pandora 0.4.4 → 0.4.5

raw patch · 92 files changed

+772/−1241 lines, 92 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• CHANGELOG.md +32/−0
• Pandora/Paradigm/Controlflow/Effect/Adaptable.hs +45/−73
• Pandora/Paradigm/Controlflow/Effect/Interpreted.hs +19/−19
• Pandora/Paradigm/Controlflow/Effect/Transformer/Comonadic.hs +8/−13
• Pandora/Paradigm/Controlflow/Effect/Transformer/Monadic.hs +9/−18
• Pandora/Paradigm/Controlflow/Observable.hs +14/−13
• Pandora/Paradigm/Controlflow/Pipeline.hs +2/−1
• Pandora/Paradigm/Inventory.hs +3/−3
• Pandora/Paradigm/Inventory/Accumulator.hs +8/−14
• Pandora/Paradigm/Inventory/Environment.hs +12/−12
• Pandora/Paradigm/Inventory/Equipment.hs +5/−7
• Pandora/Paradigm/Inventory/Imprint.hs +6/−8
• Pandora/Paradigm/Inventory/Optics.hs +14/−8
• Pandora/Paradigm/Inventory/State.hs +14/−19
• Pandora/Paradigm/Inventory/Store.hs +6/−8
• Pandora/Paradigm/Primary.hs +15/−19
• Pandora/Paradigm/Primary/Algebraic.hs +37/−7
• Pandora/Paradigm/Primary/Algebraic/Exponential.hs +11/−14
• Pandora/Paradigm/Primary/Algebraic/Product.hs +6/−9
• Pandora/Paradigm/Primary/Algebraic/Sum.hs +29/−0
• Pandora/Paradigm/Primary/Functor/Conclusion.hs +16/−24
• Pandora/Paradigm/Primary/Functor/Constant.hs +8/−10
• Pandora/Paradigm/Primary/Functor/Convergence.hs +3/−12
• Pandora/Paradigm/Primary/Functor/Edges.hs +2/−8
• Pandora/Paradigm/Primary/Functor/Endo.hs +2/−1
• Pandora/Paradigm/Primary/Functor/Fix.hs +7/−7
• Pandora/Paradigm/Primary/Functor/Identity.hs +5/−11
• Pandora/Paradigm/Primary/Functor/Maybe.hs +14/−27
• Pandora/Paradigm/Primary/Functor/Predicate.hs +5/−27
• Pandora/Paradigm/Primary/Functor/Proxy.hs +5/−16
• Pandora/Paradigm/Primary/Functor/Tagged.hs +5/−11
• Pandora/Paradigm/Primary/Functor/These.hs +2/−7
• Pandora/Paradigm/Primary/Functor/Validation.hs +15/−24
• Pandora/Paradigm/Primary/Functor/Wedge.hs +2/−7
• Pandora/Paradigm/Primary/Functor/Wye.hs +2/−8
• Pandora/Paradigm/Primary/Linear/Vector.hs +6/−5
• Pandora/Paradigm/Primary/Transformer/Backwards.hs +11/−13
• Pandora/Paradigm/Primary/Transformer/Construction.hs +16/−30
• Pandora/Paradigm/Primary/Transformer/Continuation.hs +6/−12
• Pandora/Paradigm/Primary/Transformer/Day.hs +6/−12
• Pandora/Paradigm/Primary/Transformer/Instruction.hs +13/−25
• Pandora/Paradigm/Primary/Transformer/Jack.hs +5/−25
• Pandora/Paradigm/Primary/Transformer/Jet.hs +3/−11
• Pandora/Paradigm/Primary/Transformer/Kan.hs +6/−5
• Pandora/Paradigm/Primary/Transformer/Outline.hs +5/−20
• Pandora/Paradigm/Primary/Transformer/Reverse.hs +7/−14
• Pandora/Paradigm/Primary/Transformer/Tap.hs +15/−26
• Pandora/Paradigm/Primary/Transformer/Yoneda.hs +6/−21
• Pandora/Paradigm/Schemes.hs +8/−6
• Pandora/Paradigm/Schemes/TU.hs +11/−20
• Pandora/Paradigm/Schemes/TUT.hs +15/−24
• Pandora/Paradigm/Schemes/T_U.hs +7/−10
• Pandora/Paradigm/Schemes/UT.hs +12/−14
• Pandora/Paradigm/Structure.hs +15/−15
• Pandora/Paradigm/Structure/Ability/Measurable.hs +1/−1
• Pandora/Paradigm/Structure/Ability/Monotonic.hs +2/−3
• Pandora/Paradigm/Structure/Ability/Morphable.hs +2/−1
• Pandora/Paradigm/Structure/Ability/Substructure.hs +3/−3
• Pandora/Paradigm/Structure/Interface/Set.hs +2/−1
• Pandora/Paradigm/Structure/Modification/Comprehension.hs +12/−29
• Pandora/Paradigm/Structure/Modification/Prefixed.hs +6/−16
• Pandora/Paradigm/Structure/Some/Binary.hs +15/−19
• Pandora/Paradigm/Structure/Some/List.hs +27/−28
• Pandora/Paradigm/Structure/Some/Rose.hs +41/−43
• Pandora/Paradigm/Structure/Some/Splay.hs +9/−8
• Pandora/Paradigm/Structure/Some/Stream.hs +4/−3
• Pandora/Pattern.hs +1/−0
• Pandora/Pattern/Category.hs +3/−4
• Pandora/Pattern/Functor.hs +7/−17
• Pandora/Pattern/Functor/Adjoint.hs +2/−2
• Pandora/Pattern/Functor/Alternative.hs +0/−20
• Pandora/Pattern/Functor/Applicative.hs +0/−51
• Pandora/Pattern/Functor/Avoidable.hs +0/−13
• Pandora/Pattern/Functor/Bindable.hs +2/−2
• Pandora/Pattern/Functor/Bivariant.hs +2/−2
• Pandora/Pattern/Functor/Contravariant.hs +3/−44
• Pandora/Pattern/Functor/Covariant.hs +18/−95
• Pandora/Pattern/Functor/Determinable.hs +0/−7
• Pandora/Pattern/Functor/Distributive.hs +3/−3
• Pandora/Pattern/Functor/Divariant.hs +3/−10
• Pandora/Pattern/Functor/Divisible.hs +0/−14
• Pandora/Pattern/Functor/Extendable.hs +2/−3
• Pandora/Pattern/Functor/Extractable.hs +2/−2
• Pandora/Pattern/Functor/Monad.hs +2/−2
• Pandora/Pattern/Functor/Pointable.hs +2/−2
• Pandora/Pattern/Functor/Semimonoidal.hs +6/−0
• Pandora/Pattern/Functor/Traversable.hs +6/−6
• Pandora/Pattern/Semigroupoid.hs +11/−0
• Pandora/Pattern/Transformer/Hoistable.hs +3/−3
• Pandora/Pattern/Transformer/Liftable.hs +2/−2
• Pandora/Pattern/Transformer/Lowerable.hs +2/−2
• pandora.cabal +5/−7

@@ -517,3 +517,35 @@ * Rename experimental `Applicative_` to `Semimonoidal`  # 0.4.5+* Define `Endofunctor` type family+* Define `Sum` module in `Algebraic` with `:+:` type+* Define experimental `Day_` transformer+* Define experimental `Semimonoidal_` typeclass+* Define `Semigroupoid` typeclass as generalization of `Category`+* Define `Applicative_` and `Alternative_` type class aliases of `Semimonoidal_`+* Define experimental `-*-` method of `Semonoidal_` typeclass+* Define experimental `-+-` method of `Semonoidal_` typeclass+* Use experimental `Semimonoidal_` as superclass of `Traversable`+* Remove `-<*>-` method of `Semimonoidal` typeclass+* Remove `Semimonoidal` typeclass+* Rename `Semimonoidal_` typeclass to `Semimonoidal`+* Rename `-*-` method of `Semimonoidal` to `-<*>-`+* Use `Semigroupoid` as superclass for `Semimonoidal`+* Define `*>-` and `forever_` methods of `Applicative_` typeclass+* Remove `<+*>`, `<**+>`, `<***+>` methods+* Remove `Applicative` typeclass+* Remove `satisfy` method of `Predicate`+* Remove `Alternative` typeclass+* Remove `Avoidable` typeclass+* Change `-<$$$>-`: works with endofunctors+* Define `-<$$$$>-` operator of `Covariant_` typeclass+* Use experimental `Covariant_` in `Interpreted`+* Define `$>-`, `$$>-`, `$$$>-` methods of `Covariant_` typeclass+* Remove `Covariant` typeclass+* Rename experimental `Covariant_` to `Covariant`+* Remove `Determinable` typeclass+* Remove `Divisible_` typeclass+* Remove `Contravariant` typeclass+* Rename experimental `Contravariant_` to `Contravariant`++# 0.4.6

@@ -3,8 +3,9 @@ module Pandora.Paradigm.Controlflow.Effect.Adaptable where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Category (identity, (.))-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant_)+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity)+import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Pointable (Pointable) import Pandora.Pattern.Functor.Extractable (Extractable) import Pandora.Pattern.Functor.Comonad (Comonad)@@ -17,8 +18,8 @@ 	{-# MINIMAL adapt #-} 	adapt :: t ~> u -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 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, Pointable u (->)) type Bringable t u = (Comonadic t, Extractable u (->)) @@ -39,7 +40,7 @@  instance 	( Liftable (Schematic Monad t)-	, Covariant_ (Schematic Monad u v) (->) (->)+	, Covariant (Schematic Monad u v) (->) (->) 	, Wrappable u v 	) => Adaptable u (t :> u :> v) where 	adapt = lift . wrap@@ -293,12 +294,12 @@ 	) => Adaptable (t :< u :< v :< w :< x :< y :< z :< f :< h) f where 	adapt = bring . lower . lower . lower . lower . lower . lower . lower -instance (Covariant u, Covariant_ u (->) (->), Hoistable ((:>) t), Adaptable u u') => Adaptable (t :> u) (t :> u') where+instance (Covariant u (->) (->), Hoistable ((:>) t), Adaptable u u') => Adaptable (t :> u) (t :> u') where 	adapt = hoist adapt  instance-	( Covariant_ v (->) (->)-	, Covariant_ (Schematic Monad u v) (->) (->)+	( Covariant v (->) (->)+	, Covariant (Schematic Monad u v) (->) (->) 	, Hoistable ((:>) (t :> u)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -307,12 +308,12 @@ 	adapt = hoist (hoist adapt)  instance-	( Covariant_ u (->) (->)-	, Covariant_ v (->) (->)-	, Covariant_ w (->) (->)-	, Covariant_ (Schematic Monad u v) (->) (->)-	, Covariant_ (Schematic Monad u (v :> w)) (->) (->)-	, Covariant_ (Schematic Monad v w) (->) (->)+	( Covariant u (->) (->)+	, Covariant v (->) (->)+	, Covariant w (->) (->)+	, Covariant (Schematic Monad u v) (->) (->)+	, Covariant (Schematic Monad u (v :> w)) (->) (->)+	, Covariant (Schematic Monad v w) (->) (->) 	, Hoistable ((:>) (t :> u :> v)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -322,10 +323,10 @@ 	adapt = hoist (hoist (hoist adapt))  instance-	( Covariant_ x (->) (->)-	, Covariant_ (Schematic Monad u (v :> (w :> x))) (->) (->)-	, Covariant_ (Schematic Monad v (w :> x)) (->) (->)-	, Covariant_ (Schematic Monad w x) (->) (->)+	( Covariant x (->) (->)+	, Covariant (Schematic Monad u (v :> (w :> x))) (->) (->)+	, Covariant (Schematic Monad v (w :> x)) (->) (->)+	, Covariant (Schematic Monad w x) (->) (->) 	, Hoistable ((:>) (t :> u :> v)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -336,11 +337,11 @@ 	adapt = hoist (hoist (hoist (hoist adapt)))  instance-	( Covariant_ y (->) (->)-	, Covariant_ (Schematic Monad u (v :> (w :> (x :> y)))) (->) (->)-	, Covariant_ (Schematic Monad v (w :> (x :> y))) (->) (->)-	, Covariant_ (Schematic Monad w (x :> y)) (->) (->)-	, Covariant_ (Schematic Monad x y) (->) (->)+	( Covariant y (->) (->)+	, Covariant (Schematic Monad u (v :> (w :> (x :> y)))) (->) (->)+	, Covariant (Schematic Monad v (w :> (x :> y))) (->) (->)+	, Covariant (Schematic Monad w (x :> y)) (->) (->)+	, Covariant (Schematic Monad x y) (->) (->) 	, Hoistable ((:>) (t :> u :> v :> w)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -352,12 +353,12 @@ 	adapt = hoist (hoist (hoist (hoist (hoist adapt))))  instance-	( Covariant z, Covariant_ z (->) (->)-	, Covariant_ (Schematic Monad u (v :> (w :> (x :> (y :> z))))) (->) (->)-	, Covariant_ (Schematic Monad v (w :> (x :> (y :> z)))) (->) (->)-	, Covariant_ (Schematic Monad w (x :> (y :> z))) (->) (->)-	, Covariant_ (Schematic Monad x (y :> z)) (->) (->)-	, Covariant_ (Schematic Monad y z) (->) (->)+	( Covariant z (->) (->)+	, Covariant (Schematic Monad u (v :> (w :> (x :> (y :> z))))) (->) (->)+	, Covariant (Schematic Monad v (w :> (x :> (y :> z)))) (->) (->)+	, Covariant (Schematic Monad w (x :> (y :> z))) (->) (->)+	, Covariant (Schematic Monad x (y :> z)) (->) (->)+	, Covariant (Schematic Monad y z) (->) (->) 	, Hoistable ((:>) (t :> u :> v :> w)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -371,32 +372,13 @@ 	adapt = hoist (hoist (hoist (hoist (hoist adapt))))  instance-	( Covariant f, Covariant_ f (->) (->)-	, Covariant (Schematic Monad u v)-	, Covariant (Schematic Monad u (v :> w))-	, Covariant (Schematic Monad u (v :> (w :> x)))-	, Covariant (Schematic Monad u (v :> (w :> (x :> y))))-	, Covariant (Schematic Monad u (v :> (w :> (x :> (y :> z)))))-	, Covariant (Schematic Monad u (v :> (w :> (x :> (y :> (z :> f))))))-	, Covariant_ (Schematic Monad u (v :> (w :> (x :> (y :> (z :> f)))))) (->) (->)-	, Covariant (Schematic Monad v (w :> x))-	, Covariant (Schematic Monad v (w :> (x :> y)))-	, Covariant (Schematic Monad v (w :> (x :> (y :> z))))-	, Covariant (Schematic Monad v (w :> (x :> (y :> (z :> f)))))-	, Covariant_ (Schematic Monad v (w :> (x :> (y :> (z :> f))))) (->) (->)-	, Covariant (Schematic Monad w (x :> y))-	, Covariant (Schematic Monad w (x :> (y :> z)))-	, Covariant (Schematic Monad w (x :> (y :> (z :> f))))-	, Covariant_ (Schematic Monad w (x :> (y :> (z :> f)))) (->) (->)-	, Covariant (Schematic Monad x y)-	, Covariant (Schematic Monad x (y :> z))-	, Covariant (Schematic Monad x (y :> (z :> f)))-	, Covariant_ (Schematic Monad x (y :> (z :> f))) (->) (->)-	, Covariant (Schematic Monad y z)-	, Covariant (Schematic Monad y (z :> f))-	, Covariant_ (Schematic Monad y (z :> f)) (->) (->)-	, Covariant (Schematic Monad z f)-	, Covariant_ (Schematic Monad z f) (->) (->)+	( Covariant f (->) (->)+	, Covariant (Schematic Monad u (v :> (w :> (x :> (y :> (z :> f)))))) (->) (->)+	, Covariant (Schematic Monad v (w :> (x :> (y :> (z :> f))))) (->) (->)+	, Covariant (Schematic Monad w (x :> (y :> (z :> f)))) (->) (->)+	, Covariant (Schematic Monad x (y :> (z :> f))) (->) (->)+	, Covariant (Schematic Monad y (z :> f)) (->) (->)+	, Covariant (Schematic Monad z f) (->) (->) 	, Hoistable ((:>) (t :> u :> v :> w)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)@@ -411,24 +393,14 @@ 	adapt = hoist (hoist (hoist (hoist (hoist (hoist adapt)))))  instance-	( Covariant h, Covariant_ h (->) (->)-	, Covariant_ (Schematic Monad u (v :> (w :> (x :> (y :> (z :> (f :> h))))))) (->) (->)-	, Covariant_ (Schematic Monad v (w :> (x :> (y :> (z :> (f :> h)))))) (->) (->)-	, Covariant_ (Schematic Monad w (x :> (y :> (z :> (f :> h))))) (->) (->)-	, Covariant (Schematic Monad x y)-	, Covariant (Schematic Monad x (y :> z))-	, Covariant (Schematic Monad x (y :> (z :> f)))-	, Covariant (Schematic Monad x (y :> (z :> (f :> h))))-	, Covariant_ (Schematic Monad x (y :> (z :> (f :> h)))) (->) (->)-	, Covariant (Schematic Monad y z)-	, Covariant (Schematic Monad y (z :> f))-	, Covariant (Schematic Monad y (z :> (f :> h)))-	, Covariant_ (Schematic Monad y (z :> (f :> h))) (->) (->)-	, Covariant (Schematic Monad z f)-	, Covariant (Schematic Monad z (f :> h))-	, Covariant_ (Schematic Monad z (f :> h)) (->) (->)-	, Covariant (Schematic Monad f h)-	, Covariant_ (Schematic Monad f h) (->) (->)+	( Covariant h (->) (->)+	, Covariant (Schematic Monad u (v :> (w :> (x :> (y :> (z :> (f :> h))))))) (->) (->)+	, Covariant (Schematic Monad v (w :> (x :> (y :> (z :> (f :> h)))))) (->) (->)+	, Covariant (Schematic Monad w (x :> (y :> (z :> (f :> h))))) (->) (->)+	, Covariant (Schematic Monad x (y :> (z :> (f :> h)))) (->) (->)+	, Covariant (Schematic Monad y (z :> (f :> h))) (->) (->)+	, Covariant (Schematic Monad z (f :> h)) (->) (->)+	, Covariant (Schematic Monad f h) (->) (->) 	, Hoistable ((:>) (t :> u :> v :> w)) 	, Hoistable (Schematic Monad t) 	, Hoistable (Schematic Monad u)

@@ -1,8 +1,8 @@ module Pandora.Paradigm.Controlflow.Effect.Interpreted where  import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Category ((.))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), (<$$$>), (<$$$$>)), Covariant_)+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-), (-<$$$>-), (-<$$$$>-)) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Paradigm.Primary.Algebraic.Exponential () @@ -22,38 +22,38 @@ 	(=||) :: Interpreted u => (t a -> u b) -> Primary t a -> Primary u b 	(=||) f = run . f . unite -	(<$||=) :: (Covariant j, Interpreted u)+	(<$||=) :: (Covariant j (->) (->), Interpreted u) 		=> (Primary t a -> Primary u b) -> j := t a -> j := u b-	f <$||= x = (f ||=) <$> x+	f <$||= x = (f ||=) -<$>- x -	(<$$||=) :: (Covariant j, Covariant k, Interpreted u)+	(<$$||=) :: (Covariant j (->) (->), Covariant k (->) (->), Interpreted u) 		=> (Primary t a -> Primary u b) -> j :. k := t a -> j :. k := u b-	f <$$||= x = (f ||=) <$$> x+	f <$$||= x = (f ||=) -<$$>- x -	(<$$$||=) :: (Covariant j, Covariant k, Covariant l, Interpreted u)+	(<$$$||=) :: (Covariant j (->) (->), Covariant k (->) (->), Covariant l (->) (->), Interpreted u) 		=> (Primary t a -> Primary u b) -> j :. k :. l := t a -> j :. k :. l := u b-	f <$$$||= x = (f ||=) <$$$> x+	f <$$$||= x = (f ||=) -<$$$>- x -	(<$$$$||=) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u)+	(<$$$$||=) :: (Covariant j (->) (->), Covariant k (->) (->), Covariant l (->) (->), Covariant m (->) (->), Interpreted u) 		=> (Primary t a -> Primary u b) -> j :. k :. l :. m := t a -> j :. k :. l :. m := u b-	f <$$$$||= x = (f ||=) <$$$$> x+	f <$$$$||= x = (f ||=) -<$$$$>- x -	(=||$>) :: (Covariant j, Interpreted u)+	(=||$>) :: (Covariant j (->) (->), Interpreted u) 		=> (t a -> u b) -> j := Primary t a -> j := Primary u b-	f =||$> x = (f =||) <$> x+	f =||$> x = (f =||) -<$>- x -	(=||$$>) :: (Covariant j, Covariant k, Interpreted u)+	(=||$$>) :: (Covariant j (->) (->), Covariant k (->) (->), Interpreted u) 		=> (t a -> u b) -> j :. k := Primary t a -> j :. k := Primary u b-	f =||$$> x = (f =||) <$$> x+	f =||$$> x = (f =||) -<$$>- x -	(=||$$$>) :: (Covariant j, Covariant k, Covariant l, Interpreted u)+	(=||$$$>) :: (Covariant j (->) (->), Covariant k (->) (->), Covariant l (->) (->), Interpreted u) 		=> (t a -> u b) -> j :. k :. l := Primary t a -> j :. k :. l := Primary u b-	f =||$$$> x = (f =||) <$$$> x+	f =||$$$> x = (f =||) -<$$$>- x -	(=||$$$$>) :: (Covariant j, Covariant k, Covariant l, Covariant m, Interpreted u)+	(=||$$$$>) :: (Covariant j (->) (->), Covariant k (->) (->), Covariant l (->) (->), Covariant m (->) (->), Interpreted u) 		=> (t a -> u b) -> j :. k :. l :. m := Primary t a -> j :. k :. l :. m := Primary u b-	f =||$$$$> x = (f =||) <$$$$> x+	f =||$$$$> x = (f =||) -<$$$$>- x -(-=:) :: (Liftable t, Interpreted (t u), Interpreted (t v), Covariant u, Covariant_ u (->) (->))+(-=:) :: (Liftable t, Interpreted (t u), Interpreted (t v), Covariant u (->) (->)) 	=> (t u a -> t v b) -> u a -> Primary (t v) b (-=:) f = run . f . lift

@@ -3,12 +3,12 @@ module Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic (Comonadic (..), (:<) (..)) where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -16,6 +16,7 @@ import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite))  class Interpreted t => Comonadic t where@@ -25,10 +26,7 @@ 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 <$> x--instance Covariant_ (Schematic Comonad t u) (->) (->) => Covariant_ (t :< u) (->) (->) where+instance Covariant (Schematic Comonad t u) (->) (->) => Covariant (t :< u) (->) (->) where 	f -<$>- TC x = TC $ f -<$>- x  instance Pointable (Schematic Comonad t u) (->) => Pointable (t :< u) (->) where@@ -37,11 +35,8 @@ instance Extractable (Schematic Comonad t u) (->) => Extractable (t :< u) (->) where 	extract = extract . tc -instance Applicative (Schematic Comonad t u) => Applicative (t :< u) where-	TC f <*> TC x = TC $ f <*> x--instance Alternative (Schematic Comonad t u) => Alternative (t :< u) where-	TC x <+> TC y = TC $ x <+> y+instance Semimonoidal (Schematic Comonad t u) (->) (:*:) (:*:) => Semimonoidal (t :< u) (->) (:*:) (:*:) where+	multiply_ (TC f :*: TC x) = TC $ multiply_ $ f :*: x  instance Traversable (Schematic Comonad t u) (->) (->) => Traversable (t :< u) (->) (->) where 	f <<- TC x = TC -<$>- f <<- x

@@ -3,13 +3,12 @@ module Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (..), (:>) (..)) where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -17,6 +16,7 @@ import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite))  class Interpreted t => Monadic t where@@ -26,10 +26,7 @@ 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 <$> x--instance Covariant_ (Schematic Monad t u) (->) (->) => Covariant_ (t :> u) (->) (->) where+instance Covariant (Schematic Monad t u) (->) (->) => Covariant (t :> u) (->) (->) where 	f -<$>- TM x = TM $ f -<$>- x  instance Pointable (Schematic Monad t u) (->) => Pointable (t :> u) (->) where@@ -38,14 +35,8 @@ instance Extractable (Schematic Monad t u) (->) => Extractable (t :> u) (->) where 	extract = extract . tm -instance Applicative (Schematic Monad t u) => Applicative (t :> u) where-	TM f <*> TM x = TM $ f <*> x--instance Alternative (Schematic Monad t u) => Alternative (t :> u) where-	TM x <+> TM y = TM $ x <+> y--instance Avoidable (Schematic Monad t u) => Avoidable (t :> u) where-	empty = TM empty+instance Semimonoidal (Schematic Monad t u) (->) (:*:) (:*:) => Semimonoidal (t :> u) (->) (:*:) (:*:) where+	multiply_ (TM f :*: TM x) = TM $ multiply_ $ f :*: x  instance Traversable (Schematic Monad t u) (->) (->) => Traversable (t :> u) (->) (->) where 	f <<- TM x = TM -<$>- f <<- x@@ -59,7 +50,7 @@ instance Extendable (Schematic Monad t u) (->) => Extendable (t :> u) (->) where 	f <<= TM x = TM $ f . TM <<= x -instance (Covariant_ (Schematic Monad t u) (->) (->), Pointable (t :> u) (->), Bindable (t :> u) (->)) => Monad (t :> u) where+instance (Covariant (Schematic Monad t u) (->) (->), Pointable (t :> u) (->), Bindable (t :> u) (->)) => Monad (t :> u) where  instance Liftable (Schematic Monad t) => Liftable ((:>) t) where 	lift = TM . lift

@@ -1,8 +1,9 @@ module Pandora.Paradigm.Controlflow.Observable (Observable, observe, 	notify, follow, subscribe, watch, (.:~.), (.:~*), (*:~.), (*:~*)) where -import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Applicative (Applicative (forever))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Paradigm.Primary.Algebraic (Applicative_, forever_) import Pandora.Paradigm.Primary.Transformer.Continuation (Continuation (Continuation)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) @@ -22,26 +23,26 @@ (.:~.) :: Observable t a r -> (a -> t r) -> t r (.:~.) = notify --- | Listen only first event, call back forever-follow :: Applicative t => Observable t a r -> (a -> t r) -> t r-follow r action = captured $ run r # Capture . forever . action+-- | Listen only first event, call back forever_+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 r action = forever $ captured $ run r # Capture . action+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 r action = forever $ captured $ run r # Capture . forever . action+-- | Listen all events from action, call back forever_+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

@@ -1,6 +1,7 @@ module Pandora.Paradigm.Controlflow.Pipeline (Pipeline, await, yield, finish, impact, (=*=), pipeline) where -import Pandora.Pattern.Category (($), (.), (#))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (!..))

@@ -12,8 +12,8 @@ import Pandora.Paradigm.Inventory.Accumulator as Exports  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Category ((.), ($), (#), identity)-import Pandora.Pattern.Functor.Covariant (Covariant)+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#), identity) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Functor.Extractable (extract) import Pandora.Pattern.Functor.Bivariant ((<->))@@ -45,7 +45,7 @@ (=<>) :: Stateful src t => Lens mode src tgt -> mode tgt -> t src lens =<> new = modify $ set lens new -(~<>) :: Covariant mode => Stateful src t => Lens mode src tgt -> (mode tgt -> mode tgt) -> t src+(~<>) :: Stateful src t => Lens mode src tgt -> (mode tgt -> mode tgt) -> t src lens ~<> f = modify $ over lens f  magnify :: forall bg ls t . (Accessible ls bg, Stateful bg t) => t ls

@@ -2,10 +2,11 @@  module Pandora.Paradigm.Inventory.Accumulator (Accumulator (..), Accumulated, gather) where -import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Object.Monoid (Monoid (zero))@@ -18,15 +19,12 @@  newtype Accumulator e a = Accumulator (e :*: a) -instance Covariant (Accumulator e) where-	f <$> Accumulator x = Accumulator $ f <$> x--instance Covariant_ (Accumulator e) (->) (->) where+instance Covariant (Accumulator e) (->) (->) where 	f -<$>- Accumulator x = Accumulator $ f -<$>- x -instance Semigroup e => Applicative (Accumulator e) where-	f <*> v = Accumulator $ k # run f # run v where-		k ~(e :*: g) ~(e' :*: w) = e + e' :*: g w+instance Semigroup e => Semimonoidal (Accumulator e) (->) (:*:) (:*:) where+	multiply_ (x :*: y) = Accumulator $ k # run x # run y where+		k ~(ex :*: x') ~(ey :*: y') = ex + ey :*: x' :*: y'  instance Monoid e => Pointable (Accumulator e) (->) where 	point = Accumulator . (zero :*:)@@ -46,10 +44,6 @@ 	wrap = TM . UT . point . run  type Accumulated e t = Adaptable (Accumulator e) t--instance {-# OVERLAPS #-} (Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u) where-	UT f <*> UT x = UT $ k <$> f <*> x where-		k ~(u :*: g) ~(v :*: y) = u + v :*: g y  instance {-# OVERLAPS #-} (Pointable u (->), Monoid e) => Pointable ((:*:) e <.:> u) (->) where 	point = UT . point . (zero :*:)

@@ -2,16 +2,19 @@  module Pandora.Paradigm.Inventory.Environment (Environment (..), Configured, env) where -import Pandora.Pattern.Category (identity, (.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant_ ((->$<-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Functor.Divariant (Divariant ((>->))) import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (%))+import Pandora.Paradigm.Primary.Algebraic ()+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM))@@ -20,20 +23,17 @@  newtype Environment e a = Environment (e -> a) -instance Covariant (Environment e) where-	f <$> Environment x = Environment $ f . x--instance Covariant_ (Environment e) (->) (->) where+instance Covariant (Environment e) (->) (->) where 	f -<$>- Environment x = Environment $ f . x -instance Contravariant_ (Flip Environment a) (->) (->) where+instance Contravariant (Flip Environment a) (->) (->) where 	f ->$<- Flip (Environment g) = Flip . Environment $ g . f  instance Pointable (Environment e) (->) where 	point x = Environment (x !.) -instance Applicative (Environment e) where-	f <*> x = Environment $ run f <*> run x+instance Semimonoidal (Environment e) (->) (:*:) (:*:) where+	multiply_ (x :*: y) = unite $ multiply_ $ run x :*: run y  instance Distributive (Environment e) (->) (->) where 	f -<< g = Environment $ (run -<$>- f) -<< g@@ -54,7 +54,7 @@ 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) 

@@ -2,8 +2,9 @@  module Pandora.Paradigm.Inventory.Equipment (Equipment (..), retrieve) where -import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -17,10 +18,7 @@  newtype Equipment e a = Equipment (e :*: a) -instance Covariant (Equipment e) where-	f <$> Equipment x = Equipment $ f <$> x--instance Covariant_ (Equipment e) (->) (->) where+instance Covariant (Equipment e) (->) (->) where 	f -<$>- Equipment x = Equipment $ f -<$>- x  instance Extractable (Equipment e) (->) where@@ -40,7 +38,7 @@ type instance Schematic Comonad (Equipment e) = (<:.>) ((:*:) e)  instance Comonadic (Equipment e) where-	bring (TC (TU x)) = Equipment $ extract <$> x+	bring (TC (TU x)) = Equipment $ extract @_ @(->) -<$>- x  type Equipped e t = Adaptable t (Equipment e) 

@@ -2,9 +2,10 @@  module Pandora.Paradigm.Inventory.Imprint (Imprint (..), Traceable) where -import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant_ ((->$<-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -21,13 +22,10 @@  newtype Imprint e a = Imprint (e -> a) -instance Covariant (Imprint e) where-	f <$> Imprint x = Imprint $ f . x--instance Covariant_ (Imprint e) (->) (->) where+instance Covariant (Imprint e) (->) (->) where 	f -<$>- Imprint g = Imprint $ f . g -instance Contravariant_ (Flip Imprint a) (->) (->) where+instance Contravariant (Flip Imprint a) (->) (->) where 	f ->$<- Flip (Imprint g) = Flip . Imprint $ g . f  instance Distributive (Imprint e) (->) (->) where

@@ -3,8 +3,9 @@ module Pandora.Paradigm.Inventory.Optics where  import Pandora.Core.Impliable (Impliable (Arguments, imply))-import Pandora.Pattern.Category (Category (identity, (.), ($), (#)))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$)))+import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category (identity, ($), (#)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Divariant ((>->))@@ -13,6 +14,7 @@ import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (run)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (%))+import Pandora.Paradigm.Primary.Algebraic (($>-)) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))@@ -26,14 +28,16 @@ type Lens = P_Q_T (->) Store  instance Invariant (Flip (Lens available) tgt) where-	f <$< 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+	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 = imply @(Convex Lens _ _) identity ((%) (!.))-	P_Q_T to . P_Q_T from = P_Q_T $ \source -> source <$ (to . extract @Identity . position $ from source)  instance Impliable (P_Q_T (->) Store Identity source target) where 	type Arguments (P_Q_T (->) Store Identity source target) =@@ -48,12 +52,14 @@ 		(source -> Maybe target) -> (source -> Maybe target -> source) -> Lens Maybe source target 	imply getter setter = P_Q_T $ \source -> Store $ getter source :*: setter source -instance Category (Lens Maybe) where-	identity = imply @(Obscure Lens _ _) # Just # resolve identity+instance Semigroupoid (Lens Maybe) where 	P_Q_T to . P_Q_T from = P_Q_T $ \source -> case position # from source of 		Nothing -> Store $ Nothing :*: (source !.)-		Just between -> source <$ to between+		Just between -> to between $>- source +instance Category (Lens Maybe) where+	identity = imply @(Obscure Lens _ _) # Just # resolve identity+ -- Lens as natural transformation type (#=@) source target available = forall a . Lens available (source a) (target a) @@ -66,7 +72,7 @@ set lens new = look new . run lens  -- | Modify focused target value-over :: Covariant available => Lens available source target -> (available target -> available target) -> source -> source+over :: Lens available source target -> (available target -> available target) -> source -> source over lens f = extract . retrofit f . run lens  -- | Representable based lens

@@ -3,11 +3,12 @@ module Pandora.Paradigm.Inventory.State where  import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Category (identity, (.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)), Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad)@@ -19,25 +20,19 @@ 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 ((:*:) ((:*:)), (%), (!.), (-<*>-), delta)+import Pandora.Paradigm.Primary.Algebraic ((:*:) ((:*:)), (*>-), delta)  -- | Effectful computation with a variable newtype State s a = State ((->) s :. (:*:) s := a) -instance Covariant (State s) where-	f <$> x = State $ (<$>) f . run x--instance Covariant_ (State s) (->) (->) where+instance Covariant (State s) (->) (->) where 	f -<$>- x = State $ (-<$>-) f . run x -instance Applicative (State s) where-	f <*> x = State $ ((<$>) |-) . (run x <-> identity @(->)) . run f--instance Semimonoidal (State s) (:*:) (->) (->) where-	multiply f (State g :*: State h) = State $ \s -> -		let old :*: x = g s in-		let new :*: y = h old in-		new :*: f (x :*: y)+instance Semimonoidal (State s) (->) (:*:) (:*:) where+	multiply_ (State g :*: State h) = State $ \s -> +		let old :*: x = g s in +	  	let new :*: y = h old in+		new :*: x :*: y  instance Pointable (State s) (->) where 	point = State . (identity @(->) -|)@@ -58,7 +53,7 @@ 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 @_ @(->) -<$>- run x  type Stateful s = Adaptable (State s) @@ -77,7 +72,7 @@ reconcile :: (Bindable t (->), Stateful s t, Adaptable u t) => (s -> u s) -> t s reconcile f = replace =<< adapt . f =<< current -type Memorable s t = (Pointable t (->), Semimonoidal t (:*:) (->) (->), Stateful s t)+type Memorable s t = (Pointable t (->), Semimonoidal t (->) (:*:) (:*:), Stateful s t)  fold :: (Traversable t (->) (->), Memorable s u) => (a -> s -> s) -> t a -> u s-fold op struct = ((!.) %) -<$>- (modify . op <<- struct) -<*>- current+fold op struct = (modify . op <<- struct) *>- current

@@ -3,8 +3,9 @@ module Pandora.Paradigm.Inventory.Store where  import Pandora.Core (type (:.), type (:=), type (<:=), type (~>))-import Pandora.Pattern.Category (identity, (.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), (.#..)), Covariant_ ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -12,7 +13,7 @@ import Pandora.Pattern.Functor.Bivariant ((<->)) import Pandora.Pattern.Functor.Divariant ((>->)) import Pandora.Pattern.Functor.Adjoint ((-|), (|-))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))+import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), (-.#..-)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached) import Pandora.Paradigm.Primary.Algebraic () import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))@@ -24,17 +25,14 @@ -- | Context based computation on value newtype Store s a = Store ((:*:) s :. (->) s := a) -instance Covariant (Store s) where-	f <$> Store x = Store $ f <$$> x--instance Covariant_ (Store s) (->) (->) where+instance Covariant (Store s) (->) (->) where 	f -<$>- Store x = Store $ f -<$$>- x  instance Extractable (Store s) (->) where 	extract = (($) |-) . run  instance Extendable (Store s) (->) where-	f <<= Store x = Store $ f -<$$>- (Store .#.. (identity @(->) -|) -<$>- x)+	f <<= Store x = Store $ f -<$$>- (Store -.#..- (identity @(->) -|) -<$>- x)  instance Comonad (Store s) (->) where 

@@ -9,29 +9,25 @@ import Pandora.Paradigm.Primary.Algebraic as Exports  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Category (Category ((.), ($), (#), identity))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category (($), (#), identity))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((|-), (-|))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (||=))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Inventory.Store (Store (Store)) import Pandora.Paradigm.Schemes (TU (TU), P_Q_T (P_Q_T), type (<:.>), type (<:.:>)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (resolve)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Into), premorph) import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Available, Substance, substructure)) -instance Category (Flip (->)) where-	identity = Flip identity+instance Semigroupoid (Flip (->)) where 	Flip f . Flip g = Flip $ \x -> g (f x) -instance Contravariant (Flip (->) r) where-	f >$< g = (<$> f) ||= g--instance Covariant (Flip (:*:) a) where-	f <$> (Flip (x :*: y)) = Flip $ f x :*: y+instance Category (Flip (->)) where+	identity = Flip identity  instance Extractable (Flip (:*:) a) (->) where 	extract (Flip (x :*: _)) = x@@ -103,16 +99,16 @@ 	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 @_ @(->) -<$>-)

@@ -1,22 +1,30 @@ {-# OPTIONS_GHC -fno-warn-orphans #-} -module Pandora.Paradigm.Primary.Algebraic (module Exports, (-<*>-)) where+module Pandora.Paradigm.Primary.Algebraic (module Exports, Applicative_, Alternative_, ($>-), ($$>-), ($$$>-), (-<*>-), (*>-), forever_, (-+-)) where  import Pandora.Paradigm.Primary.Algebraic.Exponential as Exports import Pandora.Paradigm.Primary.Algebraic.Product as Exports+import Pandora.Paradigm.Primary.Algebraic.Sum as Exports  import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant_ ((-<$>-)))+import Pandora.Pattern.Functor (Endofunctor)+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-), (-<$$$>-)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Applicative (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-)))  infixl 4 -<*>- -instance Semimonoidal ((->) e) (:*:) (->) (->) where-	multiply f (g :*: h) = \x -> f $ g x :*: h x+($>-) :: Covariant t (->) (->) => t a -> b -> t b+x $>- r = (r !.) -<$>- x +($$>-) :: (Covariant t (->) (->), Covariant u (->) (->)) => t (u a) -> b -> t (u b)+x $$>- r = (r !.) -<$$>- x++($$$>-) :: (Covariant t (->) (->), Covariant u (->) (->), Covariant v (->) (->)) => t (u (v a)) -> b -> t (u (v b))+x $$$>- r = (r !.) -<$$$>- x+ instance Traversable ((:*:) s) (->) (->) where 	f <<- x = (attached x :*:) -<$>- f (extract x) @@ -26,5 +34,27 @@ 	(|-) :: (a -> s -> b) -> (s :*: a) -> b 	f |- ~(s :*: x) = f x s -(-<*>-) :: forall a b t . (Semimonoidal t (:*:) (->) (->)) => t (a -> b) -> t a -> t b-(-<*>-) = (%) ((-|) @((:*:) (t (a -> b))) (multiply @t @(:*:) @(->) @(->) ((&) |-)))+instance Semimonoidal ((->) e) (->) (:*:) (:*:) where+	multiply_ :: ((e -> a) :*: (e -> b)) -> e -> (a :*: b)+	multiply_ (g :*: h) = \x -> g x :*: h x++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++type Applicative_ t = (Endofunctor Covariant t (->), Semimonoidal t (->) (:*:) (:*:))+type Alternative_ t = (Endofunctor Covariant t (->), Semimonoidal t (->) (:*:) (:+:))++(-<*>-) :: Applicative_ t => t (a -> b) -> t a -> t b+f -<*>- x = (|-) @_ @_ @(->) @(->) (&) -<$>- multiply_ @_ @_ @_ @(:*:) (f :*: x)++forever_ :: Applicative_ t => t a -> t b+forever_ x = let r = x *>- r in r++(*>-) :: Applicative_ t => t a -> t b -> t b+x *>- y = ((!.) %) -<$>- x -<*>- y++(-+-) :: Alternative_ t => t a -> t b -> (a :+: b -> r) -> t r+x -+- y = \f -> f -<$>- multiply_ (x :*: y)

@@ -2,10 +2,10 @@  module Pandora.Paradigm.Primary.Algebraic.Exponential where -import Pandora.Pattern.Category (Category ((.), ($), (#), identity))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant_ ((->$<-)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category (($), (#), identity))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -16,25 +16,22 @@ import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip))  infixr 2 !.+infixr 7 -.#..- infixr 9 % infixl 1 & -instance Category (->) where-	identity x = x+instance Semigroupoid (->) where 	f . g = \x -> f (g x) -instance Covariant ((->) a) where-	(<$>) = (.)+instance Category (->) where+	identity x = x -instance Covariant_ ((->) a) (->) (->) where+instance Covariant ((->) a) (->) (->) where 	(-<$>-) = (.) -instance Contravariant_ (Flip (->) a) (->) (->) where+instance Contravariant (Flip (->) a) (->) (->) where 	f ->$<- Flip g = Flip $ g . f -instance Applicative ((->) e) where-	(<*>) f g x = f x $ g x- instance Distributive ((->) e) (->) (->) where 	f -<< g = \e -> (f % e) -<$>- g @@ -58,7 +55,7 @@ instance Ringoid r => Ringoid (e -> r) where 	f * g = \e -> f e * g e -(-.#..-) :: (Covariant_ (v a) (->) target, Category v) => v c d -> target (v a (v b c)) (v a (v b d))+(-.#..-) :: (Covariant (v a) (->) target, Semigroupoid v) => v c d -> target (v a (v b c)) (v a (v b d)) (-.#..-) f = (-<$>-) (f .)  {-# INLINE (!.) #-}

@@ -2,8 +2,8 @@  import Pandora.Core.Functor (type (:=)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad)@@ -23,13 +23,10 @@  data (:*:) s a = s :*: a -instance Covariant ((:*:) s) where-	f <$> x = attached x :*: f # extract x--instance Covariant_ ((:*:) s) (->) (->) where+instance Covariant ((:*:) s) (->) (->) where 	f -<$>- x = attached x :*: f # extract x -instance Covariant_ (Flip (:*:) a) (->) (->) where+instance Covariant (Flip (:*:) a) (->) (->) where 	f -<$>- (Flip (x :*: y)) = Flip $ f x :*: y  instance Extractable ((:*:) a) (->) where@@ -69,8 +66,8 @@ instance (Group s, Group a) => Group (s :*: a) where 	invert x = invert # attached x :*: invert # extract x -instance {-# OVERLAPS #-} Applicative t => Applicative (t <:.:> t := (:*:)) where-	T_U (lfs :*: rfs) <*> T_U (ls :*: rs) = T_U $ lfs <*> ls :*: rfs <*> rs+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)  delta :: a -> a :*: a delta x = x :*: x

@@ -0,0 +1,29 @@+module Pandora.Paradigm.Primary.Algebraic.Sum where++import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Pointable (Pointable (point))+import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->)))+import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Primary.Transformer.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++instance Pointable ((:+:) e) (->) where+	point = Adoption++instance Bivariant (:+:) (->) (->) (->) where+	f <-> g = \case+		Option s -> Option $ f s+		Adoption x -> Adoption $ g x++instance Covariant (Flip (:+:) a) (->) (->) where+	_ -<$>- Flip (Adoption x) = Flip $ Adoption x+	f -<$>- Flip (Option y) = Flip . Option $ f y

@@ -1,11 +1,12 @@ module Pandora.Paradigm.Primary.Functor.Conclusion where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Category (identity, (.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($), (#))+import Pandora.Pattern.Functor (Endofunctor)+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad)@@ -16,6 +17,7 @@ import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False)) import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption)) import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM))@@ -24,38 +26,28 @@  data Conclusion e a = Failure e | Success a -instance Covariant (Conclusion e) where-	f <$> Success x = Success $ f x-	_ <$> Failure y = Failure y--instance Covariant_ (Conclusion e) (->) (->) where+instance Covariant (Conclusion e) (->) (->) where 	f -<$>- Success x = Success $ f x 	_ -<$>- Failure y = Failure y -instance Covariant_ (Flip Conclusion e) (->) (->) where+instance Covariant (Flip Conclusion e) (->) (->) where 	_ -<$>- Flip (Success x) = Flip $ Success x 	f -<$>- Flip (Failure y) = Flip . Failure $ f y  instance Pointable (Conclusion e) (->) where 	point = Success -instance Semimonoidal (Conclusion e) (:*:) (->) (->) where-	multiply f (Success x :*: Success y) = Success . f $ x :*: y-	multiply _ (Failure x :*: _) = Failure x-	multiply _ (_ :*: Failure x) = Failure x--instance Semimonoidal (Conclusion e) Conclusion (->) (->) where-	multiply f (Failure (Success x)) = Success . f $ Failure x-	multiply f (Success (Success y)) = Success . f $ Success y-	multiply _ (Failure (Failure e)) = Failure e-	multiply _ (Success (Failure e)) = Failure e+instance Semimonoidal (Conclusion e) (->) (:*:) (:*:) where+	multiply_ (Success x :*: Success y) = Success $ x :*: y+	multiply_ (Failure x :*: _) = Failure x+	multiply_ (_ :*: Failure x) = Failure x -instance Alternative (Conclusion e) where-	Failure _ <+> x = x-	Success x <+> _ = Success x+instance Semigroup e => Semimonoidal (Conclusion e) (->) (:*:) (:+:) where+	multiply_ (Failure _ :*: x) = Adoption -<$>- x+	multiply_ (Success x :*: _) = Option -<$>- Success x  instance Traversable (Conclusion e) (->) (->) where-	(<<-) :: (Covariant_ u (->) (->), Pointable u (->), Semimonoidal u (:*:) (->) (->))+	(<<-) :: (Endofunctor Covariant u (->), Pointable u (->), Semimonoidal u (->) (:*:) (:*:)) 		 => (a -> u b) -> Conclusion e a -> u (Conclusion e b) 	_ <<- Failure y = point $ Failure y 	f <<- Success x = Success -<$>- f x

@@ -1,8 +1,9 @@ module Pandora.Paradigm.Primary.Functor.Constant where -import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==)))@@ -19,17 +20,14 @@  newtype Constant a b = Constant a -instance Covariant (Constant a) where-	_ <$> Constant x = Constant x--instance Covariant_ (Constant a) (->) (->) where+instance Covariant (Constant a) (->) (->) where 	_ -<$>- Constant x = Constant x -instance Covariant_ (Flip Constant b) (->) (->) where+instance Covariant (Flip Constant b) (->) (->) where 	f -<$>- Flip (Constant x) = Flip . Constant $ f x -instance Contravariant (Constant a) where-	_ >$< Constant x = Constant x+instance Contravariant (Constant a) (->) (->) where+	_ ->$<- Constant x = Constant x  instance Invariant (Constant a) where 	_ <$< _ = \(Constant x) -> Constant x

@@ -1,19 +1,10 @@ module Pandora.Paradigm.Primary.Functor.Convergence where  import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)), Contravariant_ ((->$<-)))-import Pandora.Pattern.Functor.Divisible (Divisible ((>*<)))-import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-)))+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--instance Contravariant_ (Convergence r) (->) (->) where+instance Contravariant (Convergence r) (->) (->) where 	f ->$<- Convergence g = Convergence $ \x y -> g # f x # f y--instance Ringoid r => Divisible (Convergence r) where-	Convergence g >*< Convergence h = Convergence $-		\(x :*: x') (y :*: y') -> g x y * h x' y'

@@ -1,20 +1,14 @@ module Pandora.Paradigm.Primary.Functor.Edges where  import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()  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--instance Covariant_ Edges (->) (->) where+instance Covariant Edges (->) (->) where 	_ -<$>- Empty = Empty 	f -<$>- Connect x = Connect $ f x 	f -<$>- Overlay x = Overlay $ f x

@@ -1,6 +1,7 @@ module Pandora.Paradigm.Primary.Functor.Endo where -import Pandora.Pattern.Category (identity, (.), (#))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, (#)) import Pandora.Pattern.Functor.Invariant (Invariant ((<$<))) import Pandora.Pattern.Functor.Divariant ((>->)) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))

@@ -1,17 +1,17 @@ module Pandora.Paradigm.Primary.Functor.Fix where  import Pandora.Core.Functor (type (<:=), type (:=>))-import Pandora.Pattern.Category ((.))-import Pandora.Pattern.Functor.Covariant (Covariant (comap))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()  newtype Fix t = Fix { unfix :: t (Fix t) } -cata :: Covariant t => (a <:= t) -> Fix t -> a-cata f = f . comap (cata f) . unfix+cata :: Covariant t (->) (->) => (a <:= t) -> Fix t -> a+cata f = f . (cata f -<$>-) . unfix -ana :: Covariant t => (a :=> t) -> a -> Fix t-ana f = Fix . comap (ana f) . f+ana :: Covariant t (->) (->) => (a :=> t) -> a -> Fix t+ana f = Fix . (ana f -<$>-) . f -hylo :: Covariant t => (b <:= t) -> (a :=> t) -> (a -> b)+hylo :: Covariant t (->) (->) => (b <:= t) -> (a :=> t) -> (a -> b) hylo phi psi = cata phi . ana psi

@@ -1,10 +1,10 @@ module Pandora.Paradigm.Primary.Functor.Identity where -import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), comap), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -25,10 +25,7 @@  newtype Identity a = Identity a -instance Covariant Identity where-	f <$> Identity x = Identity $ f x--instance Covariant_ Identity (->) (->) where+instance Covariant Identity (->) (->) where 	f -<$>- Identity x = Identity $ f x  instance Pointable Identity (->) where@@ -37,9 +34,6 @@ instance Extractable Identity (->) where 	extract (Identity x) = x -instance Applicative Identity where-	Identity f <*> Identity x = Identity $ f x- instance Traversable Identity (->) (->) where 	f <<- Identity x = Identity -<$>- f x @@ -60,7 +54,7 @@  instance Adjoint Identity Identity (->) (->) where 	f -| x = Identity . f . Identity $ x-	g |- x = extract . extract . comap g $ x+	g |- x = extract . extract . (g -<$>-) $ x  instance Setoid a => Setoid (Identity a) where 	Identity x == Identity y = x == y

@@ -1,12 +1,11 @@ module Pandora.Paradigm.Primary.Functor.Maybe where  import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Category (identity, (.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad)@@ -25,38 +24,26 @@ import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce)) import Pandora.Paradigm.Primary.Algebraic.Exponential () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Functor.Conclusion (Conclusion (Failure, Success))+import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))  data Maybe a = Nothing | Just a -instance Covariant Maybe where-	f <$> Just x = Just $ f x-	_ <$> Nothing = Nothing--instance Covariant_ Maybe (->) (->) where+instance Covariant Maybe (->) (->) where 	f -<$>- Just x = Just $ f x 	_ -<$>- Nothing = Nothing  instance Pointable Maybe (->) where 	point = Just -instance Avoidable Maybe where-	empty = Nothing--instance Semimonoidal Maybe (:*:) (->) (->) where-	multiply f (Just x :*: Just y) = Just . f $ x :*: y-	multiply _ (Nothing :*: _) = Nothing-	multiply _ (_ :*: Nothing) = Nothing--instance Semimonoidal Maybe Conclusion (->) (->) where-	multiply f (Failure (Just x)) = Just . f $ Failure x-	multiply f (Success (Just y)) = Just . f $ Success y-	multiply _ (Failure Nothing) = Nothing-	multiply _ (Success Nothing) = Nothing+instance Semimonoidal Maybe (->) (:*:) (:*:) where+	multiply_ (Just x :*: Just y) = Just $ x :*: y+	multiply_ (Nothing :*: _) = Nothing+	multiply_ (_ :*: Nothing) = Nothing -instance Alternative Maybe where-	Nothing <+> y = y-	Just x <+> _ = Just x+instance Semimonoidal Maybe (->) (:*:) (:+:) where+	multiply_ (Just x :*: Just _) = Just $ Option x+	multiply_ (Nothing :*: Just y) = Just $ Adoption y+	multiply_ (Nothing :*: Nothing) = Nothing  instance Traversable Maybe (->) (->) where 	_ <<- Nothing = point Nothing

@@ -1,17 +1,11 @@ module Pandora.Paradigm.Primary.Functor.Predicate where  import Pandora.Core.Functor (type (~>), type (:=>))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)), Contravariant_ ((->$<-)))-import Pandora.Pattern.Functor.Divisible (Divisible ((>*<)), Divisible_ (divide))-import Pandora.Pattern.Functor.Determinable (Determinable (determine))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Object.Setoid (Setoid ((==)))-import Pandora.Pattern.Object.Ringoid ((*))-import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), bool, (?))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), bool) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype Predicate a = Predicate (a -> Boolean)@@ -21,27 +15,11 @@ 	run ~(Predicate f) = f 	unite = Predicate -instance Contravariant Predicate where-	f >$< Predicate g = Predicate $ g . f--instance Contravariant_ Predicate (->) (->) where+instance Contravariant Predicate (->) (->) where 	f ->$<- Predicate g = Predicate $ g . f -instance Divisible Predicate where-	Predicate g >*< Predicate h = Predicate $ \(b :*: c) -> g b * h c--instance Divisible_ Predicate (:*:) (->) (->) where-	divide f (Predicate g :*: Predicate h) = Predicate $ \r -> case f r of-		b :*: c -> g b * h c--instance Determinable Predicate where-	determine = Predicate (True !.)- equate :: Setoid a => a :=> Predicate equate x = Predicate (== x)--satisfy :: (Pointable t (->), Avoidable t) => Predicate a -> a -> t a-satisfy p x = run p x ? point x $ empty  not :: Predicate ~> Predicate not (Predicate p) = Predicate $ bool True False . p

@@ -1,10 +1,8 @@ module Pandora.Paradigm.Primary.Functor.Proxy where -import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -13,23 +11,14 @@  data Proxy a = Proxy -instance Covariant Proxy where-	_ <$> Proxy = Proxy--instance Covariant_ Proxy (->) (->) where+instance Covariant Proxy (->) (->) where 	_ -<$>- Proxy = Proxy -instance Contravariant Proxy where-	_ >$< _ = Proxy+instance Contravariant Proxy (->) (->) where+	_ ->$<- _ = Proxy  instance Pointable Proxy (->) where 	point _ = Proxy--instance Applicative Proxy where-	_ <*> _ = Proxy--instance Alternative Proxy where-	_ <+> _ = Proxy  instance Distributive Proxy (->) (->) where 	_ -<< _ = Proxy

@@ -1,11 +1,11 @@ module Pandora.Paradigm.Primary.Functor.Tagged where  import Pandora.Core.Functor (type (:=>), type (~>))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))@@ -30,13 +30,10 @@ infixr 0 :# type (:#) tag = Tagged tag -instance Covariant (Tagged tag) where-	f <$> Tag x = Tag $ f x--instance Covariant_ (Tagged tag) (->) (->) where+instance Covariant (Tagged tag) (->) (->) where 	f -<$>- Tag x = Tag $ f x -instance Covariant_ (Flip Tagged a) (->) (->) where+instance Covariant (Flip Tagged a) (->) (->) where 	_ -<$>- Flip (Tag x) = Flip $ Tag x  instance Pointable (Tagged tag) (->) where@@ -44,9 +41,6 @@  instance Extractable (Tagged tag) (->) where 	extract (Tag x) = x--instance Applicative (Tagged tag) where-	Tag f <*> Tag x = Tag $ f x  instance Traversable (Tagged tag) (->) (->) where 	f <<- Tag x = Tag -<$>- f x

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.These where  import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))@@ -9,12 +9,7 @@  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--instance Covariant_ (These e) (->) (->) where+instance Covariant (These e) (->) (->) where 	f -<$>- This x = This $ f x 	_ -<$>- That y = That y 	f -<$>- These y x = These y $ f x

@@ -1,10 +1,10 @@ module Pandora.Paradigm.Primary.Functor.Validation where -import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)), Semimonoidal (multiply))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==)))@@ -12,17 +12,14 @@ import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Paradigm.Primary.Algebraic.Exponential () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption)) import Pandora.Paradigm.Primary.Transformer.Flip (Flip (Flip)) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False)) import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater))  data Validation e a = Flaws e | Validated a -instance Covariant (Validation e) where-	_ <$> Flaws e = Flaws e-	f <$> Validated x = Validated $ f x--instance Covariant_ (Validation e) (->) (->) where+instance Covariant (Validation e) (->) (->) where 	_ -<$>- Flaws e = Flaws e 	f -<$>- Validated x = Validated $ f x 	_ -<$>- Flaws e = Flaws e@@ -30,7 +27,7 @@ 	_ -<$>- Flaws e = Flaws e 	f -<$>- Validated x = Validated $ f x -instance Covariant_ (Flip Validation a) (->) (->) where+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@@ -41,21 +38,15 @@ instance Pointable (Validation e) (->) where 	point = Validated -instance Semigroup e => Applicative (Validation e) where-	Flaws e <*> Flaws e' = Flaws $ e + e'-	Flaws e <*> Validated _ = Flaws e-	Validated _ <*> Flaws e' = Flaws e'-	Validated f <*> Validated x = Validated $ f x--instance Semigroup e => Semimonoidal (Validation e) (:*:) (->) (->) where-	multiply f (Validated x :*: Validated y) = Validated . f $ 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+	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 Alternative (Validation e) where-	Flaws _ <+> x = x-	Validated x <+> _ = Validated x+instance Semigroup e => Semimonoidal (Validation e) (->) (:*:) (:+:) where+	multiply_ (Flaws _ :*: y) = Adoption -<$>- y+	multiply_ (Validated x :*: _) = Option -<$>- Validated x  instance Traversable (Validation e) (->) (->) where 	f <<- Validated x = Validated -<$>- f x

@@ -1,19 +1,14 @@ module Pandora.Paradigm.Primary.Functor.Wedge where  import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Paradigm.Primary.Algebraic.Exponential ()  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--instance Covariant_ (Wedge e) (->) (->) where+instance Covariant (Wedge e) (->) (->) where 	_ -<$>- Nowhere = Nowhere 	_ -<$>- Here x = Here x 	f -<$>- There x = There $ f x

@@ -2,20 +2,14 @@  import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Category ((#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))  data Wye a = End | Left a | Right a | Both a a -instance Covariant Wye where-	_ <$> End = End-	f <$> Left x = Left # f x-	f <$> Right y = Right # f y-	f <$> Both x y = Both # f x # f y--instance Covariant_ Wye (->) (->) where+instance Covariant Wye (->) (->) where 	_ -<$>- End = End 	f -<$>- Left x = Left # f x 	f -<$>- Right y = Right # f y

@@ -2,8 +2,8 @@  module Pandora.Paradigm.Primary.Linear.Vector where +import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Pointable (point) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Ringoid (Ringoid ((*))) import Pandora.Pattern.Object.Monoid (Monoid (zero))@@ -11,8 +11,9 @@ import Pandora.Pattern.Object.Group (Group (invert)) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Functor.Maybe (Maybe)-import Pandora.Paradigm.Primary.Transformer.Construction (Construction)+import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))+import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct))+import Pandora.Paradigm.Schemes.TU (TU (TU)) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Into, Push), premorph, into, item)@@ -66,12 +67,12 @@  instance Morphable (Into List) (Vector r) where 	type Morphing (Into List) (Vector r) = List-	morphing (premorph -> Scalar x) = point x+	morphing (premorph -> Scalar x) = TU . Just $ Construct x Nothing 	morphing (premorph -> Vector x xs) = item @Push x $ into @List xs  instance Morphable (Into (Construction Maybe)) (Vector r) where 	type Morphing (Into (Construction Maybe)) (Vector r) = Construction Maybe-	morphing (premorph -> Scalar x) = point x+	morphing (premorph -> Scalar x) = Construct x Nothing 	morphing (premorph -> Vector x xs) = item @Push x $ into @(Nonempty List) xs  class Vectorize a r where

@@ -1,11 +1,12 @@ module Pandora.Paradigm.Primary.Transformer.Backwards where -import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (.#..)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Semimonoidal (multiply))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift))@@ -18,10 +19,7 @@  newtype Backwards t a = Backwards (t a) -instance Covariant t => Covariant (Backwards t) where-	f <$> Backwards x = Backwards $ f <$> x--instance Covariant_ t (->) (->) => Covariant_ (Backwards t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Backwards t) (->) (->) where 	f -<$>- Backwards x = Backwards $ f -<$>- x  instance Pointable t (->) => Pointable (Backwards t) (->) where@@ -31,9 +29,9 @@ 	extract (Backwards x) = extract x  -- TODO: check that effects evaluation goes in opposite order-instance Semimonoidal t (:*:) (->) (->) => Semimonoidal (Backwards t) (:*:) (->) (->) where-	multiply f (Backwards x :*: Backwards y) = Backwards #-		f .#.. ((:*:) %) -<$>- y -<*>- x+instance (Semimonoidal t (->) (:*:) (:*:), Covariant t (->) (->)) => Semimonoidal (Backwards t) (->) (:*:) (:*:) where+	multiply_ (Backwards x :*: Backwards y) = Backwards #+		((:*:) %) -<$>- y -<*>- x  instance Traversable t (->) (->) => Traversable (Backwards t) (->) (->) where 	f <<- Backwards x = Backwards -<$>- f <<- x@@ -41,8 +39,8 @@ 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 >$< x+instance Contravariant t (->) (->) => Contravariant (Backwards t) (->) (->) where+	f ->$<- Backwards x = Backwards $ f ->$<- x  instance Interpreted (Backwards t) where 	type Primary (Backwards t) a = t a

@@ -3,17 +3,13 @@ module Pandora.Paradigm.Primary.Transformer.Construction where  import Pandora.Core.Functor (type (:.), type (:=), type (:=>), type (~>))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), (<**>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-))-import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))-import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\), hoist))@@ -23,6 +19,7 @@ import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Primary.Algebraic ((-<*>-)) import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce)) import Pandora.Paradigm.Schemes (type (<:.>))@@ -31,33 +28,22 @@  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 <$$> xs--instance Covariant_ t (->) (->) => Covariant_ (Construction t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Construction t) (->) (->) where 	f -<$>- ~(Construct x xs) = Construct # f x # f -<$$>- xs -instance (Avoidable t, Covariant_ t (->) (->)) => Pointable (Construction t) (->) where-	point x = Construct x empty--instance Covariant_ t (->) (->) => Extractable (Construction t) (->) where+instance Covariant t (->) (->) => Extractable (Construction t) (->) where 	extract ~(Construct x _) = x -instance Applicative t => Applicative (Construction t) where-	~(Construct f fs) <*> ~(Construct x xs) = Construct # f x # fs <**> xs+instance (Covariant t (->) (->), Semimonoidal t (->) (:*:) (:*:)) => Semimonoidal (Construction t) (->) (:*:) (:*:) where+	multiply_ (Construct x xs :*: Construct y ys) = Construct (x :*: y) (multiply_ @_ @(->) @(:*:) -<$>- multiply_ (xs :*: ys))  instance Traversable t (->) (->) => Traversable (Construction t) (->) (->) where 	f <<- ~(Construct x xs) = Construct -<$>- f x -<*>- f -<<-<<- xs -instance (Covariant_ t (->) (->), Alternative t) => Bindable (Construction t) (->) where-	f =<< ~(Construct x xs) = Construct # extract (f x) # deconstruct (f x) <+> ((f =<<) -<$>- xs)--instance Covariant_ t (->) (->) => Extendable (Construction t) (->) where+instance Covariant t (->) (->) => Extendable (Construction t) (->) where 	f <<= x = Construct # f x # (f <<=) -<$>- deconstruct x -instance (Avoidable t, Alternative t, Covariant_ t (->) (->)) => Monad (Construction t) where--instance (Covariant t, Covariant_ t (->) (->)) => Comonad (Construction t) (->) where+instance (Covariant t (->) (->)) => Comonad (Construction t) (->) where  instance Lowerable Construction where 	lower x = extract @_ @(->) -<$>- deconstruct x@@ -65,13 +51,13 @@ instance Hoistable Construction where 	f /|\ x = Construct # extract x $ f # hoist f -<$>- deconstruct x -instance (Setoid a, forall b . Setoid b => Setoid (t b), Covariant t, Covariant_ t (->) (->)) => Setoid (Construction t a) where+instance (Setoid a, forall b . Setoid b => Setoid (t b), Covariant t (->) (->)) => Setoid (Construction t a) where 	x == y = (extract x == extract y) * (deconstruct x == deconstruct y) -instance (Semigroup a, forall b . Semigroup b => Semigroup (t b), Covariant t, Covariant_ t (->) (->)) => Semigroup (Construction t a) where+instance (Semigroup a, forall b . Semigroup b => Semigroup (t b), Covariant t (->) (->)) => Semigroup (Construction t a) where 	x + y = Construct # extract x + extract y # deconstruct x + deconstruct y -instance (Monoid a, forall b . Semigroup b => Monoid (t b), Covariant t, Covariant_ t (->) (->)) => Monoid (Construction t a) where+instance (Monoid a, forall b . Semigroup b => Monoid (t b), Covariant t (->) (->)) => Monoid (Construction t a) where 	zero = Construct zero zero  instance Monotonic a (t :. Construction t := a) => Monotonic a (Construction t a) where@@ -84,8 +70,8 @@ deconstruct ~(Construct _ xs) = xs  -- Generate a construction from seed using effectful computation-(.-+) :: Covariant t => a :=> t -> a :=> Construction t-f .-+ x = Construct x $ (f .-+) <$> f x+(.-+) :: Covariant t (->) (->) => a :=> t -> a :=> Construction t+f .-+ x = Construct x $ (f .-+) -<$>- f x  section :: Comonad t (->) => t ~> Construction t section xs = Construct # extract xs $ section <<= xs

@@ -2,10 +2,10 @@ module Pandora.Paradigm.Primary.Transformer.Continuation where  import Pandora.Core.Functor (type (:.), type (:=), type (::|:.))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift))@@ -19,19 +19,13 @@ 	run ~(Continuation x) = x 	unite = Continuation -instance Covariant t => Covariant (Continuation r t) where-	f <$> Continuation continuation = Continuation $ continuation . (. f)--instance Covariant_ t (->) (->) => Covariant_ (Continuation r t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Continuation r t) (->) (->) where 	f -<$>- Continuation continuation = Continuation $ continuation . (. f) -instance Covariant_ t (->) (->) => Pointable (Continuation r t) (->) where+instance Covariant t (->) (->) => Pointable (Continuation r t) (->) where 	point x = Continuation ($ x) -instance Covariant t => Applicative (Continuation r t) where-	f <*> x = Continuation $ \h -> run f $ \g -> run x # h . g--instance Covariant_ t (->) (->) => Bindable (Continuation r t) (->) where+instance Covariant t (->) (->) => Bindable (Continuation r t) (->) where 	f =<< x = Continuation $ \g -> run x $ \y -> run # f y # g  instance Monad t => Monad (Continuation r t) where

@@ -2,32 +2,23 @@  module Pandora.Paradigm.Primary.Transformer.Day where -import Pandora.Pattern.Category (($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (.#..)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Category ((#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Algebraic.Exponential ((!..), (-.#..-))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))  data Day t u a = forall b c . Day (t b) (u c) (b -> c -> a) -instance Covariant (Day t u) where-	f <$> Day tb uc g = Day tb uc # f .#.. g--instance Covariant_ (Day t u) (->) (->) where+instance Covariant (Day t u) (->) (->) where 	f -<$>- Day tb uc g = Day tb uc # f -.#..- g  instance (Pointable t (->), Pointable u (->)) => Pointable (Day t u) (->) where 	point x = Day # point () # point () # (x !..) -instance (Applicative t, Applicative u) => Applicative (Day t u) where-	Day tb uc bcad <*> Day vb wc bca = Day # (:*:) <$> tb <*> vb # (:*:) <$> uc <*> wc-		$ \(b :*: b') (c :*: c') -> bcad b c $ bca b' c'- instance (Extractable t (->), Extractable u (->)) => Extractable (Day t u) (->) where 	extract (Day tb uc bcad) = bcad # extract tb # extract uc @@ -39,3 +30,6 @@  instance Hoistable (Day t) where 	g /|\ Day tb uc bca = Day tb # g uc # bca++data Day_ category source target t u r = forall a b .+	Day_ (target (category (source a b) r) (target (t a) (u b)))

@@ -4,11 +4,9 @@  import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Category (($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad)@@ -16,34 +14,24 @@ import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\), hoist)) import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))  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 <$$> xs--instance Covariant_ t (->) (->) => Covariant_ (Instruction t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Instruction t) (->) (->) where 	f -<$>- Enter x = Enter $ f x 	f -<$>- Instruct xs = Instruct $ f -<$$>- xs -instance Covariant_ t (->) (->) => Pointable (Instruction t) (->) where+instance Covariant t (->) (->) => Pointable (Instruction t) (->) where 	point = Enter -instance Alternative t => Alternative (Instruction t) where-	Enter x <+> _ = Enter x-	_ <+> Enter y = Enter y-	Instruct xs <+> Instruct ys = Instruct $ xs <+> ys--instance Avoidable t => Avoidable (Instruction t) where-	empty = Instruct empty--instance Covariant t => Applicative (Instruction t) where-	Enter f <*> Enter y = Enter $ f y-	Enter f <*> Instruct y = Instruct $ f <$$> y-	Instruct f <*> y = Instruct $ (<*> y) <$> f+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 (->) (->) => Bindable (Instruction t) (->) where+instance Covariant t (->) (->) => Bindable (Instruction t) (->) where 	f =<< Enter x = f x 	f =<< Instruct xs = Instruct $ (f =<<) -<$>- xs @@ -60,6 +48,6 @@ 	lower (Enter x) = point x 	lower (Instruct xs) = lower =<< xs -instance (forall v . Covariant v) => Hoistable Instruction where+instance (forall v . Covariant v (->) (->)) => Hoistable Instruction where 	_ /|\ Enter x = Enter x-	f /|\ Instruct xs = Instruct $ hoist f <$> f xs+	f /|\ Instruct xs = Instruct $ hoist f -<$>- f xs

@@ -2,13 +2,11 @@  module Pandora.Paradigm.Primary.Transformer.Jack where -import Pandora.Pattern.Category (identity, (.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -22,34 +20,16 @@  data Jack t a = It a | Other (t a) -instance Covariant t => Covariant (Jack t) where-	f <$> It x = It $ f x-	f <$> Other y = Other $ f <$> y--instance Covariant_ t (->) (->) => Covariant_ (Jack t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Jack t) (->) (->) where 	f -<$>- It x = It $ f x 	f -<$>- Other y = Other $ f -<$>- y -instance Covariant_ t (->) (->) => Pointable (Jack t) (->) where+instance Covariant t (->) (->) => Pointable (Jack t) (->) where 	point = It -instance Alternative t => Alternative (Jack t) where-	It x <+> _ = It x-	Other _ <+> It y = It y-	Other x <+> Other y = Other # x <+> y--instance Avoidable t => Avoidable (Jack t) where-	empty = Other empty- instance Extractable t (->) => Extractable (Jack t) (->) where 	extract (It x) = x 	extract (Other y) = extract y--instance Applicative t => Applicative (Jack t) where-	It f <*> It x = It $ f x-	It f <*> Other y = Other $ f <$> y-	Other f <*> It x = Other $ ($ x) <$> f-	Other f <*> Other y = Other $ f <*> y  instance Traversable t (->) (->) => Traversable (Jack t) (->) (->) where 	f <<- It x = It -<$>- f x

@@ -2,26 +2,18 @@  module Pandora.Paradigm.Primary.Transformer.Jet where -import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), (<$$>), Covariant_ ((-<$>-)), (-<$$>-))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Paradigm.Primary.Algebraic ((-<*>-))  data Jet t a = Jet a (Jet t (t a)) -instance Covariant t => Covariant (Jet t) where-	f <$> Jet x xs = Jet (f x) (f <$$> xs)--instance Covariant_ t (->) (->) => Covariant_ (Jet t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Jet t) (->) (->) where 	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 -instance (forall u . Avoidable u, Covariant_ t (->) (->)) => Pointable (Jet t) (->) where-	point x = Jet x empty--instance Covariant_ t (->) (->) => Extractable (Jet t) (->) where+instance Covariant t (->) (->) => Extractable (Jet t) (->) where 	extract (Jet x _) = x

@@ -1,8 +1,9 @@ module Pandora.Paradigm.Primary.Transformer.Kan where -import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Contravariant (Contravariant_ ((->$<-)))-import Pandora.Pattern.Functor.Covariant (Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+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)) @@ -10,7 +11,7 @@  data instance Kan Left t u b a = Lan ((t b -> a) -> u b) -instance Contravariant_ (Kan Left t u b) (->) (->) where+instance Contravariant (Kan Left t u b) (->) (->) where 	f ->$<- Lan x = Lan $ x . (f .)  instance Interpreted (Kan Left t u b) where@@ -20,7 +21,7 @@  data instance Kan Right t u b a = Ran ((a -> t b) -> u b) -instance Covariant_ (Kan Right t u b) (->) (->) where+instance Covariant (Kan Right t u b) (->) (->) where 	f -<$>- Ran x = Ran $ x . (. f)  instance Interpreted (Kan Right t u b) where

@@ -2,25 +2,20 @@  module Pandora.Paradigm.Primary.Transformer.Outline where -import Pandora.Pattern.Category (identity, (.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))+import Pandora.Paradigm.Primary.Algebraic.Exponential ()  data Outline t a where 	Line :: a -> Outline t a 	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--instance Covariant_ (Outline t) (->) (->) where+instance Covariant (Outline t) (->) (->) where 	f -<$>- Line a = Line $ f a 	f -<$>- Outlined x y = Outlined x # (.) f -<$>- y @@ -31,19 +26,9 @@ 	extract (Line x) = x 	extract (Outlined x y) = extract y # extract x -instance Applicative (Outline f) where-	Line f <*> y = f <$> y-	Outlined x y <*> z = Outlined x # (%) <$> y <*> z- instance Liftable Outline where 	lift t = Outlined t (Line identity)  instance Hoistable Outline where 	_ /|\ Line x = Line x 	f /|\ Outlined x y = Outlined # f x # f /|\ y--instance (Extractable t (->), Pointable t (->), Applicative t) => Interpreted (Outline t) where-	type Primary (Outline t) a = t a-	run (Line x) = point x-	run (Outlined t f) = run f <*> t-	unite = Line . extract

@@ -2,27 +2,23 @@  module Pandora.Paradigm.Primary.Transformer.Reverse where -import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((->$<-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Semimonoidal (multiply)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) 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.Product ((:*:) ((:*:))) import Pandora.Paradigm.Primary.Transformer.Backwards (Backwards (Backwards)) 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--instance Covariant_ t (->) (->) => Covariant_ (Reverse t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Reverse t) (->) (->) where 	f -<$>- Reverse x = Reverse # f -<$>- x  instance Pointable t (->) => Pointable (Reverse t) (->) where@@ -31,17 +27,14 @@ instance Extractable t (->) => Extractable (Reverse t) (->) where 	extract (Reverse x) = extract x -instance Semimonoidal t (:*:) (->) (->) => Semimonoidal (Reverse t) (:*:) (->) (->) where-	multiply f (Reverse x :*: Reverse y) = Reverse . multiply f $ x :*: y- instance Traversable t (->) (->) => Traversable (Reverse t) (->) (->) where 	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+instance Contravariant t (->) (->) => Contravariant (Reverse t) (->) (->) where+	f ->$<- Reverse x = Reverse # f ->$<- x  instance Interpreted (Reverse t) where 	type Primary (Reverse t) a = t a

@@ -3,16 +3,13 @@ module Pandora.Paradigm.Primary.Transformer.Tap where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))-import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))@@ -31,28 +28,19 @@  data Tap t a = Tap a (t a) -instance Covariant t => Covariant (Tap t) where-	f <$> Tap x xs = Tap # f x # f <$> xs--instance Covariant_ t (->) (->) => Covariant_ (Tap t) (->) (->) where+instance Covariant t (->) (->) => Covariant (Tap t) (->) (->) where 	f -<$>- Tap x xs = Tap # f x # f -<$>- xs -instance (Avoidable t, Covariant_ t (->) (->)) => Pointable (Tap t) (->) where-	point = Tap % empty--instance (Covariant_ t (->) (->)) => Extractable (Tap t) (->) where+instance (Covariant t (->) (->)) => Extractable (Tap t) (->) where 	extract (Tap x _) = x -instance Applicative t => Applicative (Tap t) where-	Tap f fs <*> Tap x xs = Tap # f x # fs <*> xs+instance Semimonoidal t (->) (:*:) (:*:) => Semimonoidal (Tap t) (->) (:*:) (:*:) where+	multiply_ (Tap x xs :*: Tap y ys) = Tap (x :*: y) $ multiply_ $ xs :*: ys  instance Traversable t (->) (->) => Traversable (Tap t) (->) (->) where 	f <<- Tap x xs = Tap -<$>- f x -<*>- f <<- xs -instance (Extractable t (->), Alternative t, Bindable t (->)) => Bindable (Tap t) (->) where-	f =<< Tap x xs = case f x of ~(Tap y ys) -> Tap y $ ys <+> (lower . f =<< xs)--instance (Extendable t (->), Covariant_ t (->) (->)) => Extendable (Tap t) (->) where+instance (Extendable t (->), Covariant t (->) (->)) => Extendable (Tap t) (->) where 	f <<= x = Tap # f x $ f . Tap (extract x) <<= lower x  instance Lowerable Tap where@@ -61,26 +49,27 @@ instance Hoistable Tap where 	f /|\ Tap x xs = Tap x # f xs -instance {-# OVERLAPS #-} Applicative t => Applicative (Tap (t <:.:> t := (:*:))) where-	Tap f (T_U (lfs :*: rfs)) <*> Tap x (T_U (ls :*: rs)) = Tap # f x # T_U (lfs <*> ls :*: rfs <*> rs)+instance 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 #-} 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 -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Root (Tap (t <:.:> t := (:*:))) where+instance (Covariant t (->) (->)) => Substructure Root (Tap (t <:.:> t := (:*:))) where 	type Available Root (Tap (t <:.:> t := (:*:))) = Identity 	type Substance Root (Tap (t <:.:> t := (:*:))) = Identity 	substructure = P_Q_T $ \zipper -> case lower zipper of 		Tap x xs -> Store $ Identity (Identity x) :*: lift . (Tap % xs) . extract . extract -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Left (Tap (t <:.:> t := (:*:))) where+instance (Covariant t (->) (->)) => Substructure Left (Tap (t <:.:> t := (:*:))) where 	type Available Left (Tap (t <:.:> t := (:*:))) = Identity 	type Substance Left (Tap (t <:.:> t := (:*:))) = t 	substructure = P_Q_T $ \zipper -> case lower zipper of 		Tap x (T_U (future :*: past)) -> Store $ Identity future :*: lift . Tap x . T_U . (:*: past) . extract -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Right (Tap (t <:.:> t := (:*:))) where+instance (Covariant t (->) (->)) => Substructure Right (Tap (t <:.:> t := (:*:))) where 	type Available Right (Tap (t <:.:> t := (:*:))) = Identity 	type Substance Right (Tap (t <:.:> t := (:*:))) = t 	substructure = P_Q_T $ \zipper -> case lower zipper of

@@ -2,36 +2,21 @@  module Pandora.Paradigm.Primary.Transformer.Yoneda where -import Pandora.Pattern.Category (identity, (.), ($), (#))-import Pandora.Pattern.Functor ((<*+>))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.))+import Pandora.Paradigm.Primary.Algebraic.Exponential ()  newtype Yoneda t a = Yoneda 	{ yoneda :: forall b . (a -> b) -> t b } -instance Covariant (Yoneda t) where-	f <$> x = Yoneda (\k -> yoneda x (k . f))--instance Covariant_ (Yoneda t) (->) (->) where+instance Covariant (Yoneda t) (->) (->) where 	f -<$>- x = Yoneda (\k -> yoneda x (k . f)) -instance Alternative t => Alternative (Yoneda t) where-	Yoneda f <+> Yoneda g = Yoneda (f <*+> g)--instance Applicative t => Applicative (Yoneda t) where-	Yoneda f <*> Yoneda x = Yoneda (\g -> f (g .) <*> x identity)--instance Avoidable t => Avoidable (Yoneda t) where-	empty = Yoneda (empty !.)- instance Pointable t (->) => Pointable (Yoneda t) (->) where 	point x = Yoneda (\f -> point $ f x) @@ -43,4 +28,4 @@  instance (Extractable t (->), Pointable t (->), Extractable u (->) , Pointable u (->)) => Adjoint (Yoneda t) (Yoneda u) (->) (->) where 	f -| x = point . f . point # x-	g |- x = extract . extract # g <$> x+	g |- x = extract . extract # g -<$>- x

@@ -14,32 +14,34 @@ import Pandora.Paradigm.Schemes.TUT as Exports import Pandora.Paradigm.Schemes.TU as Exports -import Pandora.Pattern.Category ((.), ($))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) -instance (Covariant (v <:.> t), Covariant (u <:.> w), Adjoint t u (->) (->), Adjoint v w (->) (->))+instance (Covariant (v <:.> t) (->) (->), Covariant (u <:.> w) (->) (->), Adjoint t u (->) (->), Adjoint v w (->) (->))+ 	=> Adjoint (v <:.> t) (u <:.> w) (->) (->) where 		g |- TU y = (run . g |-) |- y 		f -| x = TU $ (f . TU -|) -| x -instance (Covariant (v <:.> t), Covariant (w <.:> u), Adjoint t u (->) (->), Adjoint v w (->) (->))+instance (Covariant (v <:.> t) (->) (->), Covariant (w <.:> u) (->) (->), Adjoint t u (->) (->), Adjoint v w (->) (->)) 	=> Adjoint (v <:.> t) (w <.:> u) (->) (->) where 		g |- TU t = (run . g |-) |- t 		f -| x = UT $ (f . TU -|) -| x -instance (Covariant (t <.:> v), Covariant (w <.:> u), Adjoint t u (->) (->), Adjoint v w (->) (->))+instance (Covariant (t <.:> v) (->) (->), Covariant (w <.:> u) (->) (->), Adjoint t u (->) (->), Adjoint v w (->) (->)) 	=> Adjoint (t <.:> v) (w <.:> u) (->) (->) where 		g |- UT t =  (run . g |-) |- t 		f -| x = UT $ (f . UT -|) -| x -instance (Covariant (t <.:> v), Covariant (w <:.> u) , Adjoint v u (->) (->), Adjoint t w (->) (->))+instance (Covariant (t <.:> v) (->) (->), Covariant (w <:.> u) (->) (->), Adjoint v u (->) (->), Adjoint t w (->) (->)) 	=> Adjoint (t <.:> v) (w <:.> u) (->) (->) where 		g |- UT x = (run . g |-) |- x 		f -| x = TU $ (f . UT -|) -| x -instance (Covariant ((t <:<.>:> u) t'), Covariant ((v <:<.>:> w) v')+instance (Covariant ((t <:<.>:> u) t') (->) (->),  Covariant ((v <:<.>:> w) v') (->) (->) 	, Adjoint t w (->) (->), Adjoint t' v' (->) (->), Adjoint t v (->) (->), Adjoint u v (->) (->), Adjoint v' t' (->) (->)) 	=> Adjoint ((t <:<.>:> u) t') ((v <:<.>:> w) v') (->) (->) where 		g |- TUT x = ((run . g |-) |-) |- x

@@ -1,13 +1,12 @@ module Pandora.Paradigm.Schemes.TU where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))-import Pandora.Pattern.Category ((.), ($), identity)-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), identity)+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), (<**>)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))@@ -16,6 +15,7 @@ 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.Product ((:*:)((:*:)))  newtype TU ct cu t u a = TU (t :. u := a) @@ -31,20 +31,11 @@ 	run ~(TU x) = x 	unite = TU -instance (Covariant t, Covariant u) => Covariant (t <:.> u) where-	f <$> x = TU $ f <$$> run x--instance (Covariant_ t (->) (->), Covariant_ u (->) (->)) => Covariant_ (t <:.> u) (->) (->) where+instance (Covariant t (->) (->), Covariant u (->) (->)) => Covariant (t <:.> u) (->) (->) where 	f -<$>- x = TU $ f -<$$>- run x -instance (Applicative t, Applicative u) => Applicative (t <:.> u) where-	TU f <*> TU x = TU $ f <**> x--instance (Covariant u, Alternative t) => Alternative (t <:.> u) where-	x <+> y = TU $ run x <+> run y--instance (Covariant u, Avoidable t) => Avoidable (t <:.> u) where-	empty = TU empty+instance (Covariant t (->) (->), Semimonoidal t (->) (:*:) (:*:), Semimonoidal u (->) (:*:) (:*:)) => Semimonoidal (t <:.> u) (->) (:*:) (:*:) where+	multiply_ (TU x :*: TU y) = TU $ multiply_ @_ @(->) @(:*:) -<$>- multiply_ (x :*: y)  instance (Pointable t (->), Pointable u (->)) => Pointable (t <:.> u) (->) where 	point = TU . point . point@@ -55,17 +46,17 @@ instance (Traversable t (->) (->), Traversable u (->) (->)) => Traversable (t <:.> u) (->) (->) where 	f <<- x = TU -<$>- f -<<-<<- run x -instance (Bindable t (->), Distributive t (->) (->), Covariant_ u (->) (->), Bindable u (->)) => Bindable (t <:.> u) (->) where+instance (Bindable t (->), Distributive t (->) (->), Covariant u (->) (->), Bindable u (->)) => Bindable (t <:.> u) (->) where 	f =<< TU x = TU $ (\i -> (identity =<<) -<$>- run . f -<< i) =<< x  instance Pointable t (->) => Liftable (TU Covariant Covariant t) where-	lift :: Covariant_ u (->) (->) => u ~> t <:.> u+	lift :: Covariant u (->) (->) => u ~> t <:.> u 	lift = TU . point  instance Extractable t (->) => Lowerable (TU Covariant Covariant t) where 	lower :: t <:.> u ~> u 	lower (TU x) = extract x -instance Covariant_ t (->) (->) => Hoistable (TU Covariant Covariant t) where+instance Covariant t (->) (->) => Hoistable (TU Covariant Covariant t) where 	(/|\) :: u ~> v -> (t <:.> u ~> t <:.> v) 	f /|\ TU x = TU $ f -<$>- x

@@ -1,9 +1,11 @@ module Pandora.Paradigm.Schemes.TUT where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))-import Pandora.Pattern.Category (identity, (.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$$>)), Covariant_ ((-<$>-)), (-<$$$>-))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (identity, ($))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-), (-<$$$>-)) import Pandora.Pattern.Functor.Contravariant (Contravariant)+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Extractable (Extractable (extract)) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -11,6 +13,7 @@ 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.Product ((:*:)((:*:))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype TUT ct ct' cu t t' u a = TUT (t :. u :. t' := a)@@ -31,37 +34,25 @@ 	run ~(TUT x) = x 	unite = TUT -instance (Covariant t, Covariant t', Covariant u) => Covariant (t <:<.>:> t' := u) where-	f <$> TUT x = TUT $ f <$$$> x--instance (Covariant_ t (->) (->), Covariant_ t' (->) (->), Covariant_ u (->) (->)) => Covariant_ (t <:<.>:> t' := u) (->) (->)where+instance (Covariant t (->) (->), Covariant t' (->) (->), Covariant u (->) (->)) => Covariant (t <:<.>:> t' := u) (->) (->) where 	f -<$>- TUT x = TUT $ f -<$$$>- x ---instance (Covariant t, Covariant t', Adjoint t' t (->) (->), Bindable u (->)) => Applicative (t <:<.>:> t' := u) where---	f <*> x = TUT $ (>>= ((<$$$> run x) |-)) <$> run f----instance (Applicative t, Covariant t', Alternative u) => Alternative (t <:<.>:> t' := u) where---	x <+> y = TUT $ run x <*+> run y----instance (Pointable t (->), Applicative t, Covariant t', Avoidable u) => Avoidable (t <:<.>:> t' := u) where---	empty = TUT $ point empty+instance (Covariant t (->) (->), Covariant t' (->) (->), Covariant u (->) (->), Semimonoidal t (->) (:*:) (:*:), Semimonoidal u (->) (:*:) (:*:), Semimonoidal t' (->) (:*:) (:*:)) => Semimonoidal (t <:<.>:> t' := u) (->) (:*:) (:*:) where+	multiply_ (TUT x :*: TUT y) = TUT $ multiply_ @_ @(->) @(:*:) -<$$>- multiply_ @_ @(->) @(:*:) -<$>- multiply_ (x :*: y) -instance (Covariant_ t (->) (->), Covariant_ t' (->) (->), Pointable u (->), Adjoint t' t (->) (->)) => Pointable (t <:<.>:> t' := u) (->) where+instance (Covariant t (->) (->), Covariant t' (->) (->), Pointable u (->), Adjoint t' t (->) (->)) => Pointable (t <:<.>:> t' := u) (->) where 	point = unite . (point @_ @(->) -|) ---instance (Covariant t, Covariant t', Adjoint t' t (->) (->), Bindable u (->)) => Bindable (t <:<.>:> t' := u) (->) where---	f =<< x = TUT $ ((run . f |-) =<<) -<$>- x--instance (Covariant t', Covariant t, Adjoint t' t (->) (->), Extendable u (->)) => Extendable (t' <:<.>:> t := u) (->) where+instance (Adjoint t' t (->) (->), Extendable u (->)) => Extendable (t' <:<.>:> t := u) (->) where 	f <<= x = TUT $ ((f . unite -|) <<=) -<$>- run x -instance (Covariant_ t (->) (->), Covariant_ t' (->) (->), Adjoint t t' (->) (->), Extractable u (->)) => Extractable (t <:<.>:> t' := u) (->) where+instance (Covariant t (->) (->), Covariant t' (->) (->), Adjoint t t' (->) (->), Extractable u (->)) => Extractable (t <:<.>:> t' := u) (->) where 	extract = (extract @_ @(->) |-) . run -instance (forall u . Covariant u, Adjoint t' t (->) (->), Distributive t(->) (->) ) => Liftable (t <:<.>:> t') where-	lift :: Covariant_ u (->) (->) => u ~> t <:<.>:> t' := u+instance (Adjoint t' t (->) (->), Distributive t(->) (->) ) => Liftable (t <:<.>:> t') where+	lift :: Covariant u (->) (->) => u ~> t <:<.>:> t' := u 	lift x = TUT $ (identity @(->) -|) -<< x -instance (forall u . Covariant u, Adjoint t t' (->) (->), Distributive t'(->) (->) ) => Lowerable (t <:<.>:> t') where-	lower :: Covariant_ u (->) (->) => (t <:<.>:> t' := u) ~> u+instance (Adjoint t t' (->) (->), Distributive t'(->) (->) ) => Lowerable (t <:<.>:> t') where+	lower :: Covariant u (->) (->) => (t <:<.>:> t' := u) ~> u 	lower (TUT x) = (identity @(->) -<<) |- x

@@ -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 ((>$<)))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant, Contravariant ((->$<-))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Functor.Divariant (Divariant ((>->))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (||=)))@@ -21,14 +21,11 @@ 	run ~(T_U x) = x 	unite = T_U -instance (forall i . Covariant (p i), Bivariant p (->) (->) (->), Covariant t, Covariant u) => Covariant (t <:.:> u := p) where-	f <$> x = (f <$>) <-> (f <$>) ||= x--instance (forall i . Covariant_ (p i) (->) (->), Bivariant p (->) (->) (->), Covariant_ t (->) (->), Covariant_ u (->) (->)) => Covariant_ (t <:.:> u := p) (->) (->) where+instance (forall i . Covariant (p i) (->) (->), Bivariant p (->) (->) (->), Covariant t (->) (->), Covariant u (->) (->)) => Covariant (t <:.:> u := p) (->) (->) where 	f -<$>- x = (f -<$>-) <-> (f -<$>-) ||= x -instance (Divariant p (->) (->) (->), Contravariant t, Covariant u) => Covariant (t >:.:> u := p) where-	f <$> x = (f >$<) >-> (f <$>) ||= x+instance (Divariant p (->) (->) (->), Contravariant t (->) (->), Covariant u (->) (->)) => Covariant (t >:.:> u := p) (->) (->) where+	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+instance (forall i . Covariant (p i) (->) (->), Bivariant p (->) (->) (->), Contravariant t (->) (->), Contravariant u (->) (->)) => Contravariant (t >:.:< u := p) (->) (->) where+	f ->$<- x = (f ->$<-) <-> (f ->$<-) ||= x

@@ -1,10 +1,11 @@ module Pandora.Paradigm.Schemes.UT where  import Pandora.Core.Functor (type (:.), type (:=), type (~>))-import Pandora.Pattern.Category ((.), ($), identity)-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), identity)+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), (<**>)), Semimonoidal)+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extractable (Extractable (extract))@@ -12,7 +13,7 @@ import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))+import Pandora.Paradigm.Primary.Algebraic ((:*:) ((:*:)))  newtype UT ct cu t u a = UT (u :. t := a) @@ -28,28 +29,25 @@ 	run ~(UT x) = x 	unite = UT -instance (Covariant t, Covariant u) => Covariant (t <.:> u) where-	f <$> UT x = UT $ f <$$> x--instance (Covariant_ t (->) (->), Covariant_ u (->) (->)) => Covariant_ (t <.:> u) (->) (->) where-	f -<$>- UT x = UT $ f -<$$>- x+instance (Covariant t (->) (->), Covariant u (->) (->)) => Covariant (t <.:> u) (->) (->) where+	f -<$>- x = UT $ f -<$$>- run x -instance (Applicative t, Applicative u) => Applicative (t <.:> u) where-	UT f <*> UT x = UT $ f <**> x+instance (Covariant u (->) (->), Semimonoidal t (->) (:*:) (:*:), Semimonoidal u (->) (:*:) (:*:)) => Semimonoidal (t <.:> u) (->) (:*:) (:*:) where+	multiply_ (UT x :*: UT y) = UT $ multiply_ @_ @(->) @(:*:) -<$>- multiply_ (x :*: y)  instance (Pointable t (->), Pointable u (->)) => Pointable (t <.:> u) (->) where 	point = UT . point . point -instance (Traversable t (->) (->), Bindable t (->), Semimonoidal u (:*:) (->) (->), Pointable u (->), Bindable u (->)) => Bindable (t <.:> u) (->) where+instance (Traversable t (->) (->), Bindable t (->), Semimonoidal u (->) (:*:) (:*:), Pointable u (->), Bindable u (->)) => Bindable (t <.:> u) (->) where 	f =<< UT x = UT $ ((identity =<<) -<$>-) . (run . f <<-) =<< x  instance (Extractable t (->), Extractable u (->)) => Extractable (t <.:> u) (->) where 	extract = extract . extract . run  instance Pointable t (->) => Liftable (UT Covariant Covariant t) where-	lift :: Covariant_ u (->) (->) => u ~> t <.:> u+	lift :: Covariant u (->) (->) => u ~> t <.:> u 	lift x = UT $ point @_ @(->) -<$>- x  instance Extractable t (->) => Lowerable (UT Covariant Covariant t) where-	lower :: Covariant_ u (->) (->) => t <.:> u ~> u+	lower :: Covariant u (->) (->) => t <.:> u ~> u 	lower (UT x) = extract @_ @(->) -<$>- x

@@ -8,10 +8,10 @@ import Pandora.Paradigm.Structure.Some as Exports  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Category (($), (.), (#))-import Pandora.Pattern.Functor.Covariant (Covariant (comap), Covariant_)+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (extract)-import Pandora.Pattern.Functor.Pointable (point) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Semigroup ((+))@@ -38,7 +38,7 @@ instance Nullable Maybe where 	null = Predicate $ \case { Just _ -> True ; _ -> False } -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Tail (Tap t) where+instance (Covariant t (->) (->)) => Substructure Tail (Tap t) where 	type Available Tail (Tap t) = Identity 	type Substance Tail (Tap t) = t 	substructure = P_Q_T $ \tap -> case extract # run tap of@@ -53,21 +53,21 @@  instance Morphable (Into (Inorder (Construction Maybe))) (Construction Wye) where 	type Morphing (Into (Inorder (Construction Maybe))) (Construction Wye) = Construction Maybe-	morphing (premorph -> Construct x End) = point x-	morphing (premorph -> Construct x (Left lst)) = into @(Inorder (Nonempty List)) lst + point x-	morphing (premorph -> Construct x (Right rst)) = point x + into @(Inorder (Nonempty List)) rst-	morphing (premorph -> Construct x (Both lst rst)) = into @(Inorder (Nonempty List)) lst + point x + into @(Inorder (Nonempty List)) rst+	morphing (premorph -> Construct x End) = Construct x Nothing+	morphing (premorph -> Construct x (Left lst)) = into @(Inorder (Nonempty List)) lst + Construct x Nothing+	morphing (premorph -> Construct x (Right rst)) = Construct x Nothing + into @(Inorder (Nonempty List)) rst+	morphing (premorph -> Construct x (Both lst rst)) = into @(Inorder (Nonempty List)) lst + Construct x Nothing + into @(Inorder (Nonempty List)) rst  instance Morphable (Into (Postorder (Construction Maybe))) (Construction Wye) where 	type Morphing (Into (Postorder (Construction Maybe))) (Construction Wye) = Construction Maybe-	morphing (premorph -> Construct x End) = point x-	morphing (premorph -> Construct x (Left lst)) = into @(Postorder (Nonempty List)) lst + point x-	morphing (premorph -> Construct x (Right rst)) = into @(Postorder (Nonempty List)) rst + point x-	morphing (premorph -> Construct x (Both lst rst)) = into @(Postorder (Nonempty List)) lst + into @(Postorder (Nonempty List)) rst + point x+	morphing (premorph -> Construct x End) = Construct x Nothing+	morphing (premorph -> Construct x (Left lst)) = into @(Postorder (Nonempty List)) lst + Construct x Nothing+	morphing (premorph -> Construct x (Right rst)) = into @(Postorder (Nonempty List)) rst + Construct x Nothing+	morphing (premorph -> Construct x (Both lst rst)) = into @(Postorder (Nonempty List)) lst + into @(Postorder (Nonempty List)) rst + Construct x Nothing  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) = comap (into @(o ds)) ||= xs+	morphing (premorph -> xs) = (into @(o ds) -<$>-) ||= xs  instance Substructure Left (Flip (:*:) a) where 	type Available Left (Flip (:*:) a) = Identity@@ -90,13 +90,13 @@ instance {-# OVERLAPS #-} Accessible b a => Accessible b (s :*: a) where 	access = access @b . access @a -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Left (t <:.:> t := (:*:)) where+instance (Covariant t (->) (->)) => Substructure Left (t <:.:> t := (:*:)) where 	type Available Left (t <:.:> t := (:*:)) = Identity 	type Substance Left (t <:.:> t := (:*:)) = t 	substructure = P_Q_T $ \x -> case run # lower x of 		ls :*: rs -> Store $ Identity ls :*: lift . (twosome % rs) . extract -instance (Covariant t, Covariant_ t (->) (->)) => Substructure Right (t <:.:> t := (:*:)) where+instance (Covariant t (->) (->)) => Substructure Right (t <:.:> t := (:*:)) where 	type Available Right (t <:.:> t := (:*:)) = Identity 	type Substance Right (t <:.:> t := (:*:)) = t 	substructure = P_Q_T $ \x -> case run # lower x of

@@ -2,7 +2,7 @@  module Pandora.Paradigm.Structure.Ability.Measurable where -import Pandora.Pattern.Category ((.))+import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag))  class Measurable f t where

@@ -1,8 +1,7 @@ module Pandora.Paradigm.Structure.Ability.Monotonic where  import Pandora.Pattern.Category ((#))-import Pandora.Pattern.Functor.Covariant ((.#..))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.))+import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (-.#..-))  class Monotonic a e where 	{-# MINIMAL reduce #-}@@ -10,7 +9,7 @@  	-- | Version of `reduce` which ignores accumulator 	resolve :: (a -> r) -> r -> e -> r-	resolve g = reduce # g .#.. (!.)+	resolve g = reduce # g -.#..- (!.)  instance Monotonic a a where 	reduce f r x = f x r

@@ -3,7 +3,8 @@ module Pandora.Paradigm.Structure.Ability.Morphable where  import Pandora.Core.Functor (type (:=), type (~>), type (:=:=>))-import Pandora.Pattern.Category ((.), (#))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((#)) import Pandora.Pattern.Functor.Extractable (extract) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Setoid (Setoid)

@@ -4,7 +4,7 @@ module Pandora.Paradigm.Structure.Ability.Substructure where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Functor.Covariant (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)@@ -23,5 +23,5 @@ 	type Substance segment structure :: * -> * 	substructure :: (Tagged segment <:.> structure) #=@ Substance segment structure := Available segment structure -	sub :: (Covariant structure, Covariant_ structure (->) (->)) => structure #=@ Substance segment structure := Available segment structure-	sub = lift >-> (lower <$>) ||= substructure @segment @structure+	sub :: (Covariant structure (->) (->)) => structure #=@ Substance segment structure := Available segment structure+	sub = lift >-> (lower -<$>-) ||= substructure @segment @structure

@@ -3,7 +3,8 @@ module Pandora.Paradigm.Structure.Interface.Set where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Category ((.), ($))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Object.Setoid (Setoid ((!=))) import Pandora.Pattern.Object.Semigroup ((+))

@@ -4,28 +4,26 @@ module Pandora.Paradigm.Structure.Modification.Comprehension where  import Pandora.Core.Functor (type (:=))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Contravariant ((>$<))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Contravariant ((->$<-))+import Pandora.Pattern.Functor.Pointable (Pointable)+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))-import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Push), premorph) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null))+import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))  newtype Comprehension t a = Comprehension (t <:.> Construction t := a) @@ -34,33 +32,18 @@ 	run ~(Comprehension x) = x 	unite = Comprehension -instance Covariant (t <:.> Construction t) => Covariant (Comprehension t) where-	f <$> Comprehension x = Comprehension $ f <$> x--instance Covariant_ (t <:.> Construction t) (->) (->) => Covariant_ (Comprehension t) (->) (->) where+instance Covariant (t <:.> Construction t) (->) (->) => Covariant (Comprehension t) (->) (->) where 	f -<$>- Comprehension x = Comprehension $ f -<$>- x -instance (Avoidable t, Pointable t (->)) => Pointable (Comprehension t) (->) where-	point = Comprehension . TU . point . Construct % empty--instance Alternative t => Alternative (Comprehension t) where-	Comprehension x <+> Comprehension y = Comprehension $ x <+> y--instance (Avoidable t, Alternative t) => Avoidable (Comprehension t) where-	empty = Comprehension empty- instance Traversable (t <:.> Construction t) (->) (->) => Traversable (Comprehension t) (->) (->) where 	f <<- Comprehension x = Comprehension -<$>- f <<- x -instance (forall a . Semigroup (t <:.> Construction t := a), Bindable t (->), Pointable t (->), Avoidable t) => Applicative (Comprehension t) where-	fs <*> xs = (\f -> Comprehension . TU . point . point . f =<< xs) =<< fs+instance (Covariant t (->) (->), Semimonoidal t (->) (:*:) (:*:)) => Semimonoidal (Comprehension t) (->) (:*:) (:*:) where+	multiply_ (Comprehension x :*: Comprehension y) = Comprehension $ multiply_ (x :*: y)  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-		-- t >>= \(Construct x xs) -> run . run $ f x + (Comprehension (TU xs) >>= f) -instance (forall a . Semigroup (t <:.> Construction t := a), Pointable t (->), Avoidable t, Bindable t (->)) => Monad (Comprehension t) where- instance Setoid (t <:.> Construction t := a) => Setoid (Comprehension t a) where 	Comprehension ls == Comprehension rs = ls == rs @@ -70,9 +53,9 @@ instance Monoid (t <:.> Construction t := a) => Monoid (Comprehension t a) where 	zero = Comprehension zero -instance (Covariant t, Covariant_ t (->) (->), Pointable t (->)) => Morphable Push (Comprehension t) where+instance (Covariant t (->) (->), Pointable 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

@@ -4,13 +4,12 @@ module Pandora.Paradigm.Structure.Modification.Prefixed where  import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Category ((.), ($))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)), Covariant_ ((-<$>-)), (-<$$>-))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)), (-<$$>-)) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (-<<-<<-)) import Pandora.Pattern.Functor.Extractable (extract)-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Primary.Algebraic () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))@@ -25,10 +24,7 @@ 	run ~(Prefixed x) = x 	unite = Prefixed -instance Covariant t => Covariant (Prefixed t k) where-	f <$> Prefixed x = Prefixed $ f <$$> x--instance Covariant_ t (->) (->) => Covariant_ (Prefixed t k) (->) (->) where+instance Covariant t (->) (->) => Covariant (Prefixed t k) (->) (->) where 	f -<$>- Prefixed x = Prefixed $ f -<$$>- x  instance Traversable t (->) (->) => Traversable (Prefixed t k) (->) (->) where@@ -37,14 +33,8 @@ instance (Monoid k, Pointable t (->)) => Pointable (Prefixed t k) (->) where 	point = Prefixed . point . (:*:) zero -instance Alternative t => Alternative (Prefixed t k) where-	x <+> y = Prefixed $ run x <+> run y--instance Avoidable t => Avoidable (Prefixed t k) where-	empty = Prefixed empty--instance Covariant t => Morphable (Into t) (Prefixed t k) where+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

@@ -3,10 +3,10 @@ module Pandora.Paradigm.Structure.Some.Binary where  import Pandora.Core.Functor (type (:.), type (:=), type (:=>), type (:::))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), ($$$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (extract)-import Pandora.Pattern.Functor.Avoidable (empty) import Pandora.Pattern.Functor.Bindable ((=<<)) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)@@ -15,6 +15,7 @@ import Pandora.Paradigm.Primary () import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), type (:*:), attached, twosome) import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), (&))+import Pandora.Paradigm.Primary.Algebraic (($$$>-)) 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))@@ -71,14 +72,14 @@ 	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 --------------------------------------- @@ -147,7 +148,7 @@ 	morphing (run . run . premorph -> Just tree) = T_U $ \(TU (key :*: Identity value)) -> 		let continue = ((vary @Element @k @_ @(Prefixed Binary _) key value =||) =||) 		in let root = extract tree in Prefixed . lift $ key <=> attached root & order-			# over (sub @Root) ($$$> value) tree+			# over (sub @Root) ($$$>- value) tree 			# over (sub @Left) continue tree 			# over (sub @Right) continue tree @@ -164,12 +165,7 @@  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--instance Covariant_ Biforked (->) (->) where+instance Covariant Biforked (->) (->) where 	_ -<$>- Top = Top 	f -<$>- Leftward l = Leftward $ f l 	f -<$>- Rightward r = Rightward $ f r@@ -188,27 +184,27 @@ 		lift $ twosome # Construct parent (resolve # Both focused # Left focused # run rest) # TU (TU next) 	morphing (run . premorph -> focused :*: TU (TU (Rightward (Construct (T_U (Identity parent :*: rest)) next)))) = 		lift $ twosome # Construct parent (resolve # Both % focused # Right focused # run rest) # TU (TU next)-	morphing (premorph -> T_U (_ :*: TU (TU Top))) = empty+	morphing (premorph -> T_U (_ :*: TU (TU Top))) = TU Nothing  instance Morphable (Rotate (Down Left)) (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) where 	type Morphing (Rotate (Down Left)) (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) 		= Maybe <:.> (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) 	morphing (run . premorph -> Construct x (Left lst) :*: TU (TU next)) =-		lift . twosome lst . TU . TU . Leftward $ Construct # twosome (Identity x) empty # next+		lift . twosome lst . TU . TU . Leftward $ Construct # twosome (Identity x) (TU Nothing) # next 	morphing (run . premorph -> Construct x (Both lst rst) :*: TU (TU next)) = 		lift . twosome lst . TU . TU . Leftward $ Construct # twosome (Identity x) (lift rst) # next-	morphing (run . premorph -> Construct _ (Right _) :*: _) = empty-	morphing (run . premorph -> Construct _ End :*: _) = empty+	morphing (run . premorph -> Construct _ (Right _) :*: _) = TU Nothing+	morphing (run . premorph -> Construct _ End :*: _) = TU Nothing  instance Morphable (Rotate (Down Right)) (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) where 	type Morphing (Rotate (Down Right)) (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) 		= Maybe <:.> (Construction Wye <:.:> Bifurcation <:.> Bicursor := (:*:)) 	morphing (run . premorph -> Construct x (Right rst) :*: TU (TU next)) =-		lift . twosome rst . TU . TU . Rightward $ Construct # twosome (Identity x) empty # next+		lift . twosome rst . TU . TU . Rightward $ Construct # twosome (Identity x) (TU Nothing) # next 	morphing (run . premorph -> Construct x (Both lst rst) :*: TU (TU next)) = 		lift . twosome rst . TU . TU . Rightward $ Construct # twosome (Identity x) (lift lst) # next-	morphing (run . premorph -> Construct _ (Left _) :*: _) = empty-	morphing (run . premorph -> Construct _ End :*: _) = empty+	morphing (run . premorph -> Construct _ (Left _) :*: _) = TU Nothing+	morphing (run . premorph -> Construct _ End :*: _) = TU Nothing  leaf :: a :=> Nonempty Binary leaf x = Construct x End

@@ -4,15 +4,16 @@  import Pandora.Core.Functor (type (:.), type (:=), type (:::)) import Pandora.Core.Impliable (imply)-import Pandora.Pattern.Category ((.), ($), (#), identity)-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (.#..)), Covariant_ ((-<$>-)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#), identity)+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((-<$>-)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_)) import Pandora.Pattern.Functor.Extractable (extract)-import Pandora.Pattern.Functor.Avoidable (empty) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Bivariant ((<->))+import Pandora.Pattern.Functor.Adjoint (Adjoint ((|-))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Setoid (Setoid ((==)))@@ -21,7 +22,7 @@ import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), (?)) import Pandora.Paradigm.Primary.Object.Numerator (Numerator (Numerator)) import Pandora.Paradigm.Primary.Object.Denumerator (Denumerator (One))-import Pandora.Paradigm.Primary.Algebraic ((-<*>-))+import Pandora.Paradigm.Primary.Algebraic ((-<*>-), (-.#..-)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached, twosome) import Pandora.Paradigm.Primary.Algebraic.Exponential ((%)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))@@ -64,7 +65,7 @@ 		$ TU @Covariant @Covariant xs + TU @Covariant @Covariant ys  instance Monoid (List a) where-	zero = empty+	zero = TU Nothing  instance Morphable Push List where 	type Morphing Push List = Identity <:.:> List := (->)@@ -106,19 +107,19 @@ 	type Available Root List = Maybe 	type Substance Root List = Identity 	substructure = P_Q_T $ \zipper -> case run # lower zipper of-		Just (Construct x xs) -> Store $ Just (Identity x) :*: lift . resolve (lift . (Construct % xs) . extract @Identity) empty-		Nothing -> Store $ Nothing :*: lift . resolve (lift . (Construct % empty) . extract @Identity) empty+		Just (Construct x xs) -> Store $ Just (Identity x) :*: lift . resolve (lift . (Construct % xs) . extract @Identity) zero+		Nothing -> Store $ Nothing :*: lift . resolve (lift . (Construct % Nothing) . extract @Identity) zero  instance Substructure Tail List where 	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-		Nothing -> Store $ Identity empty :*: lift . identity . extract+		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 ------------------------------------------- @@ -166,9 +167,6 @@  type instance Zipper List (Left ::: Right) = Tap (List <:.:> List := (:*:)) ---instance {-# OVERLAPS #-} Applicative (Tap (List <:.:> List := (:*:))) where-	--Tap f (T_U (lfs :*: rfs)) <*> Tap x (T_U (ls :*: rs)) = Tap # f x # T_U (lfs <*> ls :*: rfs <*> rs)- 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@@ -181,17 +179,17 @@ 	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@@ -212,26 +210,26 @@ 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 := (:*:))-	morphing (premorph -> ne) = Tap # extract ne $ twosome # extract (view # sub @Tail # ne) # empty+	morphing (premorph -> ne) = Tap # extract ne $ twosome # extract (view # sub @Tail # ne) # zero  instance Morphable (Into (Tap (List <:.:> List := (:*:)))) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Into (Tap (List <:.:> List := (:*:)))) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = Tap (List <:.:> List := (:*:)) 	morphing (premorph -> zipper) = Tap # extract zipper $ lift <-> lift ||= lower zipper ---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)+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)  instance Morphable (Into (Construction Maybe)) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) where 	type Morphing (Into (Construction Maybe)) (Tap (Construction Maybe <:.:> Construction Maybe := (:*:))) = Construction Maybe@@ -249,8 +247,9 @@  type instance Zipper (Comprehension Maybe) (Left ::: Right) = Tap (Comprehension Maybe <:.:> Comprehension Maybe := (:*:)) -instance {-# OVERLAPS #-} Applicative (Tap (Comprehension Maybe <:.:> Comprehension Maybe := (:*:))) where-	Tap f (T_U (lfs :*: rfs)) <*> Tap x (T_U (ls :*: rs)) = Tap # f x # T_U (lfs <*> ls :*: rfs <*> rs)+instance Semimonoidal (Tap (Comprehension Maybe <:.:> Comprehension Maybe := (:*:))) (->) (:*:) (:*:) 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)  ----------------------------------------- Prefixed list -------------------------------------------- @@ -262,5 +261,5 @@  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

@@ -3,32 +3,30 @@ module Pandora.Paradigm.Structure.Some.Rose where  import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))-import Pandora.Pattern.Functor.Contravariant ((>$<))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Contravariant ((->$<-)) import Pandora.Pattern.Functor.Extractable (extract)-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Setoid (Setoid ((==), (!=))) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), (?)) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((!.), (%))+import Pandora.Paradigm.Primary.Algebraic.Exponential ((%)) import Pandora.Paradigm.Primary.Functor.Identity (Identity (Identity)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Predicate (Predicate (Predicate), equate)-import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct)-import Pandora.Paradigm.Schemes (TU (TU), T_U (T_U), P_Q_T (P_Q_T), type (<:.>), type (<:.:>))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (=||$>))+import Pandora.Paradigm.Schemes (TU (TU), P_Q_T (P_Q_T), type (<:.>))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Inventory.Store (Store (Store)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing)-	, Morph (Lookup, Vary, Element, Key), premorph, find, vary)+	, Morph (Lookup, Element, Key), premorph, find) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null)) import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Available, Substance, substructure), Segment (Root, Tail))-import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed (Prefixed))+import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed) import Pandora.Paradigm.Structure.Some.List (List)  type Rose = Maybe <:.> Construction List@@ -37,21 +35,21 @@ 	null = Predicate $ \case { TU Nothing -> True ; _ -> False }  -- FIXME: If we want to remove root node, we ruin the whole tree-instance Substructure Root Rose where-	type Available Root Rose = Maybe-	type Substance Root Rose = Identity-	substructure = P_Q_T $ \rose -> case run # lower rose of-		Nothing -> Store $ Nothing :*: TU . Tag . TU . ((Construct % empty) . extract <$>)-		Just nonempty_rose -> Store $ Just (Identity # extract nonempty_rose) :*: \case-			Just (Identity new) -> lift . TU . Just . Construct new $ deconstruct nonempty_rose-			Nothing -> lift empty+--instance Substructure Root Rose where+--	type Available Root Rose = Maybe+--	type Substance Root Rose = Identity+--	substructure = P_Q_T $ \rose -> case run # lower rose of+--		Nothing -> Store $ Nothing :*: TU . Tag . TU . ((Construct % empty) . extract <$>)+--		Just nonempty_rose -> Store $ Just (Identity # extract nonempty_rose) :*: \case+--			Just (Identity new) -> lift . TU . Just . Construct new $ deconstruct nonempty_rose+--			Nothing -> lift empty -instance Substructure Just Rose where-	type Available Just Rose = Identity-	type Substance Just Rose = List <:.> Construction List-	substructure = P_Q_T $ \rose -> case run . extract . run # rose of-		Nothing -> Store $ Identity empty :*: (lift empty !.)-		Just (Construct x xs) -> Store $ Identity (TU xs) :*: lift . lift . Construct x . run . extract+--instance Substructure Just Rose where+--	type Available Just Rose = Identity+--	type Substance Just Rose = List <:.> Construction List+--	substructure = P_Q_T $ \rose -> case run . extract . run # rose of+--		Nothing -> Store $ Identity empty :*: (lift empty !.)+--		Just (Construct x xs) -> Store $ Identity (TU xs) :*: lift . lift . Construct x . run . extract  --------------------------------------- Non-empty rose tree ---------------------------------------- @@ -76,32 +74,32 @@ 	morphing (run . premorph -> TU (Just tree)) = TU $ find_rose_sub_tree % tree  -- TODO: Ineffiecient - we iterate over all branches in subtree, but we need to short-circuit on the first matching part of-instance Setoid k => Morphable (Vary Element) (Prefixed Rose k) where-	type Morphing (Vary Element) (Prefixed Rose k) = ((:*:) (Nonempty List k) <:.> Identity) <:.:> Prefixed Rose k := (->)-	morphing (run . run . premorph -> Nothing) = T_U $ \(TU (Construct key _ :*: Identity value)) -> Prefixed . lift $ Construct (key :*: value) empty-	morphing (run . run . premorph -> Just (Construct focused subtree)) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of-		Construct key Nothing -> Prefixed . lift $ attached focused == key ? Construct (key :*: value) subtree $ Construct focused subtree-		Construct key (Just keys) -> Prefixed . lift $ attached focused != key ? Construct focused subtree-			$ Construct focused $ vary @Element @_ @_ @(Nonempty (Prefixed Rose k)) keys value =||$> subtree+--instance Setoid k => Morphable (Vary Element) (Prefixed Rose k) where+--	type Morphing (Vary Element) (Prefixed Rose k) = ((:*:) (Nonempty List k) <:.> Identity) <:.:> Prefixed Rose k := (->)+--	morphing (run . run . premorph -> Nothing) = T_U $ \(TU (Construct key _ :*: Identity value)) -> Prefixed . lift $ Construct (key :*: value) empty+--	morphing (run . run . premorph -> Just (Construct focused subtree)) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of+--		Construct key Nothing -> Prefixed . lift $ attached focused == key ? Construct (key :*: value) subtree $ Construct focused subtree+--		Construct key (Just keys) -> Prefixed . lift $ attached focused != key ? Construct focused subtree+--			$ Construct focused $ vary @Element @_ @_ @(Nonempty (Prefixed Rose k)) keys value =||$> subtree  ---------------------------------- Non-empty prefixed rose tree ------------------------------------  -- TODO: Ineffiecient - we iterate over all branches in subtree, but we need to short-circuit on the first matching part of-instance Setoid k => Morphable (Vary Element) (Prefixed (Construction List) k) where-	type Morphing (Vary Element) (Prefixed (Construction List) k) =-		((:*:) (Nonempty List k) <:.> Identity) <:.:> Prefixed (Construction List) k := (->)-	morphing (run . premorph -> Construct x (TU Nothing)) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of-		Construct key Nothing -> Prefixed $ attached x == key ? Construct (key :*: value) empty $ Construct x empty-		Construct _ (Just _) -> Prefixed $ Construct x (TU Nothing)-	morphing (run . premorph -> Construct x (TU (Just subtree))) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of-		Construct key Nothing -> Prefixed $ attached x != key ? Construct x # lift subtree-			$ Construct (key :*: value) (lift subtree)-		Construct key (Just keys) -> Prefixed $ attached x != key ? Construct x # lift subtree-			$ Construct (key :*: value) . lift $ vary @Element @_ @_ @(Nonempty (Prefixed Rose k)) keys value =||$> subtree+--instance Setoid k => Morphable (Vary Element) (Prefixed (Construction List) k) where+--	type Morphing (Vary Element) (Prefixed (Construction List) k) =+--		((:*:) (Nonempty List k) <:.> Identity) <:.:> Prefixed (Construction List) k := (->)+--	morphing (run . premorph -> Construct x (TU Nothing)) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of+--		Construct key Nothing -> Prefixed $ attached x == key ? Construct (key :*: value) empty $ Construct x empty+--		Construct _ (Just _) -> Prefixed $ Construct x (TU Nothing)+--	morphing (run . premorph -> Construct x (TU (Just subtree))) = T_U $ \(TU (breadcrumbs :*: Identity value)) -> case breadcrumbs of+--		Construct key Nothing -> Prefixed $ attached x != key ? Construct x # lift subtree+--			$ Construct (key :*: value) (lift subtree)+--		Construct key (Just keys) -> Prefixed $ attached x != key ? Construct x # lift subtree+--			$ Construct (key :*: value) . lift $ vary @Element @_ @_ @(Nonempty (Prefixed Rose k)) keys value =||$> subtree  find_rose_sub_tree :: forall k a . Setoid k => Nonempty List k -> Nonempty Rose := k :*: a -> Maybe a find_rose_sub_tree (Construct k Nothing) tree = k == attached (extract tree) ? Just (extract $ extract tree) $ Nothing 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

@@ -4,8 +4,9 @@ module Pandora.Paradigm.Structure.Some.Splay where  import Pandora.Core.Functor (type (~>), type (:.), type (:=))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Extractable (extract) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Paradigm.Primary ()@@ -58,11 +59,11 @@  		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@@ -70,11 +71,11 @@ 	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

@@ -3,8 +3,9 @@ module Pandora.Paradigm.Structure.Some.Stream where  import Pandora.Core.Functor (type (:=), type (:=>), type (:::))-import Pandora.Pattern.Category ((.), ($), (#))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category (($), (#))+import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-))) import Pandora.Pattern.Functor.Pointable (point) import Pandora.Pattern.Functor.Extractable (extract) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))@@ -33,7 +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

@@ -4,3 +4,4 @@ import Pandora.Pattern.Transformer as Exports import Pandora.Pattern.Functor as Exports import Pandora.Pattern.Category as Exports+import Pandora.Pattern.Semigroupoid as Exports

@@ -1,19 +1,18 @@ module Pandora.Pattern.Category (Category (..)) where +import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) + infixl 2 # infixr 0 $-infixr 9 .  {- | > When providing a new instance, you should ensure it satisfies: > * Left identity: identity . f ≡ f > * Right identity: f . identity ≡ f-> * Associativity: f . (g . h) ≡ (f . g) . h -} -class Category (m :: * -> * -> *) where+class Semigroupoid m => Category m where 	identity :: m a a-	(.) :: m b c -> m a b -> m a c  	($) :: m (m a b) (m a b) 	($) = identity . identity

@@ -1,4 +1,4 @@-module Pandora.Pattern.Functor (module Exports, (<*+>), (<**+>), (<***+>)) where+module Pandora.Pattern.Functor (module Exports, Endofunctor) where  import Pandora.Pattern.Functor.Bivariant as Exports import Pandora.Pattern.Functor.Divariant as Exports@@ -10,25 +10,15 @@ import Pandora.Pattern.Functor.Bindable as Exports import Pandora.Pattern.Functor.Distributive as Exports import Pandora.Pattern.Functor.Traversable as Exports-import Pandora.Pattern.Functor.Determinable as Exports import Pandora.Pattern.Functor.Extractable as Exports import Pandora.Pattern.Functor.Pointable as Exports-import Pandora.Pattern.Functor.Avoidable as Exports-import Pandora.Pattern.Functor.Applicative as Exports-import Pandora.Pattern.Functor.Alternative as Exports+import Pandora.Pattern.Functor.Semimonoidal as Exports import Pandora.Pattern.Functor.Invariant as Exports import Pandora.Pattern.Functor.Contravariant as Exports import Pandora.Pattern.Functor.Covariant as Exports -import Pandora.Core.Functor (type (:.), type (:=))--(<*+>) :: (Applicative t, Alternative u) => t :. u := a -> t :. u := a -> t :. u := a-x <*+> y = (<+>) <$> x <*> y--(<**+>) :: (Applicative t, Applicative u, Alternative v)-	=> t :. u :. v := a -> t :. u :. v := a -> t :. u :. v := a-x <**+> y = (<+>) <$$> x <**> y--(<***+>) :: (Applicative t, Applicative u, Applicative v, Alternative w)-	=> t :. u :. v :. w := a -> t :. u :. v :. w := a -> t :. u :. v :. w := a-x <***+> y = (<+>) <$$$> x <***> y+type family Endofunctor constraint functor category where+	Endofunctor Covariant t category = Covariant t category category+	Endofunctor Contravariant t category = Contravariant t category category+	Endofunctor Traversable t category = Traversable t category category+	Endofunctor Distributive t category = Distributive t category category

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Adjoint where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  type (-|) = Adjoint @@ -14,6 +14,6 @@ > * Right adjunction interchange: psi f ≡ epsilon . comap f -} -class (Covariant_ t target source, Covariant_ u source target) => Adjoint t u source target where+class (Covariant t target source, Covariant u source target) => Adjoint t u source target where 	(-|) :: source (t a) b -> target a (u b) 	(|-) :: target a (u b) -> source (t a) b

@@ -1,20 +0,0 @@-module Pandora.Pattern.Functor.Alternative where--import Pandora.Pattern.Functor.Covariant (Covariant)--infixl 3 <+>--{- |-> When providing a new instance, you should ensure it satisfies:-> * Associativity of <+>: (x <+> y) <+> z ≡ x <+> (y <+> z)-> * Left-distributes <$> over <+>: f <$> (x <+> y) ≡ (f <$> x) <+> (f <$> y)--}--class Covariant t => Alternative t where-	{-# MINIMAL (<+>) #-}-	-- | Infix version of 'alter'--	(<+>) :: t a -> t a -> t a-	-- | Prefix version of '<+>'-	alter :: t a -> t a -> t a-	alter f g = f <+> g

@@ -1,51 +0,0 @@-module Pandora.Pattern.Functor.Applicative where--import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$)), Covariant_)-import Pandora.Pattern.Functor.Bivariant (Bivariant)--infixl 4 <*>, <*, *>-infixl 3 <**>-infixl 2 <***>-infixl 1 <****>--{- |-> When providing a new instance, you should ensure it satisfies:-> * Interpreted: (.) <$> u <*> v <*> w ≡ u <*> (v <*> w)-> * Left interchange: x <*> (f <$> y) ≡ (. f) <$> x <*> y-> * Right interchange: f <$> (x <*> y) ≡ (f .) <$> x <*> y--}--class Covariant t => Applicative t where-	{-# MINIMAL (<*>) #-}-	-- | Infix version of 'apply'-	(<*>) :: t (a -> b) -> t a -> t b-	-- | Prefix version of '<*>'-	apply :: t (a -> b) -> t a -> t b-	apply f x = f <*> x-	-- | Sequence actions, discarding the value of the first argument-	(*>) :: t a -> t b -> t b-	x *> y = ((\z -> z) <$ x) <*> y-	-- | Sequence actions, discarding the value of the second argument-	(<*) :: t a -> t b -> t a-	x <* y = y *> x-	-- | Repeat an action indefinitely-	forever :: t a -> t b-	forever x = x *> forever x-	-- | Flipped version of '<*>'-	(<%>) :: t a -> t (a -> b) -> t b-	x <%> f = (\x' f' -> f' x') <$> x <*> f-	-- | Infix versions of `apply` with various nesting levels-	(<**>) :: Applicative u => t :. u := (a -> b) -> t :. u := a -> t :. u := b-	f <**> x = (<*>) <$> f <*> x-	(<***>) :: (Applicative u, Applicative v) => t :. u :. v := (a -> b)-		-> t :. u :. v := a -> t :. u :. v := b-	f <***> x = (<**>) <$> f <*> x-	(<****>) :: (Applicative u, Applicative v, Applicative w)-		=> t :. u :. v :. w := (a -> b)-		-> t :. u :. v :. w := a-		-> t :. u :. v :. w := b-	f <****> x = (<***>) <$> f <*> x--class (Covariant_ t source target, Bivariant v source source target) => Semimonoidal t v source target where-	multiply :: source (v a b) r -> target (v (t a) (t b)) (t r)

@@ -1,13 +0,0 @@-module Pandora.Pattern.Functor.Avoidable where--import Pandora.Pattern.Functor.Alternative (Alternative)--{- |-> When providing a new instance, you should ensure it satisfies:-> * Left absorption: x <+> empty ≡ x-> * Right absorption: empty <+> x ≡ x--}--class Alternative t => Avoidable t where-	{-# MINIMAL empty #-}-	empty :: t a

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Bindable where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  infixr 1 =<< @@ -9,5 +9,5 @@ > * Interchange: t >>= f = join (f <$> t) -} -class Covariant_ t source source => Bindable t source where+class Covariant t source source => Bindable t source where 	(=<<) :: source a (t b) -> source (t a) (t b)

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Bivariant where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Paradigm.Primary.Transformer.Flip (Flip)  infixl 4 <->@@ -11,6 +11,6 @@ > * Parametricity: (f . g) <-> (h . i) ≡ f <-> h . g <-> i -} -class (forall i . Covariant_ (v i) left target, forall i . Covariant_ (Flip v i) right target)+class (forall i . Covariant (v i) left target, forall i . Covariant (Flip v i) right target) 	=> Bivariant v left right target where 	(<->) :: left a b -> right c d -> target (v a c) (v b d) 

@@ -1,56 +1,15 @@ module Pandora.Pattern.Functor.Contravariant where -import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Category (Category) -infixl 4 >$<, ->$<-, $<, >$+infixl 4 ->$<- +-- TODO: use ->$<- instead of contramap here {- | > When providing a new instance, you should ensure it satisfies: > * Identity morphism: contramap identity ≡ identity > * Interpreted of morphisms: contramap f . contramap g ≡ contramap (g . f) -} -class Contravariant (t :: * -> *) where-	{-# MINIMAL (>$<) #-}-	-- | Infix version of 'contramap'-	(>$<) :: (a -> b) -> t b -> t a--	-- | Prefix version of '>$<'-	contramap :: (a -> b) -> t b -> t a-	contramap f x = f >$< x-	-- | Replace all locations in the output with the same value-	(>$) :: b -> t b -> t a-	x >$ z = (\_ -> x) >$< z-	-- | Flipped version of '>$'-	($<) :: t b -> b -> t a-	x $< v = v >$ x-	-- | Fill the input of evaluation-	full :: t () -> t a-	full x = () >$ x-	-- | Flipped infix version of 'contramap'-	(>&<) :: t b -> (a -> b) -> t a-	x >&< f = f >$< x--	-- | Infix versions of `contramap` with various nesting levels-	(>$$<) :: Contravariant u => (a -> b) -> t :. u := a -> t :. u := b-	f >$$< x = ((f >$<) >$<) x-	(>$$$<) :: (Contravariant u, Contravariant v)-		=> (a -> b) -> t :. u :. v := b -> t :. u :. v := a-	f >$$$< x = (((f >$<) >$<) >$<) x-	(>$$$$<) :: (Contravariant u, Contravariant v, Contravariant w)-		=> (a -> b) -> t :. u :. v :. w := a -> t :. u :. v :. w := b-	f >$$$$< x = ((((f >$<) >$<) >$<) >$<) x--	-- | Infix flipped versions of `contramap` with various nesting levels-	(>&&<) :: Contravariant u => t :. u := a -> (a -> b) -> t :. u := b-	x >&&< f = f >$$< x-	(>&&&<) :: (Contravariant u, Contravariant v)-		=> t :. u :. v := b -> (a -> b) -> t :. u :. v := a-	x >&&&< f = f >$$$< x-	(>&&&&<) :: (Contravariant u, Contravariant v, Contravariant w)-		=> t :. u :. v :. w := a -> (a -> b) -> t :. u :. v :. w := b-	x >&&&&< f = f >$$$$< x--class (Category source, Category target) => Contravariant_ t source target where+class (Category source, Category target) => Contravariant t source target where 	(->$<-) :: source a b -> target (t b) (t a)

@@ -1,121 +1,44 @@ module Pandora.Pattern.Functor.Covariant where -import Pandora.Core.Functor (type (:.), type (:=), type (<:=))-import Pandora.Pattern.Category (Category ((.)))--infixl 4 <$>, -<$>-, <$, $>-infixl 3 <$$>, -<<$$>-, -<$$>>--infixl 2 <$$$>-infixl 1 <$$$$>--infixl 1 <&>-infixl 2 <&&>-infixl 3 <&&&>-infixl 4 <&&&&>+import Pandora.Pattern.Semigroupoid (Semigroupoid) -infixr 7 .#.., .#..., .#....+infixl 4 -<$>-+infixl 3 -<<$$>-, -<$$>>- +-- TODO: use -<$>- instead of comap here {- | > When providing a new instance, you should ensure it satisfies: > * Identity morphism: comap identity ≡ identity > * Interpreted of morphisms: comap (f . g) ≡ comap f . comap g -} -class Covariant (t :: * -> *) where-	{-# MINIMAL (<$>) #-}-	-- | Infix version of 'comap'-	(<$>) :: (a -> b) -> t a -> t b--	-- | Prefix version of '<$>'-	comap :: (a -> b) -> t a -> t b-	comap f x = f <$> x-	-- | Replace all locations in the input with the same value-	(<$) :: a -> t b -> t a-	x <$ z = (\_-> x) <$> z-	-- | Flipped version of '<$'-	($>) :: t a -> b -> t b-	x $> v = v <$ x-	-- | Discards the result of evaluation-	void :: t a -> t ()-	void x = () <$ x-	-- | Computing a value from a structure of values-	loeb :: t (a <:= t) -> t a-	loeb tt = let fix f = let x = f x in x in fix (\f -> (\g -> g f) <$> tt)-	-- | Flipped infix version of 'comap'-	(<&>) :: t a -> (a -> b) -> t b-	x <&> f = f <$> x--	-- | Infix versions of `comap` with various nesting levels-	(<$$>) :: Covariant u => (a -> b) -> t :. u := a -> t :. u := b-	f <$$> x = ((f <$>) <$>) x-	(<$$$>) :: (Covariant u, Covariant v)-		=> (a -> b) -> t :. u :. v := a -> t :. u :. v := b-	f <$$$> x = (((f <$>) <$>) <$>) x-	(<$$$$>) :: (Covariant u, Covariant v, Covariant w)-		=> (a -> b) -> t :. u :. v :. w := a -> t :. u :. v :. w := b-	f <$$$$> x = ((((f <$>) <$>) <$>) <$>) x--	-- | Infix flipped versions of `comap` with various nesting levels-	(<&&>) :: Covariant u => t :. u := a -> (a -> b) -> t :. u := b-	x <&&> f = f <$$> x-	(<&&&>) :: (Covariant u, Covariant v)-		=> t :. u :. v := a -> (a -> b) -> t :. u :. v := b-	x <&&&> f = f <$$$> x-	(<&&&&>) :: (Covariant u, Covariant v, Covariant w)-		=> t :. u :. v :. w := a -> (a -> b) -> t :. u :. v :. w := b-	x <&&&&> f = f <$$$$> x--	(.#..) :: (t ~ v a, Category v)-		=> v c d -> v a :. v b := c -> v a :. v b := d-	f .#.. g = (f .) <$> g--	(.#...) :: (t ~ v a, t ~ v b, Category v, Covariant (v a), Covariant (v b))-		=> v d e -> v a :. v b :. v c := d -> v a :. v b :. v c := e-	f .#... g = (f .) <$$> g--	(.#....) :: (t ~ v a, t ~ v b, t ~ v c, Category v, Covariant (v a), Covariant (v b), Covariant (v c))-		=> v e f -> v a :. v b :. v c :. v d := e -> v a :. v b :. v c :. v d := f-	f .#.... g = (f .) <$$$> g--	(<$$) :: Covariant u => b -> t :. u := a -> t :. u := b-	x <$$ s = (\_-> x) <$$> s--	(<$$$) :: (Covariant u, Covariant v) => b -> t :. u :. v := a -> t :. u :. v := b-	x <$$$ s = (\_-> x) <$$$> s--	(<$$$$) :: (Covariant u, Covariant v, Covariant w) => b -> t :. u :. v :. w := a -> t :. u :. v :. w := b-	x <$$$$ s = (\_-> x) <$$$$> s--	($$>) :: Covariant u => t :. u := a -> b -> t :. u := b-	s $$> x = (\_-> x) <$$> s--	($$$>) :: (Covariant u, Covariant v) => t :. u :. v := a -> b -> t :. u :. v := b-	s $$$> x = (\_-> x) <$$$> s--	($$$$>) :: (Covariant u, Covariant v, Covariant w) => t :. u :. v :. w := a -> b -> t :. u :. v :. w := b-	s $$$$> x = (\_-> x) <$$$$> s--class (Category source, Category target) => Covariant_ t source target where+class (Semigroupoid source, Semigroupoid target) => Covariant t source target where 	(-<$>-) :: source a b -> target (t a) (t b) 	 (-<$$>-) :: forall t u category a b -	. (Covariant_ u category category, Covariant_ t category category) +	. (Covariant u category category, Covariant t category category)  	=> category a b -> category (t (u a)) (t (u b)) (-<$$>-) s = ((-<$>-) ((-<$>-) @u @category @category s))  (-<<$$>-) :: forall t u source target a b -	. (Covariant_ u source source, Covariant_ t source target) +	. (Covariant u source source, Covariant t source target)  	=> source a b -> target (t (u a)) (t (u b)) (-<<$$>-) s = ((-<$>-) ((-<$>-) @u @source @source s))  (-<$$>>-) :: forall t u source target a b -	. (Covariant_ u source target, Covariant_ t target target) +	. (Covariant u source target, Covariant t target target)  	=> source a b -> target (t (u a)) (t (u b)) (-<$$>>-) s = ((-<$>-) ((-<$>-) @u @source @target s))  -- TODO: Figure out how to work with hidden type variables -- to put intermediate category `between`-(-<$$$>-) :: forall t u v source target a b-	. (Covariant_ u source source, Covariant_ t source target, Covariant_ v target target) -	=> source a b -> target (v (t (u a))) (v (t (u b)))-(-<$$$>-) s = ((-<$>-) ((-<$>-) @t @source @target ((-<$>-) @u @source @source s)))++(-<$$$>-) :: forall t u v category a b+	. (Covariant t category category, Covariant u category category, Covariant v category category) +	=> category a b -> category (t (u (v a))) (t (u (v b)))+(-<$$$>-) s = ((-<$>-) @t @category @category ((-<$>-) @u @category @category ((-<$>-) @v @category @category s)))++(-<$$$$>-) :: forall t u v w category a b+	. (Covariant t category category, Covariant u category category, Covariant v category category, Covariant w category category) +	=> category a b -> category (t (u (v (w a)))) (t (u (v (w b))))+(-<$$$$>-) s = ((-<$>-) @t @category @category ((-<$>-) @u @category @category ((-<$>-) @v @category @category ((-<$>-) @w @category @category s))))

@@ -1,7 +0,0 @@-module Pandora.Pattern.Functor.Determinable where--import Pandora.Pattern.Functor.Contravariant (Contravariant)--class Contravariant t => Determinable t where-	{-# MINIMAL determine #-}-	determine :: t a

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Distributive where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  {- | > Let f :: Distributive g => (a -> g b)@@ -12,5 +12,5 @@  infixl 5 -<< -class Covariant_ t source target => Distributive t source target where-	(-<<) :: Covariant_ u source target => source a (t b) -> target (u a) (t (u b))+class Covariant t source target => Distributive t source target where+	(-<<) :: Covariant u source target => source a (t b) -> target (u a) (t (u b))

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Divariant 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.Paradigm.Primary.Transformer.Flip (Flip)  infixl 4 >->@@ -12,13 +12,6 @@ > * Interpreted: f . g >-> h . i ≡ g >-> h . f >-> i -} ---class (forall i . Covariant (v i)) => Divariant (v :: * -> * -> *) where---	{-# MINIMAL (>->) #-}---	(>->) :: (a -> b) -> (c -> d) -> v b c -> v a d---	-- | Prefix version of '>->'---	dimap :: (a -> b) -> (c -> d) -> v b c -> v a d---	dimap f g x = (f >-> g) x--class (forall i . Contravariant_ (Flip v i) left target, forall i . Covariant_ (v i) right target) +class (forall i . Contravariant (Flip v i) left target, forall i . Covariant (v i) right target)  	=> Divariant v left right target where 	(>->) :: left a b -> right c d -> target (v b c) (v a d)

@@ -1,14 +0,0 @@-module Pandora.Pattern.Functor.Divisible where--import Pandora.Pattern.Functor.Contravariant (Contravariant)-import Pandora.Pattern.Functor.Bivariant (Bivariant)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))--infixr 5 >*<--class Contravariant t => Divisible t where-	{-# MINIMAL (>*<) #-}-	(>*<) :: t b -> t c -> t (b :*: c)--class Bivariant v source source target => Divisible_ t v source target where-	divide :: source r (v a b) -> target (v (t a) (t b)) (t r)

@@ -1,7 +1,6 @@ module Pandora.Pattern.Functor.Extendable where -import Pandora.Core.Functor (type (:.), type (:=))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  infixr 1 <<= @@ -11,5 +10,5 @@ > * Extension interchange: (f <<=) ≡ (f -<$>-) . (identity <<=) -} -class Covariant_ t source source => Extendable t source where+class Covariant t source source => Extendable t source where 	(<<=) :: source (t a) b -> source (t a) (t b)

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Extractable where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant) -class Covariant_ t source source => Extractable t source where+class Covariant t source source => Extractable t source where 	{-# MINIMAL extract #-} 	extract :: source (t a) a

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Monad where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Bindable (Bindable) import Pandora.Pattern.Functor.Pointable (Pointable) @@ -18,7 +18,7 @@ --infixl 1 >>=-, ->>= --infixr 1 -=<<, =<<- -class (Covariant_ t (->) (->), Pointable t (->), Bindable t (->)) => Monad t where+class (Covariant t (->) (->), Pointable t (->), Bindable t (->)) => Monad t where 	--(>>=-) :: t a -> t b -> t a 	--(>>=-) x y = x >>= \r -> y >>= \_ -> point r 	--(->>=) :: t a -> t b -> t b

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Pointable where -import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant) -class Covariant_ t source source => Pointable t source where+class Covariant t source source => Pointable t source where 	{-# MINIMAL point #-} 	point :: source a (t a)

@@ -0,0 +1,6 @@+module Pandora.Pattern.Functor.Semimonoidal where++import Pandora.Pattern.Semigroupoid (Semigroupoid)++class Semigroupoid p => Semimonoidal t p source target where+	multiply_ :: p (source (t a) (t b)) (t (target a b))

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Traversable where -import Pandora.Pattern.Functor.Covariant (Covariant_)-import Pandora.Pattern.Functor.Applicative (Semimonoidal)+import Pandora.Pattern.Functor.Covariant (Covariant)+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal) import Pandora.Pattern.Functor.Pointable (Pointable) import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)) @@ -18,10 +18,10 @@  infixl 5 <<-, -<<-<<- -class Covariant_ t source target => Traversable t source target where-	(<<-) :: (Covariant_ u source target, Pointable u target, Semimonoidal u (:*:) source target) => source a (u b) -> target (t a) (u (t b))+class Covariant t source target => Traversable t source target where+	(<<-) :: (Covariant u source target, Pointable u target, Semimonoidal u target (:*:) (:*:)) => source a (u b) -> target (t a) (u (t b)) -(-<<-<<-) :: forall t u v category a b . -	(Traversable t category category, Covariant_ u category category, Pointable u category, Semimonoidal u (:*:) category category, Traversable v category category)+(-<<-<<-) :: forall t u v category a b .+	(Traversable t category category, Covariant u category category, Pointable u category, Semimonoidal u category (:*:) (:*:), Traversable v category category) 	=> category a (u b) -> category (v (t a)) (u (v (t b))) (-<<-<<-) f = ((<<-) ((<<-) @t @category @category f))

@@ -0,0 +1,11 @@+module Pandora.Pattern.Semigroupoid where++infixr 9 .++{- |+> When providing a new instance, you should ensure it satisfies:+> * Associativity: f . (g . h) ≡ (f . g) . h+-}++class Semigroupoid (m :: * -> * -> *) where+	(.) :: m b c -> m a b -> m a c

@@ -1,7 +1,7 @@ module Pandora.Pattern.Transformer.Hoistable (Hoistable (..)) where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  {- | > When providing a new instance, you should ensure it satisfies one law:@@ -13,7 +13,7 @@  class Hoistable t where 	{-# MINIMAL (/|\) #-}-	(/|\) :: (Covariant_ u (->) (->)) => u ~> v -> t u ~> t v+	(/|\) :: (Covariant u (->) (->)) => u ~> v -> t u ~> t v -	hoist :: (Covariant_ u (->) (->)) => u ~> v -> t u ~> t v+	hoist :: (Covariant u (->) (->)) => u ~> v -> t u ~> t v 	hoist = (/|\)

@@ -1,7 +1,7 @@ module Pandora.Pattern.Transformer.Liftable (Liftable (..)) where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  {- | > When providing a new instance, you should ensure it satisfies one law:@@ -9,4 +9,4 @@ -}  class Liftable t where-	lift :: (Covariant_ u (->) (->)) => u ~> t u+	lift :: (Covariant u (->) (->)) => u ~> t u

@@ -1,7 +1,7 @@ module Pandora.Pattern.Transformer.Lowerable (Lowerable (..)) where  import Pandora.Core.Functor (type (~>))-import Pandora.Pattern.Functor.Covariant (Covariant_)+import Pandora.Pattern.Functor.Covariant (Covariant)  {- | > When providing a new instance, you should ensure it satisfies one law:@@ -9,4 +9,4 @@ -}  class Lowerable t where-	lower :: (Covariant_ u (->) (->)) => t u ~> u+	lower :: (Covariant u (->) (->)) => t u ~> u

@@ -1,5 +1,5 @@ name:                pandora-version:             0.4.4+version:             0.4.5 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@@ -31,6 +31,7 @@     Pandora.Paradigm.Primary.Algebraic     Pandora.Paradigm.Primary.Algebraic.Exponential     Pandora.Paradigm.Primary.Algebraic.Product+    Pandora.Paradigm.Primary.Algebraic.Sum     Pandora.Paradigm.Primary.Object.Boolean     Pandora.Paradigm.Primary.Object.Ordering     Pandora.Paradigm.Primary.Object.Numerator@@ -129,21 +130,18 @@     Pandora.Paradigm.Primary.Linear.Matrix      Pandora.Pattern-    -- Category typeclass+	-- Algebra typeclasses+    Pandora.Pattern.Semigroupoid     Pandora.Pattern.Category     -- Functor typeclassess     Pandora.Pattern.Functor     Pandora.Pattern.Functor.Adjoint-    Pandora.Pattern.Functor.Alternative-    Pandora.Pattern.Functor.Applicative+    Pandora.Pattern.Functor.Semimonoidal     Pandora.Pattern.Functor.Bindable     Pandora.Pattern.Functor.Comonad     Pandora.Pattern.Functor.Contravariant     Pandora.Pattern.Functor.Covariant-    Pandora.Pattern.Functor.Determinable     Pandora.Pattern.Functor.Distributive-    Pandora.Pattern.Functor.Avoidable-    Pandora.Pattern.Functor.Divisible     Pandora.Pattern.Functor.Extendable     Pandora.Pattern.Functor.Extractable     Pandora.Pattern.Functor.Invariant