Pandora.Pattern.Functor.Covariant

Documentation

class Covariant (t :: * -> *) where

When providing a new instance, you should ensure it satisfies the two laws:
* Identity morphism: comap identity ≡ identity
* Interpreted of morphisms: comap (f . g) ≡ comap f . comap g

Minimal complete definition

(<$>)

Methods

(<$>) :: (a -> b) -> t a -> t b infixl 4

Infix version of comap

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

Prefix version of <$>

(<$) :: a -> t b -> t a infixl 4

Replace all locations in the input with the same value

($>) :: t a -> b -> t b infixl 4

Flipped version of <$

void :: t a -> t ()

Discards the result of evaluation

loeb :: t (a <-| t) -> t a

Computing a value from a structure of values

(<&>) :: t a -> (a -> b) -> t b

Flipped infix version of comap

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

Infix versions of comap with various nesting levels

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((t :. (u :. v)) := a) -> (t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((t :. (u :. (v :. w))) := a) -> (t :. (u :. (v :. w))) := b

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

Infix flipped versions of comap with various nesting levels

(<&&&>) :: (Covariant u, Covariant v) => ((t :. (u :. v)) := a) -> (a -> b) -> (t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((t :. (u :. (v :. w))) := a) -> (a -> b) -> (t :. (u :. (v :. w))) := b

Instances

Insertable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

insert :: a -> Stack a -> Stack a

(forall a. Chain a) => Insertable Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

insert :: a -> Binary a -> Binary a

Covariant Wye

Defined in Pandora.Paradigm.Primary.Functor.Wye

Methods

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

comap :: (a -> b) -> Wye a -> Wye b

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

($>) :: Wye a -> b -> Wye b

void :: Wye a -> Wye ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Wye :. u) := a) -> (Wye :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Wye :. (u :. v)) := a) -> (Wye :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Wye :. (u :. (v :. w))) := a) -> (Wye :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Wye :. u) := a) -> (a -> b) -> (Wye :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Wye :. (u :. v)) := a) -> (a -> b) -> (Wye :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Wye :. (u :. (v :. w))) := a) -> (a -> b) -> (Wye :. (u :. (v :. w))) := b

Covariant Edges

Defined in Pandora.Paradigm.Primary.Functor.Edges

Methods

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

comap :: (a -> b) -> Edges a -> Edges b

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

($>) :: Edges a -> b -> Edges b

void :: Edges a -> Edges ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Edges :. u) := a) -> (Edges :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Edges :. (u :. v)) := a) -> (Edges :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Edges :. (u :. (v :. w))) := a) -> (Edges :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Edges :. u) := a) -> (a -> b) -> (Edges :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Edges :. (u :. v)) := a) -> (a -> b) -> (Edges :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Edges :. (u :. (v :. w))) := a) -> (a -> b) -> (Edges :. (u :. (v :. w))) := b

Covariant Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

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

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

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

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

void :: Identity a -> Identity ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Identity :. u) := a) -> (Identity :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Identity :. u) := a) -> (a -> b) -> (Identity :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Identity :. (u :. v)) := a) -> (a -> b) -> (Identity :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Identity :. (u :. (v :. w))) := a) -> (a -> b) -> (Identity :. (u :. (v :. w))) := b

Covariant Delta

Defined in Pandora.Paradigm.Primary.Functor.Delta

Methods

(<$>) :: (a -> b) -> Delta a -> Delta b

comap :: (a -> b) -> Delta a -> Delta b

(<$) :: a -> Delta b -> Delta a

($>) :: Delta a -> b -> Delta b

void :: Delta a -> Delta ()

loeb :: Delta (a <-| Delta) -> Delta a

(<&>) :: Delta a -> (a -> b) -> Delta b

(<$$>) :: Covariant u => (a -> b) -> ((Delta :. u) := a) -> (Delta :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Delta :. (u :. v)) := a) -> (Delta :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Delta :. (u :. (v :. w))) := a) -> (Delta :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Delta :. u) := a) -> (a -> b) -> (Delta :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Delta :. (u :. v)) := a) -> (a -> b) -> (Delta :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Delta :. (u :. (v :. w))) := a) -> (a -> b) -> (Delta :. (u :. (v :. w))) := b

Covariant Maybe

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

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

comap :: (a -> b) -> Maybe a -> Maybe b

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

($>) :: Maybe a -> b -> Maybe b

void :: Maybe a -> Maybe ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Maybe :. u) := a) -> (Maybe :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Maybe :. (u :. v)) := a) -> (Maybe :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Maybe :. (u :. (v :. w))) := a) -> (Maybe :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Maybe :. u) := a) -> (a -> b) -> (Maybe :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Maybe :. (u :. v)) := a) -> (a -> b) -> (Maybe :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Maybe :. (u :. (v :. w))) := a) -> (a -> b) -> (Maybe :. (u :. (v :. w))) := b

Covariant (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Proxy

Methods

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

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

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

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

void :: Proxy a -> Proxy ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Proxy :. u) := a) -> (Proxy :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Proxy :. (u :. v)) := a) -> (Proxy :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Proxy :. (u :. (v :. w))) := a) -> (Proxy :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Proxy :. u) := a) -> (a -> b) -> (Proxy :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Proxy :. (u :. v)) := a) -> (a -> b) -> (Proxy :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Proxy :. (u :. (v :. w))) := a) -> (a -> b) -> (Proxy :. (u :. (v :. w))) := b

Covariant (Wedge e)

Defined in Pandora.Paradigm.Primary.Functor.Wedge

Methods

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

comap :: (a -> b) -> Wedge e a -> Wedge e b

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

($>) :: Wedge e a -> b -> Wedge e b

void :: Wedge e a -> Wedge e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Wedge e :. (u :. v)) := a) -> (Wedge e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Wedge e :. (u :. (v :. w))) := a) -> (Wedge e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Wedge e :. (u :. v)) := a) -> (a -> b) -> (Wedge e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Wedge e :. (u :. (v :. w))) := a) -> (a -> b) -> (Wedge e :. (u :. (v :. w))) := b

Covariant (These e)

Defined in Pandora.Paradigm.Primary.Functor.These

Methods

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

comap :: (a -> b) -> These e a -> These e b

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

($>) :: These e a -> b -> These e b

void :: These e a -> These e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((These e :. (u :. v)) := a) -> (These e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((These e :. (u :. (v :. w))) := a) -> (These e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((These e :. (u :. v)) := a) -> (a -> b) -> (These e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((These e :. (u :. (v :. w))) := a) -> (a -> b) -> (These e :. (u :. (v :. w))) := b

Covariant t => Covariant (Jet t)

Defined in Pandora.Paradigm.Primary.Transformer.Jet

Methods

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

comap :: (a -> b) -> Jet t a -> Jet t b

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

($>) :: Jet t a -> b -> Jet t b

void :: Jet t a -> Jet t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jet t :. (u :. v)) := a) -> (Jet t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jet t :. (u :. (v :. w))) := a) -> (Jet t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Jet t :. (u :. v)) := a) -> (a -> b) -> (Jet t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jet t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jet t :. (u :. (v :. w))) := b

Covariant (Validation e)

Defined in Pandora.Paradigm.Primary.Functor.Validation

Methods

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

comap :: (a -> b) -> Validation e a -> Validation e b

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

($>) :: Validation e a -> b -> Validation e b

void :: Validation e a -> Validation e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Validation e :. (u :. v)) := a) -> (Validation e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Validation e :. (u :. (v :. w))) := a) -> (Validation e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Validation e :. (u :. v)) := a) -> (a -> b) -> (Validation e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Validation e :. (u :. (v :. w))) := a) -> (a -> b) -> (Validation e :. (u :. (v :. w))) := b

Covariant (Product s)

Defined in Pandora.Paradigm.Primary.Functor.Product

Methods

(<$>) :: (a -> b) -> Product s a -> Product s b

comap :: (a -> b) -> Product s a -> Product s b

(<$) :: a -> Product s b -> Product s a

($>) :: Product s a -> b -> Product s b

void :: Product s a -> Product s ()

loeb :: Product s (a <-| Product s) -> Product s a

(<&>) :: Product s a -> (a -> b) -> Product s b

(<$$>) :: Covariant u => (a -> b) -> ((Product s :. u) := a) -> (Product s :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Product s :. (u :. v)) := a) -> (Product s :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Product s :. (u :. (v :. w))) := a) -> (Product s :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Product s :. u) := a) -> (a -> b) -> (Product s :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Product s :. (u :. v)) := a) -> (a -> b) -> (Product s :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Product s :. (u :. (v :. w))) := a) -> (a -> b) -> (Product s :. (u :. (v :. w))) := b

Covariant (Yoneda t)

Defined in Pandora.Paradigm.Primary.Transformer.Yoneda

Methods

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

comap :: (a -> b) -> Yoneda t a -> Yoneda t b

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

($>) :: Yoneda t a -> b -> Yoneda t b

void :: Yoneda t a -> Yoneda t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Yoneda t :. (u :. v)) := a) -> (Yoneda t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Yoneda t :. (u :. (v :. w))) := a) -> (Yoneda t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Yoneda t :. (u :. v)) := a) -> (a -> b) -> (Yoneda t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Yoneda t :. (u :. (v :. w))) := a) -> (a -> b) -> (Yoneda t :. (u :. (v :. w))) := b

Covariant (Outline t)

Defined in Pandora.Paradigm.Primary.Transformer.Outline

Methods

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

comap :: (a -> b) -> Outline t a -> Outline t b

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

($>) :: Outline t a -> b -> Outline t b

void :: Outline t a -> Outline t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Outline t :. (u :. v)) := a) -> (Outline t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Outline t :. (u :. (v :. w))) := a) -> (Outline t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Outline t :. (u :. v)) := a) -> (a -> b) -> (Outline t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Outline t :. (u :. (v :. w))) := a) -> (a -> b) -> (Outline t :. (u :. (v :. w))) := b

Covariant t => Covariant (Jack t)

Defined in Pandora.Paradigm.Primary.Transformer.Jack

Methods

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

comap :: (a -> b) -> Jack t a -> Jack t b

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

($>) :: Jack t a -> b -> Jack t b

void :: Jack t a -> Jack t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jack t :. (u :. v)) := a) -> (Jack t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jack t :. (u :. (v :. w))) := a) -> (Jack t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Jack t :. (u :. v)) := a) -> (a -> b) -> (Jack t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jack t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jack t :. (u :. (v :. w))) := b

Covariant t => Covariant (Instruction t)

Defined in Pandora.Paradigm.Primary.Transformer.Instruction

Methods

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

comap :: (a -> b) -> Instruction t a -> Instruction t b

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

($>) :: Instruction t a -> b -> Instruction t b

void :: Instruction t a -> Instruction t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Instruction t :. (u :. v)) := a) -> (Instruction t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Instruction t :. (u :. (v :. w))) := a) -> (Instruction t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Instruction t :. (u :. v)) := a) -> (a -> b) -> (Instruction t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Instruction t :. (u :. (v :. w))) := a) -> (a -> b) -> (Instruction t :. (u :. (v :. w))) := b

Covariant t => Covariant (Tap t)

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

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

comap :: (a -> b) -> Tap t a -> Tap t b

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

($>) :: Tap t a -> b -> Tap t b

void :: Tap t a -> Tap t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Tap t :. (u :. v)) := a) -> (Tap t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Tap t :. (u :. (v :. w))) := a) -> (Tap t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Tap t :. (u :. v)) := a) -> (a -> b) -> (Tap t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Tap t :. (u :. (v :. w))) := a) -> (a -> b) -> (Tap t :. (u :. (v :. w))) := b

Covariant (Conclusion e)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

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

comap :: (a -> b) -> Conclusion e a -> Conclusion e b

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

($>) :: Conclusion e a -> b -> Conclusion e b

void :: Conclusion e a -> Conclusion e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Conclusion e :. (u :. v)) := a) -> (Conclusion e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Conclusion e :. (u :. (v :. w))) := a) -> (Conclusion e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Conclusion e :. (u :. v)) := a) -> (a -> b) -> (Conclusion e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Conclusion e :. (u :. (v :. w))) := a) -> (a -> b) -> (Conclusion e :. (u :. (v :. w))) := b

Covariant (State s)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

comap :: (a -> b) -> State s a -> State s b

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

($>) :: State s a -> b -> State s b

void :: State s a -> State s ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((State s :. u) := a) -> (State s :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((State s :. (u :. v)) := a) -> (State s :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((State s :. (u :. (v :. w))) := a) -> (State s :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((State s :. u) := a) -> (a -> b) -> (State s :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((State s :. (u :. v)) := a) -> (a -> b) -> (State s :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((State s :. (u :. (v :. w))) := a) -> (a -> b) -> (State s :. (u :. (v :. w))) := b

Covariant (Imprint e)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

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

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

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

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

void :: Imprint e a -> Imprint e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Imprint e :. (u :. v)) := a) -> (Imprint e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Imprint e :. (u :. (v :. w))) := a) -> (Imprint e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Imprint e :. (u :. v)) := a) -> (a -> b) -> (Imprint e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Imprint e :. (u :. (v :. w))) := a) -> (a -> b) -> (Imprint e :. (u :. (v :. w))) := b

Covariant (Equipment e)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

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

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

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

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

void :: Equipment e a -> Equipment e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Equipment e :. (u :. v)) := a) -> (Equipment e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Equipment e :. (u :. (v :. w))) := a) -> (Equipment e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Equipment e :. (u :. v)) := a) -> (a -> b) -> (Equipment e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Equipment e :. (u :. (v :. w))) := a) -> (a -> b) -> (Equipment e :. (u :. (v :. w))) := b

Covariant (Environment e)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

(<$>) :: (a -> b) -> Environment e a -> Environment e b

comap :: (a -> b) -> Environment e a -> Environment e b

(<$) :: a -> Environment e b -> Environment e a

($>) :: Environment e a -> b -> Environment e b

void :: Environment e a -> Environment e ()

loeb :: Environment e (a <-| Environment e) -> Environment e a

(<&>) :: Environment e a -> (a -> b) -> Environment e b

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Environment e :. (u :. v)) := a) -> (Environment e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Environment e :. (u :. (v :. w))) := a) -> (Environment e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Environment e :. (u :. v)) := a) -> (a -> b) -> (Environment e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Environment e :. (u :. (v :. w))) := a) -> (a -> b) -> (Environment e :. (u :. (v :. w))) := b

Covariant (Accumulator e)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

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

comap :: (a -> b) -> Accumulator e a -> Accumulator e b

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

($>) :: Accumulator e a -> b -> Accumulator e b

void :: Accumulator e a -> Accumulator e ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Accumulator e :. (u :. v)) := a) -> (Accumulator e :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Accumulator e :. (u :. (v :. w))) := a) -> (Accumulator e :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Accumulator e :. (u :. v)) := a) -> (a -> b) -> (Accumulator e :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Accumulator e :. (u :. (v :. w))) := a) -> (a -> b) -> (Accumulator e :. (u :. (v :. w))) := b

Covariant t => Covariant (Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

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

comap :: (a -> b) -> Construction t a -> Construction t b

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

($>) :: Construction t a -> b -> Construction t b

void :: Construction t a -> Construction t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Construction t :. (u :. v)) := a) -> (Construction t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Construction t :. (u :. (v :. w))) := a) -> (Construction t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Construction t :. (u :. v)) := a) -> (a -> b) -> (Construction t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Construction t :. (u :. (v :. w))) := a) -> (a -> b) -> (Construction t :. (u :. (v :. w))) := b

Covariant (t <:.> Construction t) => Covariant (Comprehension t)

Defined in Pandora.Paradigm.Structure.Ability.Comprehension

Methods

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

comap :: (a -> b) -> Comprehension t a -> Comprehension t b

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

($>) :: Comprehension t a -> b -> Comprehension t b

void :: Comprehension t a -> Comprehension t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Comprehension t :. (u :. v)) := a) -> (Comprehension t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Comprehension t :. (u :. (v :. w))) := a) -> (Comprehension t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Comprehension t :. (u :. v)) := a) -> (a -> b) -> (Comprehension t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Comprehension t :. (u :. (v :. w))) := a) -> (a -> b) -> (Comprehension t :. (u :. (v :. w))) := b

Covariant (Store p)

Defined in Pandora.Paradigm.Inventory.Store

Methods

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

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

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

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

void :: Store p a -> Store p ()

loeb :: Store p (a <-| Store p) -> Store p a

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

(<$$>) :: Covariant u => (a -> b) -> ((Store p :. u) := a) -> (Store p :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Store p :. (u :. v)) := a) -> (Store p :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Store p :. (u :. (v :. w))) := a) -> (Store p :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Store p :. u) := a) -> (a -> b) -> (Store p :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Store p :. (u :. v)) := a) -> (a -> b) -> (Store p :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Store p :. (u :. (v :. w))) := a) -> (a -> b) -> (Store p :. (u :. (v :. w))) := b

Semigroup (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

(+) :: Stack a -> Stack a -> Stack a

Monoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

zero :: Stack a

Setoid a => Setoid (Stack a)

Defined in Pandora.Paradigm.Structure.Stack

Methods

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

(/=) :: Stack a -> Stack a -> Boolean

Monad 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

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

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural 'Left Binary a

Methods

substructure :: Tagged 'Left (Binary a) :-. Substructural 'Left Binary a

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

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural 'Right Binary a

Methods

substructure :: Tagged 'Right (Binary a) :-. Substructural 'Right Binary a

Substructure ('Just :: Type -> Maybe Type) Rose

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural 'Just Rose a

Methods

substructure :: Tagged 'Just (Rose a) :-. Substructural 'Just Rose a

Focusable ('Root :: Type -> Location Type) Rose

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Focusing 'Root Rose a

Methods

focusing :: Tagged 'Root (Rose a) :-. Focusing 'Root Rose a

(forall a. Chain a) => Focusable ('Root :: Type -> Location Type) Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Focusing 'Root Binary a

Methods

focusing :: Tagged 'Root (Binary a) :-. Focusing 'Root Binary a

Focusable ('Head :: Type -> Location Type) Stack

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Focusing 'Head Stack a

Methods

focusing :: Tagged 'Head (Stack a) :-. Focusing 'Head Stack a

Substructure ('Left :: Type -> Wye Type) t => Substructure ('Left :: Type -> Wye Type) (Tap (t <:.> u))

Defined in Pandora.Paradigm.Structure

Associated Types

type Substructural 'Left (Tap (t <:.> u)) a

Methods

substructure :: Tagged 'Left (Tap (t <:.> u) a) :-. Substructural 'Left (Tap (t <:.> u)) a

Substructure ('Right :: Type -> Wye Type) t => Substructure ('Right :: Type -> Wye Type) (Tap (t <:.> u))

Defined in Pandora.Paradigm.Structure

Associated Types

type Substructural 'Right (Tap (t <:.> u)) a

Methods

substructure :: Tagged 'Right (Tap (t <:.> u) a) :-. Substructural 'Right (Tap (t <:.> u)) a

Substructure ('Just :: Type -> Maybe Type) (Construction Stack)

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural 'Just (Construction Stack) a

Methods

substructure :: Tagged 'Just (Construction Stack a) :-. Substructural 'Just (Construction Stack) a

Focusable ('Root :: Type -> Location Type) (Construction Stack)

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Focusing 'Root (Construction Stack) a

Methods

focusing :: Tagged 'Root (Construction Stack a) :-. Focusing 'Root (Construction Stack) a

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

hoist :: forall (u :: Type -> Type) (v :: Type -> Type). Covariant u => (u ~> v) -> TU Covariant Covariant t u ~> TU Covariant Covariant t v

Covariant (Tagged tag)

Defined in Pandora.Paradigm.Primary.Functor.Tagged

Methods

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

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

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

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

void :: Tagged tag a -> Tagged tag ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Tagged tag :. u) := a) -> (Tagged tag :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Tagged tag :. (u :. v)) := a) -> (Tagged tag :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Tagged tag :. (u :. (v :. w))) := a) -> (Tagged tag :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Tagged tag :. u) := a) -> (a -> b) -> (Tagged tag :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Tagged tag :. (u :. v)) := a) -> (a -> b) -> (Tagged tag :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Tagged tag :. (u :. (v :. w))) := a) -> (a -> b) -> (Tagged tag :. (u :. (v :. w))) := b

Covariant (Constant a :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Constant

Methods

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

comap :: (a0 -> b) -> Constant a a0 -> Constant a b

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

($>) :: Constant a a0 -> b -> Constant a b

void :: Constant a a0 -> Constant a ()

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

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

(<$$>) :: Covariant u => (a0 -> b) -> ((Constant a :. u) := a0) -> (Constant a :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> ((Constant a :. (u :. v)) := a0) -> (Constant a :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> ((Constant a :. (u :. (v :. w))) := a0) -> (Constant a :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Constant a :. u) := a0) -> (a0 -> b) -> (Constant a :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => ((Constant a :. (u :. v)) := a0) -> (a0 -> b) -> (Constant a :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Constant a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> (Constant a :. (u :. (v :. w))) := b

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

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

Methods

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

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

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

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

void :: (t :> u) a -> (t :> u) ()

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

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

(<$$>) :: Covariant u0 => (a -> b) -> (((t :> u) :. u0) := a) -> ((t :> u) :. u0) := b

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

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t :> u) :. (u0 :. (v :. w))) := a) -> ((t :> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((t :> u) :. u0) := a) -> (a -> b) -> ((t :> u) :. u0) := b

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

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t :> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t :> u) :. (u0 :. (v :. w))) := b

Covariant (Day t u)

Defined in Pandora.Paradigm.Primary.Transformer.Day

Methods

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

comap :: (a -> b) -> Day t u a -> Day t u b

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

($>) :: Day t u a -> b -> Day t u b

void :: Day t u a -> Day t u ()

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

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

(<$$>) :: Covariant u0 => (a -> b) -> ((Day t u :. u0) := a) -> (Day t u :. u0) := b

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

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((Day t u :. (u0 :. (v :. w))) := a) -> (Day t u :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((Day t u :. u0) := a) -> (a -> b) -> (Day t u :. u0) := b

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

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Day t u :. (u0 :. (v :. w))) := a) -> (a -> b) -> (Day t u :. (u0 :. (v :. w))) := b

Covariant t => Covariant (Backwards t)

Defined in Pandora.Paradigm.Primary.Transformer.Backwards

Methods

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

comap :: (a -> b) -> Backwards t a -> Backwards t b

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

($>) :: Backwards t a -> b -> Backwards t b

void :: Backwards t a -> Backwards t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Backwards t :. (u :. v)) := a) -> (Backwards t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Backwards t :. (u :. (v :. w))) := a) -> (Backwards t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Backwards t :. (u :. v)) := a) -> (a -> b) -> (Backwards t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Backwards t :. (u :. (v :. w))) := a) -> (a -> b) -> (Backwards t :. (u :. (v :. w))) := b

Covariant t => Covariant (Reverse t)

Defined in Pandora.Paradigm.Primary.Transformer.Reverse

Methods

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

comap :: (a -> b) -> Reverse t a -> Reverse t b

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

($>) :: Reverse t a -> b -> Reverse t b

void :: Reverse t a -> Reverse t ()

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

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

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

(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Reverse t :. (u :. v)) := a) -> (Reverse t :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Reverse t :. (u :. (v :. w))) := a) -> (Reverse t :. (u :. (v :. w))) := b

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

(<&&&>) :: (Covariant u, Covariant v) => ((Reverse t :. (u :. v)) := a) -> (a -> b) -> (Reverse t :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Reverse t :. (u :. (v :. w))) := a) -> (a -> b) -> (Reverse t :. (u :. (v :. w))) := b

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

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

Methods

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

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

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

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

void :: (t :< u) a -> (t :< u) ()

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

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

(<$$>) :: Covariant u0 => (a -> b) -> (((t :< u) :. u0) := a) -> ((t :< u) :. u0) := b

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

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t :< u) :. (u0 :. (v :. w))) := a) -> ((t :< u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((t :< u) :. u0) := a) -> (a -> b) -> ((t :< u) :. u0) := b

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

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t :< u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t :< u) :. (u0 :. (v :. w))) := b

Rotatable ('Right :: a -> Wye a) (Tap (Delta <:.> Stream))

Defined in Pandora.Paradigm.Structure.Stream

Associated Types

type Rotational 'Right (Tap (Delta <:.> Stream)) a

Methods

rotation :: Tagged 'Right (Tap (Delta <:.> Stream) a0) -> Rotational 'Right (Tap (Delta <:.> Stream)) a0

Rotatable ('Left :: a -> Wye a) (Tap (Delta <:.> Stream))

Defined in Pandora.Paradigm.Structure.Stream

Associated Types

type Rotational 'Left (Tap (Delta <:.> Stream)) a

Methods

rotation :: Tagged 'Left (Tap (Delta <:.> Stream) a0) -> Rotational 'Left (Tap (Delta <:.> Stream)) a0

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

Defined in Pandora.Pattern.Functor.Covariant

Methods

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

comap :: (a0 -> b) -> (a -> a0) -> a -> b

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

($>) :: (a -> a0) -> b -> a -> b

void :: (a -> a0) -> a -> ()

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

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

(<$$>) :: Covariant u => (a0 -> b) -> (((->) a :. u) := a0) -> ((->) a :. u) := b

(<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> (((->) a :. (u :. v)) := a0) -> ((->) a :. (u :. v)) := b

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> (((->) a :. (u :. (v :. w))) := a0) -> ((->) a :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => (((->) a :. u) := a0) -> (a0 -> b) -> ((->) a :. u) := b

(<&&&>) :: (Covariant u, Covariant v) => (((->) a :. (u :. v)) := a0) -> (a0 -> b) -> ((->) a :. (u :. v)) := b

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => (((->) a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> ((->) a :. (u :. (v :. w))) := b

Covariant t => Covariant (Continuation r t)

Defined in Pandora.Paradigm.Primary.Transformer.Continuation

Methods

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

comap :: (a -> b) -> Continuation r t a -> Continuation r t b

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

($>) :: Continuation r t a -> b -> Continuation r t b

void :: Continuation r t a -> Continuation r t ()

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

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

(<$$>) :: Covariant u => (a -> b) -> ((Continuation r t :. u) := a) -> (Continuation r t :. u) := b

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

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Continuation r t :. (u :. (v :. w))) := a) -> (Continuation r t :. (u :. (v :. w))) := b

(<&&>) :: Covariant u => ((Continuation r t :. u) := a) -> (a -> b) -> (Continuation r t :. u) := b

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

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Continuation r t :. (u :. (v :. w))) := a) -> (a -> b) -> (Continuation r t :. (u :. (v :. w))) := b

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

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

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

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

void :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) ()

loeb :: (((->) s <:<.>:> (:*:) s) := u) (a <-| (((->) s <:<.>:> (:*:) s) := u)) -> (((->) s <:<.>:> (:*:) s) := u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u)

Defined in Pandora.Paradigm.Inventory.Store

Methods

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

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

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

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

void :: (((:*:) p <:<.>:> (->) p) := u) a -> (((:*:) p <:<.>:> (->) p) := u) ()

loeb :: (((:*:) p <:<.>:> (->) p) := u) (a <-| (((:*:) p <:<.>:> (->) p) := u)) -> (((:*:) p <:<.>:> (->) p) := u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. u0) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := a) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((((:*:) p <:<.>:> (->) p) := u) :. u0) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((((:*:) p <:<.>:> (->) p) := u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (((->) e :: Type -> Type) <.:> u)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

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

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

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

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

void :: ((->) e <.:> u) a -> ((->) e <.:> u) ()

loeb :: ((->) e <.:> u) (a <-| ((->) e <.:> u)) -> ((->) e <.:> u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> ((((->) e <.:> u) :. u0) := a) -> (((->) e <.:> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((->) e <.:> u) :. (u0 :. v)) := a) -> (((->) e <.:> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((->) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((->) e <.:> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((->) e <.:> u) :. u0) := a) -> (a -> b) -> (((->) e <.:> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((->) e <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> (((->) e <.:> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((->) e <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((->) e <.:> u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

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

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

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

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

void :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) ()

loeb :: ((:*:) e <.:> u) (a <-| ((:*:) e <.:> u)) -> ((:*:) e <.:> u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((:*:) e <.:> u) :. u0) := a) -> (a -> b) -> (((:*:) e <.:> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (Maybe <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

(<$>) :: (a -> b) -> (Maybe <.:> u) a -> (Maybe <.:> u) b

comap :: (a -> b) -> (Maybe <.:> u) a -> (Maybe <.:> u) b

(<$) :: a -> (Maybe <.:> u) b -> (Maybe <.:> u) a

($>) :: (Maybe <.:> u) a -> b -> (Maybe <.:> u) b

void :: (Maybe <.:> u) a -> (Maybe <.:> u) ()

loeb :: (Maybe <.:> u) (a <-| (Maybe <.:> u)) -> (Maybe <.:> u) a

(<&>) :: (Maybe <.:> u) a -> (a -> b) -> (Maybe <.:> u) b

(<$$>) :: Covariant u0 => (a -> b) -> (((Maybe <.:> u) :. u0) := a) -> ((Maybe <.:> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((Maybe <.:> u) :. (u0 :. v)) := a) -> ((Maybe <.:> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((Maybe <.:> u) :. (u0 :. (v :. w))) := a) -> ((Maybe <.:> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((Maybe <.:> u) :. u0) := a) -> (a -> b) -> ((Maybe <.:> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((Maybe <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> ((Maybe <.:> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((Maybe <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((Maybe <.:> u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (Conclusion e <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

(<$>) :: (a -> b) -> (Conclusion e <.:> u) a -> (Conclusion e <.:> u) b

comap :: (a -> b) -> (Conclusion e <.:> u) a -> (Conclusion e <.:> u) b

(<$) :: a -> (Conclusion e <.:> u) b -> (Conclusion e <.:> u) a

($>) :: (Conclusion e <.:> u) a -> b -> (Conclusion e <.:> u) b

void :: (Conclusion e <.:> u) a -> (Conclusion e <.:> u) ()

loeb :: (Conclusion e <.:> u) (a <-| (Conclusion e <.:> u)) -> (Conclusion e <.:> u) a

(<&>) :: (Conclusion e <.:> u) a -> (a -> b) -> (Conclusion e <.:> u) b

(<$$>) :: Covariant u0 => (a -> b) -> (((Conclusion e <.:> u) :. u0) := a) -> ((Conclusion e <.:> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((Conclusion e <.:> u) :. (u0 :. v)) := a) -> ((Conclusion e <.:> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((Conclusion e <.:> u) :. (u0 :. (v :. w))) := a) -> ((Conclusion e <.:> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((Conclusion e <.:> u) :. u0) := a) -> (a -> b) -> ((Conclusion e <.:> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((Conclusion e <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> ((Conclusion e <.:> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((Conclusion e <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((Conclusion e <.:> u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

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

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

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

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

void :: ((->) e <:.> u) a -> ((->) e <:.> u) ()

loeb :: ((->) e <:.> u) (a <-| ((->) e <:.> u)) -> ((->) e <:.> u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> ((((->) e <:.> u) :. u0) := a) -> (((->) e <:.> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((->) e <:.> u) :. (u0 :. v)) := a) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((->) e <:.> u) :. u0) := a) -> (a -> b) -> (((->) e <:.> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((->) e <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(Covariant u, Covariant t) => Covariant (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<$>) :: (a -> b) -> (t <:.> Construction u) a -> (t <:.> Construction u) b

comap :: (a -> b) -> (t <:.> Construction u) a -> (t <:.> Construction u) b

(<$) :: a -> (t <:.> Construction u) b -> (t <:.> Construction u) a

($>) :: (t <:.> Construction u) a -> b -> (t <:.> Construction u) b

void :: (t <:.> Construction u) a -> (t <:.> Construction u) ()

loeb :: (t <:.> Construction u) (a <-| (t <:.> Construction u)) -> (t <:.> Construction u) a

(<&>) :: (t <:.> Construction u) a -> (a -> b) -> (t <:.> Construction u) b

(<$$>) :: Covariant u0 => (a -> b) -> (((t <:.> Construction u) :. u0) := a) -> ((t <:.> Construction u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((t <:.> Construction u) :. (u0 :. v)) := a) -> ((t <:.> Construction u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t <:.> Construction u) :. (u0 :. (v :. w))) := a) -> ((t <:.> Construction u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => (((t <:.> Construction u) :. u0) := a) -> (a -> b) -> ((t <:.> Construction u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => (((t <:.> Construction u) :. (u0 :. v)) := a) -> (a -> b) -> ((t <:.> Construction u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t <:.> Construction u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t <:.> Construction u) :. (u0 :. (v :. w))) := b

Covariant u => Covariant ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

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

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

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

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

void :: ((:*:) e <:.> u) a -> ((:*:) e <:.> u) ()

loeb :: ((:*:) e <:.> u) (a <-| ((:*:) e <:.> u)) -> ((:*:) e <:.> u) a

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

(<$$>) :: Covariant u0 => (a -> b) -> ((((:*:) e <:.> u) :. u0) := a) -> (((:*:) e <:.> u) :. u0) := b

(<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((:*:) e <:.> u) :. u0) := a) -> (a -> b) -> (((:*:) e <:.> u) :. u0) := b

(<&&&>) :: (Covariant u0, Covariant v) => ((((:*:) e <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. v)) := b

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((:*:) e <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((:*:) e <:.> u) :. (u0 :. (v :. w))) := b

Bindable u => Bindable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

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

join :: (((((->) s <:<.>:> (:*:) s) := u) :. (((->) s <:<.>:> (:*:) s) := u)) := a) -> (((->) s <:<.>:> (:*:) s) := u) a

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

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

($>>=) :: Covariant u0 => (a -> (((->) s <:<.>:> (:*:) s) := u) b) -> ((u0 :. (((->) s <:<.>:> (:*:) s) := u)) := a) -> (u0 :. (((->) s <:<.>:> (:*:) s) := u)) := b

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

(Semigroup e, Pointable u, Bindable u) => Bindable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

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

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

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

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

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

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

($>>=) :: Covariant u0 => (a -> ((:*:) e <.:> u) b) -> ((u0 :. ((:*:) e <.:> u)) := a) -> (u0 :. ((:*:) e <.:> u)) := b

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

(Pointable u, Bindable u) => Bindable (Maybe <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

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

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

bind :: (a -> (Maybe <.:> u) b) -> (Maybe <.:> u) a -> (Maybe <.:> u) b

join :: (((Maybe <.:> u) :. (Maybe <.:> u)) := a) -> (Maybe <.:> u) a

(>=>) :: (a -> (Maybe <.:> u) b) -> (b -> (Maybe <.:> u) c) -> a -> (Maybe <.:> u) c

(<=<) :: (b -> (Maybe <.:> u) c) -> (a -> (Maybe <.:> u) b) -> a -> (Maybe <.:> u) c

($>>=) :: Covariant u0 => (a -> (Maybe <.:> u) b) -> ((u0 :. (Maybe <.:> u)) := a) -> (u0 :. (Maybe <.:> u)) := b

(<>>=) :: ((Maybe <.:> u) b -> c) -> (a -> (Maybe <.:> u) b) -> (Maybe <.:> u) a -> c

(Pointable u, Bindable u) => Bindable (Conclusion e <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

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

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

bind :: (a -> (Conclusion e <.:> u) b) -> (Conclusion e <.:> u) a -> (Conclusion e <.:> u) b

join :: (((Conclusion e <.:> u) :. (Conclusion e <.:> u)) := a) -> (Conclusion e <.:> u) a

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

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

($>>=) :: Covariant u0 => (a -> (Conclusion e <.:> u) b) -> ((u0 :. (Conclusion e <.:> u)) := a) -> (u0 :. (Conclusion e <.:> u)) := b

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

Bindable u => Bindable (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

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

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

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

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

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

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

($>>=) :: Covariant u0 => (a -> ((->) e <:.> u) b) -> ((u0 :. ((->) e <:.> u)) := a) -> (u0 :. ((->) e <:.> u)) := b

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

Bindable u => Applicative ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

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

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

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

(<**>) :: Applicative u0 => (((((->) s <:<.>:> (:*:) s) := u) :. u0) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. u0) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := (a -> b)) -> (((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := a) -> ((((->) s <:<.>:> (:*:) s) := u) :. (u0 :. (v :. w))) := b

Applicative u => Applicative (((->) e :: Type -> Type) <.:> u)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

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

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

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

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

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

(<**>) :: Applicative u0 => ((((->) e <.:> u) :. u0) := (a -> b)) -> ((((->) e <.:> u) :. u0) := a) -> (((->) e <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((->) e <.:> u) :. (u0 :. v)) := (a -> b)) -> ((((->) e <.:> u) :. (u0 :. v)) := a) -> (((->) e <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((->) e <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((->) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((->) e <.:> u) :. (u0 :. (v :. w))) := b

(Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

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

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

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

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

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

(<**>) :: Applicative u0 => ((((:*:) e <.:> u) :. u0) := (a -> b)) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((:*:) e <.:> u) :. (u0 :. v)) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. (v :. w))) := a) -> (((:*:) e <.:> u) :. (u0 :. (v :. w))) := b

Applicative u => Applicative (Maybe <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

(<*>) :: (Maybe <.:> u) (a -> b) -> (Maybe <.:> u) a -> (Maybe <.:> u) b

apply :: (Maybe <.:> u) (a -> b) -> (Maybe <.:> u) a -> (Maybe <.:> u) b

(*>) :: (Maybe <.:> u) a -> (Maybe <.:> u) b -> (Maybe <.:> u) b

(<*) :: (Maybe <.:> u) a -> (Maybe <.:> u) b -> (Maybe <.:> u) a

forever :: (Maybe <.:> u) a -> (Maybe <.:> u) b

(<**>) :: Applicative u0 => (((Maybe <.:> u) :. u0) := (a -> b)) -> (((Maybe <.:> u) :. u0) := a) -> ((Maybe <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((Maybe <.:> u) :. (u0 :. v)) := (a -> b)) -> (((Maybe <.:> u) :. (u0 :. v)) := a) -> ((Maybe <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((Maybe <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> (((Maybe <.:> u) :. (u0 :. (v :. w))) := a) -> ((Maybe <.:> u) :. (u0 :. (v :. w))) := b

Applicative u => Applicative (Conclusion e <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

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

apply :: (Conclusion e <.:> u) (a -> b) -> (Conclusion e <.:> u) a -> (Conclusion e <.:> u) b

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

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

forever :: (Conclusion e <.:> u) a -> (Conclusion e <.:> u) b

(<**>) :: Applicative u0 => (((Conclusion e <.:> u) :. u0) := (a -> b)) -> (((Conclusion e <.:> u) :. u0) := a) -> ((Conclusion e <.:> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((Conclusion e <.:> u) :. (u0 :. v)) := (a -> b)) -> (((Conclusion e <.:> u) :. (u0 :. v)) := a) -> ((Conclusion e <.:> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((Conclusion e <.:> u) :. (u0 :. (v :. w))) := (a -> b)) -> (((Conclusion e <.:> u) :. (u0 :. (v :. w))) := a) -> ((Conclusion e <.:> u) :. (u0 :. (v :. w))) := b

Applicative u => Applicative (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

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

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

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

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

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

(<**>) :: Applicative u0 => ((((->) e <:.> u) :. u0) := (a -> b)) -> ((((->) e <:.> u) :. u0) := a) -> (((->) e <:.> u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((->) e <:.> u) :. (u0 :. v)) := (a -> b)) -> ((((->) e <:.> u) :. (u0 :. v)) := a) -> (((->) e <:.> u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((->) e <:.> u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((->) e <:.> u) :. (u0 :. (v :. w))) := a) -> (((->) e <:.> u) :. (u0 :. (v :. w))) := b

(Applicative u, Applicative t) => Applicative (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<*>) :: (t <:.> Construction u) (a -> b) -> (t <:.> Construction u) a -> (t <:.> Construction u) b

apply :: (t <:.> Construction u) (a -> b) -> (t <:.> Construction u) a -> (t <:.> Construction u) b

(*>) :: (t <:.> Construction u) a -> (t <:.> Construction u) b -> (t <:.> Construction u) b

(<*) :: (t <:.> Construction u) a -> (t <:.> Construction u) b -> (t <:.> Construction u) a

forever :: (t <:.> Construction u) a -> (t <:.> Construction u) b

(<**>) :: Applicative u0 => (((t <:.> Construction u) :. u0) := (a -> b)) -> (((t <:.> Construction u) :. u0) := a) -> ((t <:.> Construction u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => (((t <:.> Construction u) :. (u0 :. v)) := (a -> b)) -> (((t <:.> Construction u) :. (u0 :. v)) := a) -> ((t <:.> Construction u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => (((t <:.> Construction u) :. (u0 :. (v :. w))) := (a -> b)) -> (((t <:.> Construction u) :. (u0 :. (v :. w))) := a) -> ((t <:.> Construction u) :. (u0 :. (v :. w))) := b

Alternative u => Alternative ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

(<+>) :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a

alter :: (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a -> (((->) s <:<.>:> (:*:) s) := u) a

(Covariant u, Alternative t) => Alternative (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(<+>) :: (t <:.> Construction u) a -> (t <:.> Construction u) a -> (t <:.> Construction u) a

alter :: (t <:.> Construction u) a -> (t <:.> Construction u) a -> (t <:.> Construction u) a

Avoidable u => Avoidable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

empty :: (((->) s <:<.>:> (:*:) s) := u) a

(Covariant u, Avoidable t) => Avoidable (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

empty :: (t <:.> Construction u) a

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

Defined in Pandora.Paradigm.Inventory.Store

Methods

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

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

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

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

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

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

($=>>) :: Covariant u0 => ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> ((u0 :. (((:*:) p <:<.>:> (->) p) := u)) := a) -> (u0 :. (((:*:) p <:<.>:> (->) p) := u)) := b

(<<=$) :: Covariant u0 => ((u0 :. (((:*:) p <:<.>:> (->) p) := u)) := a) -> ((((:*:) p <:<.>:> (->) p) := u) a -> b) -> (u0 :. (((:*:) p <:<.>:> (->) p) := u)) := b

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

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

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

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

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

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

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

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

($=>>) :: Covariant u0 => (((->) e <.:> u) a -> b) -> ((u0 :. ((->) e <.:> u)) := a) -> (u0 :. ((->) e <.:> u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((->) e <.:> u)) := a) -> (((->) e <.:> u) a -> b) -> (u0 :. ((->) e <.:> u)) := b

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

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

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

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

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

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

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

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

($=>>) :: Covariant u0 => (((:*:) e <:.> u) a -> b) -> ((u0 :. ((:*:) e <:.> u)) := a) -> (u0 :. ((:*:) e <:.> u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

Pointable u => Pointable ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

point :: a |-> (((->) s <:<.>:> (:*:) s) := u)

(Pointable u, Monoid e) => Pointable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

point :: a |-> ((:*:) e <.:> u)

Pointable u => Pointable (Maybe <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

point :: a |-> (Maybe <.:> u)

Pointable u => Pointable (Conclusion e <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

point :: a |-> (Conclusion e <.:> u)

(Covariant u, Pointable u) => Pointable (((->) e :: Type -> Type) <:.> u)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

point :: a |-> ((->) e <:.> u)

(Avoidable u, Pointable t) => Pointable (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

point :: a |-> (t <:.> Construction u)

Monad u => Monad ((((->) s :: Type -> Type) <:<.>:> (:*:) s) := u)

Defined in Pandora.Paradigm.Inventory.State

Methods

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

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

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

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

Monad u => Monad (Maybe <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

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

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

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

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

Monad u => Monad (Conclusion e <.:> u)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

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

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

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

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

(Traversable u, Traversable t) => Traversable (t <:.> Construction u)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(->>) :: (Pointable u0, Applicative u0) => (t <:.> Construction u) a -> (a -> u0 b) -> (u0 :. (t <:.> Construction u)) := b

traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> (t <:.> Construction u) a -> (u0 :. (t <:.> Construction u)) := b

sequence :: (Pointable u0, Applicative u0) => (((t <:.> Construction u) :. u0) := a) -> (u0 :. (t <:.> Construction u)) := a

(->>>) :: (Pointable u0, Applicative u0, Traversable v) => ((v :. (t <:.> Construction u)) := a) -> (a -> u0 b) -> (u0 :. (v :. (t <:.> Construction u))) := b

(->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => ((w :. (v :. (t <:.> Construction u))) := a) -> (a -> u0 b) -> (u0 :. (w :. (v :. (t <:.> Construction u)))) := b

(->>>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w, Traversable j) => ((j :. (w :. (v :. (t <:.> Construction u)))) := a) -> (a -> u0 b) -> (u0 :. (j :. (w :. (v :. (t <:.> Construction u))))) := b

Extractable u => Extractable (((:*:) p <:<.>:> ((->) p :: Type -> Type)) := u)

Defined in Pandora.Paradigm.Inventory.Store

Methods

extract :: a <-| (((:*:) p <:<.>:> (->) p) := u)

(Monoid e, Extractable u) => Extractable (((->) e :: Type -> Type) <.:> u)

Defined in Pandora.Paradigm.Inventory.Imprint

Methods

extract :: a <-| ((->) e <.:> u)

Extractable u => Extractable ((:*:) e <:.> u)

Defined in Pandora.Paradigm.Inventory.Equipment

Methods

extract :: a <-| ((:*:) e <:.> u)

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

Defined in Pandora.Paradigm.Structure.Stack

Methods

bypass :: (a -> r -> r) -> r -> ((Maybe <:.> Construction Maybe) := a) -> r

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

eta :: a -> ((w <:.> u) :. (t <.:> v)) := a

epsilon :: (((t <.:> v) :. (w <:.> u)) := a) -> a

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

eta :: a -> ((w <.:> u) :. (t <.:> v)) := a

epsilon :: (((t <.:> v) :. (w <.:> u)) := a) -> a

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

eta :: a -> ((w <.:> u) :. (v <:.> t)) := a

epsilon :: (((v <:.> t) :. (w <.:> u)) := a) -> a

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

eta :: a -> ((u <:.> w) :. (v <:.> t)) := a

epsilon :: (((v <:.> t) :. (u <:.> w)) := a) -> a

Covariant (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

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

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

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

void :: Kan 'Right t u b a -> Kan 'Right t u b ()

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

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

(<$$>) :: Covariant u0 => (a -> b0) -> ((Kan 'Right t u b :. u0) := a) -> (Kan 'Right t u b :. u0) := b0

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

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b0) -> ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0

(<&&>) :: Covariant u0 => ((Kan 'Right t u b :. u0) := a) -> (a -> b0) -> (Kan 'Right t u b :. u0) := b0

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

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> (t <:<.>:> t') u

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

lower :: forall (u :: Type -> Type). Covariant u => (t <:<.>:> t') u ~> u

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

Defined in Pandora.Paradigm.Schemes

Methods

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

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

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

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

eta :: a -> ((v <:<.>:> w) v' :. (t <:<.>:> u) t') := a

epsilon :: (((t <:<.>:> u) t' :. (v <:<.>:> w) v') := a) -> a

Pointable t => Liftable (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> UT Covariant Covariant t u

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

lift :: forall (u :: Type -> Type). Covariant u => u ~> TU Covariant Covariant t u

Extractable t => Lowerable (UT Covariant Covariant t)

Defined in Pandora.Paradigm.Schemes.UT

Methods

lower :: forall (u :: Type -> Type). Covariant u => UT Covariant Covariant t u ~> u

Extractable t => Lowerable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type)

Defined in Pandora.Paradigm.Schemes.TU

Methods

lower :: forall (u :: Type -> Type). Covariant u => TU Covariant Covariant t u ~> u

type Nonempty Stack

Defined in Pandora.Paradigm.Structure.Stack

type Nonempty Stack = Construction Maybe

type Nonempty Rose

Defined in Pandora.Paradigm.Structure.Rose

type Nonempty Rose = Construction Stack

type Nonempty Binary

Defined in Pandora.Paradigm.Structure.Binary

type Nonempty Binary = Construction Wye

type Zipper Stack

Defined in Pandora.Paradigm.Structure.Stack

type Zipper Stack = Tap (Delta <:.> Stack)

type Substructural ('Left :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural ('Left :: Type -> Wye Type) Binary a = Binary a

type Substructural ('Right :: Type -> Wye Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Substructural ('Right :: Type -> Wye Type) Binary a = Binary a

type Substructural ('Just :: Type -> Maybe Type) Rose a

Defined in Pandora.Paradigm.Structure.Rose

type Substructural ('Just :: Type -> Maybe Type) Rose a = (Stack :. Construction Stack) := a

type Focusing ('Root :: Type -> Location Type) Rose a

Defined in Pandora.Paradigm.Structure.Rose

type Focusing ('Root :: Type -> Location Type) Rose a = Maybe a

type Focusing ('Root :: Type -> Location Type) Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Focusing ('Root :: Type -> Location Type) Binary a = Maybe a

type Focusing ('Head :: Type -> Location Type) Stack a

Defined in Pandora.Paradigm.Structure.Stack

type Focusing ('Head :: Type -> Location Type) Stack a = Maybe a

type Substructural ('Left :: Type -> Wye Type) (Tap (t <:.> u)) a

Defined in Pandora.Paradigm.Structure

type Substructural ('Left :: Type -> Wye Type) (Tap (t <:.> u)) a = Substructural ('Left :: Type -> Wye Type) t (u a)

type Substructural ('Right :: Type -> Wye Type) (Tap (t <:.> u)) a

Defined in Pandora.Paradigm.Structure

type Substructural ('Right :: Type -> Wye Type) (Tap (t <:.> u)) a = Substructural ('Right :: Type -> Wye Type) t (u a)

type Substructural ('Just :: Type -> Maybe Type) (Construction Stack) a

Defined in Pandora.Paradigm.Structure.Rose

type Substructural ('Just :: Type -> Maybe Type) (Construction Stack) a = (Stack :. Construction Stack) := a

type Focusing ('Root :: Type -> Location Type) (Construction Stack) a

Defined in Pandora.Paradigm.Structure.Rose

type Focusing ('Root :: Type -> Location Type) (Construction Stack) a = a

type Rotational ('Right :: a1 -> Wye a1) (Tap (Delta <:.> Stream)) a2

Defined in Pandora.Paradigm.Structure.Stream

type Rotational ('Right :: a1 -> Wye a1) (Tap (Delta <:.> Stream)) a2 = Tap (Delta <:.> Stream) a2

type Rotational ('Left :: a1 -> Wye a1) (Tap (Delta <:.> Stream)) a2

Defined in Pandora.Paradigm.Structure.Stream

type Rotational ('Left :: a1 -> Wye a1) (Tap (Delta <:.> Stream)) a2 = Tap (Delta <:.> Stream) a2