pandora 0.4.6 → 0.4.7

raw patch · 93 files changed

+898/−779 lines, 93 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• CHANGELOG.md +22/−0
• Pandora/Core.hs +1/−0
• Pandora/Core/Appliable.hs +6/−0
• Pandora/Paradigm/Controlflow/Effect/Adaptable.hs +13/−12
• Pandora/Paradigm/Controlflow/Effect/Interpreted.hs +46/−34
• Pandora/Paradigm/Controlflow/Effect/Transformer.hs +5/−5
• Pandora/Paradigm/Controlflow/Effect/Transformer/Comonadic.hs +16/−13
• Pandora/Paradigm/Controlflow/Effect/Transformer/Monadic.hs +16/−13
• Pandora/Paradigm/Controlflow/Observable.hs +7/−7
• Pandora/Paradigm/Controlflow/Pipeline.hs +6/−6
• Pandora/Paradigm/Inventory/Accumulator.hs +8/−6
• Pandora/Paradigm/Inventory/Environment.hs +18/−15
• Pandora/Paradigm/Inventory/Equipment.hs +5/−5
• Pandora/Paradigm/Inventory/Imprint.hs +8/−8
• Pandora/Paradigm/Inventory/Optics.hs +7/−3
• Pandora/Paradigm/Inventory/State.hs +18/−16
• Pandora/Paradigm/Inventory/Store.hs +12/−10
• Pandora/Paradigm/Primary.hs +10/−9
• Pandora/Paradigm/Primary/Algebraic.hs +56/−45
• Pandora/Paradigm/Primary/Algebraic/Exponential.hs +20/−12
• Pandora/Paradigm/Primary/Algebraic/Product.hs +13/−13
• Pandora/Paradigm/Primary/Algebraic/Sum.hs +6/−6
• Pandora/Paradigm/Primary/Functor/Conclusion.hs +24/−21
• Pandora/Paradigm/Primary/Functor/Constant.hs +6/−6
• Pandora/Paradigm/Primary/Functor/Convergence.hs +2/−2
• Pandora/Paradigm/Primary/Functor/Edges.hs +8/−8
• Pandora/Paradigm/Primary/Functor/Endo.hs +1/−1
• Pandora/Paradigm/Primary/Functor/Fix.hs +3/−3
• Pandora/Paradigm/Primary/Functor/Identity.hs +17/−15
• Pandora/Paradigm/Primary/Functor/Maybe.hs +24/−21
• Pandora/Paradigm/Primary/Functor/Predicate.hs +3/−3
• Pandora/Paradigm/Primary/Functor/Proxy.hs +4/−4
• Pandora/Paradigm/Primary/Functor/Tagged.hs +16/−15
• Pandora/Paradigm/Primary/Functor/These.hs +6/−6
• Pandora/Paradigm/Primary/Functor/Validation.hs +30/−27
• Pandora/Paradigm/Primary/Functor/Wedge.hs +5/−5
• Pandora/Paradigm/Primary/Functor/Wye.hs +8/−8
• Pandora/Paradigm/Primary/Transformer.hs +0/−8
• Pandora/Paradigm/Primary/Transformer/Backwards.hs +16/−18
• Pandora/Paradigm/Primary/Transformer/Construction.hs +26/−20
• Pandora/Paradigm/Primary/Transformer/Continuation.hs +8/−7
• Pandora/Paradigm/Primary/Transformer/Day.hs +2/−2
• Pandora/Paradigm/Primary/Transformer/Flip.hs +0/−3
• Pandora/Paradigm/Primary/Transformer/Instruction.hs +24/−20
• Pandora/Paradigm/Primary/Transformer/Jack.hs +7/−7
• Pandora/Paradigm/Primary/Transformer/Jet.hs +4/−4
• Pandora/Paradigm/Primary/Transformer/Kan.hs +6/−6
• Pandora/Paradigm/Primary/Transformer/Outline.hs +3/−3
• Pandora/Paradigm/Primary/Transformer/Reverse.hs +16/−16
• Pandora/Paradigm/Primary/Transformer/Tap.hs +19/−17
• Pandora/Paradigm/Primary/Transformer/Yoneda.hs +3/−3
• Pandora/Paradigm/Schemes/PQ_.hs +1/−1
• Pandora/Paradigm/Schemes/PTU.hs +1/−1
• Pandora/Paradigm/Schemes/P_Q_T.hs +1/−1
• Pandora/Paradigm/Schemes/P_T.hs +1/−1
• Pandora/Paradigm/Schemes/TU.hs +23/−24
• Pandora/Paradigm/Schemes/TUT.hs +17/−19
• Pandora/Paradigm/Schemes/TUVW.hs +1/−1
• Pandora/Paradigm/Schemes/T_U.hs +6/−6
• Pandora/Paradigm/Schemes/UT.hs +20/−21
• Pandora/Paradigm/Schemes/UTU.hs +1/−1
• Pandora/Paradigm/Schemes/U_T.hs +1/−1
• Pandora/Paradigm/Structure.hs +3/−3
• Pandora/Paradigm/Structure/Ability.hs +0/−1
• Pandora/Paradigm/Structure/Ability/Measurable.hs +0/−15
• Pandora/Paradigm/Structure/Ability/Substructure.hs +2/−2
• Pandora/Paradigm/Structure/Interface/Set.hs +1/−1
• Pandora/Paradigm/Structure/Modification/Comprehension.hs +16/−15
• Pandora/Paradigm/Structure/Modification/Prefixed.hs +7/−7
• Pandora/Paradigm/Structure/Some/Binary.hs +29/−39
• Pandora/Paradigm/Structure/Some/List.hs +19/−30
• Pandora/Paradigm/Structure/Some/Rose.hs +2/−2
• Pandora/Paradigm/Structure/Some/Splay.hs +10/−10
• Pandora/Paradigm/Structure/Some/Stream.hs +2/−2
• Pandora/Pattern.hs +2/−0
• Pandora/Pattern/Category.hs +1/−1
• Pandora/Pattern/Functor/Bivariant.hs +2/−2
• Pandora/Pattern/Functor/Comonad.hs +1/−1
• Pandora/Pattern/Functor/Contravariant.hs +4/−4
• Pandora/Pattern/Functor/Covariant.hs +19/−29
• Pandora/Pattern/Functor/Distributive.hs +1/−1
• Pandora/Pattern/Functor/Divariant.hs +2/−2
• Pandora/Pattern/Functor/Extendable.hs +2/−2
• Pandora/Pattern/Functor/Monad.hs +2/−1
• Pandora/Pattern/Functor/Monoidal.hs +1/−1
• Pandora/Pattern/Functor/Semimonoidal.hs +2/−2
• Pandora/Pattern/Functor/Traversable.hs +5/−4
• Pandora/Pattern/Groupoid.hs +11/−0
• Pandora/Pattern/Morphism.hs +8/−0
• Pandora/Pattern/Morphism/Flip.hs +27/−0
• Pandora/Pattern/Morphism/Straight.hs +26/−0
• Pandora/Pattern/Transformer/Hoistable.hs +2/−5
• pandora.cabal +6/−3

@@ -583,3 +583,25 @@ * Rearrange type parameters in `Divariant` typeclass * Generalize `Liftable` typeclass * Generalize `Lowerable` typeclass++# 0.4.7+* Remove `hoist` method from `Hoistable` typeclass+* Rename `-<$>-` method to `<$>` in `Covariant` typeclasss+* Rename `->$<-` method to `>$<` in `Contravariant` typeclass+* Define `Straight` transformer+* Define `-->` type synonymous+* Define `Opposite` type family+* Define experimental `Appliable` typeclass+* Rename `multiply` method to `mult` in `Semimonoidal` typeclass+* Generalize `Interpreted` typeclass+* Define `Groupoid` typeclass+* Remove `Measurable` typeclass+* Rename `Applicative_` typeclass to `Applicative`+* Rename `Alternative_` typeclass to `Alternative`+* Rename `-<*>-` method of Applicative to `<-*-`+* Add functional dependencies to `Appliable` typeclass+* Remove `-<$$>-`, `-<<$>-`, `-<$$>>-` in favor of `<$$>`+* Remove `-<$$$>-` in favor of `<$$$>`+* Remove `-<$$$$>-` in favor of `<$$$$>`++# 0.4.8

@@ -1,4 +1,5 @@ module Pandora.Core (module Exports) where  import Pandora.Core.Impliable as Exports+import Pandora.Core.Appliable as Exports import Pandora.Core.Functor as Exports

@@ -0,0 +1,6 @@+module Pandora.Core.Appliable where++infixr 0 !++class Appliable m a b n c d | m a b -> n c d where+	(!) :: m a b -> n c d

@@ -9,9 +9,10 @@ import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Functor.Monad (Monad)-import Pandora.Pattern.Transformer (Liftable (lift), Lowerable (lower), Hoistable (hoist))+import Pandora.Pattern.Transformer (Liftable (lift), Lowerable (lower), Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic (Extractable_)+import Pandora.Paradigm.Primary.Algebraic (Extractable) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic) import Pandora.Paradigm.Controlflow.Effect.Transformer (Monadic, Comonadic, wrap, bring, (:>), (:<)) @@ -21,8 +22,8 @@  type Lifting t u = (Monadic t, Liftable (->) (Schematic Monad t), Covariant (->) (->) u) type Lowering t u = (Comonadic t, Lowerable (->) (Schematic Comonad t), Covariant (->) (->) u)-type Wrappable t u = (Monadic t, Monoidal (->) (->) (:*:) (:*:) u)-type Bringable t u = (Comonadic t, Extractable_ u)+type Wrappable t u = (Monadic t, Monoidal (-->) (->) (:*:) (:*:) u)+type Bringable t u = (Comonadic t, Extractable u)  instance Adaptable t t where 	adapt = identity@@ -296,7 +297,7 @@ 	adapt = bring . lower . lower . lower . lower . lower . lower . lower  instance (Covariant (->) (->) u, Hoistable ((:>) t), Adaptable u u') => Adaptable (t :> u) (t :> u') where-	adapt = hoist adapt+	adapt = (adapt /|\)  instance 	( Covariant (->) (->) v@@ -306,7 +307,7 @@ 	, Hoistable (Schematic Monad u) 	, Adaptable v v' 	) => Adaptable (t :> u :> v) (t :> u :> v') where-	adapt = hoist (hoist adapt)+	adapt = ((adapt /|\) /|\)  instance 	( Covariant (->) (->) u@@ -321,7 +322,7 @@ 	, Hoistable (Schematic Monad v) 	, Adaptable w w' 	) => Adaptable (t :> u :> v :> w) (t :> u :> v :> w') where-	adapt = hoist (hoist (hoist adapt))+	adapt = (((adapt /|\) /|\) /|\)  instance 	( Covariant (->) (->) x@@ -335,7 +336,7 @@ 	, Hoistable (Schematic Monad w) 	, Adaptable x x' 	) => Adaptable (t :> u :> v :> w :> x) (t :> u :> v :> w :> x') where-	adapt = hoist (hoist (hoist (hoist adapt)))+	adapt = (((adapt /|\) /|\) /|\)  instance 	( Covariant (->) (->) y@@ -351,7 +352,7 @@ 	, Hoistable (Schematic Monad x) 	, Adaptable y y' 	) => Adaptable (t :> u :> v :> w :> x :> y) (t :> u :> v :> w :> x :> y') where-	adapt = hoist (hoist (hoist (hoist (hoist adapt))))+	adapt = ((((adapt /|\) /|\) /|\) /|\)  instance 	( Covariant (->) (->) z@@ -370,7 +371,7 @@ 	, Adaptable z z' 	) => Adaptable (t :> u :> v :> w :> x :> y :> z) 		(t :> u :> v :> w :> x :> y :> z') where-	adapt = hoist (hoist (hoist (hoist (hoist adapt))))+	adapt = (((((adapt /|\) /|\) /|\) /|\) /|\)  instance 	( Covariant (->) (->) f@@ -391,7 +392,7 @@ 	, Adaptable f f' 	) => Adaptable (t :> u :> v :> w :> x :> y :> z :> f) 		(t :> u :> v :> w :> x :> y :> z :> f') where-	adapt = hoist (hoist (hoist (hoist (hoist (hoist adapt)))))+	adapt = ((((((adapt /|\) /|\) /|\) /|\) /|\) /|\)  instance 	( Covariant (->) (->) h@@ -414,4 +415,4 @@ 	, Adaptable h h' 	) => Adaptable (t :> u :> v :> w :> x :> y :> z :> f :> h) 		(t :> u :> v :> w :> x :> y :> z :> f :> h') where-	adapt = hoist (hoist (hoist (hoist (hoist (hoist (hoist adapt))))))+	adapt = (((((((adapt /|\) /|\) /|\) /|\) /|\) /|\) /|\)

@@ -1,59 +1,71 @@ module Pandora.Paradigm.Controlflow.Effect.Interpreted where +import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-), (-<$$$>-), (-<$$$$>-))+import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>), (<$$$>), (<$$$$>)) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Paradigm.Primary.Algebraic.Exponential ()  infixr 2 ||=, =|| -type family Schematic (c :: (* -> *) -> k) (t :: * -> *) = (r :: (* -> *) -> * -> *) | r -> t+type family Schematic (c :: (* -> * -> *) -> (* -> *) -> k) (t :: * -> *) = (r :: (* -> *) -> * -> *) | r -> t -class Interpreted t where+class Interpreted m t where 	{-# MINIMAL run, unite #-} 	type Primary t a :: *-	run :: t a -> Primary t a-	unite :: Primary t a -> t a+	run :: m (t a) (Primary t a)+	unite :: m (Primary t a) (t a) -	(||=) :: Interpreted u => (Primary t a -> Primary u b) -> t a -> u b+	(||=) :: (Semigroupoid m, Interpreted m u) => m (Primary t a) (Primary u b) -> m (t a) (u b) 	(||=) f = unite . f . run -	(=||) :: Interpreted u => (t a -> u b) -> Primary t a -> Primary u b+	(=||) :: (Semigroupoid m, Interpreted m u) => m (t a) (u b) -> m (Primary t a) (Primary u b) 	(=||) f = run . f . unite -	(<$||=) :: (Covariant (->) (->) j, Interpreted u)-		=> (Primary t a -> Primary u b) -> j := t a -> j := u b-	f <$||= x = (f ||=) -<$>- x+	(<$||=) :: (Semigroupoid m, Covariant m m j, Interpreted m u)+                => m (Primary t a) (Primary u b) -> m (j := t a) (j := u b)+	(<$||=) f = (<$>) ((||=) f) -	(<$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Interpreted u)-		=> (Primary t a -> Primary u b) -> j :. k := t a -> j :. k := u b-	f <$$||= x = (f ||=) -<$$>- x+	(<$$||=) :: (Semigroupoid m, Covariant m m j, Covariant m m k, Interpreted m u)+		=> m (Primary t a) (Primary u b) -> m (j :. k := t a) (j :. k := u b)+	(<$$||=) f = (<$$>) @m @m ((||=) f) -	(<$$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Interpreted u)-		=> (Primary t a -> Primary u b) -> j :. k :. l := t a -> j :. k :. l := u b-	f <$$$||= x = (f ||=) -<$$$>- x+	(<$$$||=) :: (Semigroupoid m, Covariant m m j, Covariant m m k, Covariant m m l, Interpreted m u)+		=> m (Primary t a) (Primary u b) -> m (j :. k :. l := t a) (j :. k :. l := u b)+	(<$$$||=) f = (<$$$>) @m @m @m ((||=) f) -	(<$$$$||=) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Covariant (->) (->) m, Interpreted u)-		=> (Primary t a -> Primary u b) -> j :. k :. l :. m := t a -> j :. k :. l :. m := u b-	f <$$$$||= x = (f ||=) -<$$$$>- x+	(<$$$$||=) :: (Semigroupoid m, Covariant m m j, Covariant m m k, Covariant m m l, Covariant m m n, Interpreted m u)+		=> m (Primary t a) (Primary u b) -> m (j :. k :. l :. n := t a) (j :. k :. l :. n := u b)+	(<$$$$||=) f = (<$$$$>) @m @m @m @m ((||=) f) -	(=||$>) :: (Covariant (->) (->) j, Interpreted u)-		=> (t a -> u b) -> j := Primary t a -> j := Primary u b-	f =||$> x = (f =||) -<$>- x+	(=||$>) :: (Covariant m m j, Interpreted m u)+		=> m (t a) (u b) -> m (j := Primary t a) (j := Primary u b)+	(=||$>) f = (<$>) ((=||) f) -	(=||$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Interpreted u)-		=> (t a -> u b) -> j :. k := Primary t a -> j :. k := Primary u b-	f =||$$> x = (f =||) -<$$>- x+	(=||$$>) :: (Covariant m m j, Covariant m m k, Interpreted m u)+		=> m (t a) (u b) -> m (j :. k := Primary t a) (j :. k := Primary u b)+	(=||$$>) f = (<$$>) @m @m ((=||) f) -	(=||$$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Interpreted u)-		=> (t a -> u b) -> j :. k :. l := Primary t a -> j :. k :. l := Primary u b-	f =||$$$> x = (f =||) -<$$$>- x+	(=||$$$>) :: (Covariant m m j, Covariant m m k, Covariant m m l, Interpreted m u)+		=> m (t a) (u b) -> m (j :. k :. l := Primary t a) (j :. k :. l := Primary u b)+	(=||$$$>) f = (<$$$>) @m @m @m ((=||) f) -	(=||$$$$>) :: (Covariant (->) (->) j, Covariant (->) (->) k, Covariant (->) (->) l, Covariant (->) (->) m, Interpreted u)-		=> (t a -> u b) -> j :. k :. l :. m := Primary t a -> j :. k :. l :. m := Primary u b-	f =||$$$$> x = (f =||) -<$$$$>- x+	(=||$$$$>) :: (Covariant m m j, Covariant m m k, Covariant m m l, Covariant m m n, Interpreted m u)+		=> m (t a) (u b) -> m (j :. k :. l :. n := Primary t a) (j :. k :. l :. n := Primary u b)+	(=||$$$$>) f = (<$$$$>) @m @m @m @m ((=||) f) -(-=:) :: (Liftable (->) t, Interpreted (t u), Interpreted (t v), Covariant (->) (->) u)-	=> (t u a -> t v b) -> u a -> Primary (t v) b+(-=:) :: (Liftable m t, Interpreted m (t u), Interpreted m (t v), Covariant m m u)+	=> m (t u a) (t v b) -> m (u a) (Primary (t v) b) (-=:) f = run . f . lift++instance Interpreted (->) (Flip v a) where+	type Primary (Flip v a) e = v e a+	run ~(Flip x) = x+	unite = Flip++instance Interpreted (->) (Straight v e) where+	type Primary (Straight v e) a = v e a+	run ~(Straight x) = x+	unite = Straight

@@ -1,10 +1,10 @@-module Pandora.Paradigm.Controlflow.Effect.Transformer (module Exports) where+module Pandora.Paradigm.Controlflow.Effect.Transformer (module Exports, Transformer) where  import Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic as Exports import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic as Exports ---import Pandora.Pattern.Functor (Monad, Comonad)+import Pandora.Pattern.Functor (Monad, Comonad) ---type family Transformer c t where---	Transformer Monad t = Monadic t---	Transformer Comonad t = Comonadic t+type family Transformer c t where+	Transformer Monad t = Monadic t+	Transformer Comonad t = Comonadic t

@@ -2,11 +2,13 @@  module Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic (Comonadic (..), (:<) (..)) where +import Pandora.Core.Appliable ((!)) import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))@@ -15,29 +17,30 @@ import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (Extractable_, point)+import Pandora.Paradigm.Primary.Algebraic (Extractable, point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) -class Interpreted t => Comonadic t where+class Interpreted (->) t => Comonadic t where 	{-# MINIMAL bring #-}-	bring :: Extractable_ u => t :< u ~> t+	bring :: Extractable u => t :< u ~> t  infixr 3 :< newtype (:<) t u a = TC { tc :: Schematic Comonad t u a }  instance Covariant (->) (->) (Schematic Comonad t u) => Covariant (->) (->) (t :< u) where-	f -<$>- TC x = TC $ f -<$>- x+	f <$> TC x = TC $ f <$> x -instance Semimonoidal (->) (:*:) (:*:) (Schematic Comonad t u) => Semimonoidal (->) (:*:) (:*:) (t :< u) where-	multiply (TC f :*: TC x) = TC $ multiply $ f :*: x+instance Semimonoidal (-->) (:*:) (:*:) (Schematic Comonad t u) => Semimonoidal (-->) (:*:) (:*:) (t :< u) where+	mult = Straight $ \(TC f :*: TC x) -> TC $ mult @(-->) @(:*:) @(:*:) ! f :*: x -instance Monoidal (->) (->) (:*:) (:*:) (Schematic Comonad t u) => Monoidal (->) (->) (:*:) (:*:) (t :< u) where-	unit _ f = TC . point $ f One+instance Monoidal (-->) (->) (:*:) (:*:) (Schematic Comonad t u) => Monoidal (-->) (->) (:*:) (:*:) (t :< u) where+	unit _ = Straight $ TC . point . ($ One)  instance Traversable (->) (->) (Schematic Comonad t u) => Traversable (->) (->) (t :< u) where-	f <<- TC x = TC -<$>- f <<- x+	f <<- TC x = TC <$> f <<- x  instance Distributive (->) (->) (Schematic Comonad t u) => Distributive (->) (->) (t :< u) where 	f -<< x = TC $ tc . f -<< x@@ -48,7 +51,7 @@ instance Extendable (->) (Schematic Comonad t u) => Extendable (->) (t :< u) where 	f <<= TC x = TC $ f . TC <<= x -instance (Extractable_ (t :< u), Extendable (->) (t :< u)) => Comonad (t :< u) (->) where+instance (Extractable (t :< u), Extendable (->) (t :< u)) => Comonad (->) (t :< u) where  instance Lowerable (->) (Schematic Comonad t) => Lowerable (->) ((:<) t) where 	lower (TC x) = lower x@@ -56,7 +59,7 @@ instance Hoistable (Schematic Comonad t) => Hoistable ((:<) t) where 	f /|\ TC x = TC $ f /|\ x -instance (Interpreted (Schematic Comonad t u)) => Interpreted (t :< u) where+instance (Interpreted (->) (Schematic Comonad t u)) => Interpreted (->) (t :< u) where 	type Primary (t :< u) a = Primary (Schematic Comonad t u) a 	run ~(TC x) = run x 	unite = TC . unite

@@ -2,11 +2,13 @@  module Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (..), (:>) (..)) where +import Pandora.Core.Appliable ((!)) import Pandora.Core.Functor (type (~>))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))@@ -15,29 +17,30 @@ import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Primary.Algebraic (Pointable, point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) -class Interpreted t => Monadic t where+class Interpreted (->) t => Monadic t where 	{-# MINIMAL wrap #-}-	wrap :: Monoidal (->) (->) (:*:) (:*:) u => t ~> t :> u+	wrap :: Pointable u => t ~> t :> u  infixr 3 :> newtype (:>) t u a = TM { tm :: Schematic Monad t u a }  instance Covariant (->) (->) (Schematic Monad t u) => Covariant (->) (->) (t :> u) where-	f -<$>- TM x = TM $ f -<$>- x+	f <$> TM x = TM $ f <$> x -instance Semimonoidal (->) (:*:) (:*:) (Schematic Monad t u) => Semimonoidal (->) (:*:) (:*:) (t :> u) where-	multiply (TM f :*: TM x) = TM $ multiply $ f :*: x+instance Semimonoidal (-->) (:*:) (:*:) (Schematic Monad t u) => Semimonoidal (-->) (:*:) (:*:) (t :> u) where+	mult = Straight $ \(TM f :*: TM x) -> TM $ mult @(-->) @(:*:) @(:*:) ! f :*: x -instance Monoidal (->) (->) (:*:) (:*:) (Schematic Monad t u) => Monoidal (->) (->) (:*:) (:*:) (t :> u) where-	unit _ f = TM . point $ f One+instance Monoidal (-->) (->) (:*:) (:*:) (Schematic Monad t u) => Monoidal (-->) (->) (:*:) (:*:) (t :> u) where+	unit _ = Straight $ TM . point . ($ One)  instance Traversable (->) (->) (Schematic Monad t u) => Traversable (->) (->) (t :> u) where-	f <<- TM x = TM -<$>- f <<- x+	f <<- TM x = TM <$> f <<- x  instance Distributive (->) (->) (Schematic Monad t u) => Distributive (->) (->) (t :> u) where 	f -<< x = TM $ tm . f -<< x@@ -48,7 +51,7 @@ instance Extendable (->) (Schematic Monad t u) => Extendable (->) (t :> u) where 	f <<= TM x = TM $ f . TM <<= x -instance (Covariant (->) (->) (Schematic Monad t u), Monoidal (->) (->) (:*:) (:*:) (Schematic Monad t u), Bindable (->) (t :> u)) => Monad (t :> u) where+instance (Covariant (->) (->) (Schematic Monad t u), Monoidal (-->) (->) (:*:) (:*:) (Schematic Monad t u), Bindable (->) (t :> u)) => Monad (->) (t :> u) where  instance Liftable (->) (Schematic Monad t) => Liftable (->) ((:>) t) where 	lift = TM . lift@@ -56,7 +59,7 @@ instance Hoistable (Schematic Monad t) => Hoistable ((:>) t) where 	f /|\ TM x = TM $ f /|\ x -instance (Interpreted (Schematic Monad t u)) => Interpreted (t :> u) where+instance (Interpreted (->) (Schematic Monad t u)) => Interpreted (->) (t :> u) where 	type Primary (t :> u) a = Primary (Schematic Monad t u) a 	run ~(TM x) = run x 	unite = TM . unite

@@ -3,7 +3,7 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Paradigm.Primary.Algebraic (Applicative_, forever_)+import Pandora.Paradigm.Primary.Algebraic (Applicative, forever_) import Pandora.Paradigm.Primary.Transformer.Continuation (Continuation (Continuation)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) @@ -24,25 +24,25 @@ (.:~.) = notify  -- | Listen only first event, call back forever_-follow :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+follow :: Applicative t => Observable t a r -> (a -> t r) -> t r follow r action = captured $ run r # Capture . forever_ . action  -- | Infix version of 'follow'-(.:~*) :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+(.:~*) :: Applicative t => Observable t a r -> (a -> t r) -> t r (.:~*) = follow  -- | Listen all events from action, call back just once-subscribe :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+subscribe :: Applicative t => Observable t a r -> (a -> t r) -> t r subscribe r action = forever_ $ captured $ run r # Capture . action  -- | Infix version of 'subscribe'-(*:~.) :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+(*:~.) :: Applicative t => Observable t a r -> (a -> t r) -> t r (*:~.) = subscribe  -- | Listen all events from action, call back forever_-watch :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+watch :: Applicative t => Observable t a r -> (a -> t r) -> t r watch r action = forever_ $ captured $ run r # Capture . forever_ . action  -- | Infix version of 'watch'-(*:~*) :: Applicative_ t => Observable t a r -> (a -> t r) -> t r+(*:~*) :: Applicative t => Observable t a r -> (a -> t r) -> t r (*:~*) = watch

@@ -4,7 +4,7 @@ import Pandora.Pattern.Category (($), (#)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monoidal (Monoidal)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (!..))+import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (!..), type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)) import Pandora.Paradigm.Primary.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))@@ -12,14 +12,14 @@  newtype Producer i t r = Producer { produce :: Consumer i t r -> t r } -instance Interpreted (Producer i t) where+instance Interpreted (->) (Producer i t) where 	type Primary (Producer i t) a = Consumer i t a -> t a 	run ~(Producer f) = f 	unite = Producer  newtype Consumer o t r = Consumer { consume :: o -> Producer o t r -> t r } -instance Interpreted (Consumer o t) where+instance Interpreted (->) (Consumer o t) where 	type Primary (Consumer o t) a = o -> Producer o t a -> t a 	run ~(Consumer f) = f 	unite = Consumer@@ -43,7 +43,7 @@ yield v = Continuation $ \next -> Pipe $ \i (Consumer o) -> o v # pause next i  -- | Pipeline that does nothing-finish :: Monoidal (->) (->) (:*:) (:*:) t => Pipeline i o t () ()+finish :: Monoidal (-->) (->) (:*:) (:*:) t => Pipeline i o t () () finish = Continuation (Pipe (point () !..) !.)  -- | Do some effectful computation within pipeline@@ -51,14 +51,14 @@ impact action = Continuation $ \next -> Pipe $ \i o -> (\x -> pipe (next x) i o) =<< action  -- | Compose two pipelines into one-(=*=) :: forall i e o t . Monoidal (->) (->) (:*:) (:*:) t => Pipeline i e t () () -> Pipeline e o t () () -> Pipeline i o t () ()+(=*=) :: forall i e o t . Monoidal (-->) (->) (:*:) (:*:) t => Pipeline i e t () () -> Pipeline e o t () () -> Pipeline i o t () () p =*= q = Continuation $ \_ -> Pipe $ \i -> pipe # run q end # pause (run p end !.) i where  	end :: b -> Pipe c d () t () 	end _ = Pipe (point () !..)  -- | Run pipeline and get result-pipeline :: Monoidal (->) (->) (:*:) (:*:) t => Pipeline i o t () () -> t ()+pipeline :: Monoidal (-->) (->) (:*:) (:*:) t => Pipeline i o t () () -> t () pipeline p = pipe # run p (Pipe . (!..) . point) # i # o where  	i :: Producer i t ()

@@ -2,14 +2,16 @@  module Pandora.Paradigm.Inventory.Accumulator (Accumulator (..), Accumulated, gather) where +import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Object.Monoid (Monoid) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite))@@ -20,10 +22,10 @@ newtype Accumulator e a = Accumulator (e :*: a)  instance Covariant (->) (->) (Accumulator e) where-	f -<$>- Accumulator x = Accumulator $ f -<$>- x+	f <$> Accumulator x = Accumulator $ f <$> x -instance Semigroup e => Semimonoidal (->) (:*:) (:*:) (Accumulator e) where-	multiply (x :*: y) = Accumulator $ k # run x # run y where+instance Semigroup e => Semimonoidal (-->) (:*:) (:*:) (Accumulator e) where+	mult = Straight $ \(x :*: y) -> Accumulator $ k # run x # run y where 		k ~(ex :*: x') ~(ey :*: y') = ex + ey :*: x' :*: y'  instance Semigroup e => Bindable (->) (Accumulator e) where@@ -32,7 +34,7 @@  type instance Schematic Monad (Accumulator e) = (<.:>) ((:*:) e) -instance Interpreted (Accumulator e) where+instance Interpreted (->) (Accumulator e) where 	type Primary (Accumulator e) a = e :*: a 	run ~(Accumulator x) = x 	unite = Accumulator

@@ -2,22 +2,25 @@  module Pandora.Paradigm.Inventory.Environment (Environment (..), Configured, env) where +import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Functor.Divariant (Divariant ((>->)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))+import Pandora.Pattern.Functor.Bivariant ((<->))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), (%)) import Pandora.Paradigm.Primary.Algebraic ()-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))@@ -26,19 +29,19 @@ newtype Environment e a = Environment (e -> a)  instance Covariant (->) (->) (Environment e) where-	f -<$>- Environment x = Environment $ f . x+	f <$> Environment x = Environment $ f . x  instance Contravariant (->) (->) (Flip Environment a) where-	f ->$<- Flip (Environment g) = Flip . Environment $ g . f+	f >$< Flip (Environment g) = Flip . Environment $ g . f -instance Semimonoidal (->) (:*:) (:*:) (Environment e) where-	multiply (x :*: y) = unite $ multiply $ run x :*: run y+instance Semimonoidal (-->) (:*:) (:*:) (Environment e) where+	mult = Straight $ Environment . (mult @(-->) !) . (run @(->) <-> run @(->)) -instance Monoidal (->) (->) (:*:) (:*:) (Environment e) where-	unit _ f = Environment $ \_ -> f One+instance Monoidal (-->) (->) (:*:) (:*:) (Environment e) where+	unit _ = Straight $ \f -> Environment $ \_ -> f One  instance Distributive (->) (->) (Environment e) where-	f -<< g = Environment $ (run -<$>- f) -<< g+	f -<< g = Environment $ (run @(->) <$> f) -<< g  instance Bindable (->) (Environment e) where 	f =<< Environment x = Environment $ \e -> (run % e) . f . x $ e@@ -48,7 +51,7 @@ instance Divariant (->) (->) (->) Environment where 	(>->) ab cd bc = Environment $ ab >-> cd $ run bc -instance Interpreted (Environment e) where+instance Interpreted (->) (Environment e) where 	type Primary (Environment e) a = (->) e a 	run ~(Environment x) = x 	unite = Environment@@ -56,7 +59,7 @@ type instance Schematic Monad (Environment e) = (<:.>) ((->) e)  instance Monadic (Environment e) where-	wrap x = TM . TU $ point -<$>- run x+	wrap x = TM . TU $ point <$> run x  type Configured e = Adaptable (Environment e) 

@@ -4,7 +4,7 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad)@@ -17,15 +17,15 @@ newtype Equipment e a = Equipment (e :*: a)  instance Covariant (->) (->) (Equipment e) where-	f -<$>- Equipment x = Equipment $ f -<$>- x+	f <$> Equipment x = Equipment $ f <$> x  instance Traversable (->) (->) (Equipment e) where-	f <<- Equipment x = Equipment -<$>- f <<- x+	f <<- Equipment x = Equipment <$> f <<- x  instance Extendable (->) (Equipment e) where 	f <<= Equipment (e :*: x) = Equipment . (:*:) e . f . Equipment $ e :*: x -instance Interpreted (Equipment e) where+instance Interpreted (->) (Equipment e) where 	type Primary (Equipment e) a = e :*: a 	run ~(Equipment x) = x 	unite = Equipment@@ -38,4 +38,4 @@ 	f <<= TU (e :*: x) = TU . (:*:) e $ f . TU . (:*:) e <<= x  retrieve :: Equipped e t => t a -> e-retrieve = attached . run @(Equipment _) . adapt+retrieve = attached . run @(->) @(Equipment _) . adapt

@@ -4,15 +4,15 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Functor.Divariant (Divariant ((>->))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite, (||=))) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable) import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>))@@ -20,13 +20,13 @@ newtype Imprint e a = Imprint (e -> a)  instance Covariant (->) (->) (Imprint e) where-	f -<$>- Imprint g = Imprint $ f . g+	f <$> Imprint g = Imprint $ f . g  instance Contravariant (->) (->) (Flip Imprint a) where-	f ->$<- Flip (Imprint g) = Flip . Imprint $ g . f+	f >$< Flip (Imprint g) = Flip . Imprint $ g . f  instance Distributive (->) (->) (Imprint e) where-	f -<< g = Imprint $ (run -<$>- f) -<< g+	f -<< g = Imprint $ (run @(->) <$> f) -<< g  instance Divariant (->) (->) (->) Imprint where 	(>->) ab cd bc = ab >-> cd ||= bc@@ -34,7 +34,7 @@ instance Semigroup e => Extendable (->) (Imprint e) where 	f <<= Imprint x = Imprint $ \e -> f $ Imprint $ x . (e +) -instance Interpreted (Imprint e) where+instance Interpreted (->) (Imprint e) where 	type Primary (Imprint e) a = (->) e a 	run ~(Imprint x) = x 	unite = Imprint@@ -42,6 +42,6 @@ type instance Schematic Comonad (Imprint e) = (<.:>) ((->) e)  instance {-# OVERLAPS #-} (Semigroup e, Extendable (->) u) => Extendable (->) ((->) e <.:> u) where-	f <<= UT x = UT $ (\x' e -> f . UT . (-<$>-) (. (e +)) $ x') <<= x+	f <<= UT x = UT $ (\x' e -> f . UT . (<$>) (. (e +)) $ x') <<= x  type Traceable e t = Adaptable t (Imprint e)

@@ -5,7 +5,7 @@ import Pandora.Core.Impliable (Impliable (Arguments, imply)) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) import Pandora.Pattern.Category (Category (identity, ($), (#)))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Divariant ((>->)) import Pandora.Pattern.Functor.Representable (Representable (Representation, (<#>), tabulate))@@ -16,7 +16,7 @@ import Pandora.Paradigm.Primary.Algebraic (($>-), extract) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Primary.Object.Boolean ((?)) import Pandora.Paradigm.Inventory.Store (Store (Store), position, look, retrofit) import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))@@ -27,15 +27,17 @@ type Lens = P_Q_T (->) Store  instance Invariant (Flip (Lens available) tgt) where-	f <$< g = \(Flip (P_Q_T lens)) -> Flip . P_Q_T $ g >-> (f -<$>-) $ lens+	f <$< g = \(Flip (P_Q_T lens)) -> Flip . P_Q_T $ g >-> (f <$>) $ lens  type family Convex lens where 	Convex Lens = Lens Identity  instance Semigroupoid (Lens Identity) where+	(.) :: Convex Lens between target -> Convex Lens source between -> Convex Lens source target 	P_Q_T to . P_Q_T from = P_Q_T $ \source -> (to . extract @Identity . position $ from source) $>- source  instance Category (Lens Identity) where+	identity :: Convex Lens source source 	identity = imply @(Convex Lens _ _) identity ((%) (!.))  instance Impliable (P_Q_T (->) Store Identity source target) where@@ -52,11 +54,13 @@ 	imply getter setter = P_Q_T $ \source -> Store $ getter source :*: setter source  instance Semigroupoid (Lens Maybe) where+	(.) :: Obscure Lens between target -> Obscure Lens source between -> Obscure Lens source target 	P_Q_T to . P_Q_T from = P_Q_T $ \source -> case position # from source of 		Nothing -> Store $ Nothing :*: (source !.) 		Just between -> to between $>- source  instance Category (Lens Maybe) where+	identity :: Obscure Lens source source 	identity = imply @(Obscure Lens _ _) # Just # resolve identity  -- Lens as natural transformation

@@ -2,12 +2,14 @@  module Pandora.Paradigm.Inventory.State where +import Pandora.Pattern.Morphism.Flip (Flip)+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -15,39 +17,39 @@ import Pandora.Pattern.Functor.Adjoint ((-|), (|-)) import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Functor.Divariant ((>->))-import Pandora.Paradigm.Primary.Transformer (Flip) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)), Schematic) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Schemes.TUT (TUT (TUT), type (<:<.>:>))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic ((:*:) ((:*:)), (*>-), delta) import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Primary.Algebraic (Pointable, point)  -- | Effectful computation with a variable newtype State s a = State ((->) s :. (:*:) s := a)  instance Covariant (->) (->) (State s) where-	f -<$>- x = State $ (-<$>-) f . run x+	f <$> x = State $ (<$>) f . run x -instance Semimonoidal (->) (:*:) (:*:) (State s) where-	multiply (State g :*: State h) = State $ \s -> -		let old :*: x = g s in -	  	let new :*: y = h old in+instance Semimonoidal (-->) (:*:) (:*:) (State s) where+	mult = Straight $ \(State g :*: State h) -> State $ \s ->+		let old :*: x = g s in+		let new :*: y = h old in 		new :*: x :*: y -instance Monoidal (->) (->) (:*:) (:*:) (State s) where-	unit _ f = State . (identity @(->) -|) $ f One+instance Monoidal (-->) (->) (:*:) (:*:) (State s) where+	unit _ = Straight $ State . (identity @(->) -|) . ($ One)  instance Bindable (->) (State s) where-	f =<< x = State $ (run . f |-) -<$>- run x+	f =<< x = State $ (run . f |-) <$> run x -instance Monad (State s) where+instance Monad (->) (State s) where  instance Invariant (Flip State r) where 	f <$< g = ((g >-> ((<->) @_ @(->) @(->) f identity) ||=) ||=) -instance Interpreted (State s) where+instance Interpreted (->) (State s) where 	type Primary (State s) a = (->) s :. (:*:) s := a 	run ~(State x) = x 	unite = State@@ -55,7 +57,7 @@ type instance Schematic Monad (State s) = (->) s <:<.>:> (:*:) s  instance Monadic (State s) where-	wrap x = TM . TUT $ point -<$>- run x+	wrap x = TM . TUT $ point <$> run x  type Stateful s = Adaptable (State s) @@ -74,7 +76,7 @@ reconcile :: (Bindable (->) t, Stateful s t, Adaptable u t) => (s -> u s) -> t s reconcile f = replace =<< adapt . f =<< current -type Memorable s t = (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:*:) t,  Stateful s t)+type Memorable s t = (Covariant (->) (->) t, Pointable t,  Stateful s t)  fold :: (Traversable (->) (->) t, Memorable s u) => (a -> s -> s) -> t a -> u s fold op struct = (modify . op <<- struct) *>- current

@@ -5,8 +5,8 @@ import Pandora.Core (type (:.), type (:=), type (<:=), type (~>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -17,7 +17,7 @@ import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), (%), (!.), (-.#..-)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached) import Pandora.Paradigm.Primary.Algebraic (extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)), Schematic) import Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic (Comonadic (bring), (:<) (TC))@@ -26,26 +26,28 @@ -- | Context based computation on value newtype Store s a = Store ((:*:) s :. (->) s := a) +-- TODO: Try to generalize (->) here instance Covariant (->) (->) (Store s) where-	f -<$>- Store x = Store $ f -<$$>- x+	(<$>) f = (||=) ((<$$>) @(->) @(->) f)  instance Semimonoidal (<--) (:*:) (:*:) (Store s) where-	multiply = Flip $ \(Store (s :*: f)) -> +	mult = Flip $ \(Store (s :*: f)) -> 		let (x :*: y) = f s in 		Store (s :*: (x !.)) :*: Store (s :*: (y !.))  instance Monoidal (<--) (->) (:*:) (:*:) (Store s) where 	unit _ = Flip $ \(Store (s :*: f)) -> (\_ -> f s) +-- TODO: Try to generalize (->) here instance Extendable (->) (Store s) where-	f <<= Store x = Store $ f -<$$>- (Store -.#..- (identity @(->) -|) -<$>- x)+	f <<= Store x = Store $ (<$$>) @(->) @(->) f (Store -.#..- (identity @(->) -|) <$> x) -instance Comonad (Store s) (->) where+instance Comonad (->) (Store s) where  instance Invariant (Flip Store r) where 	f <$< g = \(Flip x) -> Flip $ (<->) @_ @(->) f (g >-> identity @(->)) ||= x -instance Interpreted (Store s) where+instance Interpreted (->) (Store s) where 	type Primary (Store s) a = (:*:) s :. (->) s := a 	run ~(Store x) = x 	unite = Store@@ -59,11 +61,11 @@  -- | Get current index position :: Storable s t => t a -> s-position = attached . run @(Store _) . adapt+position = attached . run @(->) @(Store _) . adapt  -- | Given an index return value look :: Storable s t => s -> a <:= t-look s = (extract % s) . run @(Store _) . adapt+look s = (extract % s) . run @(->) @(Store _) . adapt  -- | Change index with function retrofit :: (s -> s) -> Store s ~> Store s

@@ -8,10 +8,11 @@ import Pandora.Paradigm.Primary.Object as Exports import Pandora.Paradigm.Primary.Algebraic as Exports +import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Core.Functor (type (:=)) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) import Pandora.Pattern.Category (Category (($), (#)))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((|-), (-|))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)@@ -89,16 +90,16 @@ 	type Available Left Wye = Maybe 	type Substance Left Wye = Identity 	substructure = P_Q_T $ \new -> case lower new of-		End -> Store $ Nothing :*: lift . resolve Left End . (extract -<$>-)-		Left x -> Store $ Just (Identity x) :*: lift . resolve Left End . (extract -<$>-)-		Right y -> Store $ Nothing :*: (lift # Right y !.) . (extract -<$>-)-		Both x y -> Store $ Just (Identity x) :*: lift . resolve (Both % y) (Right y) . (extract -<$>-)+		End -> Store $ Nothing :*: lift . resolve Left End . (extract <$>)+		Left x -> Store $ Just (Identity x) :*: lift . resolve Left End . (extract <$>)+		Right y -> Store $ Nothing :*: (lift # Right y !.) . (extract <$>)+		Both x y -> Store $ Just (Identity x) :*: lift . resolve (Both % y) (Right y) . (extract <$>)  instance Substructure Right Wye where 	type Available Right Wye = Maybe 	type Substance Right Wye = Identity 	substructure = P_Q_T $ \new -> case lower new of-		End -> Store $ Nothing :*: lift . resolve Right End . (extract -<$>-)-		Left x -> Store $ Nothing :*: (lift # Left x !.) . (extract -<$>-)-		Right y -> Store $ Just (Identity y) :*: lift . resolve Right End . (extract -<$>-)-		Both x y -> Store $ Just (Identity y) :*: lift . resolve (Both x) (Left x) . (extract -<$>-)+		End -> Store $ Nothing :*: lift . resolve Right End . (extract <$>)+		Left x -> Store $ Nothing :*: (lift # Left x !.) . (extract <$>)+		Right y -> Store $ Just (Identity y) :*: lift . resolve Right End . (extract <$>)+		Both x y -> Store $ Just (Identity y) :*: lift . resolve (Both x) (Left x) . (extract <$>)

@@ -1,6 +1,6 @@ {-# OPTIONS_GHC -fno-warn-orphans #-} -module Pandora.Paradigm.Primary.Algebraic (module Exports, Applicative_, Alternative_, Extractable_, ($>-), ($$>-), ($$$>-), (-<*>-), (*>-), forever_, (-+-), void, empty, point, extract) where+module Pandora.Paradigm.Primary.Algebraic (module Exports, Applicative, Alternative, Extractable, Pointable, ($>-), ($$>-), ($$$>-), (<-*-), (*>-), forever_, (-+-), void, empty, point, extract) where  import Pandora.Paradigm.Primary.Algebraic.Exponential as Exports import Pandora.Paradigm.Primary.Algebraic.Product as Exports@@ -8,35 +8,39 @@ import Pandora.Paradigm.Primary.Algebraic.Zero as Exports import Pandora.Paradigm.Primary.Algebraic.One as Exports +import Pandora.Core.Appliable ((!))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-), (-<$$$>-))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>), (<$$$>))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit), Unit) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Paradigm.Primary.Functor.Proxy (Proxy (Proxy))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run)  type instance Unit (:*:) = One type instance Unit (:+:) = Zero -infixl 4 -<*>-+infixl 4 <-*-  ($>-) :: Covariant (->) (->) t => t a -> b -> t b-x $>- r = (r !.) -<$>- x+x $>- r = (r !.) <$> x  ($$>-) :: (Covariant (->) (->) t, Covariant (->) (->) u) => t (u a) -> b -> t (u b)-x $$>- r = (r !.) -<$$>- x+x $$>- r = (<$$>) @(->) @(->) (r !.) x  ($$$>-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Covariant (->) (->) v) => t (u (v a)) -> b -> t (u (v b))-x $$$>- r = (r !.) -<$$$>- x+x $$$>- r = (<$$$>) @(->) @(->) @(->) (r !.) x  void :: Covariant (->) (->) t => t a -> t () void x = x $>- ()  instance Traversable (->) (->) ((:*:) s) where-	f <<- x = (attached x :*:) -<$>- f (extract x)+	f <<- x = (attached x :*:) <$> f (extract x)  instance Adjoint (->) (->) ((:*:) s) ((->) s) where 	(-|) :: ((s :*: a) -> b) -> a -> (s -> b)@@ -44,65 +48,72 @@ 	(|-) :: (a -> s -> b) -> (s :*: a) -> b 	f |- ~(s :*: x) = f x s -instance Semimonoidal (->) (:*:) (:*:) ((->) e) where-	multiply :: ((e -> a) :*: (e -> b)) -> e -> (a :*: b)-	multiply (g :*: h) = \x -> g x :*: h x+instance Semimonoidal (-->) (:*:) (:*:) ((->) e) where+	mult :: ((e -> a) :*: (e -> b)) --> (e -> (a :*: b))+	mult = Straight $ \(g :*: h) -> \x -> g x :*: h x  instance Semimonoidal (<--) (:*:) (:*:) ((->) e) where-	multiply = Flip $ \f -> (\e -> attached $ f e) :*: (\e -> extract $ f e)+	mult :: ((e -> a) :*: (e -> b)) <-- (e -> a :*: b)+	mult = Flip $ \f -> attached . f :*: extract . f -instance Semimonoidal (->) (:*:) (:+:) ((:+:) e) where-	multiply :: ((e :+: a) :*: (e :+: b)) -> e :+: a :+: b-	multiply (Option _ :*: Option e') = Option e'-	multiply (Option _ :*: Adoption y) = Adoption $ Adoption y-	multiply (Adoption x :*: _) = Adoption $ Option x+instance Semimonoidal (-->) (:*:) (:+:) ((:+:) e) where+	mult :: ((e :+: a) :*: (e :+: b)) --> (e :+: a :+: b)+	mult = Straight $ \case+		Option _ :*: Option e' -> Option e'+		Option _ :*: Adoption y -> Adoption $ Adoption y+		Adoption x :*: _ -> Adoption $ Option x -instance Semimonoidal (->) (:*:) (:*:) ((:+:) e) where-	multiply (Adoption x :*: Adoption y) = Adoption $ x :*: y-	multiply (Option e :*: _) = Option e-	multiply (_ :*: Option e) = Option e+instance Semimonoidal (-->) (:*:) (:*:) ((:+:) e) where+	mult = Straight $ \case+		Adoption x :*: Adoption y -> Adoption $ x :*: y+		Option e :*: _ -> Option e+		_ :*: Option e -> Option e -instance Monoidal (->) (->) (:*:) (:*:) ((:+:) e) where-	unit _ f = Adoption $ f One+instance Monoidal (-->) (->) (:*:) (:*:) ((:+:) e) where+	unit _ = Straight $ Adoption . ($ One)  instance Semimonoidal (<--) (:*:) (:*:) ((:*:) s) where-	multiply = Flip $ \(s :*: x :*: y) -> (s :*: x) :*: (s :*: y)+	mult = Flip $ \(s :*: x :*: y) -> (s :*: x) :*: (s :*: y)  instance Monoidal (<--) (->) (:*:) (:*:) ((:*:) s) where 	unit _ = Flip $ \(_ :*: x) -> (\_ -> x) -instance Comonad ((:*:) s) (->) where+instance Comonad (->) ((:*:) s) where  instance Semimonoidal (<--) (:*:) (:*:) (Flip (:*:) a) where-	multiply = Flip $ \(Flip ((sx :*: sy) :*: r)) -> Flip (sx :*: r) :*: Flip (sy :*: r)+	mult = Flip $ \(Flip ((sx :*: sy) :*: r)) -> Flip (sx :*: r) :*: Flip (sy :*: r)  instance Monoidal (<--) (->) (:*:) (:*:) (Flip (:*:) a) where 	unit _ = Flip $ \(Flip (s :*: _)) -> (\_ -> s) -type Applicative_ t = (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t, Monoidal (->) (->) (:*:) (:*:) t)-type Alternative_ t = (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:+:) t, Monoidal (->) (->) (:*:) (:+:) t)+type Applicative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Monoidal (-->) (->) (:*:) (:*:) t)+type Alternative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (->) (:*:) (:+:) t) -(-<*>-) :: (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t)-	=> t (a -> b) -> t a -> t b-f -<*>- x = (|-) @(->) @(->) (&) -<$>- multiply @_ @_ @(:*:) (f :*: x)+(<-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b+f <-*- x = (|-) @(->) @(->) (&) <$> run (mult @(-->) @_ @(:*:)) (f :*: x) -forever_ :: (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => t a -> t b+forever_ :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t a -> t b forever_ x = let r = x *>- r in r -(*>-) :: (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => t a -> t b -> t b-x *>- y = ((!.) %) -<$>- x -<*>- y+(*>-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t a -> t b -> t b+x *>- y = ((!.) %) <$> x <-*- y -(-+-) :: (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:+:) t)-	  => t a -> t b -> (a :+: b -> r) -> t r-x -+- y = \f -> f -<$>- multiply (x :*: y)+(-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t)+	=> t a -> t b -> (a :+: b -> r) -> t r+x -+- y = \f -> f <$> (mult @(-->) ! (x :*: y)) -point :: Monoidal (->) (->) (:*:) (:*:) t => a -> t a-point x = unit (Proxy @(:*:)) (\One -> x)+type Extractable t = Monoidal (<--) (->) (:*:) (:*:) t+type Pointable t = Monoidal (-->) (->) (:*:) (:*:) t+type Emptiable t = Monoidal (-->) (->) (:*:) (:+:) t -empty :: Monoidal (->) (->) (:*:) (:+:) t => t a-empty = unit (Proxy @(:*:)) absurd+extract :: Extractable t => t a -> a+extract j = run (unit @(<--) Proxy) j One -type Extractable_ t = Monoidal (<--) (->) (:*:) (:*:) t+point :: Pointable t => a -> t a+point x = run (unit @(-->) Proxy) (\One -> x) -extract :: Extractable_ t => t a -> a-extract j = let Flip f = unit @(<--) @(->) @(:*:) @(:*:) Proxy in f j $ One+empty :: Emptiable t => t a+empty = unit @(-->) (Proxy @(:*:)) ! absurd++--instance Appliable (->) b c (->) e d => Appliable (->) a (b -> c) (->) (a :*: e) d where+--	f ! (x :*: y) = f x ! y

@@ -2,16 +2,18 @@  module Pandora.Paradigm.Primary.Algebraic.Exponential where +import Pandora.Core.Appliable (Appliable ((!))) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) import Pandora.Pattern.Category (Category (($), (#), identity))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Divariant (Divariant ((>->))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))  infixr 2 !. infixr 7 -.#..-@@ -25,10 +27,10 @@ 	identity x = x  instance Covariant (->) (->) ((->) a) where-	(-<$>-) = (.)+	(<$>) = (.)  instance Distributive (->) (->) ((->) e) where-	f -<< g = \e -> (f % e) -<$>- g+	f -<< g = \e -> (f % e) <$> g  instance Bindable (->) ((->) e) where 	f =<< g = \x -> f # g x # x@@ -44,17 +46,23 @@  type (<--) = Flip (->) -instance Semigroupoid (<--) where-	Flip f . Flip g = Flip $ \x -> g (f x)+instance Contravariant (->) (->) ((<--) a) where+	f >$< Flip g = Flip $ g . f -instance Category (<--) where-	identity = Flip identity+type (-->) = Straight (->) -instance Contravariant (->) (->) ((<--) a) where-	f ->$<- Flip g = Flip $ g . f+instance Covariant (->) (->) ((-->) b) where+	f <$> Straight g = Straight $ f . g +instance Appliable (->) c b (->) c b where+	f ! x = f x++-- TODO: Is it possible to generalize?+instance Appliable (->) a (b -> c) (->) b (a -> c) where+	(!) f = (%) f+ (-.#..-) :: (Covariant (->) target (v a), Semigroupoid v) => v c d -> target (v a (v b c)) (v a (v b d))-(-.#..-) f = (-<$>-) (f .)+(-.#..-) f = (<$>) (f .)  {-# INLINE (!.) #-} (!.) :: a -> b -> a

@@ -1,9 +1,10 @@ module Pandora.Paradigm.Primary.Algebraic.Product where  import Pandora.Core.Functor (type (:=))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==)))@@ -14,8 +15,9 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))  infixr 0 :*:@@ -23,10 +25,10 @@ data (:*:) s a = s :*: a  instance Covariant (->) (->) ((:*:) s) where-	f -<$>- ~(s :*: x) = s :*: f x+	f <$> ~(s :*: x) = s :*: f x  instance Covariant (->) (->) (Flip (:*:) a) where-	f -<$>- (Flip (x :*: y)) = Flip $ f x :*: y+	f <$> (Flip (x :*: y)) = Flip $ f x :*: y  instance Extendable (->) ((:*:) s) where 	f <<= ~(s :*: x) = s :*: f (s :*: x)@@ -60,16 +62,14 @@ instance (Group s, Group a) => Group (s :*: a) where 	invert ~(s :*: x) = invert # s :*: invert # x -instance {-# OVERLAPS #-} Semimonoidal (->) (:*:) (:*:) t => Semimonoidal (->) (:*:) (:*:) (t <:.:> t := (:*:)) where-	multiply (T_U (xls :*: xrs) :*: T_U (yls :*: yrs)) = T_U $ multiply (xls :*: yls) :*: multiply (xrs :*: yrs)+instance {-# OVERLAPS #-} Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (t <:.:> t := (:*:)) where+	mult = Straight $ \(T_U (xls :*: xrs) :*: T_U (yls :*: yrs)) -> T_U $ (mult @(-->) !) (xls :*: yls) :*: (mult @(-->) !) (xrs :*: yrs)  -- TODO: Generalize (:*:) as Bivariant p instance (Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:.:> u := (:*:)) where-	multiply = Flip $ \(T_U (lxys :*: rxys)) ->-		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let Flip g = multiply @(<--) @(:*:) @(:*:) in-		let (lxs :*: lys) = f lxys in-		let (rxs :*: rys) = g rxys in+	mult = Flip $ \(T_U lrxys) ->+		-- TODO: I need matrix transposing here+		let ((lxs :*: lys) :*: (rxs :*: rys)) = ((mult @(<--) !) <-> (mult @(<--) !)) lrxys in 		T_U (lxs :*: rxs) :*: T_U (lys :*: rys)  delta :: a -> a :*: a

@@ -2,18 +2,18 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))  infixr 0 :+:  data (:+:) s a = Option s | Adoption a  instance Covariant (->) (->) ((:+:) s) where-	_ -<$>- Option s = Option s-	f -<$>- Adoption x = Adoption $ f x+	_ <$> Option s = Option s+	f <$> Adoption x = Adoption $ f x  instance Bivariant (->) (->) (->) (:+:) where 	f <-> g = \case@@ -21,8 +21,8 @@ 		Adoption x -> Adoption $ g x  instance Covariant (->) (->) (Flip (:+:) a) where-	_ -<$>- Flip (Adoption x) = Flip $ Adoption x-	f -<$>- Flip (Option y) = Flip . Option $ f y+	_ <$> Flip (Adoption x) = Flip $ Adoption x+	f <$> Flip (Option y) = Flip . Option $ f y  sum :: (e -> r) -> (a -> r) -> e :+: a -> r sum f _ (Option x) = f x

@@ -2,10 +2,10 @@  import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Category (identity, ($), (#))---import Pandora.Pattern.Functor (Endofunctor)-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -18,41 +18,44 @@ import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point)  data Conclusion e a = Failure e | Success a  instance Covariant (->) (->) (Conclusion e) where-	f -<$>- Success x = Success $ f x-	_ -<$>- Failure y = Failure y+	f <$> Success x = Success $ f x+	_ <$> Failure y = Failure y  instance Covariant (->) (->) (Flip Conclusion e) where-	_ -<$>- Flip (Success x) = Flip $ Success x-	f -<$>- Flip (Failure y) = Flip . Failure $ f y+	_ <$> Flip (Success x) = Flip $ Success x+	f <$> Flip (Failure y) = Flip . Failure $ f y -instance Semimonoidal (->) (:*:) (:*:) (Conclusion e) where-	multiply (Success x :*: Success y) = Success $ x :*: y-	multiply (Failure x :*: _) = Failure x-	multiply (_ :*: Failure x) = Failure x+instance Semimonoidal (-->) (:*:) (:*:) (Conclusion e) where+	mult = Straight $ \case+		Success x :*: Success y -> Success $ x :*: y+		Failure x :*: _ -> Failure x+		_ :*: Failure x -> Failure x -instance Monoidal (->) (->) (:*:) (:*:) (Conclusion e) where-	unit _ f = Success $ f One+instance Monoidal (-->) (->) (:*:) (:*:) (Conclusion e) where+	unit _ = Straight $ Success . ($ One) -instance Semigroup e => Semimonoidal (->) (:*:) (:+:) (Conclusion e) where-	multiply (Failure _ :*: x) = Adoption -<$>- x-	multiply (Success x :*: _) = Option -<$>- Success x+instance Semigroup e => Semimonoidal (-->) (:*:) (:+:) (Conclusion e) where+	mult = Straight $ \case+		Failure _ :*: x -> Adoption <$> x+		Success x :*: _ -> Option <$> Success x  instance Traversable (->) (->) (Conclusion e) where-	(<<-) :: (Covariant (->) (->) u, Monoidal (->) (->) (:*:) (:*:) u, Semimonoidal (->) (:*:) (:*:)u)+	(<<-) :: (Covariant (->) (->) u, Monoidal (-->) (->) (:*:) (:*:) u, Semimonoidal (-->) (:*:) (:*:) u) 		 => (a -> u b) -> Conclusion e a -> u (Conclusion e b) 	_ <<- Failure y = point $ Failure y-	f <<- Success x = Success -<$>- f x+	f <<- Success x = Success <$> f x  instance Bindable (->) (Conclusion e) where 	f =<< Success x = f x@@ -88,7 +91,7 @@ fail f (Failure x) = Failure $ f x fail _ (Success y) = Success y -instance Interpreted (Conclusion e) where+instance Interpreted (->) (Conclusion e) where 	type Primary (Conclusion e) a = Conclusion e a 	run = identity 	unite = identity@@ -110,6 +113,6 @@ 	catch (Failure e) handle = handle e 	catch (Success x) _ = Success x -instance (Monoidal (->) (->) (:*:) (:*:) u, Bindable (->) u) => Catchable e (Conclusion e <.:> u) where+instance (Monoidal (-->) (->) (:*:) (:*:) u, Bindable (->) u) => Catchable e (Conclusion e <.:> u) where 	catch (UT x) handle = let conclude = conclusion # run . handle # point . Success 		in UT $ conclude =<< x

@@ -2,8 +2,8 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==)))@@ -16,18 +16,18 @@ import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert)) import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))  newtype Constant a b = Constant a  instance Covariant (->) (->) (Constant a) where-	_ -<$>- Constant x = Constant x+	_ <$> Constant x = Constant x  instance Covariant (->) (->) (Flip Constant b) where-	f -<$>- Flip (Constant x) = Flip . Constant $ f x+	f <$> Flip (Constant x) = Flip . Constant $ f x  instance Contravariant (->) (->) (Constant a) where-	_ ->$<- Constant x = Constant x+	_ >$< Constant x = Constant x  instance Invariant (Constant a) where 	_ <$< _ = \(Constant x) -> Constant x

@@ -1,10 +1,10 @@ module Pandora.Paradigm.Primary.Functor.Convergence where  import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Paradigm.Primary.Algebraic ()  data Convergence r a = Convergence (a -> a -> r)  instance Contravariant (->) (->) (Convergence r) where-	f ->$<- Convergence g = Convergence $ \x y -> g # f x # f y+	f >$< Convergence g = Convergence $ \x y -> g # f x # f y

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.Edges where  import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Paradigm.Primary.Algebraic.Exponential () import Pandora.Paradigm.Primary.Algebraic (point)@@ -9,16 +9,16 @@ data Edges a = Empty | Leap a | Connect a | Overlay a  instance Covariant (->) (->) Edges where-	_ -<$>- Empty = Empty-	f -<$>- Connect x = Connect $ f x-	f -<$>- Overlay x = Overlay $ f x-	f -<$>- Leap x = Leap $ f x+	_ <$> Empty = Empty+	f <$> Connect x = Connect $ f x+	f <$> Overlay x = Overlay $ f x+	f <$> Leap x = Leap $ f x  instance Traversable (->) (->) Edges where 	_ <<- Empty = point Empty-	f <<- Connect x = Connect -<$>- f x-	f <<- Overlay x = Overlay -<$>- f x-	f <<- Leap x = Leap -<$>- f x+	f <<- Connect x = Connect <$> f x+	f <<- Overlay x = Overlay <$> f x+	f <<- Leap x = Leap <$> f x  edges :: r -> (a -> r) -> (a -> r) -> (a -> r) -> Edges a -> r edges r _ _ _ Empty = r

@@ -11,7 +11,7 @@  newtype Endo a = Endo { endo :: a -> a } -instance Interpreted Endo where+instance Interpreted (->) Endo where 	type Primary Endo a = a -> a 	run ~(Endo x) = x 	unite = Endo

@@ -2,16 +2,16 @@  import Pandora.Core.Functor (type (<:=), type (:=>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()  newtype Fix t = Fix { unfix :: t (Fix t) }  cata :: Covariant (->) (->) t => (a <:= t) -> Fix t -> a-cata f = f . (cata f -<$>-) . unfix+cata f = f . (cata f <$>) . unfix  ana :: Covariant (->) (->) t => (a :=> t) -> a -> Fix t-ana f = Fix . (ana f -<$>-) . f+ana f = Fix . (ana f <$>) . f  hylo :: Covariant (->) (->) t => (b <:= t) -> (a :=> t) -> (a -> b) hylo phi psi = cata phi . ana psi

@@ -2,12 +2,15 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))+import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Functor.Comonad (Comonad) --import Pandora.Pattern.Functor.Representable (Representable (Representation, (<#>), tabulate))@@ -21,41 +24,40 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))  newtype Identity a = Identity a  instance Covariant (->) (->) Identity where-	f -<$>- Identity x = Identity $ f x+	f <$> Identity x = Identity $ f x -instance Semimonoidal (->) (:*:) (:*:) Identity where-	multiply (Identity x :*: Identity y) = Identity $ x :*: y+instance Semimonoidal (-->) (:*:) (:*:) Identity where+	mult = Straight $ Identity . (extract <-> extract) -instance Monoidal (->) (->) (:*:) (:*:) Identity where-	unit _ f = Identity $ f One+instance Monoidal (-->) (->) (:*:) (:*:) Identity where+	unit _ = Straight $ Identity . ($ One)  instance Semimonoidal (<--) (:*:) (:*:) Identity where-	multiply = Flip $ \(Identity (x :*: y)) -> Identity x :*: Identity y+	mult = Flip $ \(Identity (x :*: y)) -> Identity x :*: Identity y  instance Monoidal (<--) (->) (:*:) (:*:) Identity where 	unit _ = Flip $ \(Identity x) -> (\_ -> x)  instance Traversable (->) (->) Identity where-	f <<- Identity x = Identity -<$>- f x+	f <<- Identity x = Identity <$> f x  instance Bindable (->) Identity where-	f =<< Identity x = f x	+	f =<< Identity x = f x -instance Monad Identity+instance Monad (->) Identity  instance Extendable (->) Identity where 	f <<= x = Identity . f $ x -instance Comonad Identity (->)+instance Comonad (->) Identity  --instance Representable Identity where 	--type Representation Identity = ()@@ -64,7 +66,7 @@  instance Adjoint (->) (->) Identity Identity where 	f -| x = Identity . f . Identity $ x-	g |- x = extract . extract . (g -<$>-) $ x+	g |- x = extract . extract . (g <$>) $ x  instance Setoid a => Setoid (Identity a) where 	Identity x == Identity y = x == y

@@ -3,8 +3,10 @@ import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -22,44 +24,45 @@ import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))  data Maybe a = Nothing | Just a  instance Covariant (->) (->) Maybe where-	f -<$>- Just x = Just $ f x-	_ -<$>- Nothing = Nothing+	f <$> Just x = Just $ f x+	_ <$> Nothing = Nothing -instance Semimonoidal (->) (:*:) (:*:) Maybe where-	multiply (Just x :*: Just y) = Just $ x :*: y-	multiply (Nothing :*: _) = Nothing-	multiply (_ :*: Nothing) = Nothing+instance Semimonoidal (-->) (:*:) (:*:) Maybe where+	mult = Straight $ \case+		Just x :*: Just y -> Just $ x :*: y+		Nothing :*: _ -> Nothing+		_ :*: Nothing -> Nothing -instance Semimonoidal (->) (:*:) (:+:) Maybe where-	multiply (Just x :*: _) = Just $ Option x-	multiply (Nothing :*: Just y) = Just $ Adoption y-	multiply (Nothing :*: Nothing) = Nothing+instance Semimonoidal (-->) (:*:) (:+:) Maybe where+	mult = Straight $ \case+		Just x :*: _ -> Just $ Option x+		Nothing :*: Just y -> Just $ Adoption y+		Nothing :*: Nothing -> Nothing -instance Monoidal (->) (->) (:*:) (:*:) Maybe where-	unit _ f = Just $ f One+instance Monoidal (-->) (->) (:*:) (:*:) Maybe where+	unit _ = Straight $ Just . ($ One) -instance Monoidal (->) (->) (:*:) (:+:) Maybe where-	unit _ _ = Nothing+instance Monoidal (-->) (->) (:*:) (:+:) Maybe where+	unit _ = Straight $ \_ -> Nothing  -- TODO: Check laws instance Semimonoidal (<--) (:*:) (:*:) Maybe where-	multiply = Flip $ \case+	mult = Flip $ \case 		Just (x :*: y) -> Just x :*: Just y 		Nothing -> Nothing :*: Nothing  instance Traversable (->) (->) Maybe where 	_ <<- Nothing = point Nothing-	f <<- Just x = Just -<$>- f x+	f <<- Just x = Just <$> f x  instance Bindable (->) Maybe where 	f =<< Just x = f x@@ -100,7 +103,7 @@  type instance Schematic Monad Maybe = (<.:>) Maybe -instance Interpreted Maybe where+instance Interpreted (->) Maybe where 	type Primary Maybe a = Maybe a 	run = identity 	unite = identity

@@ -3,20 +3,20 @@ import Pandora.Core.Functor (type (~>), type (:=>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), bool) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype Predicate a = Predicate (a -> Boolean) -instance Interpreted Predicate where+instance Interpreted (->) Predicate where 	type Primary Predicate a = a -> Boolean 	run ~(Predicate f) = f 	unite = Predicate  instance Contravariant (->) (->) Predicate where-	f ->$<- Predicate g = Predicate $ g . f+	f >$< Predicate g = Predicate $ g . f  equate :: Setoid a => a :=> Predicate equate x = Predicate (== x)

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.Proxy where -import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -11,10 +11,10 @@ data Proxy a = Proxy  instance Covariant (->) (->) Proxy where-	_ -<$>- Proxy = Proxy+	_ <$> Proxy = Proxy  instance Contravariant (->) (->) Proxy where-	_ ->$<- _ = Proxy+	_ >$< _ = Proxy  instance Distributive (->) (->) Proxy where 	_ -<< _ = Proxy

@@ -2,9 +2,11 @@  import Pandora.Core.Functor (type (:=>), type (~>)) import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -22,11 +24,10 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))  newtype Tagged tag a = Tag a @@ -34,38 +35,38 @@ type (:#) tag = Tagged tag  instance Covariant (->) (->) (Tagged tag) where-	f -<$>- Tag x = Tag $ f x+	f <$> Tag x = Tag $ f x  instance Covariant (->) (->) (Flip Tagged a) where-	_ -<$>- Flip (Tag x) = Flip $ Tag x+	_ <$> Flip (Tag x) = Flip $ Tag x -instance Semimonoidal (->) (:*:) (:*:) (Tagged tag) where-	multiply (x :*: y) = Tag $ extract x :*: extract y+instance Semimonoidal (-->) (:*:) (:*:) (Tagged tag) where+	mult = Straight $ Tag . (extract <-> extract) -instance Monoidal (->) (->) (:*:) (:*:) (Tagged tag) where-	unit _ f = Tag $ f One+instance Monoidal (-->) (->) (:*:) (:*:) (Tagged tag) where+	unit _ = Straight $ Tag . ($ One)  instance Semimonoidal (<--) (:*:) (:*:) (Tagged tag) where-	multiply = Flip $ \(Tag (x :*: y)) -> Tag x :*: Tag y+	mult = Flip $ \(Tag (x :*: y)) -> Tag x :*: Tag y  instance Monoidal (<--) (->) (:*:) (:*:) (Tagged tag) where 	unit _ = Flip $ \(Tag x) -> (\_ -> x)  instance Traversable (->) (->) (Tagged tag) where-	f <<- Tag x = Tag -<$>- f x+	f <<- Tag x = Tag <$> f x  instance Distributive (->) (->) (Tagged tag) where-	f -<< x = Tag $ extract . f -<$>- x+	f -<< x = Tag $ extract . f <$> x  instance Bindable (->) (Tagged tag) where 	f =<< Tag x = f x -instance Monad (Tagged tag)+instance Monad (->) (Tagged tag)  instance Extendable (->) (Tagged tag) where 	f <<= x = Tag . f $ x -instance Comonad (Tagged tag) (->)+instance Comonad (->) (Tagged tag)  instance Bivariant (->) (->) (->) Tagged where 	_ <-> g = \(Tag x) -> Tag $ g x

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.These where  import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()@@ -10,14 +10,14 @@ data These e a = This a | That e | These e a  instance Covariant (->) (->) (These e) where-	f -<$>- This x = This $ f x-	_ -<$>- That y = That y-	f -<$>- These y x = These y $ f x+	f <$> This x = This $ f x+	_ <$> That y = That y+	f <$> These y x = These y $ f x  instance Traversable (->) (->) (These e) where-	f <<- This x = This -<$>- f x+	f <<- This x = This <$> f x 	_ <<- That y = point $ That y-	f <<- These y x = These y -<$>- f x+	f <<- These y x = These y <$> f x  instance (Semigroup e, Semigroup a) => Semigroup (These e a) where 	This x + This x' = This # x + x'

@@ -2,56 +2,59 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False)) import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater))  data Validation e a = Flaws e | Validated a  instance Covariant (->) (->) (Validation e) where-	_ -<$>- Flaws e = Flaws e-	f -<$>- Validated x = Validated $ f x-	_ -<$>- Flaws e = Flaws e-	f -<$>- Validated x = Validated $ f x-	_ -<$>- Flaws e = Flaws e-	f -<$>- Validated x = Validated $ f x+	_ <$> Flaws e = Flaws e+	f <$> Validated x = Validated $ f x+	_ <$> Flaws e = Flaws e+	f <$> Validated x = Validated $ f x+	_ <$> Flaws e = Flaws e+	f <$> Validated x = Validated $ f x  instance Covariant (->) (->) (Flip Validation a) where-	f -<$>- Flip (Flaws e) = Flip . Flaws $ f e-	_ -<$>- Flip (Validated x) = Flip $ Validated x-	f -<$>- Flip (Flaws e) = Flip . Flaws $ f e-	_ -<$>- Flip (Validated x) = Flip $ Validated x-	f -<$>- Flip (Flaws e) = Flip . Flaws $ f e-	_ -<$>- Flip (Validated x) = Flip $ Validated x+	f <$> Flip (Flaws e) = Flip . Flaws $ f e+	_ <$> Flip (Validated x) = Flip $ Validated x+	f <$> Flip (Flaws e) = Flip . Flaws $ f e+	_ <$> Flip (Validated x) = Flip $ Validated x+	f <$> Flip (Flaws e) = Flip . Flaws $ f e+	_ <$> Flip (Validated x) = Flip $ Validated x -instance Semigroup e => Semimonoidal (->) (:*:) (:*:) (Validation e) where-	multiply (Validated x :*: Validated y) = Validated $ x :*: y-	multiply (Flaws x :*: Flaws y) = Flaws $ x + y-	multiply (Validated _ :*: Flaws y) = Flaws y-	multiply (Flaws x :*: Validated _) = Flaws x+instance Semigroup e => Semimonoidal (-->) (:*:) (:*:) (Validation e) where+	mult = Straight $ \case+		Validated x :*: Validated y -> Validated $ x :*: y+		Flaws x :*: Flaws y -> Flaws $ x + y+		Validated _ :*: Flaws y -> Flaws y+		Flaws x :*: Validated _ -> Flaws x -instance Semigroup e => Monoidal (->) (->) (:*:) (:*:) (Validation e) where-	unit _ f = Validated $ f One+instance Semigroup e => Monoidal (-->) (->) (:*:) (:*:) (Validation e) where+	unit _ = Straight $ Validated . ($ One) -instance Semigroup e => Semimonoidal (->) (:*:) (:+:) (Validation e) where-	multiply (Flaws _ :*: y) = Adoption -<$>- y-	multiply (Validated x :*: _) = Option -<$>- Validated x+instance Semigroup e => Semimonoidal (-->) (:*:) (:+:) (Validation e) where+	mult = Straight $ \case+		Flaws _ :*: y -> Adoption <$> y+		Validated x :*: _ -> Option <$> Validated x  instance Traversable (->) (->) (Validation e) where-	f <<- Validated x = Validated -<$>- f x+	f <<- Validated x = Validated <$> f x 	_ <<- Flaws e = point $ Flaws e  instance Bivariant (->) (->) (->) Validation where

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.Wedge where  import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Paradigm.Primary.Algebraic.Exponential () import Pandora.Paradigm.Primary.Algebraic (point)@@ -9,14 +9,14 @@ data Wedge e a = Nowhere | Here e | There a  instance Covariant (->) (->) (Wedge e) where-	_ -<$>- Nowhere = Nowhere-	_ -<$>- Here x = Here x-	f -<$>- There x = There $ f x+	_ <$> Nowhere = Nowhere+	_ <$> Here x = Here x+	f <$> There x = There $ f x  instance Traversable (->) (->) (Wedge e) where 	_ <<- Nowhere = point Nowhere 	_ <<- Here x = point $ Here x-	f <<- There x = There -<$>- f x+	f <<- There x = There <$> f x  wedge :: (e -> r) -> (a -> r) -> r -> Wedge e a -> r wedge f _ _ (Here x) = f x

@@ -2,25 +2,25 @@  import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Category ((#), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))  data Wye a = End | Left a | Right a | Both a a  instance Covariant (->) (->) Wye where-	_ -<$>- End = End-	f -<$>- Left x = Left # f x-	f -<$>- Right y = Right # f y-	f -<$>- Both x y = Both # f x # f y+	_ <$> End = End+	f <$> Left x = Left # f x+	f <$> Right y = Right # f y+	f <$> Both x y = Both # f x # f y  instance Semimonoidal (<--) (:*:) (:*:) Wye where-	multiply = Flip $ \case+	mult = Flip $ \case 		End -> End :*: End 		Left (x :*: y) -> Left x :*: Left y 		Right (x :*: y) -> Right x :*: Right y

@@ -14,11 +14,3 @@ import Pandora.Paradigm.Primary.Transformer.Construction as Exports import Pandora.Paradigm.Primary.Transformer.Reverse as Exports import Pandora.Paradigm.Primary.Transformer.Backwards as Exports-import Pandora.Paradigm.Primary.Transformer.Flip as Exports--import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))--instance Interpreted (Flip v a) where-	type Primary (Flip v a) e = v e a-	run ~(Flip x) = x-	unite = Flip

@@ -2,9 +2,9 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -12,45 +12,43 @@ import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic ((-<*>-))+import Pandora.Paradigm.Primary.Algebraic ((<-*-)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), (%))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point, extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype Backwards t a = Backwards (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Backwards t) where-	f -<$>- Backwards x = Backwards $ f -<$>- x+	f <$> Backwards x = Backwards $ f <$> x  -- TODO: check that effects evaluation goes in opposite order-instance (Semimonoidal (->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (->) (:*:) (:*:) (Backwards t) where-	multiply (Backwards x :*: Backwards y) = Backwards #-		((:*:) %) -<$>- y -<*>- x+instance (Semimonoidal (-->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (-->) (:*:) (:*:) (Backwards t) where+	mult = Straight $ \(Backwards x :*: Backwards y) -> Backwards # ((:*:) %) <$> y <-*- x -instance (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:*:) t) => Monoidal (->) (->) (:*:) (:*:) (Backwards t) where-	unit _ f = Backwards . point $ f One+instance (Covariant (->) (->) t, Monoidal (-->) (->) (:*:) (:*:) t) => Monoidal (-->) (->) (:*:) (:*:) (Backwards t) where+	unit _ = Straight $ Backwards . point . ($ One)  instance (Semimonoidal (<--) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (<--) (:*:) (:*:) (Backwards t) where-	multiply = Flip $ \(Backwards x) -> -		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		(Backwards <-> Backwards) $ f x+	mult = Flip $ (Backwards <-> Backwards) . run (mult @(<--)) . run  instance (Covariant (->) (->) t, Monoidal (<--) (->) (:*:) (:*:) t) => Monoidal (<--) (->) (:*:) (:*:) (Backwards t) where 	unit _ = Flip $ \(Backwards x) -> (\_ -> extract x)  instance Traversable (->) (->) t => Traversable (->) (->) (Backwards t) where-	f <<- Backwards x = Backwards -<$>- f <<- x+	f <<- Backwards x = Backwards <$> f <<- x  instance Distributive (->) (->) t => Distributive (->) (->) (Backwards t) where 	f -<< x = Backwards $ run . f -<< x  instance Contravariant (->) (->) t => Contravariant (->) (->) (Backwards t) where-	f ->$<- Backwards x = Backwards $ f ->$<- x+	f >$< Backwards x = Backwards $ f >$< x -instance Interpreted (Backwards t) where+instance Interpreted (->) (Backwards t) where 	type Primary (Backwards t) a = t a 	run ~(Backwards x) = x 	unite = Backwards

@@ -3,25 +3,30 @@ module Pandora.Paradigm.Primary.Transformer.Construction where  import Pandora.Core.Functor (type (:.), type (:=), type (:=>), type (~>))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\), hoist))+import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Ringoid ((*)) import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Paradigm.Primary.Algebraic ((-<*>-), extract)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic ((<-*-), extract)+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Primary.Algebraic.One (One (One))+import Pandora.Paradigm.Primary.Algebraic (empty)+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce)) import Pandora.Paradigm.Schemes (type (<:.>))@@ -31,33 +36,34 @@ data Construction t a = Construct a (t :. Construction t := a)  instance Covariant (->) (->) t => Covariant (->) (->) (Construction t) where-	f -<$>- ~(Construct x xs) = Construct # f x # f -<$$>- xs+	f <$> ~(Construct x xs) = Construct # f x # (<$$>) @(->) @(->) f xs -instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => Semimonoidal (->) (:*:) (:*:) (Construction t) where-	multiply (Construct x xs :*: Construct y ys) = Construct (x :*: y) (multiply @(->) @(:*:) -<$>- multiply (xs :*: ys))+instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Semimonoidal (-->) (:*:) (:*:) (Construction t) where+	mult = Straight $ \(Construct x xs :*: Construct y ys) -> Construct (x :*: y) $ (mult @(-->) !) <$> (mult @(-->) ! xs :*: ys)  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Semimonoidal (<--) (:*:) (:*:) (Construction t) where-	multiply = Flip $ \(Construct (x :*: y) xys) ->-		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let Flip g = multiply @(<--) @(:*:) @(:*:) in-		(Construct x <-> Construct y) $ f $ g -<$>- xys+	mult = Flip $ \(Construct (x :*: y) xys) -> (Construct x <-> Construct y)+		$ (mult @(<--) !) $ (mult @(<--) !) <$> xys  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Monoidal (<--) (->) (:*:) (:*:) (Construction t) where 	unit _ = Flip $ \(Construct x _) -> (\_ -> x) +instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Monoidal (-->) (->) (:*:) (:+:) t) => Monoidal (-->) (->) (:*:) (:*:) (Construction t) where+	unit _ = Straight $ \f -> Construct # f One # empty+ instance Traversable (->) (->) t => Traversable (->) (->) (Construction t) where-	f <<- ~(Construct x xs) = Construct -<$>- f x -<*>- f -<<-<<- xs+	f <<- ~(Construct x xs) = Construct <$> f x <-*- f -<<-<<- xs  instance Covariant (->) (->) t => Extendable (->) (Construction t) where-	f <<= x = Construct # f x # (f <<=) -<$>- deconstruct x+	f <<= x = Construct # f x # (f <<=) <$> deconstruct x -instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Comonad (Construction t) (->) where+instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Comonad (->) (Construction t) where  instance (forall u . Semimonoidal (<--) (:*:) (:*:) u) => Lowerable (->) Construction where-	lower x = extract -<$>- deconstruct x+	lower x = extract <$> deconstruct x  instance (forall u . Semimonoidal (<--) (:*:) (:*:) u) => Hoistable Construction where-	f /|\ x = Construct # extract x $ f # hoist f -<$>- deconstruct x+	f /|\ x = Construct # extract x $ f # (f /|\) <$> deconstruct x  instance (Setoid a, forall b . Setoid b => Setoid (t b), Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Setoid (Construction t a) where 	x == y = (extract x == extract y) * (deconstruct x == deconstruct y)@@ -79,7 +85,7 @@  -- Generate a construction from seed using effectful computation (.-+) :: Covariant (->) (->) t => a :=> t -> a :=> Construction t-f .-+ x = Construct x $ (f .-+) -<$>- f x+f .-+ x = Construct x $ (f .-+) <$> f x -section :: (Comonad t (->), Monoidal (<--) (->) (:*:) (:*:) t) => t ~> Construction t+section :: (Comonad (->) t, Monoidal (<--) (->) (:*:) (:*:) t) => t ~> Construction t section xs = Construct # extract xs $ section <<= xs

@@ -1,28 +1,29 @@ {-# LANGUAGE UndecidableInstances #-}+ module Pandora.Paradigm.Primary.Transformer.Continuation where  import Pandora.Core.Functor (type (:.), type (:=), type (::|:.)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (%))+import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (%), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)) import Pandora.Paradigm.Primary.Algebraic (point)  newtype Continuation r t a = Continuation ((->) ::|:. a :. t := r) -instance Interpreted (Continuation r t) where+instance Interpreted (->) (Continuation r t) where 	type Primary (Continuation r t) a = (->) ::|:. a :. t := r 	run ~(Continuation x) = x 	unite = Continuation  instance Covariant (->) (->) t => Covariant (->) (->) (Continuation r t) where-	f -<$>- Continuation continuation = Continuation $ continuation . (. f)+	f <$> Continuation continuation = Continuation $ continuation . (. f)  instance Covariant (->) (->) t => Bindable (->) (Continuation r t) where 	f =<< x = Continuation $ \g -> run x $ \y -> run # f y # g@@ -37,12 +38,12 @@ cwcc f = Continuation $ \g -> (run % g) . f $ Continuation . (!.) . g  -- | Delimit the continuation of any 'shift'-reset :: (forall u . Bindable (->) u, Monad t) => Continuation r t r -> Continuation s t r+reset :: (forall u . Bindable (->) u, Monad (->) t) => Continuation r t r -> Continuation s t r reset = lift . (run % point)  -- | Capture the continuation up to the nearest enclosing 'reset' and pass it-shift :: Monoidal (->) (->) (:*:) (:*:) t => ((a -> t r) -> Continuation r t r) -> Continuation r t a+shift :: Monoidal (-->) (->) (:*:) (:*:) t => ((a -> t r) -> Continuation r t r) -> Continuation r t a shift f = Continuation $ (run % point) . f -interruptable :: Monoidal (->) (->) (:*:) (:*:) t => ((a -> Continuation a t a) -> Continuation a t a) -> t a+interruptable :: Monoidal (-->) (->) (:*:) (:*:) t => ((a -> Continuation a t a) -> Continuation a t a) -> t a interruptable = (run % point) . cwcc

@@ -3,7 +3,7 @@ module Pandora.Paradigm.Primary.Transformer.Day where  import Pandora.Pattern.Category ((#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Algebraic.Exponential ((!..), (-.#..-))@@ -11,7 +11,7 @@ data Day t u a = forall b c . Day (t b) (u c) (b -> c -> a)  instance Covariant (->) (->) (Day t u) where-	f -<$>- Day tb uc g = Day tb uc # f -.#..- g+	f <$> Day tb uc g = Day tb uc # f -.#..- g  instance (Extendable (->) t, Extendable (->) u) => Extendable (->) (Day t u) where 	f <<= day@(Day tb uc _) = Day tb uc (f day !..)

@@ -1,3 +0,0 @@-module Pandora.Paradigm.Primary.Transformer.Flip where--newtype Flip (v :: * -> * -> *) a e = Flip (v e a)

@@ -3,17 +3,20 @@ module Pandora.Paradigm.Primary.Transformer.Instruction where  import Pandora.Core.Functor (type (:.), type (:=))+import Pandora.Core.Appliable ((!))+import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\), hoist))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point)@@ -21,35 +24,36 @@ data Instruction t a = Enter a | Instruct (t :. Instruction t := a)  instance Covariant (->) (->) t => Covariant (->) (->) (Instruction t) where-	f -<$>- Enter x = Enter $ f x-	f -<$>- Instruct xs = Instruct $ f -<$$>- xs+	f <$> Enter x = Enter $ f x+	f <$> Instruct xs = Instruct $ (<$$>) @(->) @(->) f xs -instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => Semimonoidal (->) (:*:) (:*:) (Instruction t) where-	multiply (Enter x :*: Enter y) = Enter $ x :*: y-	multiply (Enter x :*: Instruct y) = (x :*:) -<$>- Instruct y-	multiply (Instruct x :*: Enter y) = (:*: y) -<$>- Instruct x-	multiply (Instruct x :*: Instruct y) = Instruct $ multiply @(->) @(:*:) -<$>- multiply (x :*: y)+instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Semimonoidal (-->) (:*:) (:*:) (Instruction t) where+	mult = Straight $ \case+		Enter x :*: Enter y -> Enter $ x :*: y+		Enter x :*: Instruct y -> (x :*:) <$> Instruct y+		Instruct x :*: Enter y -> (:*: y) <$> Instruct x+		Instruct x :*: Instruct y -> Instruct $ (mult @(-->) !) <$> (mult @(-->) ! x :*: y) -instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => Monoidal (->) (->) (:*:) (:*:) (Instruction t) where-	unit _ f = Enter $ f One+instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Monoidal (-->) (->) (:*:) (:*:) (Instruction t) where+	unit _ = Straight $ Enter . ($ One)  instance Covariant (->) (->) t => Bindable (->) (Instruction t) where 	f =<< Enter x = f x-	f =<< Instruct xs = Instruct $ (f =<<) -<$>- xs+	f =<< Instruct xs = Instruct $ (f =<<) <$> xs -instance Monad t => Monad (Instruction t) where+instance Monad (->) t => Monad (->) (Instruction t) where  instance Traversable (->) (->) t => Traversable (->) (->) (Instruction t) where-	f <<- Enter x = Enter -<$>- f x-	f <<- Instruct xs = Instruct -<$>- f -<<-<<- xs+	f <<- Enter x = Enter <$> f x+	f <<- Instruct xs = Instruct <$> f -<<-<<- xs  instance Liftable (->) Instruction where-	lift x = Instruct $ Enter -<$>- x+	lift x = Instruct $ Enter <$> x -instance (forall t . Bindable (->) t, forall t . Monoidal (->) (->) (:*:) (:*:) t) => Lowerable (->) Instruction where+instance (forall t . Bindable (->) t, forall t . Monoidal (-->) (->) (:*:) (:*:) t) => Lowerable (->) Instruction where 	lower (Enter x) = point x 	lower (Instruct xs) = lower =<< xs  instance (forall v . Covariant (->) (->) v) => Hoistable Instruction where 	_ /|\ Enter x = Enter x-	f /|\ Instruct xs = Instruct $ hoist f -<$>- f xs+	f /|\ Instruct xs = Instruct $ (f /|\) <$> f xs

@@ -4,7 +4,7 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -13,7 +13,7 @@ import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)) import Pandora.Paradigm.Primary.Algebraic (point) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False))@@ -22,14 +22,14 @@ data Jack t a = It a | Other (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Jack t) where-	f -<$>- It x = It $ f x-	f -<$>- Other y = Other $ f -<$>- y+	f <$> It x = It $ f x+	f <$> Other y = Other $ f <$> y  instance Traversable (->) (->) t => Traversable (->) (->) (Jack t) where-	f <<- It x = It -<$>- f x-	f <<- Other y = Other -<$>- f <<- y+	f <<- It x = It <$> f x+	f <<- Other y = Other <$> f <<- y -instance (Monoidal (->) (->) (:*:) (:*:) t, Bindable (->) t) => Bindable (->) (Jack t) where+instance (Monoidal (-->) (->) (:*:) (:*:) t, Bindable (->) t) => Bindable (->) (Jack t) where 	f =<< It x = f x 	f =<< Other x = Other $ jack point identity . f =<< x 

@@ -2,14 +2,14 @@  module Pandora.Paradigm.Primary.Transformer.Jet where -import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-))-import Pandora.Paradigm.Primary.Algebraic ((-<*>-))+import Pandora.Paradigm.Primary.Algebraic ((<-*-))  data Jet t a = Jet a (Jet t (t a))  instance Covariant (->) (->) t => Covariant (->) (->) (Jet t) where-	f -<$>- Jet x xs = Jet (f x) (f -<$$>- xs)+	f <$> Jet x xs = Jet (f x) ((<$$>) @(->) @(->) f xs)  instance Traversable (->) (->) t => Traversable (->) (->) (Jet t) where-	f <<- Jet x xs = Jet -<$>- f x -<*>- f -<<-<<- xs+	f <<- Jet x xs = Jet <$> f x <-*- f -<<-<<- xs

@@ -2,8 +2,8 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right)) @@ -12,9 +12,9 @@ data instance Kan Left t u b a = Lan ((t b -> a) -> u b)  instance Contravariant (->) (->) (Kan Left t u b) where-	f ->$<- Lan x = Lan $ x . (f .)+	f >$< Lan x = Lan $ x . (f .) -instance Interpreted (Kan Left t u b) where+instance Interpreted (->) (Kan Left t u b) where 	type Primary (Kan Left t u b) a = (t b -> a) -> u b 	run ~(Lan x) = x 	unite = Lan@@ -22,9 +22,9 @@ data instance Kan Right t u b a = Ran ((a -> t b) -> u b)  instance Covariant (->) (->) (Kan Right t u b) where-	f -<$>- Ran x = Ran $ x . (. f)+	f <$> Ran x = Ran $ x . (. f) -instance Interpreted (Kan Right t u b) where+instance Interpreted (->) (Kan Right t u b) where 	type Primary (Kan Right t u b) a = (a -> t b) -> u b 	run ~(Ran x) = x 	unite = Ran

@@ -4,7 +4,7 @@  import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()@@ -14,8 +14,8 @@ 	Outlined :: t a -> Outline t (a -> b) -> Outline t b  instance Covariant (->) (->) (Outline t) where-	f -<$>- Line a = Line $ f a-	f -<$>- Outlined x y = Outlined x # (.) f -<$>- y+	f <$> Line a = Line $ f a+	f <$> Outlined x y = Outlined x # (.) f <$> y  instance Liftable (->) Outline where 	lift t = Outlined t (Line identity)

@@ -2,11 +2,12 @@  module Pandora.Paradigm.Primary.Transformer.Reverse where +import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -15,42 +16,41 @@ import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Transformer.Backwards (Backwards (Backwards))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point, extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype Reverse t a = Reverse (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Reverse t) where-	f -<$>- Reverse x = Reverse # f -<$>- x+	f <$> Reverse x = Reverse # f <$> x -instance (Semimonoidal (->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (->) (:*:) (:*:) (Reverse t) where-	multiply (Reverse x :*: Reverse y) = Reverse # multiply (x :*: y)+instance (Semimonoidal (-->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (-->) (:*:) (:*:) (Reverse t) where+	mult = Straight $ \(Reverse x :*: Reverse y) -> Reverse ! mult @(-->) ! (x :*: y) -instance (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:*:) t) => Monoidal (->) (->) (:*:) (:*:) (Reverse t) where-	unit _ f = Reverse . point $ f One+instance (Covariant (->) (->) t, Monoidal (-->) (->) (:*:) (:*:) t) => Monoidal (-->) (->) (:*:) (:*:) (Reverse t) where+	unit _ = Straight $ Reverse . point . ($ One)  instance (Semimonoidal (<--) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (<--) (:*:) (:*:) (Reverse t) where-	multiply = Flip $ \(Reverse x) -> -		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		(Reverse <-> Reverse) $ f x+	mult = Flip $ (Reverse <-> Reverse) . run (mult @(<--)) . run  instance (Covariant (->) (->) t, Monoidal (<--) (->) (:*:) (:*:) t) => Monoidal (<--) (->) (:*:) (:*:) (Reverse t) where 	unit _ = Flip $ \(Reverse x) -> (\_ -> extract x)  instance Traversable (->) (->) t => Traversable (->) (->) (Reverse t) where-	f <<- Reverse x = Reverse -<$>- run (Backwards . f <<- x)+	f <<- Reverse x = Reverse <$> run (Backwards . f <<- x)  instance Distributive (->) (->) t => Distributive (->) (->) (Reverse t) where 	f -<< x = Reverse $ run . f -<< x  instance Contravariant (->) (->) t => Contravariant (->) (->) (Reverse t) where-	f ->$<- Reverse x = Reverse # f ->$<- x+	f >$< Reverse x = Reverse # f >$< x -instance Interpreted (Reverse t) where+instance Interpreted (->) (Reverse t) where 	type Primary (Reverse t) a = t a 	run ~(Reverse x) = x 	unite = Reverse

@@ -3,24 +3,27 @@ module Pandora.Paradigm.Primary.Transformer.Tap where  import Pandora.Core.Functor (type (:=))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))+import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Inventory.Store (Store (Store))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) -import Pandora.Paradigm.Primary.Algebraic ((-<*>-), extract)+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run)+import Pandora.Paradigm.Primary.Algebraic ((<-*-), extract) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), twosome)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), (%))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%)) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse (Reverse)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>)) import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))@@ -30,21 +33,20 @@ data Tap t a = Tap a (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Tap t) where-	f -<$>- Tap x xs = Tap # f x # f -<$>- xs+	f <$> Tap x xs = Tap # f x # f <$> xs -instance Semimonoidal (->) (:*:) (:*:) t => Semimonoidal (->) (:*:) (:*:) (Tap t) where-	multiply (Tap x xs :*: Tap y ys) = Tap (x :*: y) $ multiply $ xs :*: ys+instance Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap t) where+	mult = Straight $ \(Tap x xs :*: Tap y ys) -> Tap (x :*: y) $ mult @(-->) ! xs :*: ys  instance Semimonoidal (<--) (:*:) (:*:) t => Semimonoidal (<--) (:*:) (:*:) (Tap t) where-	multiply = Flip $ \(Tap (x :*: y) xys) -> -		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let (xs :*: ys) = f xys in Tap x xs :*: Tap y ys+	mult = Flip $ \(Tap (x :*: y) xys) ->+		(Tap x <-> Tap y) $ mult @(<--) ! xys  instance Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (->) (:*:) (:*:) (Tap t) where 	unit _ = Flip $ \(Tap x _) -> (\_ -> x)  instance Traversable (->) (->) t => Traversable (->) (->) (Tap t) where-	f <<- Tap x xs = Tap -<$>- f x -<*>- f <<- xs+	f <<- Tap x xs = Tap <$> f x <-*- f <<- xs  instance (Semimonoidal (<--) (:*:) (:*:) t, Extendable (->) t, Covariant (->) (->) t) => Extendable (->) (Tap t) where 	f <<= x = Tap # f x $ f . Tap (extract x) <<= lower x@@ -55,13 +57,13 @@ instance Hoistable Tap where 	f /|\ Tap x xs = Tap x # f xs -instance {-# OVERLAPS #-} Semimonoidal (->) (:*:) (:*:) t => Semimonoidal (->) (:*:) (:*:) (Tap (t <:.:> t := (:*:))) where-	multiply (Tap x (T_U (xls :*: xrs)) :*: Tap y (T_U (yls :*: yrs))) = Tap (x :*: y)-		$ T_U $ multiply (xls :*: yls) :*: multiply (xrs :*: yrs)+instance {-# OVERLAPS #-} Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap (t <:.:> t := (:*:))) where+	mult = Straight $ \(Tap x (T_U (xls :*: xrs)) :*: Tap y (T_U (yls :*: yrs))) -> Tap (x :*: y)+		$ T_U $ (mult @(-->) ! (xls :*: yls)) :*: (mult @(-->) ! (xrs :*: yrs))  instance {-# OVERLAPS #-} Traversable (->) (->) t => Traversable (->) (->) (Tap (t <:.:> t := (:*:))) where 	f <<- Tap x (T_U (future :*: past)) = (\past' x' future' -> Tap x' $ twosome # future' # run past')-		-<$>- f <<- Reverse past -<*>- f x -<*>- f <<- future+		<$> f <<- Reverse past <-*- f x <-*- f <<- future  instance (Covariant (->) (->) t) => Substructure Root (Tap (t <:.:> t := (:*:))) where 	type Available Root (Tap (t <:.:> t := (:*:))) = Identity

@@ -3,7 +3,7 @@ module Pandora.Paradigm.Primary.Transformer.Yoneda where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Paradigm.Primary.Algebraic.Exponential () @@ -11,7 +11,7 @@ 	{ yoneda :: forall b . (a -> b) -> t b }  instance Covariant (->) (->) (Yoneda t) where-	f -<$>- x = Yoneda (\k -> yoneda x (k . f))+	f <$> x = Yoneda (\k -> yoneda x (k . f))  instance Liftable (->) Yoneda where-	lift x = Yoneda (-<$>- x)+	lift x = Yoneda (<$> x)

@@ -4,7 +4,7 @@  newtype PQ_ p q a b = PQ_ (p a (q b a)) -instance Interpreted (PQ_ p q a) where+instance Interpreted (->) (PQ_ p q a) where 	type Primary (PQ_ p q a) b = p a (q b a) 	run ~(PQ_ x) = x 	unite = PQ_

@@ -4,7 +4,7 @@  newtype PTU p t u a b = PTU (p (t a) (u b)) -instance Interpreted (PTU p t u a) where+instance Interpreted (->) (PTU p t u a) where 	type Primary (PTU p t u a) b = p (t a) (u b) 	run ~(PTU x) = x 	unite = PTU

@@ -4,7 +4,7 @@  newtype P_Q_T (p :: * -> * -> *) (q :: * -> * -> *) (t :: * -> *) (a :: *) (b :: *) = P_Q_T (p a (q (t b) a)) -instance Interpreted (P_Q_T p q t a) where+instance Interpreted (->) (P_Q_T p q t a) where 	type Primary (P_Q_T p q t a) b = (p a (q (t b) a)) 	run ~(P_Q_T x) = x 	unite = P_Q_T

@@ -4,7 +4,7 @@  newtype P_T p t a b = P_T (p (t a) b) -instance Interpreted (P_T p t a) where+instance Interpreted (->) (P_T p t a) where 	type Primary (P_T p t a) b = p (t a) b 	run ~(P_T x) = x 	unite = P_T

@@ -1,11 +1,12 @@ module Pandora.Paradigm.Schemes.TU where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), identity)-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>)) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -14,13 +15,14 @@ import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption), sum) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (empty, point, extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))  newtype TU ct cu t u a = TU (t :. u := a) @@ -31,42 +33,39 @@ type (<:.<) = TU Covariant Contravariant type (>:.<) = TU Contravariant Contravariant -instance Interpreted (TU ct cu t u) where+instance Interpreted (->) (TU ct cu t u) where 	type Primary (TU ct cu t u) a = t :. u := a 	run ~(TU x) = x 	unite = TU -instance (Covariant (->) (->) t, Covariant (->) (->) u) => Covariant (->) (->) (t <:.> u) where-	f -<$>- x = TU $ f -<$$>- run x+instance (Covariant m m t, Covariant m m u, Interpreted m (t <:.> u)) => Covariant m m (t <:.> u) where+	(<$>) f = (||=) ((<$$>) @m @m f) -instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t, Semimonoidal (->) (:*:) (:*:) u) => Semimonoidal (->) (:*:) (:*:) (t <:.> u) where-	multiply (TU x :*: TU y) = TU $ multiply @(->) @(:*:) -<$>- multiply (x :*: y)+instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <:.> u) where+	mult = Straight $ TU . (<$>) (mult @(-->) !) . (mult @(-->) !) . (run @(->) <-> run @(->)) -instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (->) (:*:) (:*:) u, Monoidal (->) (->) (:*:) (:*:) t, Monoidal (->) (->) (:*:) (:*:) u) => Monoidal (->) (->) (:*:) (:*:) (t <:.> u) where-	unit _ f = TU . point . point $ f One+instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (->) (:*:) (:*:) t, Monoidal (-->) (->) (:*:) (:*:) u) => Monoidal (-->) (->) (:*:) (:*:) (t <:.> u) where+	unit _ = Straight $ TU . point . point . ($ One) -instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (->) (:*:) (:+:) t) => Semimonoidal (->) (:*:) (:+:) (t <:.> u) where-	multiply (TU x :*: TU y) = TU $ sum (Option -<$>-) (Adoption -<$>-) -<$>- multiply @(->) @(:*:) @(:+:) (x :*: y)+instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:+:) t) => Semimonoidal (-->) (:*:) (:+:) (t <:.> u) where+	mult = Straight $ \(TU x :*: TU y) -> TU $ sum (Option <$>) (Adoption <$>) <$> (mult @(-->) ! x :*: y) -instance (Covariant (->) (->) t, Covariant (->) (->) u, Monoidal (->) (->) (:*:) (:+:) t) => Monoidal (->) (->) (:*:) (:+:) (t <:.> u) where-	unit _ _ = TU empty+instance (Covariant (->) (->) t, Covariant (->) (->) u, Monoidal (-->) (->) (:*:) (:+:) t) => Monoidal (-->) (->) (:*:) (:+:) (t <:.> u) where+	unit _ = Straight $ \_ -> TU empty  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:.> u) where-	multiply = Flip $ \(TU xys) ->-		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let Flip g = multiply @(<--) @(:*:) @(:*:) in-		(TU <-> TU) $ g (f -<$>- xys) where+	mult = Flip $ \(TU xys) -> (TU <-> TU) . (mult @(<--) !) $ (mult @(<--) !) <$> xys  instance (Covariant (->) (->) t, Monoidal (<--) (->) (:*:) (:*:) t, Monoidal (<--) (->) (:*:) (:*:) u) => Monoidal (<--) (->) (:*:) (:*:) (t <:.> u) where 	unit _ = Flip $ \(TU x) -> (\_ -> extract $ extract x)  instance (Traversable (->) (->) t, Traversable (->) (->) u) => Traversable (->) (->) (t <:.> u) where-	f <<- x = TU -<$>- f -<<-<<- run x+	f <<- x = TU <$> f -<<-<<- run x  instance (Bindable (->) t, Distributive (->) (->) t, Covariant (->) (->) u, Bindable (->) u) => Bindable (->) (t <:.> u) where-	f =<< TU x = TU $ (\i -> (identity =<<) -<$>- run . f -<< i) =<< x+	f =<< TU x = TU $ (\i -> (identity =<<) <$> run . f -<< i) =<< x -instance Monoidal (->) (->) (:*:) (:*:) t => Liftable (->) (TU Covariant Covariant t) where+instance Monoidal (-->) (->) (:*:) (:*:) t => Liftable (->) (TU Covariant Covariant t) where 	lift :: Covariant (->) (->) u => u ~> t <:.> u 	lift = TU . point @@ -76,4 +75,4 @@  instance Covariant (->) (->) t => Hoistable (TU Covariant Covariant t) where 	(/|\) :: u ~> v -> (t <:.> u ~> t <:.> v)-	f /|\ TU x = TU $ f -<$>- x+	f /|\ TU x = TU $ f <$> x

@@ -1,11 +1,12 @@ module Pandora.Paradigm.Schemes.TUT where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (identity, ($))-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-), (-<$$$>-))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<$>)), (<$$>), (<$$$>)) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -14,12 +15,13 @@ import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic (point, extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))  newtype TUT ct ct' cu t t' u a = TUT (t :. u :. t' := a) @@ -34,35 +36,31 @@ type (<:>.<:<) = TUT Covariant Contravariant Contravariant type (>:>.<:<) = TUT Contravariant Contravariant Contravariant -instance Interpreted (TUT ct ct' cu t t' u) where+instance Interpreted (->) (TUT ct ct' cu t t' u) where 	type Primary (TUT ct ct' cu t t' u) a = t :. u :. t' := a 	run ~(TUT x) = x 	unite = TUT -instance (Covariant (->) (->) t, Covariant (->) (->) t', Covariant (->) (->) u) => Covariant (->) (->) (t <:<.>:> t' := u) where-	f -<$>- TUT x = TUT $ f -<$$$>- x+instance (Covariant m m t, Covariant m m u, Covariant m m t', Interpreted m (t <:<.>:> t' := u)) => Covariant m m (t <:<.>:> t' := u) where+	(<$>) f = (||=) ((<$$$>) @m @m @m f) -instance (Covariant (->) (->) t, Covariant (->) (->) t', Covariant (->) (->) u, Semimonoidal (->) (:*:) (:*:) t, Semimonoidal (->) (:*:) (:*:) u, Semimonoidal (->) (:*:) (:*:) t') => Semimonoidal (->) (:*:) (:*:) (t <:<.>:> t' := u) where-	multiply (TUT x :*: TUT y) = TUT $ multiply @(->) @(:*:) -<$$>- multiply @(->) @(:*:) -<$>- multiply (x :*: y)+instance (Covariant (->) (->) t, Covariant (->) (->) t', Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u, Semimonoidal (-->) (:*:) (:*:) t') => Semimonoidal (-->) (:*:) (:*:) (t <:<.>:> t' := u) where+	mult = Straight $ TUT . (<$$>) @_ @(->) (mult @(-->) !) . (<$>) (mult @(-->) !) . (mult @(-->) !) . (run @(->) <-> run @(->))  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Covariant (->) (->) u, Semimonoidal (<--) (:*:) (:*:) u, Covariant (->) (->) t', Semimonoidal (<--) (:*:) (:*:) t') => Semimonoidal (<--) (:*:) (:*:) (t <:<.>:> t' := u) where-	multiply = Flip $ \(TUT xys) ->-		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let Flip g = multiply @(<--) @(:*:) @(:*:) in-		let Flip h = multiply @(<--) @(:*:) @(:*:) in-		(TUT <-> TUT) $ f (g -<$>- (h -<$$>- xys)) where+	mult = Flip $ (TUT <-> TUT) . (mult @(<--) !) . (<$>) (mult @(<--) !) . (<$$>) @_ @(->) (mult @(<--) !) . run  instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) t', Monoidal (<--) (->) (:*:) (:*:) u, Adjoint (->) (->) t t') => Monoidal (<--) (->) (:*:) (:*:) (t <:<.>:> t' := u) where 	unit _ = Flip $ \(TUT xys) -> (\_ -> (extract |-) xys)  instance (Covariant (->) (->) t, Covariant (->) (->) t', Adjoint (->) (->) t' t, Bindable (->) u) => Bindable (->) (t <:<.>:> t' := u) where-	f =<< x = TUT $ ((run . f |-) =<<) -<$>- run x+	f =<< x = TUT $ ((run . f |-) =<<) <$> run x -instance (Covariant (->) (->) t, Covariant (->) (->) u, Covariant (->) (->) t', Semimonoidal (->) (:*:) (:*:) t, Semimonoidal (->) (:*:) (:*:) t', Monoidal (->) (->) (:*:) (:*:) u, Adjoint (->) (->) t' t) => Monoidal (->) (->) (:*:) (:*:) (t <:<.>:> t' := u) where-	unit _ f = unite . (point -|) . f $ One+instance (Covariant (->) (->) t, Covariant (->) (->) u, Covariant (->) (->) t', Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) t', Monoidal (-->) (->) (:*:) (:*:) u, Adjoint (->) (->) t' t) => Monoidal (-->) (->) (:*:) (:*:) (t <:<.>:> t' := u) where+	unit _ = Straight $ unite . (point -|) . ($ One)  instance (Adjoint (->) (->) t' t, Extendable (->) u) => Extendable (->) (t' <:<.>:> t := u) where-	f <<= x = TUT $ ((f . unite -|) <<=) -<$>- run x+	f <<= x = TUT $ ((f . unite -|) <<=) <$> run x  instance (Adjoint (->) (->) t' t, Distributive (->) (->) t) => Liftable (->) (t <:<.>:> t') where 	lift :: Covariant (->) (->) u => u ~> t <:<.>:> t' := u

@@ -5,7 +5,7 @@  newtype TUVW ct cu cv cw t u v w a = TUVW (t :. u :. v :. w := a) -instance Interpreted (TUVW ct cu cv cw t u v w) where+instance Interpreted (->) (TUVW ct cu cv cw t u v w) where 	type Primary (TUVW ct cu cv cw t u v w) a = t :. u :. v :. w := a 	run ~(TUVW x) = x 	unite = TUVW

@@ -1,8 +1,8 @@ module Pandora.Paradigm.Schemes.T_U where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant, Contravariant ((->$<-)))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant, Contravariant ((>$<))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Functor.Divariant (Divariant ((>->))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))@@ -16,16 +16,16 @@ type (<:.:<) t u p = T_U Covariant Contravariant p t u type (>:.:<) t u p = T_U Contravariant Contravariant p t u -instance Interpreted (T_U ct cu p t u) where+instance Interpreted (->) (T_U ct cu p t u) where 	type Primary (T_U ct cu p t u) a = p (t a) (u a) 	run ~(T_U x) = x 	unite = T_U  instance (forall i . Covariant (->) (->) (p i), Bivariant (->) (->) (->) p,  Covariant (->) (->) t, Covariant (->) (->) u) => Covariant (->) (->) (t <:.:> u := p) where-	f -<$>- x = (f -<$>-) <-> (f -<$>-) ||= x+	f <$> x = (f <$>) <-> (f <$>) ||= x  instance (Divariant (->) (->) (->) p, Contravariant (->) (->) t, Covariant (->) (->) u) => Covariant (->) (->) (t >:.:> u := p) where-	f -<$>- x = (f ->$<-) >-> (f -<$>-) ||= x+	f <$> x = (f >$<) >-> (f <$>) ||= x  instance (forall i . Covariant (->) (->) (p i), Bivariant (->) (->) (->) p, Contravariant (->) (->) t, Contravariant (->) (->) u) => Contravariant (->) (->) (t >:.:< u := p) where-	f ->$<- x = (f ->$<-) <-> (f ->$<-) ||= x+	f >$< x = (f >$<) <-> (f >$<) ||= x

@@ -1,22 +1,24 @@ module Pandora.Paradigm.Schemes.UT where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), identity)-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>)) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.One (One (One)) import Pandora.Paradigm.Primary.Algebraic ((:*:) ((:*:)), point, extract)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))  newtype UT ct cu t u a = UT (u :. t := a) @@ -27,36 +29,33 @@ type (<.:<) = UT Covariant Contravariant type (>.:<) = UT Contravariant Contravariant -instance Interpreted (UT ct cu t u) where+instance Interpreted (->) (UT ct cu t u) where 	type Primary (UT ct cu t u) a = u :. t := a 	run ~(UT x) = x 	unite = UT -instance (Covariant (->) (->) t, Covariant (->) (->) u) => Covariant (->) (->) (t <.:> u) where-	f -<$>- x = UT $ f -<$$>- run x+instance (Covariant m m t, Covariant m m u, Interpreted m (t <.:> u)) => Covariant m m (t <.:> u) where+	(<$>) f = (||=) ((<$$>) @m @m f) -instance (Covariant (->) (->) u, Semimonoidal (->) (:*:) (:*:) t, Semimonoidal (->) (:*:) (:*:) u) => Semimonoidal (->) (:*:) (:*:) (t <.:> u) where-	multiply (UT x :*: UT y) = UT $ multiply @(->) @(:*:) -<$>- multiply (x :*: y)+instance (Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <.:> u) where+	mult = Straight $ UT . (<$>) (mult @(-->) !) . (mult @(-->) !) . (run @(->) <-> run @(->)) -instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (->) (:*:) (:*:) u, Monoidal (->) (->) (:*:) (:*:) t, Monoidal (->) (->) (:*:) (:*:) u) => Monoidal (->) (->) (:*:) (:*:) (t <.:> u) where-	unit _ f = UT . point . point $ f One+instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (->) (:*:) (:*:) t, Monoidal (-->) (->) (:*:) (:*:) u) => Monoidal (-->) (->) (:*:) (:*:) (t <.:> u) where+	unit _ = Straight $ UT . point . point . ($ One) -instance (Traversable (->) (->) t, Bindable (->) t, Semimonoidal (->) (:*:) (:*:) u, Monoidal (->) (->) (:*:) (:*:) u, Bindable (->) u) => Bindable (->) (t <.:> u) where-	f =<< UT x = UT $ ((identity =<<) -<$>-) . (run . f <<-) =<< x+instance (Traversable (->) (->) t, Bindable (->) t, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (->) (:*:) (:*:) u, Bindable (->) u) => Bindable (->) (t <.:> u) where+	f =<< UT x = UT $ ((identity =<<) <$>) . (run . f <<-) =<< x  instance (Covariant (->) (->) u, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <.:> u) where-	multiply = Flip $ \(UT xys) ->-		let Flip f = multiply @(<--) @(:*:) @(:*:) in-		let Flip g = multiply @(<--) @(:*:) @(:*:) in-		(UT <-> UT) $ f (g -<$>- xys) where+	mult = Flip $ \(UT xys) -> (UT <-> UT) . (mult @(<--) !) $ (mult @(<--) !) <$> xys  instance (Covariant (->) (->) u, Monoidal (<--) (->) (:*:) (:*:) t, Monoidal (<--) (->) (:*:) (:*:) u) => Monoidal (<--) (->) (:*:) (:*:) (t <.:> u) where 	unit _ = Flip $ \(UT x) -> (\_ -> extract $ extract x) -instance Monoidal (->) (->) (:*:) (:*:) t => Liftable (->) (UT Covariant Covariant t) where+instance Monoidal (-->) (->) (:*:) (:*:) t => Liftable (->) (UT Covariant Covariant t) where 	lift :: Covariant (->) (->) u => u ~> t <.:> u-	lift x = UT $ point -<$>- x+	lift x = UT $ point <$> x  instance Monoidal (<--) (->) (:*:) (:*:) t => Lowerable (->) (UT Covariant Covariant t) where 	lower :: Covariant (->) (->) u => t <.:> u ~> u-	lower (UT x) = extract -<$>- x+	lower (UT x) = extract <$> x

@@ -16,7 +16,7 @@ type (<.>:<.<) = UTU Covariant Contravariant Contravariant type (>.>:<.<) = UTU Contravariant Contravariant Contravariant -instance Interpreted (UTU ct cu t u u') where+instance Interpreted (->) (UTU ct cu t u u') where 	type Primary (UTU ct cu t u u') a = u :. t :. u' := a 	run ~(UTU x) = x 	unite = UTU

@@ -4,7 +4,7 @@  newtype U_T ct cu t p u a = U_T (p (u a) (t a)) -instance Interpreted (U_T ct cu t p u) where+instance Interpreted (->) (U_T ct cu t p u) where 	type Primary (U_T ct cu t p u) a = p (u a) (t a) 	run ~(U_T x) = x 	unite = U_T

@@ -10,7 +10,7 @@ import Pandora.Core.Functor (type (:=)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Semigroup ((+))@@ -26,7 +26,7 @@ import Pandora.Paradigm.Primary.Functor.Predicate (Predicate (Predicate)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Both, Left, Right, End)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct))-import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Primary.Transformer.Tap (Tap (Tap)) import Pandora.Paradigm.Schemes.TU (type (<:.>)) import Pandora.Paradigm.Schemes.T_U ( type (<:.:>))@@ -67,7 +67,7 @@  instance Morphable (Into (o ds)) (Construction Wye) => Morphable (Into (o ds)) Binary where 	type Morphing (Into (o ds)) Binary = Maybe <:.> Morphing (Into (o ds)) (Construction Wye)-	morphing (premorph -> xs) = (into @(o ds) -<$>-) ||= xs+	morphing (premorph -> xs) = (into @(o ds) <$>) ||= xs  instance Substructure Left (Flip (:*:) a) where 	type Available Left (Flip (:*:) a) = Identity

@@ -3,7 +3,6 @@ import Pandora.Paradigm.Structure.Ability.Monotonic as Exports import Pandora.Paradigm.Structure.Ability.Zipper as Exports import Pandora.Paradigm.Structure.Ability.Substructure as Exports-import Pandora.Paradigm.Structure.Ability.Measurable as Exports import Pandora.Paradigm.Structure.Ability.Morphable as Exports import Pandora.Paradigm.Structure.Ability.Accessible as Exports import Pandora.Paradigm.Structure.Ability.Nullable as Exports

@@ -1,15 +0,0 @@-{-# LANGUAGE AllowAmbiguousTypes #-}--module Pandora.Paradigm.Structure.Ability.Measurable where--import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag))--class Measurable f t where-	type Measural (f :: k) (t :: * -> *) a-	measurement :: Tagged f (t a) -> Measural f t a--measure :: forall f t a . Measurable f t => t a -> Measural f t a-measure = measurement . Tag @f--data Scale = Length | Heighth | Depth

@@ -4,7 +4,7 @@ module Pandora.Paradigm.Structure.Ability.Substructure where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Divariant ((>->)) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)@@ -24,4 +24,4 @@ 	substructure :: (Tagged segment <:.> structure) #=@ Substance segment structure := Available segment structure  	sub :: (Covariant (->) (->) structure) => structure #=@ Substance segment structure := Available segment structure-	sub = lift @(->) >-> (lower @(->) -<$>-) ||= substructure @segment @structure+	sub = lift @(->) >-> (lower @(->) <$>) ||= substructure @segment @structure

@@ -28,4 +28,4 @@ subset = Convergence $ \s ss -> Nothing != (find @f @t @Maybe % s) . equate <<- ss  cardinality :: Traversable (->) (->) t => t a -> Numerator-cardinality s = attached . run @(State _) % Zero $ (modify @Numerator (+ one) !.) <<- s+cardinality s = attached . run @(->) @(State _) % Zero $ (modify @Numerator (+ one) !.) <<- s

@@ -4,14 +4,17 @@ module Pandora.Paradigm.Structure.Modification.Comprehension where  import Pandora.Core.Functor (type (:=))+import Pandora.Core.Appliable ((!)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant ((->$<-))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant ((>$<))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))+import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))@@ -23,31 +26,29 @@ import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Push), premorph) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null))+import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:)) import Pandora.Paradigm.Primary.Algebraic (empty)  newtype Comprehension t a = Comprehension (t <:.> Construction t := a) -instance Interpreted (Comprehension t) where+instance Interpreted (->) (Comprehension t) where 	type Primary (Comprehension t) a = t <:.> Construction t := a 	run ~(Comprehension x) = x 	unite = Comprehension  instance Covariant (->) (->) (t <:.> Construction t) => Covariant (->) (->) (Comprehension t) where-	f -<$>- Comprehension x = Comprehension $ f -<$>- x+	f <$> Comprehension x = Comprehension $ f <$> x  instance Traversable (->) (->) (t <:.> Construction t) => Traversable (->) (->) (Comprehension t) where-	f <<- Comprehension x = Comprehension -<$>- f <<- x--instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:*:) t) => Semimonoidal (->) (:*:) (:*:) (Comprehension t) where-	multiply (Comprehension x :*: Comprehension y) = Comprehension $ multiply (x :*: y)+	f <<- Comprehension x = Comprehension <$> f <<- x -instance (Covariant (->) (->) t, Semimonoidal (->) (:*:) (:+:) t) => Semimonoidal (->) (:*:) (:+:) (Comprehension t) where-	multiply (Comprehension x :*: Comprehension y) = Comprehension $ multiply (x :*: y)+instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) right t, Semimonoidal (-->) (:*:) right (t <:.> Construction t)) => Semimonoidal (-->) (:*:) right (Comprehension t) where+	mult = Straight $ Comprehension . (mult @(-->) @(:*:) @right !) . (run @(->) <-> run @(->)) -instance (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:+:) t) => Monoidal (->) (->) (:*:) (:+:) (Comprehension t) where-	unit _ _ = Comprehension empty+instance (Covariant (->) (->) t, Monoidal (-->) (->) (:*:) (:+:) t) => Monoidal (-->) (->) (:*:) (:+:) (Comprehension t) where+	unit _ = Straight $ \_ -> Comprehension empty  instance (forall a . Semigroup (t <:.> Construction t := a), Bindable (->) t) => Bindable (->) (Comprehension t) where 	f =<< Comprehension (TU t) = Comprehension . TU $ (\(Construct x xs) -> run . run $ f x + (f =<< Comprehension (TU xs))) =<< t@@ -61,9 +62,9 @@ instance Monoid (t <:.> Construction t := a) => Monoid (Comprehension t a) where 	zero = Comprehension zero -instance (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:*:) t)  => Morphable Push (Comprehension t) where+instance (Covariant (->) (->) t, Monoidal (-->) (->) (:*:) (:*:) t)  => Morphable Push (Comprehension t) where 	type Morphing Push (Comprehension t) = Identity <:.:> Comprehension t := (->) 	morphing (run . premorph -> xs) = T_U $ \(Identity x) -> Comprehension . lift . Construct x . run $ xs  instance Nullable (t <:.> Construction t) => Nullable (Comprehension t) where-	null = run ->$<- null+	null = run @(->) >$< null

@@ -5,30 +5,30 @@  import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Paradigm.Primary.Algebraic (extract) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=))) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Into), premorph) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)  newtype Prefixed t k a = Prefixed (t :. (:*:) k := a) -instance Interpreted (Prefixed t k) where+instance Interpreted (->) (Prefixed t k) where 	type Primary (Prefixed t k) a = t :. (:*:) k := a 	run ~(Prefixed x) = x 	unite = Prefixed +-- TODO: Try to generalize (->) here instance Covariant (->) (->) t => Covariant (->) (->) (Prefixed t k) where-	f -<$>- Prefixed x = Prefixed $ f -<$$>- x+	(<$>) f = (||=) ((<$$>) @(->) @(->) f)  instance Traversable (->) (->) t => Traversable (->) (->) (Prefixed t k) where-	f <<- Prefixed x = Prefixed -<$>- f -<<-<<- x+	f <<- Prefixed x = Prefixed <$> f -<<-<<- x  instance Covariant (->) (->) t => Morphable (Into t) (Prefixed t k) where 	type Morphing (Into t) (Prefixed t k) = t-	morphing (run . premorph -> prefixed) = extract -<$>- prefixed+	morphing (run . premorph -> prefixed) = extract <$> prefixed  type instance Nonempty (Prefixed t k) = Prefixed (Nonempty t) k

@@ -2,37 +2,34 @@  module Pandora.Paradigm.Structure.Some.Binary where -import Pandora.Core.Functor (type (:.), type (:=), type (:=>), type (:::))+import Pandora.Core.Functor (type (:=), type (:=>), type (:::)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable ((=<<)) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Paradigm.Primary () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), type (:*:), attached, twosome) import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), (&))-import Pandora.Paradigm.Primary.Algebraic (($$$>-), extract)+import Pandora.Paradigm.Primary.Algebraic (($$$>-), (<-*-), extract) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False)) import Pandora.Paradigm.Primary.Object.Ordering (order)-import Pandora.Paradigm.Primary.Object.Numerator (Numerator (Numerator, Zero))-import Pandora.Paradigm.Primary.Object.Denumerator (Denumerator (Single)) import Pandora.Paradigm.Primary.Functor (Comparison) import Pandora.Paradigm.Primary.Functor.Convergence (Convergence (Convergence)) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Predicate (Predicate (Predicate)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (End, Left, Right, Both))-import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct)+import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Schemes (TU (TU), T_U (T_U), P_Q_T (P_Q_T), type (<:.>), type (<:.:>)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (=||)) import Pandora.Paradigm.Inventory.Store (Store (Store)) import Pandora.Paradigm.Inventory.Optics (over, view) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null))-import Pandora.Paradigm.Structure.Ability.Measurable (Measurable (Measural, measurement), Scale (Heighth), measure) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (resolve)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), morph, premorph 	, Morph (Rotate, Into, Insert, Lookup, Vary, Key, Element), Vertical (Up, Down), lookup, vary)@@ -42,26 +39,28 @@  type Binary = Maybe <:.> Construction Wye -rebalance :: Chain a => (Wye :. Construction Wye := a) -> Nonempty Binary a-rebalance (Both x y) = extract x <=> extract y & order-	# Construct (extract x) (Both # rebalance (deconstruct x) # rebalance (deconstruct y))-	# Construct (extract y) (Both # x # rebalance (deconstruct y))-	# Construct (extract x) (Both # rebalance (deconstruct x) # y)+instance {-# OVERLAPS #-} Traversable (->) (->) (Construction Wye) where+	f <<- (Construct x (Left l)) = Construct <$> f x <-*- (Left <$> f <<- l)+	f <<- (Construct x (Right r)) = Construct <$> f x <-*- (Right <$> f <<- r)+	f <<- (Construct x (Both l r)) = Construct <$> f x <-*- (Both <$> f <<- l <-*- f <<- r)+	f <<- (Construct x End) = Construct % End <$> f x +--rebalance :: Chain a => (Wye :. Construction Wye := a) -> Nonempty Binary a+--rebalance (Both x y) = extract x <=> extract y & order+--	# Construct (extract x) (Both # rebalance (deconstruct x) # rebalance (deconstruct y))+--	# Construct (extract y) (Both # x # rebalance (deconstruct y))+--	# Construct (extract x) (Both # rebalance (deconstruct x) # y)+ instance Morphable Insert Binary where 	type Morphing Insert Binary = (Identity <:.:> Comparison := (:*:)) <:.:> Binary := (->)-	morphing (run . premorph -> Nothing) = T_U $ \(T_U (Identity x :*: _)) -> lift $ leaf x-	morphing (run . premorph -> Just ne) = T_U $ \(T_U (Identity x :*: Convergence f)) ->-		let continue xs = run # morph @Insert @(Nonempty Binary) xs $ twosome # Identity x # Convergence f in-		let change = Just . resolve continue (leaf x) in-		lift $ f x # extract ne & order # ne-			# over (sub @Left) change ne-			# over (sub @Right) change ne--instance Measurable Heighth Binary where-	type Measural Heighth Binary a = Numerator-	measurement (run . extract -> Just bt) = Numerator $ measure @Heighth bt-	measurement (run . extract -> Nothing) = Zero+	morphing binary = case run # premorph binary of+		Nothing -> T_U $ \(T_U (Identity x :*: _)) -> lift $ leaf x+		Just non_empty_binary -> T_U $ \(T_U (Identity x :*: Convergence f)) ->+			let continue xs = run # morph @Insert @(Nonempty Binary) xs $ twosome # Identity x # Convergence f in+			let change = Just . resolve continue (leaf x) in+			lift $ f x # extract non_empty_binary & order # non_empty_binary+				# over (sub @Left) change non_empty_binary+				# over (sub @Right) change non_empty_binary  instance Nullable Binary where 	null = Predicate $ \case { TU Nothing -> True ; _ -> False }@@ -71,14 +70,14 @@ 	type Substance Left Binary = Construction Wye 	substructure = P_Q_T $ \bintree -> case run . lower # bintree of 		Nothing -> Store $ Nothing :*: lift . TU-		Just tree -> lift . lift @(->) -<$>- run (sub @Left) tree+		Just tree -> lift . lift @(->) <$> run (sub @Left) tree  instance Substructure Right Binary where 	type Available Right Binary = Maybe 	type Substance Right Binary = Construction Wye 	substructure = P_Q_T $ \bintree -> case run . extract . run # bintree of 		Nothing -> Store $ Nothing :*: lift . TU-		Just tree -> lift . lift @(->) -<$>- run (sub @Right) tree+		Just tree -> lift . lift @(->) <$> run (sub @Right) tree  -------------------------------------- Non-empty binary tree --------------------------------------- @@ -98,15 +97,6 @@ 			# over (sub @Right) change nonempty_list 			# f x (extract nonempty_list) -instance Measurable Heighth (Construction Wye) where-	type Measural Heighth (Construction Wye) a = Denumerator-	measurement (deconstruct . extract -> End) = Single-	measurement (deconstruct . extract -> Left lst) = Single + measure @Heighth lst-	measurement (deconstruct . extract -> Right rst) = Single + measure @Heighth rst-	measurement (deconstruct . extract -> Both lst rst) = Single +-		let (lm :*: rm) = measure @Heighth lst :*: measure @Heighth rst-		in lm <=> rm & order lm rm lm- instance Substructure Root (Construction Wye) where 	type Available Root (Construction Wye) = Identity 	type Substance Root (Construction Wye) = Identity@@ -165,9 +155,9 @@ data Biforked a = Top | Leftward a | Rightward a  instance Covariant (->) (->) Biforked where-	_ -<$>- Top = Top-	f -<$>- Leftward l = Leftward $ f l-	f -<$>- Rightward r = Rightward $ f r+	_ <$> Top = Top+	f <$> Leftward l = Leftward $ f l+	f <$> Rightward r = Rightward $ f r  type Bifurcation = Biforked <:.> Construction Biforked 

@@ -6,7 +6,7 @@ import Pandora.Core.Impliable (imply) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#), identity)-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<$>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -20,7 +20,7 @@ import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), (?)) import Pandora.Paradigm.Primary.Object.Numerator (Numerator (Numerator)) import Pandora.Paradigm.Primary.Object.Denumerator (Denumerator (Single))-import Pandora.Paradigm.Primary.Algebraic ((-<*>-), (-.#..-), extract)+import Pandora.Paradigm.Primary.Algebraic ((<-*-), (-.#..-), extract) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached, twosome) import Pandora.Paradigm.Primary.Algebraic.Exponential ((%)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))@@ -40,7 +40,6 @@ import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null)) import Pandora.Paradigm.Structure.Ability.Zipper (Zipper)-import Pandora.Paradigm.Structure.Ability.Measurable (Measurable (Measural, measurement), Scale (Length), measure) import Pandora.Paradigm.Structure.Ability.Monotonic (resolve) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing) 	, Morph (Rotate, Into, Push, Pop, Delete, Find, Lookup, Element, Key)@@ -93,11 +92,6 @@  instance Stack List where -instance Measurable Length List where-	type Measural Length List a = Numerator-	measurement (run . extract -> Nothing) = zero-	measurement (run . extract -> Just xs) = Numerator $ measure @Length xs- instance Nullable List where 	null = Predicate $ \case { TU Nothing -> True ; _ -> False } @@ -112,12 +106,12 @@ 	type Available Tail List = Identity 	type Substance Tail List = List 	substructure = P_Q_T $ \x -> case run . extract . run $ x of-		Just ns -> lift . lift @(->) -<$>- run (sub @Tail) ns+		Just ns -> lift . lift @(->) <$> run (sub @Tail) ns 		Nothing -> Store $ Identity zero :*: lift . identity . extract  -- | Transform any traversable structure into a stack linearize :: forall t a . Traversable (->) (->) t => t a -> List a-linearize = TU . extract . (run @(State (Maybe :. Nonempty List := a)) % Nothing) . fold (Just -.#..- Construct)+linearize = TU . extract . (run @(->) @(State (Maybe :. Nonempty List := a)) % Nothing) . fold (Just -.#..- Construct)  ----------------------------------------- Non-empty list ------------------------------------------- @@ -140,11 +134,6 @@ 	type Morphing Push (Construction Maybe) = Identity <:.:> Construction Maybe := (->) 	morphing (premorph -> xs) = T_U $ \(Identity x) -> Construct x $ Just xs -instance Measurable Length (Construction Maybe) where-	type Measural Length (Construction Maybe) a = Denumerator-	measurement (deconstruct . extract -> Nothing) = Single-	measurement (deconstruct . extract -> Just xs) = Single + measure @Length xs- instance Substructure Root (Construction Maybe) where 	type Available Root (Construction Maybe) = Identity 	type Substance Root (Construction Maybe) = Identity@@ -167,37 +156,37 @@  instance {-# OVERLAPS #-} Traversable (->) (->) (Tap (List <:.:> List := (:*:))) where 	f <<- Tap x (T_U (future :*: past)) = (\past' x' future' -> Tap x' $ twosome # future' # run past')-		-<$>- f <<- Reverse past -<*>- f x -<*>- f <<- future+		<$> f <<- Reverse past <-*- f x <-*- f <<- future  instance {-# OVERLAPS #-} Extendable (->) (Tap (List <:.:> List := (:*:))) where 	f <<= z = let move rtt = TU . deconstruct $ run . rtt .-+ z in-		Tap # f z $ twosome # f -<$>- move (rotate @Left) # f -<$>- move (rotate @Right)+		Tap # f z $ twosome # f <$> move (rotate @Left) # f <$> move (rotate @Right)  instance Morphable (Rotate Left) (Tap (List <:.:> List := (:*:))) where 	type Morphing (Rotate Left) (Tap (List <:.:> List := (:*:))) = Maybe <:.> Tap (List <:.:> List := (:*:)) 	morphing (premorph -> Tap x (T_U (future :*: past))) = 		let subtree = twosome # extract (view (sub @Tail) future) # item @Push x past in-		TU $ (Tap . extract) % subtree -<$>- view (sub @Root) future+		TU $ (Tap . extract) % subtree <$> view (sub @Root) future  instance Morphable (Rotate Right) (Tap (List <:.:> List := (:*:))) where 	type Morphing (Rotate Right) (Tap (List <:.:> List := (:*:))) = Maybe <:.> Tap (List <:.:> List := (:*:)) 	morphing (premorph -> Tap x (T_U (future :*: past))) = 		let subtree = twosome # item @Push x future # extract (view (sub @Tail) past) in-		TU $ (Tap . extract) % subtree -<$>- view (sub @Root) past+		TU $ (Tap . extract) % subtree <$> view (sub @Root) past  instance Morphable (Into (Tap (List <:.:> List := (:*:)))) List where 	type Morphing (Into (Tap (List <:.:> List := (:*:)))) List = Maybe <:.> Tap (List <:.:> List := (:*:))-	morphing (premorph -> list) = (into @(Zipper List (Left ::: Right)) -<$>-) ||= list+	morphing (premorph -> list) = (into @(Zipper List (Left ::: Right)) <$>) ||= list  instance Morphable (Into List) (Tap (List <:.:> List := (:*:))) where 	type Morphing (Into List) (Tap (List <:.:> List := (:*:))) = List-	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(State _)+	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(->) @(State _) 		# modify . item @Push @List <<- past 		# item @Push x future  instance Morphable (Into (Comprehension Maybe)) (Tap (List <:.:> List := (:*:))) where 	type Morphing (Into (Comprehension Maybe)) (Tap (List <:.:> List := (:*:))) = Comprehension Maybe-	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(State _)+	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(->) @(State _) 		# modify . item @Push @(Comprehension Maybe) <<- past 		# item @Push x (Comprehension future) @@ -208,12 +197,12 @@ instance Morphable (Rotate Left) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Rotate Left) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = 		Maybe <:.> Tap (Construction Maybe <:.:> Construction Maybe := (:*:))-	morphing (premorph -> Tap x (T_U (future :*: past))) = TU $ Tap (extract future) . twosome % item @Push x past -<$>- deconstruct future+	morphing (premorph -> Tap x (T_U (future :*: past))) = TU $ Tap (extract future) . twosome % item @Push x past <$> deconstruct future  instance Morphable (Rotate Right) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Rotate Right) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = 		Maybe <:.> Tap (Construction Maybe <:.:> Construction Maybe := (:*:))-	morphing (premorph -> Tap x (T_U (future :*: past))) = TU $ Tap (extract past) . twosome (item @Push x future) -<$>- deconstruct past+	morphing (premorph -> Tap x (T_U (future :*: past))) = TU $ Tap (extract past) . twosome (item @Push x future) <$> deconstruct past  instance Morphable (Into (Tap (List <:.:> List := (:*:)))) (Construction Maybe) where 	type Morphing (Into (Tap (List <:.:> List := (:*:)))) (Construction Maybe) = Tap (List <:.:> List := (:*:))@@ -226,18 +215,18 @@ instance Morphable (Into (Tap (Construction Maybe <:.:> Construction Maybe := (:*:)))) (Tap (List <:.:> List := (:*:))) where 	type Morphing (Into (Tap (Construction Maybe <:.:> Construction Maybe := (:*:)))) (Tap (List <:.:> List := (:*:))) = 		Maybe <:.> Tap (Construction Maybe <:.:> Construction Maybe := (:*:))-	morphing (premorph -> zipper) = let spread x y = (:*:) -<$>- x -<*>- y in TU $-		Tap (extract zipper) . T_U -<$>- ((spread |-) . (run <-> run) . run $ lower zipper)+	morphing (premorph -> zipper) = let spread x y = (:*:) <$> x <-*- y in TU $+		Tap (extract zipper) . T_U <$> ((spread |-) . (run @(->) <-> run @(->)) . run $ lower zipper)  instance Morphable (Into (Construction Maybe)) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Into (Construction Maybe)) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = Construction Maybe-	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(State _)+	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(->) @(State _) 		# modify . item @Push @(Nonempty List) <<- past 		# item @Push x future  instance Morphable (Into List) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Into List) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = List-	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(State _)+	morphing (premorph -> Tap x (T_U (future :*: past))) = attached $ run @(->) @(State _) 		# modify . item @Push @List <<- past 		# item @Push x (lift future) @@ -249,11 +238,11 @@  instance Setoid key => Morphable (Lookup Key) (Prefixed List key) where 	type Morphing (Lookup Key) (Prefixed List key) = (->) key <:.> Maybe-	morphing (run . premorph -> list) = TU $ \key -> lookup @Key key =<< Prefixed -<$>- run list +	morphing (run . premorph -> list) = TU $ \key -> lookup @Key key =<< Prefixed <$> run list   ------------------------------------ Prefixed non-empty list ---------------------------------------  instance Setoid key => Morphable (Lookup Key) (Prefixed (Construction Maybe) key) where 	type Morphing (Lookup Key) (Prefixed (Construction Maybe) key) = (->) key <:.> Maybe-	morphing (run . premorph -> Construct x xs) = TU $ \key -> extract -<$>- search key where+	morphing (run . premorph -> Construct x xs) = TU $ \key -> extract <$> search key where 		search key = key == attached x ? Just x $ find @Element # Predicate ((key ==) . attached) =<< xs

@@ -5,7 +5,7 @@ import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Contravariant ((->$<-))+import Pandora.Pattern.Functor.Contravariant ((>$<)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)@@ -102,4 +102,4 @@ find_rose_sub_tree (Construct k (Just ks)) tree = k != attached (extract tree) ? Nothing $ find_rose_sub_tree ks =<< subtree where  	subtree :: Maybe :. Nonempty Rose := k :*: a-	subtree = find @Element # attached . extract ->$<- equate (extract ks) # deconstruct tree+	subtree = find @Element # attached . extract >$< equate (extract ks) # deconstruct tree

@@ -6,10 +6,10 @@ import Pandora.Core.Functor (type (~>), type (:.), type (:=)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Paradigm.Primary ()-import Pandora.Paradigm.Primary.Algebraic ((-<*>-), extract)+import Pandora.Paradigm.Primary.Algebraic ((<-*-), extract) import Pandora.Paradigm.Primary.Algebraic.Product (twosome) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just)) import Pandora.Paradigm.Primary.Functor.Tagged (type (:#))@@ -54,27 +54,27 @@ instance Morphable (Rotate (Left Zig)) (Construction Wye) where 	type Morphing (Rotate (Left Zig)) (Construction Wye) = Binary 	morphing :: forall a . (:#) (Rotate (Left Zig)) <:.> Construction Wye := a -> Binary a-	morphing (premorph -> Construct x xs) = TU $ Construct -<$>- parent -<*>- Just nodes where+	morphing (premorph -> Construct x xs) = TU $ Construct <$> parent <-*- Just nodes where  		nodes :: Wye :. Nonempty Binary := a 		nodes = into @Wye . twosome (branch @Left xs) . Just . Construct x-			. into @Wye $ twosome (branch @Left =<< deconstruct -<$>- branch @Right xs)-				(branch @Right =<< deconstruct -<$>- branch @Right xs)+			. into @Wye $ twosome (branch @Left =<< deconstruct <$> branch @Right xs)+				(branch @Right =<< deconstruct <$> branch @Right xs)  		parent :: Maybe a-		parent = extract -<$>- branch @Right xs+		parent = extract <$> branch @Right xs  instance Morphable (Rotate (Right Zig)) (Construction Wye) where 	type Morphing (Rotate (Right Zig)) (Construction Wye) = Binary 	morphing :: forall a . (:#) (Rotate (Right Zig)) <:.> Construction Wye := a -> Binary a-	morphing (premorph -> Construct x xs) = TU $ Construct -<$>- parent -<*>- Just nodes where+	morphing (premorph -> Construct x xs) = TU $ Construct <$> parent <-*- Just nodes where  		nodes :: Wye :. Nonempty Binary := a-		nodes = into @Wye . twosome (branch @Left =<< deconstruct -<$>- branch @Left xs) . Just . Construct x-			. into @Wye $ twosome (branch @Right =<< deconstruct -<$>- branch @Left xs) # branch @Right xs+		nodes = into @Wye . twosome (branch @Left =<< deconstruct <$> branch @Left xs) . Just . Construct x+			. into @Wye $ twosome (branch @Right =<< deconstruct <$> branch @Left xs) # branch @Right xs  		parent :: Maybe a-		parent = extract -<$>- branch @Left xs+		parent = extract <$> branch @Left xs  -- TODO: Morphing ... = Conclussion Error <:.> Nonempty Binary instance Morphable (Rotate (Left (Zig Zig))) (Construction Wye) where

@@ -5,7 +5,7 @@ import Pandora.Core.Functor (type (:=), type (:=>), type (:::)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), twosome) import Pandora.Paradigm.Primary.Algebraic (extract)@@ -34,7 +34,7 @@  instance {-# OVERLAPS #-} Extendable (->) (Tap (Stream <:.:> Stream := (:*:))) where 	f <<= z = let move rtt = extract . deconstruct $ point . rtt .-+ z-		in f -<$>- Tap z (twosome # (move $ rotate @Left) # (move $ rotate @Right))+		in f <$> Tap z (twosome # (move $ rotate @Left) # (move $ rotate @Right))  repeat :: a :=> Stream repeat x = Construct x . Identity $ repeat x

@@ -3,5 +3,7 @@ import Pandora.Pattern.Object as Exports import Pandora.Pattern.Transformer as Exports import Pandora.Pattern.Functor as Exports+import Pandora.Pattern.Morphism as Exports+import Pandora.Pattern.Groupoid as Exports import Pandora.Pattern.Category as Exports import Pandora.Pattern.Semigroupoid as Exports

@@ -1,6 +1,6 @@ module Pandora.Pattern.Category (Category (..)) where -import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) +import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))  infixl 2 # infixr 0 $

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Bivariant where  import Pandora.Pattern.Functor.Covariant (Covariant)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip)+import Pandora.Pattern.Morphism.Flip (Flip)  infixl 4 <-> @@ -13,4 +13,4 @@  class (forall i . Covariant left target (v i), forall i . Covariant right target (Flip v i)) 	=> Bivariant left right target v where-	(<->) :: left a b -> right c d -> target (v a c) (v b d) +	(<->) :: left a b -> right c d -> target (v a c) (v b d)

@@ -15,4 +15,4 @@ > * Associativity: extend f . extend g ≡ extend (f . extend g) -} -class (Monoidal (<--) source (:*:) (:*:) t, Extendable source t) => Comonad t source+class (Monoidal (<--) source (:*:) (:*:) t, Extendable source t) => Comonad source t

@@ -2,13 +2,13 @@  import Pandora.Pattern.Category (Category) -infixl 4 ->$<-+infixl 4 >$<  {- | > When providing a new instance, you should ensure it satisfies:-> * Identity morphism: (identity ->$<-) ≡ identity-> * Interpreted of morphisms: (f ->$<-) . (g ->$<-) ≡ (g . f ->$<-)+> * Identity morphism: (identity >$<) ≡ identity+> * Interpreted of morphisms: (f >$<) . (g >$<) ≡ (g . f >$<) -}  class (Category source, Category target) => Contravariant source target t where-	(->$<-) :: source a b -> target (t b) (t a)+	(>$<) :: source a b -> target (t b) (t a)

@@ -1,43 +1,33 @@+{-# LANGUAGE AllowAmbiguousTypes #-}+ module Pandora.Pattern.Functor.Covariant where  import Pandora.Pattern.Semigroupoid (Semigroupoid) -infixl 4 -<$>--infixl 3 -<<$$>-, -<$$>>-+infixl 4 <$>+infixl 3 <$$>+infixl 4 <$$$>  {- | > When providing a new instance, you should ensure it satisfies:-> * Identity morphism: (identity -<$>-) ≡ identity-> * Interpreted of morphisms: (f . g -<$>-) ≡ (f -<$>-) . (g -<$>-)+> * Identity morphism: (identity <$>) ≡ identity+> * Interpreted of morphisms: (f . g <$>) ≡ (f <$>) . (g <$>) -}  class (Semigroupoid source, Semigroupoid target) => Covariant source target t where-	(-<$>-) :: source a b -> target (t a) (t b)-	-(-<$$>-) :: forall t u category a b -	. (Covariant category category u, Covariant category category t) -	=> category a b -> category (t (u a)) (t (u b))-(-<$$>-) s = ((-<$>-) ((-<$>-) @category @category @u s))--(-<<$$>-) :: forall t u source target a b -	. (Covariant source source u, Covariant source target t) -	=> source a b -> target (t (u a)) (t (u b))-(-<<$$>-) s = ((-<$>-) ((-<$>-) @source @source @u s))+	(<$>) :: source a b -> target (t a) (t b) -(-<$$>>-) :: forall source target t u a b -	. (Covariant source target u, Covariant target target t) +(<$$>) :: forall source between target t u a b+	. (Covariant source between u, Covariant between target t) 	=> source a b -> target (t (u a)) (t (u b))-(-<$$>>-) s = ((-<$>-) ((-<$>-) @source @target @u s))---- TODO: Figure out how to work with hidden type variables--- to put intermediate category `between`+(<$$>) s = ((<$>) ((<$>) @source @between @u s)) -(-<$$$>-) :: forall t u v category a b-	. (Covariant category category t, Covariant category category u, Covariant category category v) -	=> category a b -> category (t (u (v a))) (t (u (v b)))-(-<$$$>-) s = ((-<$>-) @category @category @t ((-<$>-) @category @category @u ((-<$>-) @category @category @v s)))+(<$$$>) :: forall source between1 between2 target t u v a b+	. (Covariant source between1 v, Covariant between1 between2 u, Covariant between2 target t)+	=> source a b -> target (t (u (v a))) (t (u (v b)))+(<$$$>) s = ((<$>) @between2 @target ((<$>) @between1 @between2 @u ((<$>) @source @between1 @v s))) -(-<$$$$>-) :: forall category t u v w a b-	. (Covariant category category t, Covariant category category u, Covariant category category v, Covariant category category w) -	=> category a b -> category (t (u (v (w a)))) (t (u (v (w b))))-(-<$$$$>-) s = ((-<$>-) @category @category @t ((-<$>-) @category @category @u ((-<$>-) @category @category @v ((-<$>-) @category @category @w s))))+(<$$$$>) :: forall source between1 between2 between3 target t u v w a b+	. (Covariant source between1 w, Covariant between1 between2 v, Covariant between2 between3 u, Covariant between3 target t)+	=> source a b -> target (t (u (v (w a)))) (t (u (v (w b))))+(<$$$$>) s = ((<$>) @between3 @target @t ((<$>) @between2 @between3 @u ((<$>) @between1 @between2 @v ((<$>) @source @between1 @w s))))

@@ -7,7 +7,7 @@  > When providing a new instance, you should ensure it satisfies: > * Identity morphism: (identity -<<) . (identity -<<) ≡ identity-> * Interchange collection: (f -<<) ≡ (identity -<<) . (f -<$>-)+> * Interchange collection: (f -<<) ≡ (identity -<<) . (f <$>) -}  infixl 5 -<<

@@ -2,7 +2,7 @@  import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Paradigm.Primary.Transformer.Flip (Flip)+import Pandora.Pattern.Morphism.Flip (Flip)  infixl 4 >-> @@ -12,6 +12,6 @@ > * Interpreted: f . g >-> h . i ≡ g >-> h . f >-> i -} -class (forall i . Contravariant left target (Flip v i), forall i . Covariant right target (v i)) +class (forall i . Contravariant left target (Flip v i), forall i . Covariant right target (v i)) 	=> Divariant left right target v where 	(>->) :: left a b -> right c d -> target (v b c) (v a d)

@@ -6,8 +6,8 @@  {- | > When providing a new instance, you should ensure it satisfies:-> * Duplication interchange: (f -<$$>-) . (identity <<=) ≡ (identity <<=) . (f -<$>-)-> * Extension interchange: (f <<=) ≡ (f -<$>-) . (identity <<=)+> * Duplication interchange: (f -<$$>-) . (identity <<=) ≡ (identity <<=) . (f <$>)+> * Extension interchange: (f <<=) ≡ (f <$>) . (identity <<=) -}  class Covariant source source t => Extendable source t where

@@ -1,5 +1,6 @@ module Pandora.Pattern.Functor.Monad where +import Pandora.Pattern.Morphism.Straight (Straight) import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Bindable (Bindable) import Pandora.Pattern.Functor.Monoidal (Monoidal)@@ -19,7 +20,7 @@ --infixl 1 >>=-, ->>= --infixr 1 -=<<, =<<- -class (Covariant (->) (->) t, Monoidal (->) (->) (:*:) (:*:) t, Bindable (->) t) => Monad t where+class (Covariant category category t, Monoidal (Straight category) category (:*:) (:*:) t, Bindable category t) => Monad category t where 	--(>>=-) :: t a -> t b -> t a 	--(>>=-) x y = x >>= \r -> y >>= \_ -> point r 	--(->>=) :: t a -> t b -> t b

@@ -5,5 +5,5 @@  type family Unit (p :: * -> * -> *) = r | r -> p -class Semimonoidal p source target t => Monoidal p q source target t where+class Semimonoidal p source target t => Monoidal p q source target t | p target -> source where 	unit :: Proxy source -> p (q (Unit target) a) (t a)

@@ -2,5 +2,5 @@  import Pandora.Pattern.Semigroupoid (Semigroupoid) -class Semigroupoid p => Semimonoidal p source target t where-	multiply :: p (source (t a) (t b)) (t (target a b))+class Semigroupoid p => Semimonoidal p source target t | p target -> source where+	mult :: p (source (t a) (t b)) (t (target a b))

@@ -2,6 +2,7 @@  import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Monoidal (Monoidal)+import Pandora.Pattern.Morphism.Straight (Straight) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))  {- |@@ -10,17 +11,17 @@  > When providing a new instance, you should ensure it satisfies: > * Numeratority of traversing: g . (f <<--) ≡ (g . f <<--)-> * Numeratority of sequencing: f . (identity <<--)= (identity <<--) . (f -<$>-)+> * Numeratority of sequencing: f . (identity <<--)= (identity <<--) . (f <$>) > * Preserving point: p (point x) ≡ point x-> * Preserving apply: f (x -<*>- y) ≡ f x -<*>- f y+> * Preserving apply: f (x <-*- y) ≡ f x <-*- f y -}  infixl 5 <<-, -<<-<<-  class Covariant source target t => Traversable source target t where-	(<<-) :: (Covariant source target u, Monoidal source target (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b))+	(<<-) :: (Covariant source target u, Monoidal (Straight source) target (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b))  (-<<-<<-) :: forall t u v category a b .-	(Traversable category category t, Covariant category category u, Monoidal category category (:*:) (:*:) u, Traversable category category v) +	(Traversable category category t, Covariant category category u, Monoidal (Straight category) category (:*:) (:*:) u, Traversable category category v) 	=> category a (u b) -> category (v (t a)) (u (v (t b))) (-<<-<<-) f = ((<<-) ((<<-) @category @category @t f))

@@ -0,0 +1,11 @@+module Pandora.Pattern.Groupoid (Groupoid (..)) where++import Pandora.Pattern.Category (Category)++{- |+> When providing a new instance, you should ensure it satisfies:+> * Inversion absence: inversion . inversion ≡ identity+-}++class Category m => Groupoid m where+  inversion :: m a b -> m b a

@@ -0,0 +1,8 @@+module Pandora.Pattern.Morphism (module Exports, Opposite) where++import Pandora.Pattern.Morphism.Flip as Exports+import Pandora.Pattern.Morphism.Straight as Exports++type family Opposite m where+	Opposite Straight = Flip+	Opposite Flip = Straight

@@ -0,0 +1,27 @@+module Pandora.Pattern.Morphism.Flip where++import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category (identity))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Core.Appliable (Appliable ((!)))++newtype Flip (v :: * -> * -> *) a e = Flip (v e a)++instance Semigroupoid m => Semigroupoid (Flip m) where+  Flip g . Flip f = Flip (f . g)++instance Category m => Category (Flip m) where+	identity = Flip identity++instance (Category m, Covariant m m t) => Contravariant (Flip m) m t where+	(>$<) (Flip f) = (<$>) f++instance (Category m, Covariant m m t) => Contravariant m (Flip m) t where+	(>$<) f = Flip ((<$>) f)++instance (Category m, Covariant m m t) => Covariant  (Flip m) (Flip m) t where+	(<$>) (Flip f) = Flip ((<$>) f)++instance Appliable (Flip m) b c m c b where+	(!) (Flip m) = m

@@ -0,0 +1,26 @@+module Pandora.Pattern.Morphism.Straight where++import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category (identity))+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Core.Appliable (Appliable ((!)))++newtype Straight (v :: * -> * -> *) a e = Straight (v a e)++instance Semigroupoid m => Semigroupoid (Straight m) where+  Straight g . Straight f = Straight (g . f)++instance Category m => Category (Straight m) where+	identity = Straight identity++instance Covariant m m t => Covariant (Straight m) m t where+	(<$>) (Straight f) = (<$>) f++instance Covariant m m t => Covariant m (Straight m) t where+	(<$>) f = Straight ((<$>) f)++instance Covariant m m t => Covariant (Straight m) (Straight m) t where+	(<$>) (Straight f) = Straight ((<$>) f)++instance Appliable (Straight m) c b m c b where+	(!) (Straight m) = m

@@ -5,8 +5,8 @@  {- | > When providing a new instance, you should ensure it satisfies one law:-> * Identity morphism: hoist identity ≡ identity-> * Interpreted of morphisms: hoist (f . g) ≡ hoist f . hoist g+> * Identity morphism: (identity /|\) ≡ identity+> * Interpreted of morphisms: (f . g /|\) ≡ (f /|\) . (g /|\) -}  infixr 5 /|\@@ -14,6 +14,3 @@ class Hoistable t where 	{-# MINIMAL (/|\) #-} 	(/|\) :: (Covariant (->) (->) u) => u ~> v -> t u ~> t v--	hoist :: (Covariant (->) (->) u) => u ~> v -> t u ~> t v-	hoist = (/|\)

@@ -1,5 +1,5 @@ name:                pandora-version:             0.4.6+version:             0.4.7 synopsis:            A box of patterns and paradigms description:         Humble attempt to define a library for problem solving based on math abstractions. homepage:            https://github.com/iokasimov/pandora@@ -23,6 +23,7 @@     Pandora.Core     Pandora.Core.Functor     Pandora.Core.Impliable+    Pandora.Core.Appliable      Pandora.Paradigm     -- Basic constructions@@ -57,7 +58,8 @@     Pandora.Paradigm.Primary.Transformer     Pandora.Paradigm.Primary.Transformer.Backwards     Pandora.Paradigm.Primary.Transformer.Reverse-    Pandora.Paradigm.Primary.Transformer.Flip+    Pandora.Pattern.Morphism.Flip+    Pandora.Pattern.Morphism.Straight     Pandora.Paradigm.Primary.Transformer.Continuation     Pandora.Paradigm.Primary.Transformer.Construction     Pandora.Paradigm.Primary.Transformer.Instruction@@ -106,7 +108,6 @@     Pandora.Paradigm.Structure.Ability     Pandora.Paradigm.Structure.Ability.Morphable     Pandora.Paradigm.Structure.Ability.Accessible-    Pandora.Paradigm.Structure.Ability.Measurable     Pandora.Paradigm.Structure.Ability.Substructure     Pandora.Paradigm.Structure.Ability.Nonempty     Pandora.Paradigm.Structure.Ability.Nullable@@ -135,6 +136,8 @@ 	-- Algebra typeclasses     Pandora.Pattern.Semigroupoid     Pandora.Pattern.Category+    Pandora.Pattern.Groupoid+    Pandora.Pattern.Morphism     -- Functor typeclassess     Pandora.Pattern.Functor     Pandora.Pattern.Functor.Adjoint