u <:.> Construction t) a -> (u <:.> Construction t) b

(*>) :: (u <:.> Construction t) a -> (u <:.> Construction t) b -> (u <:.> Construction t) b

(<*) :: (u <:.> Construction t) a -> (u <:.> Construction t) b -> (u <:.> Construction t) a

forever :: (u <:.> Construction t) a -> (u <:.> Construction t) b

(<**>) :: Applicative u0 => (((u <:.> Construction t) :. u0) := (a -> b)) -> (((u <:.> Construction t) :. u0) := a) -> ((u <:.> Construction t) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((u <:.> Construction t) :. (u0 :. v)) := (a -> b)) -> (((u <:.> Construction t) :. (u0 :. v)) := a) -> ((u <:.> Construction t) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((u <:.> Construction t) :. (u0 :. (v :. w))) := (a -> b)) -> (((u <:.> Construction t) :. (u0 :. (v :. w))) := a) -> ((u <:.> Construction t) :. (u0 :. (v :. w))) := b

(Covariant t, Alternative u) => Alternative (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<+>) :: (u <:.> Construction t) a -> (u <:.> Construction t) a -> (u <:.> Construction t) a

alter :: (u <:.> Construction t) a -> (u <:.> Construction t) a -> (u <:.> Construction t) a

(Covariant t, Avoidable u) => Avoidable (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

empty :: (u <:.> Construction t) a

Extendable u => Extendable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(=>>) :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) b

(<<=) :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

extend :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b

duplicate :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) :. ((:*:) e <:.> u)) := a

(=<=) :: (((:*:) e <:.> u) b -> c) -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> c

(=>=) :: (((:*:) e <:.> u) a -> b) -> (((:*:) e <:.> u) b -> c) -> ((:*:) e <:.> u) a -> c

($=>>) :: Covariant u0 => (((:*:) e <:.> u) a -> b) -> ((u0 :. ((:*:) e <:.> u)) := a) -> (u0 :. ((:*:) e <:.> u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

(Covariant u, Pointable u) => Pointable (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

point :: a |-> ((->) e <:.> u)

(Avoidable t, Pointable u) => Pointable (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

point :: a |-> (u <:.> Construction t)

(Traversable t, Traversable u) => Traversable (u <:.> Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(->>) :: (Pointable u0, Applicative u0) => (u <:.> Construction t) a -> (a -> u0 b) -> (u0 :. (u <:.> Construction t)) := b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> (u <:.> Construction t) a -> (u0 :. (u <:.> Construction t)) := b

sequence :: (Pointable u0, Applicative u0) => (((u <:.> Construction t) :. u0) := a) -> (u0 :. (u <:.> Construction t)) := a

(->>>) :: (Pointable u0, Applicative u0, Traversable v) => ((v :. (u <:.> Construction t)) := a) -> (a -> u0 b) -> (u0 :. (v :. (u <:.> Construction t))) := b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => ((w :. (v :. (u <:.> Construction t))) := a) -> (a -> u0 b) -> (u0 :. (w :. (v :. (u <:.> Construction t)))) := b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. (u <:.> Construction t)))) := a) -> (a -> u0 b) -> (u0 :. (j :. (w :. (v :. (u <:.> Construction t))))) := b

Extractable u => Extractable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

extract :: a <-| ((:*:) e <:.> u)

(Covariant (t <.:> v), Covariant (w <:.> u), Adjoint v u, Adjoint t w) => Adjoint (t <.:> v) (w <:.> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((t <.:> v) a -> b) -> (w <:.> u) b

(|-) :: (t <.:> v) a -> (a -> (w <:.> u) b) -> b

phi :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b

psi :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b

eta :: a -> ((w <:.> u) :. (t <.:> v)) := a

epsilon :: (((t <.:> v) :. (w <:.> u)) := a) -> a

(Covariant (v <:.> t), Covariant (w <.:> u), Adjoint t u, Adjoint v w) => Adjoint (v <:.> t) (w <.:> u)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((v <:.> t) a -> b) -> (w <.:> u) b

(|-) :: (v <:.> t) a -> (a -> (w <.:> u) b) -> b

phi :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b

psi :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b

eta :: a -> ((w <.:> u) :. (v <:.> t)) := a

epsilon :: (((v <:.> t) :. (w <.:> u)) := a) -> a

(Covariant (v <:.> t), Covariant (u <:.> w), Adjoint t u, Adjoint v w) => Adjoint (v <:.> t) (u <:.> w)

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((v <:.> t) a -> b) -> (u <:.> w) b

(|-) :: (v <:.> t) a -> (a -> (u <:.> w) b) -> b

phi :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b

psi :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b

eta :: a -> ((u <:.> w) :. (v <:.> t)) := a

epsilon :: (((v <:.> t) :. (u <:.> w)) := a) -> a

Pointable t => Liftable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

lift :: Covariant u => u ~> TU Covariant Covariant t u

Extractable t => Lowerable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

lower :: Covariant u => TU Covariant Covariant t u ~> u

Interpreted (TU ct cu t u)

Defined in Pandora.Paradigm.Schemes.TU

Associated Types

type Primary (TU ct cu t u) a :: Type

Methods

run :: TU ct cu t u a -> Primary (TU ct cu t u) a

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Binary

type Nonempty Binary = Construction Wye

type Nonempty Stack

Defined in Pandora.Paradigm.Structure.Stack

type Nonempty Stack = Construction Maybe

type Nonempty Rose

Defined in Pandora.Paradigm.Structure.Rose

type Nonempty Rose = Construction Stack

type Zipper Stack

Defined in Pandora.Paradigm.Structure.Stack

type Zipper Stack = Tap (Delta <:.> Stack)

type Substructural (Left :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Left :: Type -> Wye Type) Binary a = Binary a

type Substructural (Right :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural (Right :: Type -> Wye Type) Binary a = Binary a

type Substructural (Just :: Type -> Maybe Type) Rose a

Defined in Pandora.Paradigm.Structure.Rose

type Substructural (Just :: Type -> Maybe Type) Rose a = (Stack :. Construction Stack) := a

type Focusing (Root :: Type -> Location Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Focusing (Root :: Type -> Location Type) Binary a = Maybe a

type Focusing (Root :: Type -> Location Type) Rose a

Defined in Pandora.Paradigm.Structure.Rose

type Focusing (Root :: Type -> Location Type) Rose a = Maybe a

type Focusing (Head :: Type -> Location Type) Stack a

Defined in Pandora.Paradigm.Structure.Stack

type Focusing (Head :: Type -> Location Type) Stack a = Maybe a

type Substructural (Just :: Type -> Maybe Type) (Construction Stack) a

Defined in Pandora.Paradigm.Structure.Rose

type Substructural (Just :: Type -> Maybe Type) (Construction Stack) a = (Stack :. Construction Stack) := a

type Focusing (Root :: Type -> Location Type) (Construction Stack) a

Defined in Pandora.Paradigm.Structure.Rose

type Focusing (Root :: Type -> Location Type) (Construction Stack) a = a

type Primary (TU ct cu t u) a

Defined in Pandora.Paradigm.Schemes.TU

type Primary (TU ct cu t u) a = (t :. u) := a

type (<:.>) = TU Covariant Covariant

type (>:.>) = TU Contravariant Covariant

type (<:.<) = TU Covariant Contravariant

type (>:.<) = TU Contravariant Contravariant