Pandora.Paradigm.Schemes.TUT

Documentation

newtype TUT ct ct' cu t t' u a

Constructors

TUT ((t :. (u :. t')) := a)

Instances

(Covariant t, Covariant t', Covariant u) => Covariant ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(<$>) :: (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

comap :: (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

(<$) :: a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) a

($>) :: ((t <:<.>:> t') := u) a -> b -> ((t <:<.>:> t') := u) b

void :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) ()

loeb :: ((t <:<.>:> t') := u) (a <-| ((t <:<.>:> t') := u)) -> ((t <:<.>:> t') := u) a

(<&>) :: ((t <:<.>:> t') := u) a -> (a -> b) -> ((t <:<.>:> t') := u) b

(<$$>) :: Covariant u0 => (a -> b) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((t <:<.>:> t') := u) :. u0) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

(Adjoint t' t, Bindable u) => Bindable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(>>=) :: ((t <:<.>:> t') := u) a -> (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) b

(=<<) :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

bind :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

join :: ((((t <:<.>:> t') := u) :. ((t <:<.>:> t') := u)) := a) -> ((t <:<.>:> t') := u) a

(>=>) :: (a -> ((t <:<.>:> t') := u) b) -> (b -> ((t <:<.>:> t') := u) c) -> a -> ((t <:<.>:> t') := u) c

(<=<) :: (b -> ((t <:<.>:> t') := u) c) -> (a -> ((t <:<.>:> t') := u) b) -> a -> ((t <:<.>:> t') := u) c

($>>=) :: Covariant u0 => ((u0 :. ((t <:<.>:> t') := u)) := a) -> (a -> ((t <:<.>:> t') := u) b) -> (u0 :. ((t <:<.>:> t') := u)) := b

(<>>=) :: (((t <:<.>:> t') := u) b -> c) -> (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> c

(Adjoint t' t, Bindable u) => Applicative ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(<*>) :: ((t <:<.>:> t') := u) (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

apply :: ((t <:<.>:> t') := u) (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

(*>) :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) b

(<*) :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) a

forever :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

(<**>) :: Applicative u0 => ((((t <:<.>:> t') := u) :. u0) := (a -> b)) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((t <:<.>:> t') := u) :. (u0 :. v)) := (a -> b)) -> ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

(Applicative t, Covariant t', Alternative u) => Alternative ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(<+>) :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) a

alter :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) a

(Pointable t, Applicative t, Covariant t', Avoidable u) => Avoidable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

empty :: ((t <:<.>:> t') := u) a

(Adjoint t' t, Extendable u) => Extendable ((t' <:<.>:> t) := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(=>>) :: ((t' <:<.>:> t) := u) a -> (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) b

(<<=) :: (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> ((t' <:<.>:> t) := u) b

extend :: (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> ((t' <:<.>:> t) := u) b

duplicate :: ((t' <:<.>:> t) := u) a -> (((t' <:<.>:> t) := u) :. ((t' <:<.>:> t) := u)) := a

(=<=) :: (((t' <:<.>:> t) := u) b -> c) -> (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> c

(=>=) :: (((t' <:<.>:> t) := u) a -> b) -> (((t' <:<.>:> t) := u) b -> c) -> ((t' <:<.>:> t) := u) a -> c

($=>>) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := u)) := b

(Pointable u, Adjoint t' t) => Pointable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

point :: a |-> ((t <:<.>:> t') := u)

(Adjoint t t', Extractable u) => Extractable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

extract :: a <-| ((t <:<.>:> t') := u)

(Adjoint t' t, Distributive t) => Liftable (t <:<.>:> t')

Defined in Pandora.Paradigm.Schemes.TUT

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> (t <:<.>:> t') u

(Adjoint t t', Distributive t') => Lowerable (t <:<.>:> t')

Defined in Pandora.Paradigm.Schemes.TUT

Methods

lower :: forall (u :: Type -> Type). Covariant u => (t <:<.>:> t') u ~> u

(Covariant ((t <:<.>:> u) t'), Covariant ((v <:<.>:> w) v'), Adjoint t w, Adjoint t' v', Adjoint t v, Adjoint u v, Adjoint v' t') => Adjoint ((t <:<.>:> u) t') ((v <:<.>:> w) v')

Defined in Pandora.Paradigm.Schemes

Methods

(-|) :: a -> ((t <:<.>:> u) t' a -> b) -> (v <:<.>:> w) v' b

(|-) :: (t <:<.>:> u) t' a -> (a -> (v <:<.>:> w) v' b) -> b

phi :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b

psi :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b

eta :: a -> ((v <:<.>:> w) v' :. (t <:<.>:> u) t') := a

epsilon :: (((t <:<.>:> u) t' :. (v <:<.>:> w) v') := a) -> a

(-|$) :: Covariant v0 => v0 a -> ((t <:<.>:> u) t' a -> b) -> v0 ((v <:<.>:> w) v' b)

($|-) :: Covariant v0 => v0 ((t <:<.>:> u) t' a) -> (a -> (v <:<.>:> w) v' b) -> v0 b

Interpreted (TUT ct ct' cu t t' u)

Defined in Pandora.Paradigm.Schemes.TUT

Associated Types

type Primary (TUT ct ct' cu t t' u) a

Methods

run :: TUT ct ct' cu t t' u a -> Primary (TUT ct ct' cu t t' u) a

unite :: Primary (TUT ct ct' cu t t' u) a -> TUT ct ct' cu t t' u a

type Primary (TUT ct ct' cu t t' u) a

Defined in Pandora.Paradigm.Schemes.TUT

type Primary (TUT ct ct' cu t t' u) a = (t :. (u :. t')) := a

type (<:<.>:>) = TUT Covariant Covariant Covariant

type (>:<.>:>) = TUT Contravariant Covariant Covariant

type (<:<.>:<) = TUT Covariant Covariant Contravariant

type (>:<.>:<) = TUT Contravariant Covariant Contravariant

type (<:>.<:>) = TUT Covariant Contravariant Covariant

type (>:>.<:>) = TUT Contravariant Contravariant Covariant

type (<:>.<:<) = TUT Covariant Contravariant Contravariant

type (>:>.<:<) = TUT Contravariant Contravariant Contravariant