Pandora.Paradigm.Schemes.TUT

Documentation

newtype TUT ct ct' cu t t' u a

Constructors

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

Instances

(Bindable ((->) :: Type -> Type -> Type) u, Monoidal (-->) (-->) (:*:) (:*:) u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t' t) => Monoidal (-->) (-->) (:*:) (:*:) ((t <:<.>:> t') >>>>>>>> u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) --> ((t <:<.>:> t') >>>>>>>> u) a

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) t', Monoidal (<--) (-->) (:*:) (:*:) u, Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t t') => Monoidal (<--) (-->) (:*:) (:*:) ((t <:<.>:> t') >>>>>>>> u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

unit :: Proxy (:*:) -> (Unit (:*:) --> a) <-- ((t <:<.>:> t') >>>>>>>> u) a

(Semigroupoid m, Covariant m m t, Covariant (Betwixt (Betwixt m m) m) m t, Covariant (Betwixt m (Betwixt m m)) (Betwixt (Betwixt m m) m) u, Covariant m (Betwixt m (Betwixt m m)) t', Interpreted m ((t <:<.>:> t') >>>>>>>> u)) => Covariant m m ((t <:<.>:> t') >>>>>>>> u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

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

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

(<-|-|-) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

(<-|-|--) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

(<-|-|---) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

(<-|-|----) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

(<-|-|-----) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

(<-|-|------) :: (Covariant m (Betwixt m m) u0, Covariant (Betwixt m m) m ((t <:<.>:> t') >>>>>>>> u)) => m a b -> m (((t <:<.>:> t') >>>>>>>> u) (u0 a)) (((t <:<.>:> t') >>>>>>>> u) (u0 b))

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

(Adjoint ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t' t, Bindable ((->) :: Type -> Type -> Type) u) => Semimonoidal (-->) (:*:) (:*:) ((t <:<.>:> t') >>>>>>>> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

mult :: forall (a :: k) (b :: k). (((t <:<.>:> t') >>>>>>>> u) a :*: ((t <:<.>:> t') >>>>>>>> u) b) --> ((t <:<.>:> t') >>>>>>>> u) (a :*: b)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (<--) (:*:) (:*:) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Semimonoidal (<--) (:*:) (:*:) u, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t', Semimonoidal (<--) (:*:) (:*:) t') => Semimonoidal (<--) (:*:) (:*:) ((t <:<.>:> t') >>>>>>>> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

mult :: forall (a :: k) (b :: k). (((t <:<.>:> t') >>>>>>>> u) a :*: ((t <:<.>:> t') >>>>>>>> u) b) <-- ((t <:<.>:> t') >>>>>>>> u) (a :*: b)

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

Interpreted ((->) :: Type -> Type -> Type) (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

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

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

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

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

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

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

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

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

(=#-) :: (Semigroupoid (->), Interpreted (->) u0) => (((->) < Primary (TUT ct ct' cu t t' u) a) < Primary u0 b) -> ((->) < TUT ct ct' cu t t' u a) < u0 b

(-#=) :: (Semigroupoid (->), Interpreted (->) u0) => (((->) < TUT ct ct' cu t t' u a) < u0 b) -> ((->) < Primary (TUT ct ct' cu t t' u) a) < Primary u0 b

(<$=#-) :: (Semigroupoid (->), Covariant (->) (->) j, Interpreted (->) u0) => (((->) < Primary (TUT ct ct' cu t t' u) a) < Primary u0 b) -> (j > TUT ct ct' cu t t' u a) -> (j > u0 b)

(-#=$>) :: (Covariant (->) (->) j, Interpreted (->) u0) => (((->) < TUT ct ct' cu t t' u a) < u0 b) -> (j > Primary (TUT ct ct' cu t t' u) a) -> (j > Primary u0 b)

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 infix 3

type (>:<.>:>) = TUT Contravariant Covariant Covariant infix 3

type (<:<.>:<) = TUT Covariant Covariant Contravariant infix 3

type (>:<.>:<) = TUT Contravariant Covariant Contravariant infix 3

type (<:>.<:>) = TUT Covariant Contravariant Covariant infix 3

type (>:>.<:>) = TUT Contravariant Contravariant Covariant infix 3

type (<:>.<:<) = TUT Covariant Contravariant Contravariant infix 3

type (>:>.<:<) = TUT Contravariant Contravariant Contravariant infix 3

product_over_sum :: ((s :*: a) :+: (s :*: b)) -> s :*: (a :+: b)