Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
Synopsis
- class Covariant (t :: * -> *) where
- (<$>) :: (a -> b) -> t a -> t b
- comap :: (a -> b) -> t a -> t b
- (<$) :: a -> t b -> t a
- ($>) :: t a -> b -> t b
- void :: t a -> t ()
- loeb :: t (a <:= t) -> t a
- (<&>) :: t a -> (a -> b) -> t b
- (<$$>) :: Covariant u => (a -> b) -> ((t :. u) := a) -> (t :. u) := b
- (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((t :. (u :. v)) := a) -> (t :. (u :. v)) := b
- (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((t :. (u :. (v :. w))) := a) -> (t :. (u :. (v :. w))) := b
- (<&&>) :: Covariant u => ((t :. u) := a) -> (a -> b) -> (t :. u) := b
- (<&&&>) :: (Covariant u, Covariant v) => ((t :. (u :. v)) := a) -> (a -> b) -> (t :. (u :. v)) := b
- (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((t :. (u :. (v :. w))) := a) -> (a -> b) -> (t :. (u :. (v :. w))) := b
Documentation
class Covariant (t :: * -> *) where Source #
When providing a new instance, you should ensure it satisfies the two laws: * Identity morphism: comap identity ≡ identity * Interpreted of morphisms: comap (f . g) ≡ comap f . comap g
(<$>) :: (a -> b) -> t a -> t b infixl 4 Source #
Infix version of comap
comap :: (a -> b) -> t a -> t b Source #
Prefix version of <$>
(<$) :: a -> t b -> t a infixl 4 Source #
Replace all locations in the input with the same value
($>) :: t a -> b -> t b infixl 4 Source #
Flipped version of <$
Discards the result of evaluation
loeb :: t (a <:= t) -> t a Source #
Computing a value from a structure of values
(<&>) :: t a -> (a -> b) -> t b infixl 1 Source #
Flipped infix version of comap
(<$$>) :: Covariant u => (a -> b) -> ((t :. u) := a) -> (t :. u) := b infixl 3 Source #
Infix versions of comap
with various nesting levels
(<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((t :. (u :. v)) := a) -> (t :. (u :. v)) := b infixl 2 Source #
(<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((t :. (u :. (v :. w))) := a) -> (t :. (u :. (v :. w))) := b infixl 1 Source #
(<&&>) :: Covariant u => ((t :. u) := a) -> (a -> b) -> (t :. u) := b infixl 2 Source #
Infix flipped versions of comap
with various nesting levels
(<&&&>) :: (Covariant u, Covariant v) => ((t :. (u :. v)) := a) -> (a -> b) -> (t :. (u :. v)) := b infixl 3 Source #
(<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((t :. (u :. (v :. w))) := a) -> (a -> b) -> (t :. (u :. (v :. w))) := b infixl 4 Source #
Instances
Covariant Edges Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Edges (<$>) :: (a -> b) -> Edges a -> Edges b Source # comap :: (a -> b) -> Edges a -> Edges b Source # (<$) :: a -> Edges b -> Edges a Source # ($>) :: Edges a -> b -> Edges b Source # void :: Edges a -> Edges () Source # loeb :: Edges (a <:= Edges) -> Edges a Source # (<&>) :: Edges a -> (a -> b) -> Edges b Source # (<$$>) :: Covariant u => (a -> b) -> ((Edges :. u) := a) -> (Edges :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Edges :. (u :. v)) := a) -> (Edges :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Edges :. (u :. (v :. w))) := a) -> (Edges :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Edges :. u) := a) -> (a -> b) -> (Edges :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Edges :. (u :. v)) := a) -> (a -> b) -> (Edges :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Edges :. (u :. (v :. w))) := a) -> (a -> b) -> (Edges :. (u :. (v :. w))) := b Source # | |
Covariant Identity Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Identity (<$>) :: (a -> b) -> Identity a -> Identity b Source # comap :: (a -> b) -> Identity a -> Identity b Source # (<$) :: a -> Identity b -> Identity a Source # ($>) :: Identity a -> b -> Identity b Source # void :: Identity a -> Identity () Source # loeb :: Identity (a <:= Identity) -> Identity a Source # (<&>) :: Identity a -> (a -> b) -> Identity b Source # (<$$>) :: Covariant u => (a -> b) -> ((Identity :. u) := a) -> (Identity :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Identity :. (u :. v)) := a) -> (Identity :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Identity :. (u :. (v :. w))) := a) -> (Identity :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Identity :. u) := a) -> (a -> b) -> (Identity :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Identity :. (u :. v)) := a) -> (a -> b) -> (Identity :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Identity :. (u :. (v :. w))) := a) -> (a -> b) -> (Identity :. (u :. (v :. w))) := b Source # | |
Covariant Wye Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Wye (<$>) :: (a -> b) -> Wye a -> Wye b Source # comap :: (a -> b) -> Wye a -> Wye b Source # (<$) :: a -> Wye b -> Wye a Source # ($>) :: Wye a -> b -> Wye b Source # void :: Wye a -> Wye () Source # loeb :: Wye (a <:= Wye) -> Wye a Source # (<&>) :: Wye a -> (a -> b) -> Wye b Source # (<$$>) :: Covariant u => (a -> b) -> ((Wye :. u) := a) -> (Wye :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Wye :. (u :. v)) := a) -> (Wye :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Wye :. (u :. (v :. w))) := a) -> (Wye :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Wye :. u) := a) -> (a -> b) -> (Wye :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Wye :. (u :. v)) := a) -> (a -> b) -> (Wye :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Wye :. (u :. (v :. w))) := a) -> (a -> b) -> (Wye :. (u :. (v :. w))) := b Source # | |
Covariant Maybe Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Maybe (<$>) :: (a -> b) -> Maybe a -> Maybe b Source # comap :: (a -> b) -> Maybe a -> Maybe b Source # (<$) :: a -> Maybe b -> Maybe a Source # ($>) :: Maybe a -> b -> Maybe b Source # void :: Maybe a -> Maybe () Source # loeb :: Maybe (a <:= Maybe) -> Maybe a Source # (<&>) :: Maybe a -> (a -> b) -> Maybe b Source # (<$$>) :: Covariant u => (a -> b) -> ((Maybe :. u) := a) -> (Maybe :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Maybe :. (u :. v)) := a) -> (Maybe :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Maybe :. (u :. (v :. w))) := a) -> (Maybe :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Maybe :. u) := a) -> (a -> b) -> (Maybe :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Maybe :. (u :. v)) := a) -> (a -> b) -> (Maybe :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Maybe :. (u :. (v :. w))) := a) -> (a -> b) -> (Maybe :. (u :. (v :. w))) := b Source # | |
Covariant Biforked Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary (<$>) :: (a -> b) -> Biforked a -> Biforked b Source # comap :: (a -> b) -> Biforked a -> Biforked b Source # (<$) :: a -> Biforked b -> Biforked a Source # ($>) :: Biforked a -> b -> Biforked b Source # void :: Biforked a -> Biforked () Source # loeb :: Biforked (a <:= Biforked) -> Biforked a Source # (<&>) :: Biforked a -> (a -> b) -> Biforked b Source # (<$$>) :: Covariant u => (a -> b) -> ((Biforked :. u) := a) -> (Biforked :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Biforked :. (u :. v)) := a) -> (Biforked :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Biforked :. (u :. (v :. w))) := a) -> (Biforked :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Biforked :. u) := a) -> (a -> b) -> (Biforked :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Biforked :. (u :. v)) := a) -> (a -> b) -> (Biforked :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Biforked :. (u :. (v :. w))) := a) -> (a -> b) -> (Biforked :. (u :. (v :. w))) := b Source # | |
Deletable List Source # | |
Stack List Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
Measurable 'Length List Source # | |
Measurable 'Heighth Binary Source # | |
Monotonic a ((Maybe <:.> Construction Maybe) := a) Source # | |
Covariant (Proxy :: Type -> Type) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Proxy (<$>) :: (a -> b) -> Proxy a -> Proxy b Source # comap :: (a -> b) -> Proxy a -> Proxy b Source # (<$) :: a -> Proxy b -> Proxy a Source # ($>) :: Proxy a -> b -> Proxy b Source # void :: Proxy a -> Proxy () Source # loeb :: Proxy (a <:= Proxy) -> Proxy a Source # (<&>) :: Proxy a -> (a -> b) -> Proxy b Source # (<$$>) :: Covariant u => (a -> b) -> ((Proxy :. u) := a) -> (Proxy :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Proxy :. (u :. v)) := a) -> (Proxy :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Proxy :. (u :. (v :. w))) := a) -> (Proxy :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Proxy :. u) := a) -> (a -> b) -> (Proxy :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Proxy :. (u :. v)) := a) -> (a -> b) -> (Proxy :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Proxy :. (u :. (v :. w))) := a) -> (a -> b) -> (Proxy :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Jet t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Jet (<$>) :: (a -> b) -> Jet t a -> Jet t b Source # comap :: (a -> b) -> Jet t a -> Jet t b Source # (<$) :: a -> Jet t b -> Jet t a Source # ($>) :: Jet t a -> b -> Jet t b Source # void :: Jet t a -> Jet t () Source # loeb :: Jet t (a <:= Jet t) -> Jet t a Source # (<&>) :: Jet t a -> (a -> b) -> Jet t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Jet t :. u) := a) -> (Jet t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jet t :. (u :. v)) := a) -> (Jet t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jet t :. (u :. (v :. w))) := a) -> (Jet t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Jet t :. u) := a) -> (a -> b) -> (Jet t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Jet t :. (u :. v)) := a) -> (a -> b) -> (Jet t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jet t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jet t :. (u :. (v :. w))) := b Source # | |
Covariant (Wedge e) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Wedge (<$>) :: (a -> b) -> Wedge e a -> Wedge e b Source # comap :: (a -> b) -> Wedge e a -> Wedge e b Source # (<$) :: a -> Wedge e b -> Wedge e a Source # ($>) :: Wedge e a -> b -> Wedge e b Source # void :: Wedge e a -> Wedge e () Source # loeb :: Wedge e (a <:= Wedge e) -> Wedge e a Source # (<&>) :: Wedge e a -> (a -> b) -> Wedge e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Wedge e :. u) := a) -> (Wedge e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Wedge e :. (u :. v)) := a) -> (Wedge e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Wedge e :. (u :. (v :. w))) := a) -> (Wedge e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Wedge e :. u) := a) -> (a -> b) -> (Wedge e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Wedge e :. (u :. v)) := a) -> (a -> b) -> (Wedge e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Wedge e :. (u :. (v :. w))) := a) -> (a -> b) -> (Wedge e :. (u :. (v :. w))) := b Source # | |
Covariant (These e) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.These (<$>) :: (a -> b) -> These e a -> These e b Source # comap :: (a -> b) -> These e a -> These e b Source # (<$) :: a -> These e b -> These e a Source # ($>) :: These e a -> b -> These e b Source # void :: These e a -> These e () Source # loeb :: These e (a <:= These e) -> These e a Source # (<&>) :: These e a -> (a -> b) -> These e b Source # (<$$>) :: Covariant u => (a -> b) -> ((These e :. u) := a) -> (These e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((These e :. (u :. v)) := a) -> (These e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((These e :. (u :. (v :. w))) := a) -> (These e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((These e :. u) := a) -> (a -> b) -> (These e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((These e :. (u :. v)) := a) -> (a -> b) -> (These e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((These e :. (u :. (v :. w))) := a) -> (a -> b) -> (These e :. (u :. (v :. w))) := b Source # | |
Covariant (Validation e) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Validation (<$>) :: (a -> b) -> Validation e a -> Validation e b Source # comap :: (a -> b) -> Validation e a -> Validation e b Source # (<$) :: a -> Validation e b -> Validation e a Source # ($>) :: Validation e a -> b -> Validation e b Source # void :: Validation e a -> Validation e () Source # loeb :: Validation e (a <:= Validation e) -> Validation e a Source # (<&>) :: Validation e a -> (a -> b) -> Validation e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Validation e :. u) := a) -> (Validation e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Validation e :. (u :. v)) := a) -> (Validation e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Validation e :. (u :. (v :. w))) := a) -> (Validation e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Validation e :. u) := a) -> (a -> b) -> (Validation e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Validation e :. (u :. v)) := a) -> (a -> b) -> (Validation e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Validation e :. (u :. (v :. w))) := a) -> (a -> b) -> (Validation e :. (u :. (v :. w))) := b Source # | |
Covariant (Yoneda t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Yoneda (<$>) :: (a -> b) -> Yoneda t a -> Yoneda t b Source # comap :: (a -> b) -> Yoneda t a -> Yoneda t b Source # (<$) :: a -> Yoneda t b -> Yoneda t a Source # ($>) :: Yoneda t a -> b -> Yoneda t b Source # void :: Yoneda t a -> Yoneda t () Source # loeb :: Yoneda t (a <:= Yoneda t) -> Yoneda t a Source # (<&>) :: Yoneda t a -> (a -> b) -> Yoneda t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Yoneda t :. u) := a) -> (Yoneda t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Yoneda t :. (u :. v)) := a) -> (Yoneda t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Yoneda t :. (u :. (v :. w))) := a) -> (Yoneda t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Yoneda t :. u) := a) -> (a -> b) -> (Yoneda t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Yoneda t :. (u :. v)) := a) -> (a -> b) -> (Yoneda t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Yoneda t :. (u :. (v :. w))) := a) -> (a -> b) -> (Yoneda t :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Jack t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Jack (<$>) :: (a -> b) -> Jack t a -> Jack t b Source # comap :: (a -> b) -> Jack t a -> Jack t b Source # (<$) :: a -> Jack t b -> Jack t a Source # ($>) :: Jack t a -> b -> Jack t b Source # void :: Jack t a -> Jack t () Source # loeb :: Jack t (a <:= Jack t) -> Jack t a Source # (<&>) :: Jack t a -> (a -> b) -> Jack t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Jack t :. u) := a) -> (Jack t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Jack t :. (u :. v)) := a) -> (Jack t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Jack t :. (u :. (v :. w))) := a) -> (Jack t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Jack t :. u) := a) -> (a -> b) -> (Jack t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Jack t :. (u :. v)) := a) -> (a -> b) -> (Jack t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Jack t :. (u :. (v :. w))) := a) -> (a -> b) -> (Jack t :. (u :. (v :. w))) := b Source # | |
Covariant (Product s) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Product (<$>) :: (a -> b) -> Product s a -> Product s b Source # comap :: (a -> b) -> Product s a -> Product s b Source # (<$) :: a -> Product s b -> Product s a Source # ($>) :: Product s a -> b -> Product s b Source # void :: Product s a -> Product s () Source # loeb :: Product s (a <:= Product s) -> Product s a Source # (<&>) :: Product s a -> (a -> b) -> Product s b Source # (<$$>) :: Covariant u => (a -> b) -> ((Product s :. u) := a) -> (Product s :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Product s :. (u :. v)) := a) -> (Product s :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Product s :. (u :. (v :. w))) := a) -> (Product s :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Product s :. u) := a) -> (a -> b) -> (Product s :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Product s :. (u :. v)) := a) -> (a -> b) -> (Product s :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Product s :. (u :. (v :. w))) := a) -> (a -> b) -> (Product s :. (u :. (v :. w))) := b Source # | |
Covariant (Outline t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Outline (<$>) :: (a -> b) -> Outline t a -> Outline t b Source # comap :: (a -> b) -> Outline t a -> Outline t b Source # (<$) :: a -> Outline t b -> Outline t a Source # ($>) :: Outline t a -> b -> Outline t b Source # void :: Outline t a -> Outline t () Source # loeb :: Outline t (a <:= Outline t) -> Outline t a Source # (<&>) :: Outline t a -> (a -> b) -> Outline t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Outline t :. u) := a) -> (Outline t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Outline t :. (u :. v)) := a) -> (Outline t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Outline t :. (u :. (v :. w))) := a) -> (Outline t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Outline t :. u) := a) -> (a -> b) -> (Outline t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Outline t :. (u :. v)) := a) -> (a -> b) -> (Outline t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Outline t :. (u :. (v :. w))) := a) -> (a -> b) -> (Outline t :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Tap t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Tap (<$>) :: (a -> b) -> Tap t a -> Tap t b Source # comap :: (a -> b) -> Tap t a -> Tap t b Source # (<$) :: a -> Tap t b -> Tap t a Source # ($>) :: Tap t a -> b -> Tap t b Source # void :: Tap t a -> Tap t () Source # loeb :: Tap t (a <:= Tap t) -> Tap t a Source # (<&>) :: Tap t a -> (a -> b) -> Tap t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Tap t :. u) := a) -> (Tap t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Tap t :. (u :. v)) := a) -> (Tap t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Tap t :. (u :. (v :. w))) := a) -> (Tap t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Tap t :. u) := a) -> (a -> b) -> (Tap t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Tap t :. (u :. v)) := a) -> (a -> b) -> (Tap t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Tap t :. (u :. (v :. w))) := a) -> (a -> b) -> (Tap t :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Instruction t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Instruction (<$>) :: (a -> b) -> Instruction t a -> Instruction t b Source # comap :: (a -> b) -> Instruction t a -> Instruction t b Source # (<$) :: a -> Instruction t b -> Instruction t a Source # ($>) :: Instruction t a -> b -> Instruction t b Source # void :: Instruction t a -> Instruction t () Source # loeb :: Instruction t (a <:= Instruction t) -> Instruction t a Source # (<&>) :: Instruction t a -> (a -> b) -> Instruction t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Instruction t :. u) := a) -> (Instruction t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Instruction t :. (u :. v)) := a) -> (Instruction t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Instruction t :. (u :. (v :. w))) := a) -> (Instruction t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Instruction t :. u) := a) -> (a -> b) -> (Instruction t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Instruction t :. (u :. v)) := a) -> (a -> b) -> (Instruction t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Instruction t :. (u :. (v :. w))) := a) -> (a -> b) -> (Instruction t :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Construction t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Construction (<$>) :: (a -> b) -> Construction t a -> Construction t b Source # comap :: (a -> b) -> Construction t a -> Construction t b Source # (<$) :: a -> Construction t b -> Construction t a Source # ($>) :: Construction t a -> b -> Construction t b Source # void :: Construction t a -> Construction t () Source # loeb :: Construction t (a <:= Construction t) -> Construction t a Source # (<&>) :: Construction t a -> (a -> b) -> Construction t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Construction t :. u) := a) -> (Construction t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Construction t :. (u :. v)) := a) -> (Construction t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Construction t :. (u :. (v :. w))) := a) -> (Construction t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Construction t :. u) := a) -> (a -> b) -> (Construction t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Construction t :. (u :. v)) := a) -> (a -> b) -> (Construction t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Construction t :. (u :. (v :. w))) := a) -> (a -> b) -> (Construction t :. (u :. (v :. w))) := b Source # | |
Covariant (t <:.> Construction t) => Covariant (Comprehension t) Source # | |
Defined in Pandora.Paradigm.Structure.Modification.Comprehension (<$>) :: (a -> b) -> Comprehension t a -> Comprehension t b Source # comap :: (a -> b) -> Comprehension t a -> Comprehension t b Source # (<$) :: a -> Comprehension t b -> Comprehension t a Source # ($>) :: Comprehension t a -> b -> Comprehension t b Source # void :: Comprehension t a -> Comprehension t () Source # loeb :: Comprehension t (a <:= Comprehension t) -> Comprehension t a Source # (<&>) :: Comprehension t a -> (a -> b) -> Comprehension t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Comprehension t :. u) := a) -> (Comprehension t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Comprehension t :. (u :. v)) := a) -> (Comprehension t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Comprehension t :. (u :. (v :. w))) := a) -> (Comprehension t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Comprehension t :. u) := a) -> (a -> b) -> (Comprehension t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Comprehension t :. (u :. v)) := a) -> (a -> b) -> (Comprehension t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Comprehension t :. (u :. (v :. w))) := a) -> (a -> b) -> (Comprehension t :. (u :. (v :. w))) := b Source # | |
Covariant (Conclusion e) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Conclusion (<$>) :: (a -> b) -> Conclusion e a -> Conclusion e b Source # comap :: (a -> b) -> Conclusion e a -> Conclusion e b Source # (<$) :: a -> Conclusion e b -> Conclusion e a Source # ($>) :: Conclusion e a -> b -> Conclusion e b Source # void :: Conclusion e a -> Conclusion e () Source # loeb :: Conclusion e (a <:= Conclusion e) -> Conclusion e a Source # (<&>) :: Conclusion e a -> (a -> b) -> Conclusion e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Conclusion e :. u) := a) -> (Conclusion e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Conclusion e :. (u :. v)) := a) -> (Conclusion e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Conclusion e :. (u :. (v :. w))) := a) -> (Conclusion e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Conclusion e :. u) := a) -> (a -> b) -> (Conclusion e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Conclusion e :. (u :. v)) := a) -> (a -> b) -> (Conclusion e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Conclusion e :. (u :. (v :. w))) := a) -> (a -> b) -> (Conclusion e :. (u :. (v :. w))) := b Source # | |
Covariant (Store s) Source # | |
Defined in Pandora.Paradigm.Inventory.Store (<$>) :: (a -> b) -> Store s a -> Store s b Source # comap :: (a -> b) -> Store s a -> Store s b Source # (<$) :: a -> Store s b -> Store s a Source # ($>) :: Store s a -> b -> Store s b Source # void :: Store s a -> Store s () Source # loeb :: Store s (a <:= Store s) -> Store s a Source # (<&>) :: Store s a -> (a -> b) -> Store s b Source # (<$$>) :: Covariant u => (a -> b) -> ((Store s :. u) := a) -> (Store s :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Store s :. (u :. v)) := a) -> (Store s :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Store s :. (u :. (v :. w))) := a) -> (Store s :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Store s :. u) := a) -> (a -> b) -> (Store s :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Store s :. (u :. v)) := a) -> (a -> b) -> (Store s :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Store s :. (u :. (v :. w))) := a) -> (a -> b) -> (Store s :. (u :. (v :. w))) := b Source # | |
Covariant (State s) Source # | |
Defined in Pandora.Paradigm.Inventory.State (<$>) :: (a -> b) -> State s a -> State s b Source # comap :: (a -> b) -> State s a -> State s b Source # (<$) :: a -> State s b -> State s a Source # ($>) :: State s a -> b -> State s b Source # void :: State s a -> State s () Source # loeb :: State s (a <:= State s) -> State s a Source # (<&>) :: State s a -> (a -> b) -> State s b Source # (<$$>) :: Covariant u => (a -> b) -> ((State s :. u) := a) -> (State s :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((State s :. (u :. v)) := a) -> (State s :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((State s :. (u :. (v :. w))) := a) -> (State s :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((State s :. u) := a) -> (a -> b) -> (State s :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((State s :. (u :. v)) := a) -> (a -> b) -> (State s :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((State s :. (u :. (v :. w))) := a) -> (a -> b) -> (State s :. (u :. (v :. w))) := b Source # | |
Covariant (Imprint e) Source # | |
Defined in Pandora.Paradigm.Inventory.Imprint (<$>) :: (a -> b) -> Imprint e a -> Imprint e b Source # comap :: (a -> b) -> Imprint e a -> Imprint e b Source # (<$) :: a -> Imprint e b -> Imprint e a Source # ($>) :: Imprint e a -> b -> Imprint e b Source # void :: Imprint e a -> Imprint e () Source # loeb :: Imprint e (a <:= Imprint e) -> Imprint e a Source # (<&>) :: Imprint e a -> (a -> b) -> Imprint e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Imprint e :. u) := a) -> (Imprint e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Imprint e :. (u :. v)) := a) -> (Imprint e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Imprint e :. (u :. (v :. w))) := a) -> (Imprint e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Imprint e :. u) := a) -> (a -> b) -> (Imprint e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Imprint e :. (u :. v)) := a) -> (a -> b) -> (Imprint e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Imprint e :. (u :. (v :. w))) := a) -> (a -> b) -> (Imprint e :. (u :. (v :. w))) := b Source # | |
Covariant (Equipment e) Source # | |
Defined in Pandora.Paradigm.Inventory.Equipment (<$>) :: (a -> b) -> Equipment e a -> Equipment e b Source # comap :: (a -> b) -> Equipment e a -> Equipment e b Source # (<$) :: a -> Equipment e b -> Equipment e a Source # ($>) :: Equipment e a -> b -> Equipment e b Source # void :: Equipment e a -> Equipment e () Source # loeb :: Equipment e (a <:= Equipment e) -> Equipment e a Source # (<&>) :: Equipment e a -> (a -> b) -> Equipment e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Equipment e :. u) := a) -> (Equipment e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Equipment e :. (u :. v)) := a) -> (Equipment e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Equipment e :. (u :. (v :. w))) := a) -> (Equipment e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Equipment e :. u) := a) -> (a -> b) -> (Equipment e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Equipment e :. (u :. v)) := a) -> (a -> b) -> (Equipment e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Equipment e :. (u :. (v :. w))) := a) -> (a -> b) -> (Equipment e :. (u :. (v :. w))) := b Source # | |
Covariant (Environment e) Source # | |
Defined in Pandora.Paradigm.Inventory.Environment (<$>) :: (a -> b) -> Environment e a -> Environment e b Source # comap :: (a -> b) -> Environment e a -> Environment e b Source # (<$) :: a -> Environment e b -> Environment e a Source # ($>) :: Environment e a -> b -> Environment e b Source # void :: Environment e a -> Environment e () Source # loeb :: Environment e (a <:= Environment e) -> Environment e a Source # (<&>) :: Environment e a -> (a -> b) -> Environment e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Environment e :. u) := a) -> (Environment e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Environment e :. (u :. v)) := a) -> (Environment e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Environment e :. (u :. (v :. w))) := a) -> (Environment e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Environment e :. u) := a) -> (a -> b) -> (Environment e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Environment e :. (u :. v)) := a) -> (a -> b) -> (Environment e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Environment e :. (u :. (v :. w))) := a) -> (a -> b) -> (Environment e :. (u :. (v :. w))) := b Source # | |
Covariant (Accumulator e) Source # | |
Defined in Pandora.Paradigm.Inventory.Accumulator (<$>) :: (a -> b) -> Accumulator e a -> Accumulator e b Source # comap :: (a -> b) -> Accumulator e a -> Accumulator e b Source # (<$) :: a -> Accumulator e b -> Accumulator e a Source # ($>) :: Accumulator e a -> b -> Accumulator e b Source # void :: Accumulator e a -> Accumulator e () Source # loeb :: Accumulator e (a <:= Accumulator e) -> Accumulator e a Source # (<&>) :: Accumulator e a -> (a -> b) -> Accumulator e b Source # (<$$>) :: Covariant u => (a -> b) -> ((Accumulator e :. u) := a) -> (Accumulator e :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Accumulator e :. (u :. v)) := a) -> (Accumulator e :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Accumulator e :. (u :. (v :. w))) := a) -> (Accumulator e :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Accumulator e :. u) := a) -> (a -> b) -> (Accumulator e :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Accumulator e :. (u :. v)) := a) -> (a -> b) -> (Accumulator e :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Accumulator e :. (u :. (v :. w))) := a) -> (a -> b) -> (Accumulator e :. (u :. (v :. w))) := b Source # | |
Extendable (Tap ((Stream <:.:> Stream) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Stream (=>>) :: Tap ((Stream <:.:> Stream) := (:*:)) a -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) b Source # (<<=) :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> Tap ((Stream <:.:> Stream) := (:*:)) b Source # extend :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> Tap ((Stream <:.:> Stream) := (:*:)) b Source # duplicate :: Tap ((Stream <:.:> Stream) := (:*:)) a -> (Tap ((Stream <:.:> Stream) := (:*:)) :. Tap ((Stream <:.:> Stream) := (:*:))) := a Source # (=<=) :: (Tap ((Stream <:.:> Stream) := (:*:)) b -> c) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> c Source # (=>=) :: (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (Tap ((Stream <:.:> Stream) := (:*:)) b -> c) -> Tap ((Stream <:.:> Stream) := (:*:)) a -> c Source # ($=>>) :: Covariant u => ((u :. Tap ((Stream <:.:> Stream) := (:*:))) := a) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (u :. Tap ((Stream <:.:> Stream) := (:*:))) := b Source # (<<=$) :: Covariant u => ((u :. Tap ((Stream <:.:> Stream) := (:*:))) := a) -> (Tap ((Stream <:.:> Stream) := (:*:)) a -> b) -> (u :. Tap ((Stream <:.:> Stream) := (:*:))) := b Source # | |
Extendable (Tap ((List <:.:> List) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List (=>>) :: Tap ((List <:.:> List) := (:*:)) a -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) b Source # (<<=) :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> Tap ((List <:.:> List) := (:*:)) b Source # extend :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> Tap ((List <:.:> List) := (:*:)) b Source # duplicate :: Tap ((List <:.:> List) := (:*:)) a -> (Tap ((List <:.:> List) := (:*:)) :. Tap ((List <:.:> List) := (:*:))) := a Source # (=<=) :: (Tap ((List <:.:> List) := (:*:)) b -> c) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> Tap ((List <:.:> List) := (:*:)) a -> c Source # (=>=) :: (Tap ((List <:.:> List) := (:*:)) a -> b) -> (Tap ((List <:.:> List) := (:*:)) b -> c) -> Tap ((List <:.:> List) := (:*:)) a -> c Source # ($=>>) :: Covariant u => ((u :. Tap ((List <:.:> List) := (:*:))) := a) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> (u :. Tap ((List <:.:> List) := (:*:))) := b Source # (<<=$) :: Covariant u => ((u :. Tap ((List <:.:> List) := (:*:))) := a) -> (Tap ((List <:.:> List) := (:*:)) a -> b) -> (u :. Tap ((List <:.:> List) := (:*:))) := b Source # | |
Semigroup (List a) Source # | |
Monoid (List a) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
Setoid a => Setoid (List a) Source # | |
Nullable List Source # | |
Nullable Rose Source # | |
Nullable Binary Source # | |
Monad u => Catchable e (Conclusion e <.:> u :: Type -> Type) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Conclusion catch :: forall (a :: k). (Conclusion e <.:> u) a -> (e -> (Conclusion e <.:> u) a) -> (Conclusion e <.:> u) a Source # | |
Focusable ('Root :: Type -> Location Type) Rose Source # | |
(forall a. Chain a) => Focusable ('Root :: Type -> Location Type) Binary Source # | |
Focusable ('Head :: Type -> Location Type) List Source # | |
Focusable ('Root :: Type -> Location Type) (Construction List) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose | |
Morphable ('Into (o ds)) (Construction Wye) => Morphable ('Into (o ds) :: Morph a) Binary Source # | |
Morphable ('Into List) (Construction Maybe) Source # | |
Morphable ('Into Binary) (Construction Wye) Source # | |
Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Stream | |
Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) Source # | |
Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
Morphable ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) Source # | |
Morphable ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) Source # | |
Morphable ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) Source # | |
Morphable ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
Morphable ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
Morphable ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
Covariant t => Hoistable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type) Source # | |
Covariant (Tagged tag) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Tagged (<$>) :: (a -> b) -> Tagged tag a -> Tagged tag b Source # comap :: (a -> b) -> Tagged tag a -> Tagged tag b Source # (<$) :: a -> Tagged tag b -> Tagged tag a Source # ($>) :: Tagged tag a -> b -> Tagged tag b Source # void :: Tagged tag a -> Tagged tag () Source # loeb :: Tagged tag (a <:= Tagged tag) -> Tagged tag a Source # (<&>) :: Tagged tag a -> (a -> b) -> Tagged tag b Source # (<$$>) :: Covariant u => (a -> b) -> ((Tagged tag :. u) := a) -> (Tagged tag :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Tagged tag :. (u :. v)) := a) -> (Tagged tag :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Tagged tag :. (u :. (v :. w))) := a) -> (Tagged tag :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Tagged tag :. u) := a) -> (a -> b) -> (Tagged tag :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Tagged tag :. (u :. v)) := a) -> (a -> b) -> (Tagged tag :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Tagged tag :. (u :. (v :. w))) := a) -> (a -> b) -> (Tagged tag :. (u :. (v :. w))) := b Source # | |
Covariant (Constant a :: Type -> Type) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Constant (<$>) :: (a0 -> b) -> Constant a a0 -> Constant a b Source # comap :: (a0 -> b) -> Constant a a0 -> Constant a b Source # (<$) :: a0 -> Constant a b -> Constant a a0 Source # ($>) :: Constant a a0 -> b -> Constant a b Source # void :: Constant a a0 -> Constant a () Source # loeb :: Constant a (a0 <:= Constant a) -> Constant a a0 Source # (<&>) :: Constant a a0 -> (a0 -> b) -> Constant a b Source # (<$$>) :: Covariant u => (a0 -> b) -> ((Constant a :. u) := a0) -> (Constant a :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> ((Constant a :. (u :. v)) := a0) -> (Constant a :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> ((Constant a :. (u :. (v :. w))) := a0) -> (Constant a :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Constant a :. u) := a0) -> (a0 -> b) -> (Constant a :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Constant a :. (u :. v)) := a0) -> (a0 -> b) -> (Constant a :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Constant a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> (Constant a :. (u :. (v :. w))) := b Source # | |
Covariant (Schematic Monad t u) => Covariant (t :> u) Source # | |
Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (<$>) :: (a -> b) -> (t :> u) a -> (t :> u) b Source # comap :: (a -> b) -> (t :> u) a -> (t :> u) b Source # (<$) :: a -> (t :> u) b -> (t :> u) a Source # ($>) :: (t :> u) a -> b -> (t :> u) b Source # void :: (t :> u) a -> (t :> u) () Source # loeb :: (t :> u) (a <:= (t :> u)) -> (t :> u) a Source # (<&>) :: (t :> u) a -> (a -> b) -> (t :> u) b Source # (<$$>) :: Covariant u0 => (a -> b) -> (((t :> u) :. u0) := a) -> ((t :> u) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((t :> u) :. (u0 :. v)) := a) -> ((t :> u) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t :> u) :. (u0 :. (v :. w))) := a) -> ((t :> u) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => (((t :> u) :. u0) := a) -> (a -> b) -> ((t :> u) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => (((t :> u) :. (u0 :. v)) := a) -> (a -> b) -> ((t :> u) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t :> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t :> u) :. (u0 :. (v :. w))) := b Source # | |
Covariant (Day t u) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Day (<$>) :: (a -> b) -> Day t u a -> Day t u b Source # comap :: (a -> b) -> Day t u a -> Day t u b Source # (<$) :: a -> Day t u b -> Day t u a Source # ($>) :: Day t u a -> b -> Day t u b Source # void :: Day t u a -> Day t u () Source # loeb :: Day t u (a <:= Day t u) -> Day t u a Source # (<&>) :: Day t u a -> (a -> b) -> Day t u b Source # (<$$>) :: Covariant u0 => (a -> b) -> ((Day t u :. u0) := a) -> (Day t u :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((Day t u :. (u0 :. v)) := a) -> (Day t u :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((Day t u :. (u0 :. (v :. w))) := a) -> (Day t u :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => ((Day t u :. u0) := a) -> (a -> b) -> (Day t u :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => ((Day t u :. (u0 :. v)) := a) -> (a -> b) -> (Day t u :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Day t u :. (u0 :. (v :. w))) := a) -> (a -> b) -> (Day t u :. (u0 :. (v :. w))) := b Source # | |
Covariant t => Covariant (Backwards t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Backwards (<$>) :: (a -> b) -> Backwards t a -> Backwards t b Source # comap :: (a -> b) -> Backwards t a -> Backwards t b Source # (<$) :: a -> Backwards t b -> Backwards t a Source # ($>) :: Backwards t a -> b -> Backwards t b Source # void :: Backwards t a -> Backwards t () Source # loeb :: Backwards t (a <:= Backwards t) -> Backwards t a Source # (<&>) :: Backwards t a -> (a -> b) -> Backwards t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Backwards t :. u) := a) -> (Backwards t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Backwards t :. (u :. v)) := a) -> (Backwards t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Backwards t :. (u :. (v :. w))) := a) -> (Backwards t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Backwards t :. u) := a) -> (a -> b) -> (Backwards t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Backwards t :. (u :. v)) := a) -> (a -> b) -> (Backwards t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Backwards t :. (u :. (v :. w))) := a) -> (a -> b) -> (Backwards t :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Reverse t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Reverse (<$>) :: (a -> b) -> Reverse t a -> Reverse t b Source # comap :: (a -> b) -> Reverse t a -> Reverse t b Source # (<$) :: a -> Reverse t b -> Reverse t a Source # ($>) :: Reverse t a -> b -> Reverse t b Source # void :: Reverse t a -> Reverse t () Source # loeb :: Reverse t (a <:= Reverse t) -> Reverse t a Source # (<&>) :: Reverse t a -> (a -> b) -> Reverse t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Reverse t :. u) := a) -> (Reverse t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Reverse t :. (u :. v)) := a) -> (Reverse t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Reverse t :. (u :. (v :. w))) := a) -> (Reverse t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Reverse t :. u) := a) -> (a -> b) -> (Reverse t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Reverse t :. (u :. v)) := a) -> (a -> b) -> (Reverse t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Reverse t :. (u :. (v :. w))) := a) -> (a -> b) -> (Reverse t :. (u :. (v :. w))) := b Source # | |
Covariant (Schematic Comonad t u) => Covariant (t :< u) Source # | |
Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic (<$>) :: (a -> b) -> (t :< u) a -> (t :< u) b Source # comap :: (a -> b) -> (t :< u) a -> (t :< u) b Source # (<$) :: a -> (t :< u) b -> (t :< u) a Source # ($>) :: (t :< u) a -> b -> (t :< u) b Source # void :: (t :< u) a -> (t :< u) () Source # loeb :: (t :< u) (a <:= (t :< u)) -> (t :< u) a Source # (<&>) :: (t :< u) a -> (a -> b) -> (t :< u) b Source # (<$$>) :: Covariant u0 => (a -> b) -> (((t :< u) :. u0) := a) -> ((t :< u) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((t :< u) :. (u0 :. v)) := a) -> ((t :< u) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t :< u) :. (u0 :. (v :. w))) := a) -> ((t :< u) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => (((t :< u) :. u0) := a) -> (a -> b) -> ((t :< u) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => (((t :< u) :. (u0 :. v)) := a) -> (a -> b) -> ((t :< u) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t :< u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t :< u) :. (u0 :. (v :. w))) := b Source # | |
Covariant t => Covariant (Prefixed t k) Source # | |
Defined in Pandora.Paradigm.Structure.Modification.Prefixed (<$>) :: (a -> b) -> Prefixed t k a -> Prefixed t k b Source # comap :: (a -> b) -> Prefixed t k a -> Prefixed t k b Source # (<$) :: a -> Prefixed t k b -> Prefixed t k a Source # ($>) :: Prefixed t k a -> b -> Prefixed t k b Source # void :: Prefixed t k a -> Prefixed t k () Source # loeb :: Prefixed t k (a <:= Prefixed t k) -> Prefixed t k a Source # (<&>) :: Prefixed t k a -> (a -> b) -> Prefixed t k b Source # (<$$>) :: Covariant u => (a -> b) -> ((Prefixed t k :. u) := a) -> (Prefixed t k :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Prefixed t k :. (u :. v)) := a) -> (Prefixed t k :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Prefixed t k :. (u :. (v :. w))) := a) -> (Prefixed t k :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Prefixed t k :. u) := a) -> (a -> b) -> (Prefixed t k :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Prefixed t k :. (u :. v)) := a) -> (a -> b) -> (Prefixed t k :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Prefixed t k :. (u :. (v :. w))) := a) -> (a -> b) -> (Prefixed t k :. (u :. (v :. w))) := b Source # | |
Morphable ('Pop :: a -> Morph a) List Source # | |
Morphable ('Push :: a -> Morph a) List Source # | |
(forall a1. Chain a1) => Morphable ('Insert :: a -> Morph a) Binary Source # | |
Substructure ('Tail :: a -> Segment a) List Source # | |
Defined in Pandora.Paradigm.Structure.Some.List type Substructural 'Tail List :: Type -> Type Source # substructure :: (Tagged 'Tail <:.> List) :~. Substructural 'Tail List Source # sub :: List :~. Substructural 'Tail List Source # subview :: List ~> Substructural 'Tail List Source # substitute :: (Substructural 'Tail List a0 -> Substructural 'Tail List a0) -> List a0 -> List a0 Source # subplace :: Substructural 'Tail List a0 -> List a0 -> List a0 Source # | |
Substructure ('Just :: a -> Maybe a) Rose Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose type Substructural 'Just Rose :: Type -> Type Source # substructure :: (Tagged 'Just <:.> Rose) :~. Substructural 'Just Rose Source # sub :: Rose :~. Substructural 'Just Rose Source # subview :: Rose ~> Substructural 'Just Rose Source # substitute :: (Substructural 'Just Rose a0 -> Substructural 'Just Rose a0) -> Rose a0 -> Rose a0 Source # subplace :: Substructural 'Just Rose a0 -> Rose a0 -> Rose a0 Source # | |
Substructure ('Right :: a -> Wye a) Binary Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary type Substructural 'Right Binary :: Type -> Type Source # substructure :: (Tagged 'Right <:.> Binary) :~. Substructural 'Right Binary Source # sub :: Binary :~. Substructural 'Right Binary Source # subview :: Binary ~> Substructural 'Right Binary Source # substitute :: (Substructural 'Right Binary a0 -> Substructural 'Right Binary a0) -> Binary a0 -> Binary a0 Source # subplace :: Substructural 'Right Binary a0 -> Binary a0 -> Binary a0 Source # | |
Substructure ('Left :: a -> Wye a) Binary Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary type Substructural 'Left Binary :: Type -> Type Source # substructure :: (Tagged 'Left <:.> Binary) :~. Substructural 'Left Binary Source # sub :: Binary :~. Substructural 'Left Binary Source # subview :: Binary ~> Substructural 'Left Binary Source # substitute :: (Substructural 'Left Binary a0 -> Substructural 'Left Binary a0) -> Binary a0 -> Binary a0 Source # subplace :: Substructural 'Left Binary a0 -> Binary a0 -> Binary a0 Source # | |
Substructure ('Just :: a -> Maybe a) (Construction List) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose type Substructural 'Just (Construction List) :: Type -> Type Source # substructure :: (Tagged 'Just <:.> Construction List) :~. Substructural 'Just (Construction List) Source # sub :: Construction List :~. Substructural 'Just (Construction List) Source # subview :: Construction List ~> Substructural 'Just (Construction List) Source # substitute :: (Substructural 'Just (Construction List) a0 -> Substructural 'Just (Construction List) a0) -> Construction List a0 -> Construction List a0 Source # subplace :: Substructural 'Just (Construction List) a0 -> Construction List a0 -> Construction List a0 Source # | |
Covariant ((->) a :: Type -> Type) Source # | |
Defined in Pandora.Paradigm.Primary.Functor.Function (<$>) :: (a0 -> b) -> (a -> a0) -> a -> b Source # comap :: (a0 -> b) -> (a -> a0) -> a -> b Source # (<$) :: a0 -> (a -> b) -> a -> a0 Source # ($>) :: (a -> a0) -> b -> a -> b Source # void :: (a -> a0) -> a -> () Source # loeb :: (a -> (a0 <:= (->) a)) -> a -> a0 Source # (<&>) :: (a -> a0) -> (a0 -> b) -> a -> b Source # (<$$>) :: Covariant u => (a0 -> b) -> (((->) a :. u) := a0) -> ((->) a :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a0 -> b) -> (((->) a :. (u :. v)) := a0) -> ((->) a :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a0 -> b) -> (((->) a :. (u :. (v :. w))) := a0) -> ((->) a :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => (((->) a :. u) := a0) -> (a0 -> b) -> ((->) a :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => (((->) a :. (u :. v)) := a0) -> (a0 -> b) -> ((->) a :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => (((->) a :. (u :. (v :. w))) := a0) -> (a0 -> b) -> ((->) a :. (u :. (v :. w))) := b Source # | |
Covariant t => Covariant (Continuation r t) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Continuation (<$>) :: (a -> b) -> Continuation r t a -> Continuation r t b Source # comap :: (a -> b) -> Continuation r t a -> Continuation r t b Source # (<$) :: a -> Continuation r t b -> Continuation r t a Source # ($>) :: Continuation r t a -> b -> Continuation r t b Source # void :: Continuation r t a -> Continuation r t () Source # loeb :: Continuation r t (a <:= Continuation r t) -> Continuation r t a Source # (<&>) :: Continuation r t a -> (a -> b) -> Continuation r t b Source # (<$$>) :: Covariant u => (a -> b) -> ((Continuation r t :. u) := a) -> (Continuation r t :. u) := b Source # (<$$$>) :: (Covariant u, Covariant v) => (a -> b) -> ((Continuation r t :. (u :. v)) := a) -> (Continuation r t :. (u :. v)) := b Source # (<$$$$>) :: (Covariant u, Covariant v, Covariant w) => (a -> b) -> ((Continuation r t :. (u :. (v :. w))) := a) -> (Continuation r t :. (u :. (v :. w))) := b Source # (<&&>) :: Covariant u => ((Continuation r t :. u) := a) -> (a -> b) -> (Continuation r t :. u) := b Source # (<&&&>) :: (Covariant u, Covariant v) => ((Continuation r t :. (u :. v)) := a) -> (a -> b) -> (Continuation r t :. (u :. v)) := b Source # (<&&&&>) :: (Covariant u, Covariant v, Covariant w) => ((Continuation r t :. (u :. (v :. w))) := a) -> (a -> b) -> (Continuation r t :. (u :. (v :. w))) := b Source # | |
(Divariant p, Contravariant t, Covariant u) => Covariant ((t >:.:> u) := p) Source # | |
Defined in Pandora.Paradigm.Schemes.T_U (<$>) :: (a -> b) -> ((t >:.:> u) := p) a -> ((t >:.:> u) := p) b Source # comap :: (a -> b) -> ((t >:.:> u) := p) a -> ((t >:.:> u) := p) b Source # (<$) :: a -> ((t >:.:> u) := p) b -> ((t >:.:> u) := p) a Source # ($>) :: ((t >:.:> u) := p) a -> b -> ((t >:.:> u) := p) b Source # void :: ((t >:.:> u) := p) a -> ((t >:.:> u) := p) () Source # loeb :: ((t >:.:> u) := p) (a <:= ((t >:.:> u) := p)) -> ((t >:.:> u) := p) a Source # (<&>) :: ((t >:.:> u) := p) a -> (a -> b) -> ((t >:.:> u) := p) b Source # (<$$>) :: Covariant u0 => (a -> b) -> ((((t >:.:> u) := p) :. u0) := a) -> (((t >:.:> u) := p) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((t >:.:> u) := p) :. (u0 :. v)) := a) -> (((t >:.:> u) := p) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((t >:.:> u) := p) :. (u0 :. (v :. w))) := a) -> (((t >:.:> u) := p) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => ((((t >:.:> u) := p) :. u0) := a) -> (a -> b) -> (((t >:.:> u) := p) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => ((((t >:.:> u) := p) :. (u0 :. v)) := a) -> (a -> b) -> (((t >:.:> u) := p) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((t >:.:> u) := p) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t >:.:> u) := p) :. (u0 :. (v :. w))) := b Source # | |
(Bivariant p, Covariant t, Covariant u) => Covariant ((t <:.:> u) := p) Source # | |
Defined in Pandora.Paradigm.Schemes.T_U (<$>) :: (a -> b) -> ((t <:.:> u) := p) a -> ((t <:.:> u) := p) b Source # comap :: (a -> b) -> ((t <:.:> u) := p) a -> ((t <:.:> u) := p) b Source # (<$) :: a -> ((t <:.:> u) := p) b -> ((t <:.:> u) := p) a Source # ($>) :: ((t <:.:> u) := p) a -> b -> ((t <:.:> u) := p) b Source # void :: ((t <:.:> u) := p) a -> ((t <:.:> u) := p) () Source # loeb :: ((t <:.:> u) := p) (a <:= ((t <:.:> u) := p)) -> ((t <:.:> u) := p) a Source # (<&>) :: ((t <:.:> u) := p) a -> (a -> b) -> ((t <:.:> u) := p) b Source # (<$$>) :: Covariant u0 => (a -> b) -> ((((t <:.:> u) := p) :. u0) := a) -> (((t <:.:> u) := p) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((t <:.:> u) := p) :. (u0 :. v)) := a) -> (((t <:.:> u) := p) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((t <:.:> u) := p) :. (u0 :. (v :. w))) := a) -> (((t <:.:> u) := p) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => ((((t <:.:> u) := p) :. u0) := a) -> (a -> b) -> (((t <:.:> u) := p) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => ((((t <:.:> u) := p) :. (u0 :. v)) := a) -> (a -> b) -> (((t <:.:> u) := p) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((t <:.:> u) := p) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t <:.:> u) := p) :. (u0 :. (v :. w))) := b Source # | |
(Covariant t, Covariant t', Covariant u) => Covariant ((t <:<.>:> t') := u) Source # | |
Defined in Pandora.Paradigm.Schemes.TUT (<$>) :: (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # comap :: (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # (<$) :: a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) a Source # ($>) :: ((t <:<.>:> t') := u) a -> b -> ((t <:<.>:> t') := u) b Source # void :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) () Source # loeb :: ((t <:<.>:> t') := u) (a <:= ((t <:<.>:> t') := u)) -> ((t <:<.>:> t') := u) a Source # (<&>) :: ((t <:<.>:> t') := u) a -> (a -> b) -> ((t <:<.>:> t') := u) b Source # (<$$>) :: Covariant u0 => (a -> b) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => ((((t <:<.>:> t') := u) :. u0) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> (((t <:<.>:> t') := u) :. (u0 :. (v :. w))) := b Source # | |
(Covariant t, Covariant u) => Covariant (t <.:> u) Source # | |
Defined in Pandora.Paradigm.Schemes.UT (<$>) :: (a -> b) -> (t <.:> u) a -> (t <.:> u) b Source # comap :: (a -> b) -> (t <.:> u) a -> (t <.:> u) b Source # (<$) :: a -> (t <.:> u) b -> (t <.:> u) a Source # ($>) :: (t <.:> u) a -> b -> (t <.:> u) b Source # void :: (t <.:> u) a -> (t <.:> u) () Source # loeb :: (t <.:> u) (a <:= (t <.:> u)) -> (t <.:> u) a Source # (<&>) :: (t <.:> u) a -> (a -> b) -> (t <.:> u) b Source # (<$$>) :: Covariant u0 => (a -> b) -> (((t <.:> u) :. u0) := a) -> ((t <.:> u) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((t <.:> u) :. (u0 :. v)) := a) -> ((t <.:> u) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t <.:> u) :. (u0 :. (v :. w))) := a) -> ((t <.:> u) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => (((t <.:> u) :. u0) := a) -> (a -> b) -> ((t <.:> u) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => (((t <.:> u) :. (u0 :. v)) := a) -> (a -> b) -> ((t <.:> u) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t <.:> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t <.:> u) :. (u0 :. (v :. w))) := b Source # | |
(Covariant t, Covariant u) => Covariant (t <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes.TU (<$>) :: (a -> b) -> (t <:.> u) a -> (t <:.> u) b Source # comap :: (a -> b) -> (t <:.> u) a -> (t <:.> u) b Source # (<$) :: a -> (t <:.> u) b -> (t <:.> u) a Source # ($>) :: (t <:.> u) a -> b -> (t <:.> u) b Source # void :: (t <:.> u) a -> (t <:.> u) () Source # loeb :: (t <:.> u) (a <:= (t <:.> u)) -> (t <:.> u) a Source # (<&>) :: (t <:.> u) a -> (a -> b) -> (t <:.> u) b Source # (<$$>) :: Covariant u0 => (a -> b) -> (((t <:.> u) :. u0) := a) -> ((t <:.> u) :. u0) := b Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b) -> (((t <:.> u) :. (u0 :. v)) := a) -> ((t <:.> u) :. (u0 :. v)) := b Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b) -> (((t <:.> u) :. (u0 :. (v :. w))) := a) -> ((t <:.> u) :. (u0 :. (v :. w))) := b Source # (<&&>) :: Covariant u0 => (((t <:.> u) :. u0) := a) -> (a -> b) -> ((t <:.> u) :. u0) := b Source # (<&&&>) :: (Covariant u0, Covariant v) => (((t <:.> u) :. (u0 :. v)) := a) -> (a -> b) -> ((t <:.> u) :. (u0 :. v)) := b Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => (((t <:.> u) :. (u0 :. (v :. w))) := a) -> (a -> b) -> ((t <:.> u) :. (u0 :. (v :. w))) := b Source # | |
(Adjoint t' t, Bindable u) => Bindable ((t <:<.>:> t') := u) Source # | |
Defined in Pandora.Paradigm.Schemes.TUT (>>=) :: ((t <:<.>:> t') := u) a -> (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) b Source # (=<<) :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # bind :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # join :: ((((t <:<.>:> t') := u) :. ((t <:<.>:> t') := u)) := a) -> ((t <:<.>:> t') := u) a Source # (>=>) :: (a -> ((t <:<.>:> t') := u) b) -> (b -> ((t <:<.>:> t') := u) c) -> a -> ((t <:<.>:> t') := u) c Source # (<=<) :: (b -> ((t <:<.>:> t') := u) c) -> (a -> ((t <:<.>:> t') := u) b) -> a -> ((t <:<.>:> t') := u) c Source # ($>>=) :: Covariant u0 => ((u0 :. ((t <:<.>:> t') := u)) := a) -> (a -> ((t <:<.>:> t') := u) b) -> (u0 :. ((t <:<.>:> t') := u)) := b Source # | |
(Traversable t, Bindable t, Applicative u, Monad u) => Bindable (t <.:> u) Source # | |
Defined in Pandora.Paradigm.Schemes.UT (>>=) :: (t <.:> u) a -> (a -> (t <.:> u) b) -> (t <.:> u) b Source # (=<<) :: (a -> (t <.:> u) b) -> (t <.:> u) a -> (t <.:> u) b Source # bind :: (a -> (t <.:> u) b) -> (t <.:> u) a -> (t <.:> u) b Source # join :: (((t <.:> u) :. (t <.:> u)) := a) -> (t <.:> u) a Source # (>=>) :: (a -> (t <.:> u) b) -> (b -> (t <.:> u) c) -> a -> (t <.:> u) c Source # (<=<) :: (b -> (t <.:> u) c) -> (a -> (t <.:> u) b) -> a -> (t <.:> u) c Source # ($>>=) :: Covariant u0 => ((u0 :. (t <.:> u)) := a) -> (a -> (t <.:> u) b) -> (u0 :. (t <.:> u)) := b Source # | |
(Semigroup e, Pointable u, Bindable u) => Bindable ((:*:) e <.:> u) Source # | |
Defined in Pandora.Paradigm.Inventory.Accumulator (>>=) :: ((:*:) e <.:> u) a -> (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) b Source # (=<<) :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b Source # bind :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b Source # join :: ((((:*:) e <.:> u) :. ((:*:) e <.:> u)) := a) -> ((:*:) e <.:> u) a Source # (>=>) :: (a -> ((:*:) e <.:> u) b) -> (b -> ((:*:) e <.:> u) c) -> a -> ((:*:) e <.:> u) c Source # (<=<) :: (b -> ((:*:) e <.:> u) c) -> (a -> ((:*:) e <.:> u) b) -> a -> ((:*:) e <.:> u) c Source # ($>>=) :: Covariant u0 => ((u0 :. ((:*:) e <.:> u)) := a) -> (a -> ((:*:) e <.:> u) b) -> (u0 :. ((:*:) e <.:> u)) := b Source # | |
(Bindable t, Distributive t, Bindable u) => Bindable (t <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes.TU (>>=) :: (t <:.> u) a -> (a -> (t <:.> u) b) -> (t <:.> u) b Source # (=<<) :: (a -> (t <:.> u) b) -> (t <:.> u) a -> (t <:.> u) b Source # bind :: (a -> (t <:.> u) b) -> (t <:.> u) a -> (t <:.> u) b Source # join :: (((t <:.> u) :. (t <:.> u)) := a) -> (t <:.> u) a Source # (>=>) :: (a -> (t <:.> u) b) -> (b -> (t <:.> u) c) -> a -> (t <:.> u) c Source # (<=<) :: (b -> (t <:.> u) c) -> (a -> (t <:.> u) b) -> a -> (t <:.> u) c Source # ($>>=) :: Covariant u0 => ((u0 :. (t <:.> u)) := a) -> (a -> (t <:.> u) b) -> (u0 :. (t <:.> u)) := b Source # | |
(Adjoint t' t, Bindable u) => Applicative ((t <:<.>:> t') := u) Source # | |
Defined in Pandora.Paradigm.Schemes.TUT (<*>) :: ((t <:<.>:> t') := u) (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # apply :: ((t <:<.>:> t') := u) (a -> b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # (*>) :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) b Source # (<*) :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b -> ((t <:<.>:> t') := u) a Source # forever :: ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b Source # (<**>) :: Applicative u0 => ((((t <:<.>:> t') := u) :. u0) := (a -> b)) -> ((((t <:<.>:> t') := u) :. u0) := a) -> (((t <:<.>:> t') := u) :. u0) := b Source # (<***>) :: (Applicative u0, Applicative v) => ((((t <:<.>:> t') := u) :. (u0 :. v)) := (a -> b)) -> ((((t <:<.>:> t') := u) :. (u0 :. v)) := a) -> (((t <:<.>:> t') := u) :. (u0 :. v)) := b Source # (<****>) :: (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 Source # | |
(Applicative t, Applicative u) => Applicative (t <.:> u) Source # | |
Defined in Pandora.Paradigm.Schemes.UT (<*>) :: (t <.:> u) (a -> b) -> (t <.:> u) a -> (t <.:> u) b Source # apply :: (t <.:> u) (a -> b) -> (t <.:> u) a -> (t <.:> u) b Source # (*>) :: (t <.:> u) a -> (t <.:> u) b -> (t <.:> u) b Source # (<*) :: (t <.:> u) a -> (t <.:> u) b -> (t <.:> u) a Source # forever :: (t <.:> u) a -> (t <.:> u) b Source # (<**>) :: Applicative u0 => (((t <.:> u) :. u0) := (a -> b)) -> (((t <.:> u) :. u0) := a) -> ((t <.:> u) :. u0) := b Source # (<***>) :: (Applicative u0, Applicative v) => (((t <.:> u) :. (u0 :. v)) := (a -> b)) -> (((t <.:> u) :. (u0 :. v)) := a) -> ((t <.:> u) :. (u0 :. v)) := b Source # (<****>) :: (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 Source # | |
(Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u) Source # | |
Defined in Pandora.Paradigm.Inventory.Accumulator (<*>) :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b Source # apply :: ((:*:) e <.:> u) (a -> b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b Source # (*>) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) b Source # (<*) :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b -> ((:*:) e <.:> u) a Source # forever :: ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b Source # (<**>) :: Applicative u0 => ((((:*:) e <.:> u) :. u0) := (a -> b)) -> ((((:*:) e <.:> u) :. u0) := a) -> (((:*:) e <.:> u) :. u0) := b Source # (<***>) :: (Applicative u0, Applicative v) => ((((:*:) e <.:> u) :. (u0 :. v)) := (a -> b)) -> ((((:*:) e <.:> u) :. (u0 :. v)) := a) -> (((:*:) e <.:> u) :. (u0 :. v)) := b Source # (<****>) :: (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 Source # | |
(Applicative t, Applicative u) => Applicative (t <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes.TU (<*>) :: (t <:.> u) (a -> b) -> (t <:.> u) a -> (t <:.> u) b Source # apply :: (t <:.> u) (a -> b) -> (t <:.> u) a -> (t <:.> u) b Source # (*>) :: (t <:.> u) a -> (t <:.> u) b -> (t <:.> u) b Source # (<*) :: (t <:.> u) a -> (t <:.> u) b -> (t <:.> u) a Source # forever :: (t <:.> u) a -> (t <:.> u) b Source # (<**>) :: Applicative u0 => (((t <:.> u) :. u0) := (a -> b)) -> (((t <:.> u) :. u0) := a) -> ((t <:.> u) :. u0) := b Source # (<***>) :: (Applicative u0, Applicative v) => (((t <:.> u) :. (u0 :. v)) := (a -> b)) -> (((t <:.> u) :. (u0 :. v)) := a) -> ((t <:.> u) :. (u0 :. v)) := b Source # (<****>) :: (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 Source # | |
(Applicative t, Covariant t', Alternative u) => Alternative ((t <:<.>:> t') := u) Source # | |
(Covariant u, Alternative t) => Alternative (t <:.> u) Source # | |
(Pointable t, Applicative t, Covariant t', Avoidable u) => Avoidable ((t <:<.>:> t') := u) Source # | |
(Covariant u, Avoidable t) => Avoidable (t <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes.TU | |
(Adjoint t' t, Extendable u) => Extendable ((t' <:<.>:> t) := u) Source # | |
Defined in Pandora.Paradigm.Schemes.TUT (=>>) :: ((t' <:<.>:> t) := u) a -> (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) b Source # (<<=) :: (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> ((t' <:<.>:> t) := u) b Source # extend :: (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> ((t' <:<.>:> t) := u) b Source # duplicate :: ((t' <:<.>:> t) := u) a -> (((t' <:<.>:> t) := u) :. ((t' <:<.>:> t) := u)) := a Source # (=<=) :: (((t' <:<.>:> t) := u) b -> c) -> (((t' <:<.>:> t) := u) a -> b) -> ((t' <:<.>:> t) := u) a -> c Source # (=>=) :: (((t' <:<.>:> t) := u) a -> b) -> (((t' <:<.>:> t) := u) b -> c) -> ((t' <:<.>:> t) := u) a -> c Source # ($=>>) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := u)) := b Source # (<<=$) :: Covariant u0 => ((u0 :. ((t' <:<.>:> t) := u)) := a) -> (((t' <:<.>:> t) := u) a -> b) -> (u0 :. ((t' <:<.>:> t) := u)) := b Source # | |
(Semigroup e, Extendable u) => Extendable (((->) e :: Type -> Type) <.:> u) Source # | |
Defined in Pandora.Paradigm.Inventory.Imprint (=>>) :: ((->) e <.:> u) a -> (((->) e <.:> u) a -> b) -> ((->) e <.:> u) b Source # (<<=) :: (((->) e <.:> u) a -> b) -> ((->) e <.:> u) a -> ((->) e <.:> u) b Source # extend :: (((->) e <.:> u) a -> b) -> ((->) e <.:> u) a -> ((->) e <.:> u) b Source # duplicate :: ((->) e <.:> u) a -> (((->) e <.:> u) :. ((->) e <.:> u)) := a Source # (=<=) :: (((->) e <.:> u) b -> c) -> (((->) e <.:> u) a -> b) -> ((->) e <.:> u) a -> c Source # (=>=) :: (((->) e <.:> u) a -> b) -> (((->) e <.:> u) b -> c) -> ((->) e <.:> u) a -> c Source # ($=>>) :: Covariant u0 => ((u0 :. ((->) e <.:> u)) := a) -> (((->) e <.:> u) a -> b) -> (u0 :. ((->) e <.:> u)) := b Source # (<<=$) :: Covariant u0 => ((u0 :. ((->) e <.:> u)) := a) -> (((->) e <.:> u) a -> b) -> (u0 :. ((->) e <.:> u)) := b Source # | |
Extendable u => Extendable ((:*:) e <:.> u) Source # | |
Defined in Pandora.Paradigm.Inventory.Equipment (=>>) :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) b Source # (<<=) :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b Source # extend :: (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> ((:*:) e <:.> u) b Source # duplicate :: ((:*:) e <:.> u) a -> (((:*:) e <:.> u) :. ((:*:) e <:.> u)) := a Source # (=<=) :: (((:*:) e <:.> u) b -> c) -> (((:*:) e <:.> u) a -> b) -> ((:*:) e <:.> u) a -> c Source # (=>=) :: (((:*:) e <:.> u) a -> b) -> (((:*:) e <:.> u) b -> c) -> ((:*:) e <:.> u) a -> c Source # ($=>>) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b Source # (<<=$) :: Covariant u0 => ((u0 :. ((:*:) e <:.> u)) := a) -> (((:*:) e <:.> u) a -> b) -> (u0 :. ((:*:) e <:.> u)) := b Source # | |
(Adjoint t t', Extractable u) => Extractable ((t <:<.>:> t') := u) Source # | |
(Extractable t, Extractable u) => Extractable (t <.:> u) Source # | |
(Extractable t, Extractable u) => Extractable (t <:.> u) Source # | |
(Pointable u, Adjoint t' t) => Pointable ((t <:<.>:> t') := u) Source # | |
(Pointable t, Pointable u) => Pointable (t <.:> u) Source # | |
(Pointable u, Monoid e) => Pointable ((:*:) e <.:> u) Source # | |
(Pointable t, Pointable u) => Pointable (t <:.> u) Source # | |
(Traversable t, Traversable u) => Traversable (t <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes.TU (->>) :: (Pointable u0, Applicative u0) => (t <:.> u) a -> (a -> u0 b) -> (u0 :. (t <:.> u)) := b Source # traverse :: (Pointable u0, Applicative u0) => (a -> u0 b) -> (t <:.> u) a -> (u0 :. (t <:.> u)) := b Source # sequence :: (Pointable u0, Applicative u0) => (((t <:.> u) :. u0) := a) -> (u0 :. (t <:.> u)) := a Source # (->>>) :: (Pointable u0, Applicative u0, Traversable v) => ((v :. (t <:.> u)) := a) -> (a -> u0 b) -> (u0 :. (v :. (t <:.> u))) := b Source # (->>>>) :: (Pointable u0, Applicative u0, Traversable v, Traversable w) => ((w :. (v :. (t <:.> u))) := a) -> (a -> u0 b) -> (u0 :. (w :. (v :. (t <:.> u)))) := b Source # (->>>>>) :: (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 Source # | |
(Covariant (t <.:> v), Covariant (w <:.> u), Adjoint v u, Adjoint t w) => Adjoint (t <.:> v) (w <:.> u) Source # | |
Defined in Pandora.Paradigm.Schemes (-|) :: a -> ((t <.:> v) a -> b) -> (w <:.> u) b Source # (|-) :: (t <.:> v) a -> (a -> (w <:.> u) b) -> b Source # phi :: ((t <.:> v) a -> b) -> a -> (w <:.> u) b Source # psi :: (a -> (w <:.> u) b) -> (t <.:> v) a -> b Source # eta :: a -> ((w <:.> u) :. (t <.:> v)) := a Source # epsilon :: (((t <.:> v) :. (w <:.> u)) := a) -> a Source # (-|$) :: Covariant v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <:.> u) b) Source # ($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <:.> u) b) -> v0 b Source # ($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <:.> u) b) -> (v0 :. w0) := b Source # ($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. x)) := b Source # ($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <:.> u) b) -> (v0 :. (w0 :. (x :. y))) := b Source # | |
(Covariant (t <.:> v), Covariant (w <.:> u), Adjoint t u, Adjoint v w) => Adjoint (t <.:> v) (w <.:> u) Source # | |
Defined in Pandora.Paradigm.Schemes (-|) :: a -> ((t <.:> v) a -> b) -> (w <.:> u) b Source # (|-) :: (t <.:> v) a -> (a -> (w <.:> u) b) -> b Source # phi :: ((t <.:> v) a -> b) -> a -> (w <.:> u) b Source # psi :: (a -> (w <.:> u) b) -> (t <.:> v) a -> b Source # eta :: a -> ((w <.:> u) :. (t <.:> v)) := a Source # epsilon :: (((t <.:> v) :. (w <.:> u)) := a) -> a Source # (-|$) :: Covariant v0 => v0 a -> ((t <.:> v) a -> b) -> v0 ((w <.:> u) b) Source # ($|-) :: Covariant v0 => v0 ((t <.:> v) a) -> (a -> (w <.:> u) b) -> v0 b Source # ($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <.:> v))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b Source # ($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <.:> v)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b Source # ($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (t <.:> v))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b Source # | |
(Covariant (v <:.> t), Covariant (w <.:> u), Adjoint t u, Adjoint v w) => Adjoint (v <:.> t) (w <.:> u) Source # | |
Defined in Pandora.Paradigm.Schemes (-|) :: a -> ((v <:.> t) a -> b) -> (w <.:> u) b Source # (|-) :: (v <:.> t) a -> (a -> (w <.:> u) b) -> b Source # phi :: ((v <:.> t) a -> b) -> a -> (w <.:> u) b Source # psi :: (a -> (w <.:> u) b) -> (v <:.> t) a -> b Source # eta :: a -> ((w <.:> u) :. (v <:.> t)) := a Source # epsilon :: (((v <:.> t) :. (w <.:> u)) := a) -> a Source # (-|$) :: Covariant v0 => v0 a -> ((v <:.> t) a -> b) -> v0 ((w <.:> u) b) Source # ($|-) :: Covariant v0 => v0 ((v <:.> t) a) -> (a -> (w <.:> u) b) -> v0 b Source # ($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (v <:.> t))) := a) -> (a -> (w <.:> u) b) -> (v0 :. w0) := b Source # ($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (v <:.> t)))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. x)) := b Source # ($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (v <:.> t))))) := a) -> (a -> (w <.:> u) b) -> (v0 :. (w0 :. (x :. y))) := b Source # | |
(Covariant (v <:.> t), Covariant (u <:.> w), Adjoint t u, Adjoint v w) => Adjoint (v <:.> t) (u <:.> w) Source # | |
Defined in Pandora.Paradigm.Schemes (-|) :: a -> ((v <:.> t) a -> b) -> (u <:.> w) b Source # (|-) :: (v <:.> t) a -> (a -> (u <:.> w) b) -> b Source # phi :: ((v <:.> t) a -> b) -> a -> (u <:.> w) b Source # psi :: (a -> (u <:.> w) b) -> (v <:.> t) a -> b Source # eta :: a -> ((u <:.> w) :. (v <:.> t)) := a Source # epsilon :: (((v <:.> t) :. (u <:.> w)) := a) -> a Source # (-|$) :: Covariant v0 => v0 a -> ((v <:.> t) a -> b) -> v0 ((u <:.> w) b) Source # ($|-) :: Covariant v0 => v0 ((v <:.> t) a) -> (a -> (u <:.> w) b) -> v0 b Source # ($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (v <:.> t))) := a) -> (a -> (u <:.> w) b) -> (v0 :. w0) := b Source # ($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (v <:.> t)))) := a) -> (a -> (u <:.> w) b) -> (v0 :. (w0 :. x)) := b Source # ($$$$|-) :: (Covariant v0, Covariant w0, Covariant x, Covariant y) => ((v0 :. (w0 :. (x :. (y :. (v <:.> t))))) := a) -> (a -> (u <:.> w) b) -> (v0 :. (w0 :. (x :. y))) := b Source # | |
Covariant (Kan ('Right :: Type -> Wye Type) t u b) Source # | |
Defined in Pandora.Paradigm.Primary.Transformer.Kan (<$>) :: (a -> b0) -> Kan 'Right t u b a -> Kan 'Right t u b b0 Source # comap :: (a -> b0) -> Kan 'Right t u b a -> Kan 'Right t u b b0 Source # (<$) :: a -> Kan 'Right t u b b0 -> Kan 'Right t u b a Source # ($>) :: Kan 'Right t u b a -> b0 -> Kan 'Right t u b b0 Source # void :: Kan 'Right t u b a -> Kan 'Right t u b () Source # loeb :: Kan 'Right t u b (a <:= Kan 'Right t u b) -> Kan 'Right t u b a Source # (<&>) :: Kan 'Right t u b a -> (a -> b0) -> Kan 'Right t u b b0 Source # (<$$>) :: Covariant u0 => (a -> b0) -> ((Kan 'Right t u b :. u0) := a) -> (Kan 'Right t u b :. u0) := b0 Source # (<$$$>) :: (Covariant u0, Covariant v) => (a -> b0) -> ((Kan 'Right t u b :. (u0 :. v)) := a) -> (Kan 'Right t u b :. (u0 :. v)) := b0 Source # (<$$$$>) :: (Covariant u0, Covariant v, Covariant w) => (a -> b0) -> ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0 Source # (<&&>) :: Covariant u0 => ((Kan 'Right t u b :. u0) := a) -> (a -> b0) -> (Kan 'Right t u b :. u0) := b0 Source # (<&&&>) :: (Covariant u0, Covariant v) => ((Kan 'Right t u b :. (u0 :. v)) := a) -> (a -> b0) -> (Kan 'Right t u b :. (u0 :. v)) := b0 Source # (<&&&&>) :: (Covariant u0, Covariant v, Covariant w) => ((Kan 'Right t u b :. (u0 :. (v :. w))) := a) -> (a -> b0) -> (Kan 'Right t u b :. (u0 :. (v :. w))) := b0 Source # | |
(Adjoint t' t, Distributive t) => Liftable (t <:<.>:> t') Source # | |
(Adjoint t t', Distributive t') => Lowerable (t <:<.>:> t') Source # | |
(Covariant ((t <:<.>:> u) t'), Covariant ((v <:<.>:> w) v'), Adjoint t w, Adjoint t' v', Adjoint t v, Adjoint u v, Adjoint v' t') => Adjoint ((t <:<.>:> u) t') ((v <:<.>:> w) v') Source # | |
Defined in Pandora.Paradigm.Schemes (-|) :: a -> ((t <:<.>:> u) t' a -> b) -> (v <:<.>:> w) v' b Source # (|-) :: (t <:<.>:> u) t' a -> (a -> (v <:<.>:> w) v' b) -> b Source # phi :: ((t <:<.>:> u) t' a -> b) -> a -> (v <:<.>:> w) v' b Source # psi :: (a -> (v <:<.>:> w) v' b) -> (t <:<.>:> u) t' a -> b Source # eta :: a -> ((v <:<.>:> w) v' :. (t <:<.>:> u) t') := a Source # epsilon :: (((t <:<.>:> u) t' :. (v <:<.>:> w) v') := a) -> a Source # (-|$) :: Covariant v0 => v0 a -> ((t <:<.>:> u) t' a -> b) -> v0 ((v <:<.>:> w) v' b) Source # ($|-) :: Covariant v0 => v0 ((t <:<.>:> u) t' a) -> (a -> (v <:<.>:> w) v' b) -> v0 b Source # ($$|-) :: (Covariant v0, Covariant w0) => ((v0 :. (w0 :. (t <:<.>:> u) t')) := a) -> (a -> (v <:<.>:> w) v' b) -> (v0 :. w0) := b Source # ($$$|-) :: (Covariant v0, Covariant w0, Covariant x) => ((v0 :. (w0 :. (x :. (t <:<.>:> u) t'))) := a) -> (a -> (v <:<.>:> w) v' b) -> (v0 :. (w0 :. x)) := b Source # ($$$$|-) :: (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 Source # | |
Pointable t => Liftable (UT Covariant Covariant t) Source # | |
Pointable t => Liftable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type) Source # | |
Extractable t => Lowerable (UT Covariant Covariant t) Source # | |
Extractable t => Lowerable (TU Covariant Covariant t :: (Type -> Type) -> Type -> Type) Source # | |
type Nonempty List Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Nonempty Rose Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose | |
type Nonempty Binary Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Zipper List Source # | |
type Measural 'Length List a Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Measural 'Heighth Binary a Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Focusing ('Root :: Type -> Location Type) Rose a Source # | |
type Focusing ('Root :: Type -> Location Type) Binary a Source # | |
type Focusing ('Head :: Type -> Location Type) List a Source # | |
type Focusing ('Root :: Type -> Location Type) (Construction List) a Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose | |
type Morphing ('Into (o ds) :: Morph a) Binary Source # | |
type Morphing ('Into List) (Construction Maybe) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Morphing ('Into Binary) (Construction Wye) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) Source # | |
type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Stream <:.:> Stream) := (:*:))) Source # | |
type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((Construction Maybe <:.:> Construction Maybe) := (:*:))) Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Morphing ('Rotate ('Right :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) Source # | |
type Morphing ('Rotate ('Left :: a -> Wye a) :: Morph (a -> Wye a)) (Tap ((List <:.:> List) := (:*:))) Source # | |
type Morphing ('Into Wye) ((Maybe <:.:> Maybe) := (:*:)) Source # | |
type Morphing ('Rotate ('Up :: a -> Vertical a) :: Morph (a -> Vertical a)) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Morphing ('Rotate ('Down ('Right :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
type Morphing ('Rotate ('Down ('Left :: a -> Wye a)) :: Morph (Vertical (a -> Wye a))) ((Construction Wye <:.:> (Bifurcation <:.> Bicursor)) := (:*:)) Source # | |
type Morphing ('Pop :: a -> Morph a) List Source # | |
type Morphing ('Push :: a -> Morph a) List Source # | |
type Morphing ('Insert :: a -> Morph a) Binary Source # | |
type Substructural ('Tail :: a -> Segment a) List Source # | |
Defined in Pandora.Paradigm.Structure.Some.List | |
type Substructural ('Just :: a -> Maybe a) Rose Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose | |
type Substructural ('Right :: a -> Wye a) Binary Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Substructural ('Left :: a -> Wye a) Binary Source # | |
Defined in Pandora.Paradigm.Structure.Some.Binary | |
type Substructural ('Just :: a -> Maybe a) (Construction List) Source # | |
Defined in Pandora.Paradigm.Structure.Some.Rose |