Pandora.Pattern.Functor.Extendable

Documentation

class Covariant t => Extendable t where

When providing a new instance, you should ensure it satisfies the three laws:
* Duplication interchange: comap (comap f) . duplicate ≡ duplicate . comap f
* Extension interchange: extend f ≡ comap f . duplicate

Minimal complete definition

(=>>)

Methods

(=>>) :: t a -> (t a -> b) -> t b infixl 1

Infix and flipped version of extend, the dual of >>=

(<<=) :: (t a -> b) -> t a -> t b infixr 1

Flipped version of >>=, the dual of =<<

extend :: (t a -> b) -> t a -> t b

Prefix and flipped version of =>>, the dual of bind

duplicate :: t a -> (t :. t) := a

Clone existing structure, the dual of join

(=<=) :: (t b -> c) -> (t a -> b) -> t a -> c infixr 1

Right-to-left Cokleisli composition

(=>=) :: (t a -> b) -> (t b -> c) -> t a -> c infixr 1

Left-to-right Cokleisli composition

Instances

Extendable Identity

Defined in Pandora.Paradigm.Basis.Identity

Methods

(=>>) :: Identity a -> (Identity a -> b) -> Identity b

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

extend :: (Identity a -> b) -> Identity a -> Identity b

duplicate :: Identity a -> (Identity :. Identity) := a

(=<=) :: (Identity b -> c) -> (Identity a -> b) -> Identity a -> c

(=>=) :: (Identity a -> b) -> (Identity b -> c) -> Identity a -> c

Extendable (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Basis.Proxy

Methods

(=>>) :: Proxy a -> (Proxy a -> b) -> Proxy b

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

extend :: (Proxy a -> b) -> Proxy a -> Proxy b

duplicate :: Proxy a -> (Proxy :. Proxy) := a

(=<=) :: (Proxy b -> c) -> (Proxy a -> b) -> Proxy a -> c

(=>=) :: (Proxy a -> b) -> (Proxy b -> c) -> Proxy a -> c

Extendable (Product a)

Defined in Pandora.Paradigm.Basis.Product

Methods

(=>>) :: Product a a0 -> (Product a a0 -> b) -> Product a b

(<<=) :: (Product a a0 -> b) -> Product a a0 -> Product a b

extend :: (Product a a0 -> b) -> Product a a0 -> Product a b

duplicate :: Product a a0 -> (Product a :. Product a) := a0

(=<=) :: (Product a b -> c) -> (Product a a0 -> b) -> Product a a0 -> c

(=>=) :: (Product a a0 -> b) -> (Product a b -> c) -> Product a a0 -> c

Extendable (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

(=>>) :: Store p a -> (Store p a -> b) -> Store p b

(<<=) :: (Store p a -> b) -> Store p a -> Store p b

extend :: (Store p a -> b) -> Store p a -> Store p b

duplicate :: Store p a -> (Store p :. Store p) := a

(=<=) :: (Store p b -> c) -> (Store p a -> b) -> Store p a -> c

(=>=) :: (Store p a -> b) -> (Store p b -> c) -> Store p a -> c

Semigroup e => Extendable (Imprint e)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

(=>>) :: Imprint e a -> (Imprint e a -> b) -> Imprint e b

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

extend :: (Imprint e a -> b) -> Imprint e a -> Imprint e b

duplicate :: Imprint e a -> (Imprint e :. Imprint e) := a

(=<=) :: (Imprint e b -> c) -> (Imprint e a -> b) -> Imprint e a -> c

(=>=) :: (Imprint e a -> b) -> (Imprint e b -> c) -> Imprint e a -> c

Extendable (Equipment e)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(=>>) :: Equipment e a -> (Equipment e a -> b) -> Equipment e b

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

extend :: (Equipment e a -> b) -> Equipment e a -> Equipment e b

duplicate :: Equipment e a -> (Equipment e :. Equipment e) := a

(=<=) :: (Equipment e b -> c) -> (Equipment e a -> b) -> Equipment e a -> c

(=>=) :: (Equipment e a -> b) -> (Equipment e b -> c) -> Equipment e a -> c

Covariant t => Extendable (Twister t)

Defined in Pandora.Paradigm.Basis.Twister

Methods

(=>>) :: Twister t a -> (Twister t a -> b) -> Twister t b

(<<=) :: (Twister t a -> b) -> Twister t a -> Twister t b

extend :: (Twister t a -> b) -> Twister t a -> Twister t b

duplicate :: Twister t a -> (Twister t :. Twister t) := a

(=<=) :: (Twister t b -> c) -> (Twister t a -> b) -> Twister t a -> c

(=>=) :: (Twister t a -> b) -> (Twister t b -> c) -> Twister t a -> c

Extendable (Schematic Monad t u) => Extendable (t :> u)

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

Methods

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

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

extend :: ((t :> u) a -> b) -> (t :> u) a -> (t :> u) b

duplicate :: (t :> u) a -> ((t :> u) :. (t :> u)) := a

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

(=>=) :: ((t :> u) a -> b) -> ((t :> u) b -> c) -> (t :> u) a -> c

Extendable (Schematic Comonad t u) => Extendable (t :< u)

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

Methods

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

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

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

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

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

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

Extendable (Tagged tag)

Defined in Pandora.Paradigm.Basis.Tagged

Methods

(=>>) :: Tagged tag a -> (Tagged tag a -> b) -> Tagged tag b

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

extend :: (Tagged tag a -> b) -> Tagged tag a -> Tagged tag b

duplicate :: Tagged tag a -> (Tagged tag :. Tagged tag) := a

(=<=) :: (Tagged tag b -> c) -> (Tagged tag a -> b) -> Tagged tag a -> c

(=>=) :: (Tagged tag a -> b) -> (Tagged tag b -> c) -> Tagged tag a -> c

(Semigroup e, Extendable u) => Extendable (UT Covariant Covariant ((->) e :: Type -> Type) u)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

(=>>) :: UT Covariant Covariant ((->) e) u a -> (UT Covariant Covariant ((->) e) u a -> b) -> UT Covariant Covariant ((->) e) u b

(<<=) :: (UT Covariant Covariant ((->) e) u a -> b) -> UT Covariant Covariant ((->) e) u a -> UT Covariant Covariant ((->) e) u b

extend :: (UT Covariant Covariant ((->) e) u a -> b) -> UT Covariant Covariant ((->) e) u a -> UT Covariant Covariant ((->) e) u b

duplicate :: UT Covariant Covariant ((->) e) u a -> (UT Covariant Covariant ((->) e) u :. UT Covariant Covariant ((->) e) u) := a

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

(=>=) :: (UT Covariant Covariant ((->) e) u a -> b) -> (UT Covariant Covariant ((->) e) u b -> c) -> UT Covariant Covariant ((->) e) u a -> c

Extendable u => Extendable (TU Covariant Covariant ((:*:) e) u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

(=>>) :: TU Covariant Covariant ((:*:) e) u a -> (TU Covariant Covariant ((:*:) e) u a -> b) -> TU Covariant Covariant ((:*:) e) u b

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

extend :: (TU Covariant Covariant ((:*:) e) u a -> b) -> TU Covariant Covariant ((:*:) e) u a -> TU Covariant Covariant ((:*:) e) u b

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

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

(=>=) :: (TU Covariant Covariant ((:*:) e) u a -> b) -> (TU Covariant Covariant ((:*:) e) u b -> c) -> TU Covariant Covariant ((:*:) e) u a -> c

Extendable u => Extendable (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p :: Type -> Type))

Defined in Pandora.Paradigm.Inventory.Store

Methods

(=>>) :: TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> b) -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) b

(<<=) :: (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> b) -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) b

extend :: (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> b) -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) b

duplicate :: TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) :. TUT Covariant Covariant Covariant ((:*:) p) u ((->) p)) := a

(=<=) :: (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) b -> c) -> (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> b) -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> c

(=>=) :: (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> b) -> (TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) b -> c) -> TUT Covariant Covariant Covariant ((:*:) p) u ((->) p) a -> c