Pandora.Pattern.Functor.Covariant

Documentation

class (Semigroupoid source, Semigroupoid target) => Covariant source target t where

When providing a new instance, you should ensure it satisfies:
* Identity morphism: (identity <-|-) ≡ identity
* Interpreted of morphisms: (f . g <-|-) ≡ (f <-|-) . (g <-|-)

Minimal complete definition

(<-|-)

Methods

(<-|-) :: source a b -> target (t a) (t b) infixl 4

(<-|-|-) :: (Covariant source (Betwixt source target) u, Covariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) infixl 3

(<-|-|-|-) :: (Covariant source (Betwixt source (Betwixt source target)) v, Covariant (Betwixt source (Betwixt source target)) (Betwixt (Betwixt source target) target) u, Covariant (Betwixt (Betwixt source target) target) target t) => source a b -> target (t (u (v a))) (t (u (v b))) infixl 2

Instances

Stack List

Defined in Pandora.Paradigm.Structure.Some.List

Zippable List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Breadcrumbs List :: Type -> Type

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t', Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) t) => Monoidal (-->) (-->) (:*:) (:+:) (t <::> t')

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (-->) (:*:) (:*:) ((Identity <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Methods

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

(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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Monoidal (<--) (-->) (:*:) (:*:) t, Monoidal (<--) (-->) (:*:) (:*:) t') => Monoidal (<--) (-->) (:*:) (:*:) (t <::> t')

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

(Covariant m m t, Interpreted m (Turnover t)) => Covariant m m (Turnover t)

Defined in Pandora.Paradigm.Structure.Modification.Turnover

Methods

(<-|-) :: m a b -> m (Turnover t a) (Turnover t b)

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

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

(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)

(<-|-|-) :: (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)))

(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)

(<-|-|-) :: (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)))

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

(<-|-) :: 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 (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)))

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

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

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

Covariant m m t => Covariant m (Straight m) t

Defined in Pandora.Pattern.Morphism.Straight

Methods

(<-|-) :: m a b -> Straight m (t a) (t b)

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

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

Monotonic a ((t :. Construction t) := a) => Monotonic a ((t <::> Construction t) := a)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

reduce :: (a -> r -> r) -> r -> ((t <::> Construction t) := a) -> r

resolve :: (a -> r) -> r -> ((t <::> Construction t) := a) -> r

Semigroup (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(+) :: List a -> List a -> List a

Monoid (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

zero :: List a

Setoid a => Setoid (List a)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

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

(!=) :: List a -> List a -> Boolean

Nullable Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Methods

null :: forall (a :: k). (Predicate :. Binary) := a

Nullable List

Defined in Pandora.Paradigm.Structure.Some.List

Methods

null :: forall (a :: k). (Predicate :. List) := a

Nullable Rose

Defined in Pandora.Paradigm.Structure.Some.Rose

Methods

null :: forall (a :: k). (Predicate :. Rose) := a

Covariant m m t => Covariant (Straight m) m t

Defined in Pandora.Pattern.Morphism.Straight

Methods

(<-|-) :: Straight m a b -> m (t a) (t b)

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

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

Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap ((t <:.:> t) := (:*:)) :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

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

Defined in Pandora.Paradigm.Primary

Methods

mult :: forall (a :: k) (b :: k). (((t <:.:> u) := (:*:)) a :*: ((t <:.:> u) := (:*:)) b) --> ((t <:.:> 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) 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) t, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <:.> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

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

Defined in Pandora.Paradigm.Primary.Algebraic

Methods

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

Semimonoidal (<--) (:*:) (:*:) t => Semimonoidal (<--) (:*:) (:*:) ((Identity <:.:> t) := (:*:) :: Type -> Type)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Methods

mult :: forall (a :: k) (b :: k). (((Identity <:.:> t) := (:*:)) a :*: ((Identity <:.:> t) := (:*:)) b) <-- ((Identity <:.:> t) := (:*:)) (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) 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) t, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:.> u :: Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

mult :: forall (a :: k) (b :: k). ((t <::> t') a :*: (t <::> t') b) <-- (t <::> t') (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 m m t => Covariant (Straight m) (Straight m) t

Defined in Pandora.Pattern.Morphism.Straight

Methods

(<-|-) :: Straight m a b -> Straight m (t a) (t b)

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

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

(Category m, Covariant m m t) => Covariant (Flip m) (Flip m) t

Defined in Pandora.Pattern.Morphism.Flip

Methods

(<-|-) :: Flip m a b -> Flip m (t a) (t b)

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

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

Morphable ('Into (Tape List)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tape List)) List :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tape List)) <::> List) ~> Morphing ('Into (Tape List)) List

Morphable ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Delete 'All) List :: Type -> Type

Methods

morphing :: (Tagged ('Delete 'All) <::> List) ~> Morphing ('Delete 'All) List

Morphable ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Delete 'First) List :: Type -> Type

Methods

morphing :: (Tagged ('Delete 'First) <::> List) ~> Morphing ('Delete 'First) List

Morphable ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Find 'Element) List :: Type -> Type

Methods

morphing :: (Tagged ('Find 'Element) <::> List) ~> Morphing ('Find 'Element) List

Morphable ('Into (o ds)) (Construction Wye) => Morphable ('Into (o ds) :: Morph a) Binary

Defined in Pandora.Paradigm.Structure

Associated Types

type Morphing ('Into (o ds)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Into (o ds)) <::> Binary) ~> Morphing ('Into (o ds)) Binary

Morphable ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right 'Zig)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right 'Zig)) <::> Binary) ~> Morphing ('Rotate ('Right 'Zig)) Binary

Morphable ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left 'Zig)) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left 'Zig)) <::> Binary) ~> Morphing ('Rotate ('Left 'Zig)) Binary

Morphable ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right ('Zig 'Zag))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right ('Zig 'Zag))) <::> Binary) ~> Morphing ('Rotate ('Right ('Zig 'Zag))) Binary

Morphable ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left ('Zig 'Zag))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left ('Zig 'Zag))) <::> Binary) ~> Morphing ('Rotate ('Left ('Zig 'Zag))) Binary

Morphable ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Right ('Zig 'Zig))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Right ('Zig 'Zig))) <::> Binary) ~> Morphing ('Rotate ('Right ('Zig 'Zig))) Binary

Morphable ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

Associated Types

type Morphing ('Rotate ('Left ('Zig 'Zig))) Binary :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Left ('Zig 'Zig))) <::> Binary) ~> Morphing ('Rotate ('Left ('Zig 'Zig))) Binary

Morphable ('Into (Construction Maybe)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Construction Maybe)) (Tape (Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Construction Maybe)) <::> Tape (Construction Maybe)) ~> Morphing ('Into (Construction Maybe)) (Tape (Construction Maybe))

Morphable ('Into (Comprehension Maybe)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Comprehension Maybe)) (Tape List) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Comprehension Maybe)) <::> Tape List) ~> Morphing ('Into (Comprehension Maybe)) (Tape List)

Morphable ('Into (Tape (Construction Maybe))) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tape (Construction Maybe))) (Tape List) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tape (Construction Maybe))) <::> Tape List) ~> Morphing ('Into (Tape (Construction Maybe))) (Tape List)

Morphable ('Into (Tape List)) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tape List)) (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tape List)) <::> Construction Maybe) ~> Morphing ('Into (Tape List)) (Construction Maybe)

Morphable ('Into (Tape List)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into (Tape List)) (Tape (Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Into (Tape List)) <::> Tape (Construction Maybe)) ~> Morphing ('Into (Tape List)) (Tape (Construction Maybe))

Morphable ('Into Binary) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Into Binary) (Construction Wye) :: Type -> Type

Methods

morphing :: (Tagged ('Into Binary) <::> Construction Wye) ~> Morphing ('Into Binary) (Construction Wye)

Morphable ('Into List) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <::> Construction Maybe) ~> Morphing ('Into List) (Construction Maybe)

Morphable ('Into List) (Vector r)

Defined in Pandora.Paradigm.Structure

Associated Types

type Morphing ('Into List) (Vector r) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <::> Vector r) ~> Morphing ('Into List) (Vector r)

Morphable ('Into List) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Tape (Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <::> Tape (Construction Maybe)) ~> Morphing ('Into List) (Tape (Construction Maybe))

Morphable ('Into List) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Tape List) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <::> Tape List) ~> Morphing ('Into List) (Tape List)

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream)

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Right) (Tape Stream) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <::> Tape Stream) ~> Morphing ('Rotate 'Right) (Tape Stream)

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream)

Defined in Pandora.Paradigm.Structure.Some.Stream

Associated Types

type Morphing ('Rotate 'Left) (Tape Stream) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <::> Tape Stream) ~> Morphing ('Rotate 'Left) (Tape Stream)

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) (Tape (Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <::> Tape (Construction Maybe)) ~> Morphing ('Rotate 'Right) (Tape (Construction Maybe))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) (Tape (Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <::> Tape (Construction Maybe)) ~> Morphing ('Rotate 'Left) (Tape (Construction Maybe))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) (Tape List) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <::> Tape List) ~> Morphing ('Rotate 'Right) (Tape List)

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) (Tape List) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <::> Tape List) ~> Morphing ('Rotate 'Left) (Tape List)

Chain k => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Lookup 'Key) (Prefixed Binary k) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <::> Prefixed Binary k) ~> Morphing ('Lookup 'Key) (Prefixed Binary k)

Setoid key => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Lookup 'Key) (Prefixed List key) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <::> Prefixed List key) ~> Morphing ('Lookup 'Key) (Prefixed List key)

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Right) (Turnover (Tape List)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <::> Turnover (Tape List)) ~> Morphing ('Rotate 'Right) (Turnover (Tape List))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List))

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Rotate 'Left) (Turnover (Tape List)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <::> Turnover (Tape List)) ~> Morphing ('Rotate 'Left) (Turnover (Tape List))

Setoid k => Morphable ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Morphing ('Lookup 'Key) (Prefixed Rose k) :: Type -> Type

Methods

morphing :: (Tagged ('Lookup 'Key) <::> Prefixed Rose k) ~> Morphing ('Lookup 'Key) (Prefixed Rose k)

Morphable ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

Associated Types

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Into Wye) <::> ((Maybe <:.:> Maybe) := (:*:))) ~> Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Morphable ('Into List) (Construction Maybe <::> Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing ('Into List) (Construction Maybe <::> Maybe) :: Type -> Type

Methods

morphing :: (Tagged ('Into List) <::> (Construction Maybe <::> Maybe)) ~> Morphing ('Into List) (Construction Maybe <::> Maybe)

Morphable ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate 'Up) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Up) <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))) ~> Morphing ('Rotate 'Up) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Right)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Right)) <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Right)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Morphable ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing ('Rotate ('Down 'Left)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate ('Down 'Left)) <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))) ~> Morphing ('Rotate ('Down 'Left)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

(/|\) :: Covariant (->) (->) u => (forall a. u a -> v a) -> forall (a :: k). TU Covariant Covariant t u a -> TU Covariant Covariant t v a

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

(/|\) :: Covariant (->) (->) u => (forall a. u a -> v a) -> forall (a :: k). TT Covariant Covariant t u a -> TT Covariant Covariant t v a

Extendable ((->) :: Type -> Type -> Type) (Tape Stream)

Defined in Pandora.Paradigm.Structure.Some.Stream

Methods

(<<=) :: (Tape Stream a -> b) -> Tape Stream a -> Tape Stream b

Extendable ((->) :: Type -> Type -> Type) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(<<=) :: (Tape List a -> b) -> Tape List a -> Tape List b

Morphable ('Insert :: a -> Morph a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Morphing 'Insert Binary :: Type -> Type

Methods

morphing :: (Tagged 'Insert <::> Binary) ~> Morphing 'Insert Binary

Morphable ('Pop :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing 'Pop List :: Type -> Type

Methods

morphing :: (Tagged 'Pop <::> List) ~> Morphing 'Pop List

Morphable ('Push :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Morphing 'Push List :: Type -> Type

Methods

morphing :: (Tagged 'Push <::> List) ~> Morphing 'Push List

Substructure ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Available 'Right Binary :: Type -> Type

type Substance 'Right Binary :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Binary) #=@ Substance 'Right Binary) := Available 'Right Binary

sub :: (Binary #=@ Substance 'Right Binary) := Available 'Right Binary

Substructure ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

Associated Types

type Available 'Left Binary :: Type -> Type

type Substance 'Left Binary :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Binary) #=@ Substance 'Left Binary) := Available 'Left Binary

sub :: (Binary #=@ Substance 'Left Binary) := Available 'Left Binary

Substructure ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Available 'Tail List :: Type -> Type

type Substance 'Tail List :: Type -> Type

Methods

substructure :: ((Tagged 'Tail <:.> List) #=@ Substance 'Tail List) := Available 'Tail List

sub :: (List #=@ Substance 'Tail List) := Available 'Tail List

Substructure ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

Associated Types

type Available 'Root List :: Type -> Type

type Substance 'Root List :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> List) #=@ Substance 'Root List) := Available 'Root List

sub :: (List #=@ Substance 'Root List) := Available 'Root List

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Right (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Right (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Right (Tap ((t <:.:> t) := (:*:)))) := Available 'Right (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Right (Tap ((t <:.:> t) := (:*:)))) := Available 'Right (Tap ((t <:.:> t) := (:*:)))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Left (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Left (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Left (Tap ((t <:.:> t) := (:*:)))) := Available 'Left (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Left (Tap ((t <:.:> t) := (:*:)))) := Available 'Left (Tap ((t <:.:> t) := (:*:)))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Associated Types

type Available 'Root (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

type Substance 'Root (Tap ((t <:.:> t) := (:*:))) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Tap ((t <:.:> t) := (:*:))) #=@ Substance 'Root (Tap ((t <:.:> t) := (:*:)))) := Available 'Root (Tap ((t <:.:> t) := (:*:)))

sub :: (Tap ((t <:.:> t) := (:*:)) #=@ Substance 'Root (Tap ((t <:.:> t) := (:*:)))) := Available 'Root (Tap ((t <:.:> t) := (:*:)))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Right (Tape t) :: Type -> Type

type Substance 'Right (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> Tape t) #=@ Substance 'Right (Tape t)) := Available 'Right (Tape t)

sub :: (Tape t #=@ Substance 'Right (Tape t)) := Available 'Right (Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Left (Tape t) :: Type -> Type

type Substance 'Left (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> Tape t) #=@ Substance 'Left (Tape t)) := Available 'Left (Tape t)

sub :: (Tape t #=@ Substance 'Left (Tape t)) := Available 'Left (Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Root (Tape t) :: Type -> Type

type Substance 'Root (Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Tape t) #=@ Substance 'Root (Tape t)) := Available 'Root (Tape t)

sub :: (Tape t #=@ Substance 'Root (Tape t)) := Available 'Root (Tape t)

Substructure ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Available 'Tail (Construction List) :: Type -> Type

type Substance 'Tail (Construction List) :: Type -> Type

Methods

substructure :: ((Tagged 'Tail <:.> Construction List) #=@ Substance 'Tail (Construction List)) := Available 'Tail (Construction List)

sub :: (Construction List #=@ Substance 'Tail (Construction List)) := Available 'Tail (Construction List)

Substructure ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

Associated Types

type Available 'Root (Construction List) :: Type -> Type

type Substance 'Root (Construction List) :: Type -> Type

Methods

substructure :: ((Tagged 'Root <:.> Construction List) #=@ Substance 'Root (Construction List)) := Available 'Root (Construction List)

sub :: (Construction List #=@ Substance 'Root (Construction List)) := Available 'Root (Construction List)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure ('Right :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Right (Tape t <::> Tape t) :: Type -> Type

type Substance 'Right (Tape t <::> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> (Tape t <::> Tape t)) #=@ Substance 'Right (Tape t <::> Tape t)) := Available 'Right (Tape t <::> Tape t)

sub :: ((Tape t <::> Tape t) #=@ Substance 'Right (Tape t <::> Tape t)) := Available 'Right (Tape t <::> Tape t)

(Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure ('Left :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Left (Tape t <::> Tape t) :: Type -> Type

type Substance 'Left (Tape t <::> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> (Tape t <::> Tape t)) #=@ Substance 'Left (Tape t <::> Tape t)) := Available 'Left (Tape t <::> Tape t)

sub :: ((Tape t <::> Tape t) #=@ Substance 'Left (Tape t <::> Tape t)) := Available 'Left (Tape t <::> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Down :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Down (Tape t <::> Tape t) :: Type -> Type

type Substance 'Down (Tape t <::> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Down <:.> (Tape t <::> Tape t)) #=@ Substance 'Down (Tape t <::> Tape t)) := Available 'Down (Tape t <::> Tape t)

sub :: ((Tape t <::> Tape t) #=@ Substance 'Down (Tape t <::> Tape t)) := Available 'Down (Tape t <::> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Up :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

Associated Types

type Available 'Up (Tape t <::> Tape t) :: Type -> Type

type Substance 'Up (Tape t <::> Tape t) :: Type -> Type

Methods

substructure :: ((Tagged 'Up <:.> (Tape t <::> Tape t)) #=@ Substance 'Up (Tape t <::> Tape t)) := Available 'Up (Tape t <::> Tape t)

sub :: ((Tape t <::> Tape t) #=@ Substance 'Up (Tape t <::> Tape t)) := Available 'Up (Tape t <::> Tape t)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

Associated Types

type Available 'Right ((t <:.:> t) := (:*:)) :: Type -> Type

type Substance 'Right ((t <:.:> t) := (:*:)) :: Type -> Type

Methods

substructure :: ((Tagged 'Right <:.> ((t <:.:> t) := (:*:))) #=@ Substance 'Right ((t <:.:> t) := (:*:))) := Available 'Right ((t <:.:> t) := (:*:))

sub :: (((t <:.:> t) := (:*:)) #=@ Substance 'Right ((t <:.:> t) := (:*:))) := Available 'Right ((t <:.:> t) := (:*:))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Substructure ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

Associated Types

type Available 'Left ((t <:.:> t) := (:*:)) :: Type -> Type

type Substance 'Left ((t <:.:> t) := (:*:)) :: Type -> Type

Methods

substructure :: ((Tagged 'Left <:.> ((t <:.:> t) := (:*:))) #=@ Substance 'Left ((t <:.:> t) := (:*:))) := Available 'Left ((t <:.:> t) := (:*:))

sub :: (((t <:.:> t) := (:*:)) #=@ Substance 'Left ((t <:.:> t) := (:*:))) := Available 'Left ((t <:.:> t) := (:*:))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Wye

Defined in Pandora.Paradigm.Primary.Functor.Wye

Methods

(<-|-) :: (a -> b) -> Wye a -> Wye b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Wye) => (a -> b) -> Wye (u a) -> Wye (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Wye) => (a -> b) -> Wye (u (v a)) -> Wye (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(<-|-) :: (a -> b) -> Identity a -> Identity b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Identity) => (a -> b) -> Identity (u a) -> Identity (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Identity) => (a -> b) -> Identity (u (v a)) -> Identity (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Edges

Defined in Pandora.Paradigm.Primary.Functor.Edges

Methods

(<-|-) :: (a -> b) -> Edges a -> Edges b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Edges) => (a -> b) -> Edges (u a) -> Edges (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Edges) => (a -> b) -> Edges (u (v a)) -> Edges (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Maybe

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

(<-|-) :: (a -> b) -> Maybe a -> Maybe b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Maybe) => (a -> b) -> Maybe (u a) -> Maybe (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Maybe) => (a -> b) -> Maybe (u (v a)) -> Maybe (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) Biforked

Defined in Pandora.Paradigm.Structure.Some.Binary

Methods

(<-|-) :: (a -> b) -> Biforked a -> Biforked b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Biforked) => (a -> b) -> Biforked (u a) -> Biforked (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Biforked) => (a -> b) -> Biforked (u (v a)) -> Biforked (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((-->) b)

Defined in Pandora.Paradigm.Primary.Algebraic.Exponential

Methods

(<-|-) :: (a -> b0) -> (b --> a) -> (b --> b0)

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) ((-->) b)) => (a -> b0) -> (b --> u a) -> (b --> u b0)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) ((-->) b)) => (a -> b0) -> (b --> u (v a)) -> (b --> u (v b0))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Proxy

Methods

(<-|-) :: (a -> b) -> Proxy a -> Proxy b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) Proxy) => (a -> b) -> Proxy (u a) -> Proxy (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) Proxy) => (a -> b) -> Proxy (u (v a)) -> Proxy (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Yoneda t)

Defined in Pandora.Paradigm.Primary.Transformer.Yoneda

Methods

(<-|-) :: (a -> b) -> Yoneda t a -> Yoneda t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Yoneda t)) => (a -> b) -> Yoneda t (u a) -> Yoneda t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Outline t)

Defined in Pandora.Paradigm.Primary.Transformer.Outline

Methods

(<-|-) :: (a -> b) -> Outline t a -> Outline t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Outline t)) => (a -> b) -> Outline t (u a) -> Outline t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((:+:) o)

Defined in Pandora.Paradigm.Primary.Algebraic.Sum

Methods

(<-|-) :: (a -> b) -> (o :+: a) -> (o :+: b)

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) ((:+:) o)) => (a -> b) -> (o :+: u a) -> (o :+: u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) ((:+:) o)) => (a -> b) -> (o :+: u (v a)) -> (o :+: u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((:*:) s)

Defined in Pandora.Paradigm.Primary.Algebraic.Product

Methods

(<-|-) :: (a -> b) -> (s :*: a) -> (s :*: b)

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) ((:*:) s)) => (a -> b) -> (s :*: u a) -> (s :*: u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) ((:*:) s)) => (a -> b) -> (s :*: u (v a)) -> (s :*: u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Jet t)

Defined in Pandora.Paradigm.Primary.Transformer.Jet

Methods

(<-|-) :: (a -> b) -> Jet t a -> Jet t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Jet t)) => (a -> b) -> Jet t (u a) -> Jet t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Jack t)

Defined in Pandora.Paradigm.Primary.Transformer.Jack

Methods

(<-|-) :: (a -> b) -> Jack t a -> Jack t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Jack t)) => (a -> b) -> Jack t (u a) -> Jack t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Wedge e)

Defined in Pandora.Paradigm.Primary.Functor.Wedge

Methods

(<-|-) :: (a -> b) -> Wedge e a -> Wedge e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Wedge e)) => (a -> b) -> Wedge e (u a) -> Wedge e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Wedge e)) => (a -> b) -> Wedge e (u (v a)) -> Wedge e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Validation e)

Defined in Pandora.Paradigm.Primary.Functor.Validation

Methods

(<-|-) :: (a -> b) -> Validation e a -> Validation e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Validation e)) => (a -> b) -> Validation e (u a) -> Validation e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Validation e)) => (a -> b) -> Validation e (u (v a)) -> Validation e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (These e)

Defined in Pandora.Paradigm.Primary.Functor.These

Methods

(<-|-) :: (a -> b) -> These e a -> These e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (These e)) => (a -> b) -> These e (u a) -> These e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (These e)) => (a -> b) -> These e (u (v a)) -> These e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Instruction t)

Defined in Pandora.Paradigm.Primary.Transformer.Instruction

Methods

(<-|-) :: (a -> b) -> Instruction t a -> Instruction t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Instruction t)) => (a -> b) -> Instruction t (u a) -> Instruction t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<-|-) :: (a -> b) -> Construction t a -> Construction t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Construction t)) => (a -> b) -> Construction t (u a) -> Construction t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Conclusion e)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

(<-|-) :: (a -> b) -> Conclusion e a -> Conclusion e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Conclusion e)) => (a -> b) -> Conclusion e (u a) -> Conclusion e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Conclusion e)) => (a -> b) -> Conclusion e (u (v a)) -> Conclusion e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <::> Construction t) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Comprehension t)

Defined in Pandora.Paradigm.Structure.Modification.Comprehension

Methods

(<-|-) :: (a -> b) -> Comprehension t a -> Comprehension t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Comprehension t)) => (a -> b) -> Comprehension t (u a) -> Comprehension t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Store s)

Defined in Pandora.Paradigm.Inventory.Some.Store

Methods

(<-|-) :: (a -> b) -> Store s a -> Store s b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Store s)) => (a -> b) -> Store s (u a) -> Store s (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Store s)) => (a -> b) -> Store s (u (v a)) -> Store s (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tap t)

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

(<-|-) :: (a -> b) -> Tap t a -> Tap t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Tap t)) => (a -> b) -> Tap t (u a) -> Tap t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (State s)

Defined in Pandora.Paradigm.Inventory.Some.State

Methods

(<-|-) :: (a -> b) -> State s a -> State s b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (State s)) => (a -> b) -> State s (u a) -> State s (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (State s)) => (a -> b) -> State s (u (v a)) -> State s (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Provision e)

Defined in Pandora.Paradigm.Inventory.Some.Provision

Methods

(<-|-) :: (a -> b) -> Provision e a -> Provision e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Provision e)) => (a -> b) -> Provision e (u a) -> Provision e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Provision e)) => (a -> b) -> Provision e (u (v a)) -> Provision e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Imprint e)

Defined in Pandora.Paradigm.Inventory.Some.Imprint

Methods

(<-|-) :: (a -> b) -> Imprint e a -> Imprint e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Imprint e)) => (a -> b) -> Imprint e (u a) -> Imprint e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Imprint e)) => (a -> b) -> Imprint e (u (v a)) -> Imprint e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Equipment e)

Defined in Pandora.Paradigm.Inventory.Some.Equipment

Methods

(<-|-) :: (a -> b) -> Equipment e a -> Equipment e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Equipment e)) => (a -> b) -> Equipment e (u a) -> Equipment e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Equipment e)) => (a -> b) -> Equipment e (u (v a)) -> Equipment e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Accumulator e)

Defined in Pandora.Paradigm.Inventory.Some.Accumulator

Methods

(<-|-) :: (a -> b) -> Accumulator e a -> Accumulator e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Accumulator e)) => (a -> b) -> Accumulator e (u a) -> Accumulator e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Accumulator e)) => (a -> b) -> Accumulator e (u (v a)) -> Accumulator e (u (v b))

Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> Tape List a -> u (Tape List b)

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (Constant :: Type -> Type -> Type) b)

Defined in Pandora.Paradigm.Primary.Functor.Constant

Methods

(<-|-) :: (a -> b0) -> Flip Constant b a -> Flip Constant b b0

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip Constant b)) => (a -> b0) -> Flip Constant b (u a) -> Flip Constant b (u b0)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip Constant b)) => (a -> b0) -> Flip Constant b (u (v a)) -> Flip Constant b (u (v b0))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (:+:) a)

Defined in Pandora.Paradigm.Primary.Algebraic.Sum

Methods

(<-|-) :: (a0 -> b) -> Flip (:+:) a a0 -> Flip (:+:) a b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip (:+:) a)) => (a0 -> b) -> Flip (:+:) a (u a0) -> Flip (:+:) a (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip (:+:) a)) => (a0 -> b) -> Flip (:+:) a (u (v a0)) -> Flip (:+:) a (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (:*:) a)

Defined in Pandora.Paradigm.Primary.Algebraic.Product

Methods

(<-|-) :: (a0 -> b) -> Flip (:*:) a a0 -> Flip (:*:) a b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip (:*:) a)) => (a0 -> b) -> Flip (:*:) a (u a0) -> Flip (:*:) a (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip (:*:) a)) => (a0 -> b) -> Flip (:*:) a (u (v a0)) -> Flip (:*:) a (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip Validation a)

Defined in Pandora.Paradigm.Primary.Functor.Validation

Methods

(<-|-) :: (a0 -> b) -> Flip Validation a a0 -> Flip Validation a b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip Validation a)) => (a0 -> b) -> Flip Validation a (u a0) -> Flip Validation a (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip Validation a)) => (a0 -> b) -> Flip Validation a (u (v a0)) -> Flip Validation a (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip (Tagged :: Type -> Type -> Type) a)

Defined in Pandora.Paradigm.Primary.Functor.Tagged

Methods

(<-|-) :: (a0 -> b) -> Flip Tagged a a0 -> Flip Tagged a b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip Tagged a)) => (a0 -> b) -> Flip Tagged a (u a0) -> Flip Tagged a (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip Tagged a)) => (a0 -> b) -> Flip Tagged a (u (v a0)) -> Flip Tagged a (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip Conclusion e)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

(<-|-) :: (a -> b) -> Flip Conclusion e a -> Flip Conclusion e b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Flip Conclusion e)) => (a -> b) -> Flip Conclusion e (u a) -> Flip Conclusion e (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Flip Conclusion e)) => (a -> b) -> Flip Conclusion e (u (v a)) -> Flip Conclusion e (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Day t u)

Defined in Pandora.Paradigm.Primary.Transformer.Day

Methods

(<-|-) :: (a -> b) -> Day t u a -> Day t u b

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

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Constant

Methods

(<-|-) :: (a0 -> b) -> Constant a a0 -> Constant a b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Constant a)) => (a0 -> b) -> Constant a (u a0) -> Constant a (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Constant a)) => (a0 -> b) -> Constant a (u (v a0)) -> Constant a (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Tagged tag)

Defined in Pandora.Paradigm.Primary.Functor.Tagged

Methods

(<-|-) :: (a -> b) -> Tagged tag a -> Tagged tag b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Tagged tag)) => (a -> b) -> Tagged tag (u a) -> Tagged tag (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Tagged tag)) => (a -> b) -> Tagged tag (u (v a)) -> Tagged tag (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Schematic Monad t u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t :> u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic

Methods

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

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

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

(<-|-) :: (a -> b) -> Backwards t a -> Backwards t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Backwards t)) => (a -> b) -> Backwards t (u a) -> Backwards t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Reverse t)

Defined in Pandora.Paradigm.Primary.Transformer.Reverse

Methods

(<-|-) :: (a -> b) -> Reverse t a -> Reverse t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Reverse t)) => (a -> b) -> Reverse t (u a) -> Reverse t (u b)

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Schematic Comonad t u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t :< u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic

Methods

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

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

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Prefixed t k)

Defined in Pandora.Paradigm.Structure.Modification.Prefixed

Methods

(<-|-) :: (a -> b) -> Prefixed t k a -> Prefixed t k b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Prefixed t k)) => (a -> b) -> Prefixed t k (u a) -> Prefixed t k (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Prefixed t k)) => (a -> b) -> Prefixed t k (u (v a)) -> Prefixed t k (u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((->) a :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Algebraic.Exponential

Methods

(<-|-) :: (a0 -> b) -> (a -> a0) -> (a -> b)

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) ((->) a)) => (a0 -> b) -> (a -> u a0) -> (a -> u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) ((->) a)) => (a0 -> b) -> (a -> u (v a0)) -> (a -> u (v b))

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Continuation r t)

Defined in Pandora.Paradigm.Primary.Transformer.Continuation

Methods

(<-|-) :: (a -> b) -> Continuation r t a -> Continuation r t b

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u, Covariant (Betwixt (->) (->)) (->) (Continuation r t)) => (a -> b) -> Continuation r t (u a) -> Continuation r t (u b)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Continuation r t)) => (a -> b) -> Continuation r t (u (v a)) -> Continuation r t (u (v b))

(Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, forall a. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (p (t a)), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, forall b. Contravariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip p (u b))) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t >:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

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

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

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

(forall i. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (p i), forall o. Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Flip p o), Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) ((t <:.:> u) := p)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

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

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

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

(Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u) => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

(<<-) :: (Covariant (->) (->) u0, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u0) => (a -> u0 b) -> (t <:.> u) a -> u0 ((t <:.> u) b)

(Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t') => Traversable ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (t <::> t')

Defined in Pandora.Paradigm.Schemes.TT

Methods

(<<-) :: (Covariant (->) (->) u, Monoidal (Straight (->)) (Straight (->)) (:*:) (:*:) u) => (a -> u b) -> (t <::> t') a -> u ((t <::> t') 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) 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

(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

(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

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) (Kan ('Right :: Type -> Wye Type) t u b)

Defined in Pandora.Paradigm.Primary.Transformer.Kan

Methods

(<-|-) :: (a -> b0) -> Kan 'Right t u b a -> Kan 'Right t u b b0

(<-|-|-) :: (Covariant (->) (Betwixt (->) (->)) u0, Covariant (Betwixt (->) (->)) (->) (Kan 'Right t u b)) => (a -> b0) -> Kan 'Right t u b (u0 a) -> Kan 'Right t u b (u0 b0)

(<-|-|-|-) :: (Covariant (->) (Betwixt (->) (Betwixt (->) (->))) v, Covariant (Betwixt (->) (Betwixt (->) (->))) (Betwixt (Betwixt (->) (->)) (->)) u0, Covariant (Betwixt (Betwixt (->) (->)) (->)) (->) (Kan 'Right t u b)) => (a -> b0) -> Kan 'Right t u b (u0 (v a)) -> Kan 'Right t u b (u0 (v b0))

(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

(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

(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

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

Defined in Pandora.Paradigm.Inventory.Some.Equipment

Methods

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

(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

(Bindable ((->) :: Type -> Type -> Type) t, Distributive ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) u, Bindable ((->) :: Type -> Type -> Type) u) => Bindable ((->) :: Type -> Type -> Type) (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

(Bindable ((->) :: Type -> Type -> Type) t, Distributive ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t, Covariant ((->) :: Type -> Type -> Type) ((->) :: Type -> Type -> Type) t', Bindable ((->) :: Type -> Type -> Type) t') => Bindable ((->) :: Type -> Type -> Type) (t <::> t')

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

lift :: Covariant (->) (->) u => u a -> TT 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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TT

Methods

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

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Nonempty Binary = Construction Wye

type Nonempty List

Defined in Pandora.Paradigm.Structure.Some.List

type Nonempty List = Construction Maybe

type Nonempty Rose

Defined in Pandora.Paradigm.Structure.Some.Rose

type Nonempty Rose = Construction List

type Combinative List

Defined in Pandora.Paradigm.Structure.Some.List

type Combinative List = Comprehension Maybe

type Breadcrumbs List

Defined in Pandora.Paradigm.Structure.Some.List

type Breadcrumbs List = (Reverse List <:.:> List) := (:*:)

type Morphing ('Into (Tape List)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tape List)) List = Maybe <::> Tape List

type Morphing ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Delete ('All :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List = (Predicate <:.:> List) := ((->) :: Type -> Type -> Type)

type Morphing ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Delete ('First :: a -> Occurrence a) :: Morph (a -> Occurrence a)) List = (Predicate <:.:> List) := ((->) :: Type -> Type -> Type)

type Morphing ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Find ('Element :: a -> Morph a) :: Morph (a -> Morph a)) List = (Predicate <:.:> Maybe) := ((->) :: Type -> Type -> Type)

type Morphing ('Into (o ds) :: Morph a) Binary

Defined in Pandora.Paradigm.Structure

type Morphing ('Into (o ds) :: Morph a) Binary = Maybe <:.> Morphing ('Into (o ds)) (Construction Wye)

type Morphing ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig :: a -> Splay a)) :: Morph (Wye (a -> Splay a))) Binary = Binary

type Morphing ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig ('Zag :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Right ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary

Defined in Pandora.Paradigm.Structure.Some.Splay

type Morphing ('Rotate ('Left ('Zig ('Zig :: a -> Splay a))) :: Morph (Wye (Splay (a -> Splay a)))) Binary = Binary

type Morphing ('Into (Construction Maybe)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Construction Maybe)) (Tape (Construction Maybe)) = Construction Maybe

type Morphing ('Into (Comprehension Maybe)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Comprehension Maybe)) (Tape List) = Comprehension Maybe

type Morphing ('Into (Tape (Construction Maybe))) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tape (Construction Maybe))) (Tape List) = Maybe <::> Tape (Construction Maybe)

type Morphing ('Into (Tape List)) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tape List)) (Construction Maybe) = Tape List

type Morphing ('Into (Tape List)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into (Tape List)) (Tape (Construction Maybe)) = Tape List

type Morphing ('Into Binary) (Construction Wye)

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Into Binary) (Construction Wye) = Binary

type Morphing ('Into List) (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Construction Maybe) = List

type Morphing ('Into List) (Vector r)

Defined in Pandora.Paradigm.Structure

type Morphing ('Into List) (Vector r) = List

type Morphing ('Into List) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Tape (Construction Maybe)) = List

type Morphing ('Into List) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Tape List) = List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream)

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream) = Tape Stream

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream)

Defined in Pandora.Paradigm.Structure.Some.Stream

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape Stream) = Tape Stream

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe)) = Maybe <::> Tape (Construction Maybe)

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape (Construction Maybe)) = Maybe <::> Tape (Construction Maybe)

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List) = Maybe <::> Tape List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tape List) = Maybe <::> Tape List

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k)

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Binary k) = ((->) k :: Type -> Type) <::> Maybe

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed List key) = ((->) key :: Type -> Type) <::> Maybe

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List)) = Turnover (Tape List)

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List))

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Turnover (Tape List)) = Turnover (Tape List)

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Morphing ('Lookup ('Key :: a -> Morph a) :: Morph (a -> Morph a)) (Prefixed Rose k) = ((->) (Nonempty List k) :: Type -> Type) <:.> Maybe

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:))

Defined in Pandora.Paradigm.Primary

type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) = Wye

type Morphing ('Into List) (Construction Maybe <::> Maybe)

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Into List) (Construction Maybe <::> Maybe) = List

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) = Maybe <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) = Maybe <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:)) = Maybe <::> ((((Identity <:.:> (Wye <::> Construction Wye)) := (:*:)) <:.:> (Bifurcation <::> Bicursor)) := (:*:))

type Morphing ('Insert :: a -> Morph a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Morphing ('Insert :: a -> Morph a) Binary = (((Identity <:.:> Comparison) := (:*:)) <:.:> Binary) := ((->) :: Type -> Type -> Type)

type Morphing ('Pop :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Pop :: a -> Morph a) List = List

type Morphing ('Push :: a -> Morph a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Morphing ('Push :: a -> Morph a) List = (Identity <:.:> List) := ((->) :: Type -> Type -> Type)

type Available ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Available ('Right :: a -> Wye a) Binary = Maybe

type Available ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Available ('Left :: a -> Wye a) Binary = Maybe

type Available ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Available ('Tail :: a -> Segment a) List = Identity

type Available ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Available ('Root :: a -> Segment a) List = Maybe

type Substance ('Right :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Substance ('Right :: a -> Wye a) Binary = Construction Wye

type Substance ('Left :: a -> Wye a) Binary

Defined in Pandora.Paradigm.Structure.Some.Binary

type Substance ('Left :: a -> Wye a) Binary = Construction Wye

type Substance ('Tail :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Substance ('Tail :: a -> Segment a) List = List

type Substance ('Root :: a -> Segment a) List

Defined in Pandora.Paradigm.Structure.Some.List

type Substance ('Root :: a -> Segment a) List = Identity

type Available ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Available ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Available ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Right :: a -> Wye a) (Tape t) = Identity

type Available ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Left :: a -> Wye a) (Tape t) = Identity

type Available ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Root :: a -> Segment a) (Tape t) = Identity

type Available ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Available ('Tail :: a -> Segment a) (Construction List) = Identity

type Available ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Available ('Root :: a -> Segment a) (Construction List) = Identity

type Substance ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Right :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = t

type Substance ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Left :: a -> Wye a) (Tap ((t <:.:> t) := (:*:))) = t

type Substance ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:)))

Defined in Pandora.Paradigm.Primary.Transformer.Tap

type Substance ('Root :: a -> Segment a) (Tap ((t <:.:> t) := (:*:))) = Identity

type Substance ('Right :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Right :: a -> Wye a) (Tape t) = t

type Substance ('Left :: a -> Wye a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Left :: a -> Wye a) (Tape t) = Reverse t

type Substance ('Root :: a -> Segment a) (Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Root :: a -> Segment a) (Tape t) = Identity

type Substance ('Tail :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Substance ('Tail :: a -> Segment a) (Construction List) = List <:.> Construction List

type Substance ('Root :: a -> Segment a) (Construction List)

Defined in Pandora.Paradigm.Structure.Some.Rose

type Substance ('Root :: a -> Segment a) (Construction List) = Identity

type Available ('Right :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Right :: a -> Wye a) (Tape t <::> Tape t) = Identity

type Available ('Left :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Left :: a -> Wye a) (Tape t <::> Tape t) = Identity

type Available ('Down :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Down :: a -> Vertical a) (Tape t <::> Tape t) = Identity

type Available ('Up :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Available ('Up :: a -> Vertical a) (Tape t <::> Tape t) = Identity

type Available ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Available ('Right :: a -> Wye a) ((t <:.:> t) := (:*:)) = Identity

type Available ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Available ('Left :: a -> Wye a) ((t <:.:> t) := (:*:)) = Identity

type Substance ('Right :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Right :: a -> Wye a) (Tape t <::> Tape t) = Tape t <::> t

type Substance ('Left :: a -> Wye a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Left :: a -> Wye a) (Tape t <::> Tape t) = Tape t <::> Reverse t

type Substance ('Down :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Down :: a -> Vertical a) (Tape t <::> Tape t) = Reverse t <::> Tape t

type Substance ('Up :: a -> Vertical a) (Tape t <::> Tape t)

Defined in Pandora.Paradigm.Structure.Ability.Zipper

type Substance ('Up :: a -> Vertical a) (Tape t <::> Tape t) = t <::> Tape t

type Substance ('Right :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Substance ('Right :: a -> Wye a) ((t <:.:> t) := (:*:)) = t

type Substance ('Left :: a -> Wye a) ((t <:.:> t) := (:*:))

Defined in Pandora.Paradigm.Structure

type Substance ('Left :: a -> Wye a) ((t <:.:> t) := (:*:)) = t

(<$>) :: Covariant source target t => source a b -> target (t a) (t b) infixl 4

(<$$>) :: (Covariant source target t, Covariant source (Betwixt source target) u, Covariant (Betwixt source target) target t) => source a b -> target (t (u a)) (t (u b)) infixl 3

(<$$$>) :: (Covariant source target t, Covariant source (Betwixt source (Betwixt source target)) v, Covariant (Betwixt source (Betwixt source target)) (Betwixt (Betwixt source target) target) u, Covariant (Betwixt (Betwixt source target) target) target t) => source a b -> target (t (u (v a))) (t (u (v b))) infixl 2