Pandora.Paradigm.Schemes.UT

Documentation

newtype UT ct cu t u a

Constructors

UT ((u :. t) >>> a)

Instances

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (-->) (:*:) (:*:) t, Monoidal (-->) (-->) (:*:) (:*:) u) => Monoidal (-->) (-->) (:*:) (:*:) (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) --> (t <.:> u) a

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Monoidal (<--) (-->) (:*:) (:*:) t, Monoidal (<--) (-->) (:*:) (:*:) u) => Monoidal (<--) (-->) (:*:) (:*:) (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) <-- (t <.:> u) a

(Semigroupoid m, Covariant m m u, Covariant m m t, Covariant m (Betwixt m m) t, Covariant (Betwixt m m) m u, Interpreted m (t <.:> u)) => Covariant m m (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

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

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

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

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

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

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

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

(<-|-|-) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|--) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|---) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|----) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|-----) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|------) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|-------) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 a)) ((t <.:> u) (u0 b))

(<-|-|-|-) :: (Covariant m (Betwixt m (Betwixt m m)) v, Covariant (Betwixt m (Betwixt m m)) (Betwixt (Betwixt m m) m) u0, Covariant (Betwixt (Betwixt m m) m) m (t <.:> u)) => m a b -> m ((t <.:> u) (u0 (v a))) ((t <.:> u) (u0 (v b)))

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) u, Semimonoidal (-->) (:*:) (:+:) t) => Semimonoidal (-->) (:*:) (:+:) (t <.:> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.UT

Methods

mult :: forall (a :: k) (b :: k). ((t <.:> u) a :*: (t <.:> u) b) --> (t <.:> u) (a :+: b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <.:> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.UT

Methods

mult :: forall (a :: k) (b :: k). ((t <.:> u) a :*: (t <.:> u) b) --> (t <.:> u) (a :*: b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <.:> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.UT

Methods

mult :: forall (a :: k) (b :: k). ((t <.:> u) a :*: (t <.:> u) b) <-- (t <.:> u) (a :*: b)

(Monoidal (-->) (-->) (:*:) (:*:) u, Bindable ((->) :: Type -> Type -> Type) u) => Catchable e (Conclusion e <.:> u :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

catch :: forall (a :: k). (Conclusion e <.:> u) a -> (e -> (Conclusion e <.:> u) a) -> (Conclusion e <.:> u) a

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(Semigroup e, Extendable ((->) :: Type -> Type -> Type) u) => Extendable ((->) :: Type -> Type -> Type) (((->) e :: Type -> Type) <.:> u)

Defined in Pandora.Paradigm.Inventory.Some.Imprint

Methods

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

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

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

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

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

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

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

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

(Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Bindable ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (-->) (:*:) (:*:) u, Bindable ((->) :: Type -> Type -> Type) u) => Bindable ((->) :: Type -> Type -> Type) (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

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

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

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

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

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

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

Monoidal (-->) (-->) (:*:) (:*:) t => Liftable ((->) :: Type -> Type -> Type) (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lift :: Covariant (->) (->) u => u a -> UT Covariant Covariant t u a

Monoidal (<--) (-->) (:*:) (:*:) t => Lowerable ((->) :: Type -> Type -> Type) (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lower :: Covariant (->) (->) u => UT Covariant Covariant t u a -> u a

Interpreted ((->) :: Type -> Type -> Type) (UT ct cu t u)

Defined in Pandora.Paradigm.Schemes.UT

Associated Types

type Primary (UT ct cu t u) a

Methods

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

unite :: ((->) < Primary (UT ct cu t u) a) < UT ct cu t u a

(<~~~~~~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~~~~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~~~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(<~) :: ((->) < UT ct cu t u a) < Primary (UT ct cu t u) a

(=#-) :: (Semigroupoid (->), Interpreted (->) u0) => (((->) < Primary (UT ct cu t u) a) < Primary u0 b) -> ((->) < UT ct cu t u a) < u0 b

(-#=) :: (Semigroupoid (->), Interpreted (->) u0) => (((->) < UT ct cu t u a) < u0 b) -> ((->) < Primary (UT ct cu t u) a) < Primary u0 b

(<$=#-) :: (Semigroupoid (->), Covariant (->) (->) j, Interpreted (->) u0) => (((->) < Primary (UT ct cu t u) a) < Primary u0 b) -> (j > UT ct cu t u a) -> (j > u0 b)

(-#=$>) :: (Covariant (->) (->) j, Interpreted (->) u0) => (((->) < UT ct cu t u a) < u0 b) -> (j > Primary (UT ct cu t u) a) -> (j > Primary u0 b)

type Primary (UT ct cu t u) a

Defined in Pandora.Paradigm.Schemes.UT

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

type (<.:>) = UT Covariant Covariant infixr 3

type (>.:>) = UT Contravariant Covariant infixr 3

type (<.:<) = UT Covariant Contravariant infixr 3

type (>.:<) = UT Contravariant Contravariant infixr 3