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

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 (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 (Storage p)

Defined in Pandora.Paradigm.Inventory.Storage

Methods

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

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

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

duplicate :: Storage p a -> (Storage p :.: Storage p) >< a

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

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