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 infixl 1

Flipped infix version of comap

(<$$>) :: Covariant u => (a -> b) -> ((t :. u) := a) -> (t :. u) := b infixl 3

Infix versions of comap with various nesting levels

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

(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((t :. (u :. (v :. w))) := a) -> (t :. (u :. (v :. w))) := b infixl 1

(<&&>) :: Covariant u => ((t :. u) := a) -> (a -> b) -> (t :. u) := b infixl 2

Infix flipped versions of comap with various nesting levels

(<&&&>) :: (Covariant u, Covariant v) => ((t :. (u :. v)) := a) -> (a -> b) -> (t :. (u :. v)) := b infixl 3

(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((t :. (u :. (v :. w))) := a) -> (a -> b) -> (t :. (u :. (v :. w))) := b infixl 4

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 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

Deletable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

delete :: Setoid a => a -> Stack a -> Stack a

Measurable 'Length Stack

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Measural 'Length Stack a

Methods

measurement :: Tagged 'Length (Stack a) -> Measural 'Length Stack a

Measurable 'Heighth Binary

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Measural 'Heighth Binary a

Methods

measurement :: Tagged 'Heighth (Binary a) -> Measural 'Heighth Binary a

Morphable o (Construction Wye) => Morphable (o :: k) Binary

Defined in Pandora.Paradigm.Structure

Associated Types

type Morphing o Binary :: Type -> Type

Methods

morphing :: (Tagged o <:.> Binary) ~> Morphing o Binary

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

Defined in Pandora.Paradigm.Structure.Stack

Methods

reduce :: (a -> r -> r) -> r -> ((Maybe <:.> Construction Maybe) := a) -> r

resolve :: (a -> r) -> r -> ((Maybe <:.> Construction Maybe) := a) -> r

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 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 (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 (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 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 (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 (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 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 (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 (Store s)

Defined in Pandora.Paradigm.Inventory.Store

Methods

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

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

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

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

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

loeb :: Store s (a <:= Store s) -> Store s a

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

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

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

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

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

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

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

Extendable (Tap ((:*:) <:.:> Stream))

Defined in Pandora.Paradigm.Structure.Stream

Methods

(=>>) :: Tap ((:*:) <:.:> Stream) a -> (Tap ((:*:) <:.:> Stream) a -> b) -> Tap ((:*:) <:.:> Stream) b

(<<=) :: (Tap ((:*:) <:.:> Stream) a -> b) -> Tap ((:*:) <:.:> Stream) a -> Tap ((:*:) <:.:> Stream) b

extend :: (Tap ((:*:) <:.:> Stream) a -> b) -> Tap ((:*:) <:.:> Stream) a -> Tap ((:*:) <:.:> Stream) b

duplicate :: Tap ((:*:) <:.:> Stream) a -> (Tap ((:*:) <:.:> Stream) :. Tap ((:*:) <:.:> Stream)) := a

(=<=) :: (Tap ((:*:) <:.:> Stream) b -> c) -> (Tap ((:*:) <:.:> Stream) a -> b) -> Tap ((:*:) <:.:> Stream) a -> c

(=>=) :: (Tap ((:*:) <:.:> Stream) a -> b) -> (Tap ((:*:) <:.:> Stream) b -> c) -> Tap ((:*:) <:.:> Stream) a -> c

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

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

Extendable (Tap ((:*:) <:.:> Stack))

Defined in Pandora.Paradigm.Structure.Stack

Methods

(=>>) :: Tap ((:*:) <:.:> Stack) a -> (Tap ((:*:) <:.:> Stack) a -> b) -> Tap ((:*:) <:.:> Stack) b

(<<=) :: (Tap ((:*:) <:.:> Stack) a -> b) -> Tap ((:*:) <:.:> Stack) a -> Tap ((:*:) <:.:> Stack) b

extend :: (Tap ((:*:) <:.:> Stack) a -> b) -> Tap ((:*:) <:.:> Stack) a -> Tap ((:*:) <:.:> Stack) b

duplicate :: Tap ((:*:) <:.:> Stack) a -> (Tap ((:*:) <:.:> Stack) :. Tap ((:*:) <:.:> Stack)) := a

(=<=) :: (Tap ((:*:) <:.:> Stack) b -> c) -> (Tap ((:*:) <:.:> Stack) a -> b) -> Tap ((:*:) <:.:> Stack) a -> c

(=>=) :: (Tap ((:*:) <:.:> Stack) a -> b) -> (Tap ((:*:) <:.:> Stack) b -> c) -> Tap ((:*:) <:.:> Stack) a -> c

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

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

Nullable Stack

Defined in Pandora.Paradigm.Structure.Stack

Methods

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

Nullable Rose

Defined in Pandora.Paradigm.Structure.Rose

Methods

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

Nullable Binary

Defined in Pandora.Paradigm.Structure.Binary

Methods

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

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

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

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

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream))

Defined in Pandora.Paradigm.Structure.Stream

Associated Types

type Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Stream)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((:*:) <:.:> Stream)) ~> Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Stream))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream))

Defined in Pandora.Paradigm.Structure.Stream

Associated Types

type Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Stream)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((:*:) <:.:> Stream)) ~> Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Stream))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe))

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((:*:) <:.:> Construction Maybe)) ~> Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Construction Maybe))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe))

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Construction Maybe)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((:*:) <:.:> Construction Maybe)) ~> Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Construction Maybe))

Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack))

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Stack)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Right) <:.> Tap ((:*:) <:.:> Stack)) ~> Morphing ('Rotate 'Right) (Tap ((:*:) <:.:> Stack))

Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack))

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Stack)) :: Type -> Type

Methods

morphing :: (Tagged ('Rotate 'Left) <:.> Tap ((:*:) <:.:> Stack)) ~> Morphing ('Rotate 'Left) (Tap ((:*:) <:.:> Stack))

Morphable ('Down ('Right :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Morphing ('Down 'Right) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) :: Type -> Type

Methods

morphing :: (Tagged ('Down 'Right) <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) ~> Morphing ('Down 'Right) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Morphable ('Down ('Left :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Morphing ('Down 'Left) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) :: Type -> Type

Methods

morphing :: (Tagged ('Down 'Left) <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) ~> Morphing ('Down 'Left) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

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

Morphable Stack (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Morphing Stack (Construction Maybe) :: Type -> Type

Methods

morphing :: (Tagged Stack <:.> Construction Maybe) ~> Morphing Stack (Construction Maybe)

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

Defined in Pandora.Paradigm.Structure.Stack

Associated Types

type Substructural 'Tail Stack :: Type -> Type

Methods

substructure :: (Tagged 'Tail <:.> Stack) :~. Substructural 'Tail Stack

sub :: Stack :~. Substructural 'Tail Stack

subview :: Stack ~> Substructural 'Tail Stack

substitute :: (Substructural 'Tail Stack a0 -> Substructural 'Tail Stack a0) -> Stack a0 -> Stack a0

subplace :: Substructural 'Tail Stack a0 -> Stack a0 -> Stack a0

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

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural 'Just Rose :: Type -> Type

Methods

substructure :: (Tagged 'Just <:.> Rose) :~. Substructural 'Just Rose

sub :: Rose :~. Substructural 'Just Rose

subview :: Rose ~> Substructural 'Just Rose

substitute :: (Substructural 'Just Rose a0 -> Substructural 'Just Rose a0) -> Rose a0 -> Rose a0

subplace :: Substructural 'Just Rose a0 -> Rose a0 -> Rose a0

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

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural 'Right Binary :: Type -> Type

Methods

substructure :: (Tagged 'Right <:.> Binary) :~. Substructural 'Right Binary

sub :: Binary :~. Substructural 'Right Binary

subview :: Binary ~> Substructural 'Right Binary

substitute :: (Substructural 'Right Binary a0 -> Substructural 'Right Binary a0) -> Binary a0 -> Binary a0

subplace :: Substructural 'Right Binary a0 -> Binary a0 -> Binary a0

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

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Substructural 'Left Binary :: Type -> Type

Methods

substructure :: (Tagged 'Left <:.> Binary) :~. Substructural 'Left Binary

sub :: Binary :~. Substructural 'Left Binary

subview :: Binary ~> Substructural 'Left Binary

substitute :: (Substructural 'Left Binary a0 -> Substructural 'Left Binary a0) -> Binary a0 -> Binary a0

subplace :: Substructural 'Left Binary a0 -> Binary a0 -> Binary a0

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

Defined in Pandora.Paradigm.Structure.Rose

Associated Types

type Substructural 'Just (Construction Stack) :: Type -> Type

Methods

substructure :: (Tagged 'Just <:.> Construction Stack) :~. Substructural 'Just (Construction Stack)

sub :: Construction Stack :~. Substructural 'Just (Construction Stack)

subview :: Construction Stack ~> Substructural 'Just (Construction Stack)

substitute :: (Substructural 'Just (Construction Stack) a0 -> Substructural 'Just (Construction Stack) a0) -> Construction Stack a0 -> Construction Stack a0

subplace :: Substructural 'Just (Construction Stack) a0 -> Construction Stack a0 -> Construction Stack a0

Morphable ('Up :: a -> Vertical a) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

Associated Types

type Morphing 'Up (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) :: Type -> Type

Methods

morphing :: (Tagged 'Up <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) ~> Morphing 'Up (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

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

Defined in Pandora.Paradigm.Primary.Functor.Function

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 t, Covariant t', Covariant u) => Covariant ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

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

(<$$>) :: Covariant u0 => (a -> b) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b

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

(<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

(<&&>) :: Covariant u0 => ((((t <:<.>:> t') := u) :. u0) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. u0) := b

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

(<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

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

Defined in Pandora.Paradigm.Schemes.UT

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

Defined in Pandora.Paradigm.Schemes.TU

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

($>>=) :: Covariant u0 => ((u0 :. ((t <:<.>:> t') := u)) := a) -> (a -> ((t <:<.>:> t') := u) b) -> (u0 :. ((t <:<.>:> t') := u)) := b

(Traversable t, Bindable t, Applicative u, Monad u) => Bindable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

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

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

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

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

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

(Adjoint t' t, Bindable u) => Applicative ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

(<**>) :: Applicative u0 => ((((t <:<.>:> t') := u) :. u0) := (a -> b)) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b

(<***>) :: (Applicative u0, Applicative v) => ((((t <:<.>:> t') := u) :. (u0 :. v)) := (a -> b)) -> ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b

(<****>) :: (Applicative u0, Applicative v, Applicative w) => ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := (a -> b)) -> ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b

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

Defined in Pandora.Paradigm.Schemes.UT

Methods

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

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

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

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

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

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

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

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

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

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

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

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

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

(Applicative t, Covariant t', Alternative u) => Alternative ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

(Pointable t, Applicative t, Covariant t', Avoidable u) => Avoidable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

empty :: ((t <:<.>:> t') := u) a

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

Defined in Pandora.Paradigm.Schemes.TUT

Methods

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

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

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

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

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

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

($=>>) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := u)) := b

(<<=$) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := 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 => ((u0 :. ((->) e <.:> u)) := a) -> (((->) e <.:> u) a -> b) -> (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 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b

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

(Adjoint t t', Extractable u) => Extractable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

extract :: a <:= ((t <:<.>:> t') := u)

(Extractable t, Extractable u) => Extractable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

extract :: a <:= (t <.:> u)

(Extractable t, Extractable u) => Extractable (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

extract :: a <:= (t <:.> u)

(Pointable u, Adjoint t' t) => Pointable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

point :: a :=> ((t <:<.>:> t') := u)

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

Defined in Pandora.Paradigm.Schemes.UT

Methods

point :: a :=> (t <.:> u)

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

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

point :: a :=> ((:*:) e <.:> u)

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

point :: a :=> (t <:.> u)

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

Defined in Pandora.Paradigm.Schemes.TU

Methods

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

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

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

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

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

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

(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 v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <:.> u) b)

($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <:.> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <:.> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. (x :. y))) := b

(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 v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <.:> u) b)

($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <.:> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b

(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 v0 => v0 a -> ((v <:.> t) a -> b) -> v0 ((w <.:> u) b)

($|-) :: Covariant v0 => v0 ((v <:.> t) a) -> (a -> (w <.:> u) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (v <:.> t))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (v <:.> t)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (v <:.> t))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b

(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 v0 => v0 a -> ((v <:.> t) a -> b) -> v0 ((u <:.> w) b)

($|-) :: Covariant v0 => v0 ((v <:.> t) a) -> (a -> (u <:.> w) b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (v <:.> t))) := a) -> (a -> (u <:.> w) b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (v <:.> t)))) := a) -> (a -> (u <:.> w) b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (v <:.> t))))) := a) -> (a -> (u <:.> w) b) -> (v0 :. (w0 :. (x :. y))) := b

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

(-|$) :: Covariant v0 => v0 a -> ((t <:<.>:> u) t' a -> b) -> v0 ((v <:<.>:> w) v' b)

($|-) :: Covariant v0 => v0 ((t <:<.>:> u) t' a) -> (a -> (v <:<.>:> w) v' b) -> v0 b

($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <:<.>:> u) t')) := a) -> (a -> (v <:<.>:> w) v' b) -> (v0 :. w0) := b

($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <:<.>:> u) t'))) := a) -> (a -> (v <:<.>:> w) v' b) -> (v0 :. (w0 :. x)) := b

($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <:<.>:> u) t')))) := a) -> (a -> (v <:<.>:> w) v' b) -> (v0 :. (w0 :. (x :. y))) := b

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

(Bivariant p, Covariant t, Covariant u) => Covariant (T_U Covariant Covariant t p u)

Defined in Pandora.Paradigm.Schemes.T_U

Methods

(<$>) :: (a -> b) -> T_U Covariant Covariant t p u a -> T_U Covariant Covariant t p u b

comap :: (a -> b) -> T_U Covariant Covariant t p u a -> T_U Covariant Covariant t p u b

(<$) :: a -> T_U Covariant Covariant t p u b -> T_U Covariant Covariant t p u a

($>) :: T_U Covariant Covariant t p u a -> b -> T_U Covariant Covariant t p u b

void :: T_U Covariant Covariant t p u a -> T_U Covariant Covariant t p u ()

loeb :: T_U Covariant Covariant t p u (a <:= T_U Covariant Covariant t p u) -> T_U Covariant Covariant t p u a

(<&>) :: T_U Covariant Covariant t p u a -> (a -> b) -> T_U Covariant Covariant t p u b

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

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

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

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

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

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

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 ((:*:) <:.:> Stack)

type Morphing (o :: k) Binary

Defined in Pandora.Paradigm.Structure

type Morphing (o :: k) Binary = Maybe <:.> Morphing o (Construction Wye)

type Measural 'Length Stack a

Defined in Pandora.Paradigm.Structure.Stack

type Measural 'Length Stack a = Numerator

type Measural 'Heighth Binary a

Defined in Pandora.Paradigm.Structure.Binary

type Measural 'Heighth Binary a = Numerator

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 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 Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream))

Defined in Pandora.Paradigm.Structure.Stream

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream)) = Tap ((:*:) <:.:> Stream)

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream))

Defined in Pandora.Paradigm.Structure.Stream

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stream)) = Tap ((:*:) <:.:> Stream)

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe))

Defined in Pandora.Paradigm.Structure.Stack

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe)) = Maybe <:.> Zipper (Construction Maybe)

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe))

Defined in Pandora.Paradigm.Structure.Stack

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Construction Maybe)) = Maybe <:.> Zipper (Construction Maybe)

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack))

Defined in Pandora.Paradigm.Structure.Stack

type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack)) = Maybe <:.> Zipper Stack

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack))

Defined in Pandora.Paradigm.Structure.Stack

type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((:*:) <:.:> Stack)) = Maybe <:.> Zipper Stack

type Morphing ('Down ('Right :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

type Morphing ('Down ('Right :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) = Maybe <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))

type Morphing ('Down ('Left :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

type Morphing ('Down ('Left :: a -> Wye a) :: Vertical (a -> Wye a)) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) = Maybe <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))

type Morphing Stack (Construction Maybe)

Defined in Pandora.Paradigm.Structure.Stack

type Morphing Stack (Construction Maybe) = Stack

type Substructural ('Tail :: a -> Segment a) Stack

Defined in Pandora.Paradigm.Structure.Stack

type Substructural ('Tail :: a -> Segment a) Stack = Stack

type Substructural ('Just :: a -> Maybe a) Rose

Defined in Pandora.Paradigm.Structure.Rose

type Substructural ('Just :: a -> Maybe a) Rose = Stack <:.> Construction Stack

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

Defined in Pandora.Paradigm.Structure.Binary

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

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

Defined in Pandora.Paradigm.Structure.Binary

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

type Substructural ('Just :: a -> Maybe a) (Construction Stack)

Defined in Pandora.Paradigm.Structure.Rose

type Substructural ('Just :: a -> Maybe a) (Construction Stack) = Stack <:.> Construction Stack

type Morphing ('Up :: a -> Vertical a) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye)))

Defined in Pandora.Paradigm.Structure.Binary

type Morphing ('Up :: a -> Vertical a) (T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))) = Maybe <:.> T_U Covariant Covariant (Construction Wye) (:*:) ((Biforked <:.> Construction Biforked) <:.> T_ Covariant (Maybe <:.> Construction Wye))