pandora 0.5.2 → 0.5.3

raw patch · 100 files changed

+1355/−1365 lines, 100 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• CHANGELOG.md +15/−1
• Pandora/Paradigm.hs +1/−0
• Pandora/Paradigm/Algebraic.hs +84/−0
• Pandora/Paradigm/Algebraic/Exponential.hs +69/−0
• Pandora/Paradigm/Algebraic/Functor.hs +141/−0
• Pandora/Paradigm/Algebraic/One.hs +3/−0
• Pandora/Paradigm/Algebraic/Product.hs +74/−0
• Pandora/Paradigm/Algebraic/Sum.hs +35/−0
• Pandora/Paradigm/Algebraic/Zero.hs +8/−0
• Pandora/Paradigm/Controlflow/Effect.hs +0/−1
• Pandora/Paradigm/Controlflow/Effect/Adaptable.hs +3/−3
• Pandora/Paradigm/Controlflow/Effect/Conditional.hs +0/−24
• Pandora/Paradigm/Controlflow/Effect/Interpreted.hs +10/−12
• Pandora/Paradigm/Controlflow/Effect/Transformer/Comonadic.hs +8/−8
• Pandora/Paradigm/Controlflow/Effect/Transformer/Monadic.hs +9/−9
• Pandora/Paradigm/Controlflow/Observable.hs +1/−1
• Pandora/Paradigm/Controlflow/Pipeline.hs +3/−3
• Pandora/Paradigm/Inventory.hs +5/−5
• Pandora/Paradigm/Inventory/Some/Accumulator.hs +5/−5
• Pandora/Paradigm/Inventory/Some/Equipment.hs +9/−9
• Pandora/Paradigm/Inventory/Some/Imprint.hs +4/−4
• Pandora/Paradigm/Inventory/Some/Optics.hs +8/−8
• Pandora/Paradigm/Inventory/Some/Provision.hs +9/−9
• Pandora/Paradigm/Inventory/Some/State.hs +15/−15
• Pandora/Paradigm/Inventory/Some/Store.hs +6/−6
• Pandora/Paradigm/Primary.hs +4/−96
• Pandora/Paradigm/Primary/Algebraic.hs +0/−73
• Pandora/Paradigm/Primary/Algebraic/Exponential.hs +0/−69
• Pandora/Paradigm/Primary/Algebraic/Functor.hs +0/−143
• Pandora/Paradigm/Primary/Algebraic/One.hs +0/−3
• Pandora/Paradigm/Primary/Algebraic/Product.hs +0/−69
• Pandora/Paradigm/Primary/Algebraic/Sum.hs +0/−35
• Pandora/Paradigm/Primary/Algebraic/Zero.hs +0/−8
• Pandora/Paradigm/Primary/Functor/Conclusion.hs +6/−6
• Pandora/Paradigm/Primary/Functor/Constant.hs +1/−1
• Pandora/Paradigm/Primary/Functor/Convergence.hs +3/−3
• Pandora/Paradigm/Primary/Functor/Edges.hs +2/−2
• Pandora/Paradigm/Primary/Functor/Endo.hs +3/−3
• Pandora/Paradigm/Primary/Functor/Exactly.hs +6/−6
• Pandora/Paradigm/Primary/Functor/Fix.hs +1/−1
• Pandora/Paradigm/Primary/Functor/Maybe.hs +5/−5
• Pandora/Paradigm/Primary/Functor/Predicate.hs +3/−3
• Pandora/Paradigm/Primary/Functor/Proxy.hs +1/−1
• Pandora/Paradigm/Primary/Functor/Tagged.hs +6/−6
• Pandora/Paradigm/Primary/Functor/These.hs +2/−2
• Pandora/Paradigm/Primary/Functor/Validation.hs +5/−5
• Pandora/Paradigm/Primary/Functor/Wedge.hs +2/−2
• Pandora/Paradigm/Primary/Functor/Wye.hs +2/−2
• Pandora/Paradigm/Primary/Linear/Vector.hs +1/−1
• Pandora/Paradigm/Primary/Transformer/Backwards.hs +10/−10
• Pandora/Paradigm/Primary/Transformer/Construction.hs +21/−23
• Pandora/Paradigm/Primary/Transformer/Continuation.hs +3/−3
• Pandora/Paradigm/Primary/Transformer/Day.hs +1/−1
• Pandora/Paradigm/Primary/Transformer/Instruction.hs +11/−11
• Pandora/Paradigm/Primary/Transformer/Jack.hs +7/−7
• Pandora/Paradigm/Primary/Transformer/Jet.hs +6/−4
• Pandora/Paradigm/Primary/Transformer/Outline.hs +3/−3
• Pandora/Paradigm/Primary/Transformer/Reverse.hs +15/−8
• Pandora/Paradigm/Primary/Transformer/Tap.hs +11/−35
• Pandora/Paradigm/Primary/Transformer/Yoneda.hs +1/−1
• Pandora/Paradigm/Schemes.hs +11/−12
• Pandora/Paradigm/Schemes/TT.hs +12/−12
• Pandora/Paradigm/Schemes/TU.hs +13/−13
• Pandora/Paradigm/Schemes/TUT.hs +11/−11
• Pandora/Paradigm/Schemes/UT.hs +10/−10
• Pandora/Paradigm/Structure.hs +87/−11
• Pandora/Paradigm/Structure/Ability.hs +0/−1
• Pandora/Paradigm/Structure/Ability/Monotonic.hs +1/−1
• Pandora/Paradigm/Structure/Ability/Morphable.hs +4/−3
• Pandora/Paradigm/Structure/Ability/Substructure.hs +34/−23
• Pandora/Paradigm/Structure/Ability/Zipper.hs +0/−107
• Pandora/Paradigm/Structure/Interface.hs +1/−0
• Pandora/Paradigm/Structure/Interface/Set.hs +5/−5
• Pandora/Paradigm/Structure/Interface/Stack.hs +1/−0
• Pandora/Paradigm/Structure/Interface/Zipper.hs +55/−0
• Pandora/Paradigm/Structure/Modification.hs +1/−0
• Pandora/Paradigm/Structure/Modification/Comprehension.hs +7/−7
• Pandora/Paradigm/Structure/Modification/Prefixed.hs +4/−4
• Pandora/Paradigm/Structure/Modification/Tape.hs +78/−0
• Pandora/Paradigm/Structure/Modification/Turnover.hs +2/−2
• Pandora/Paradigm/Structure/Some/Binary.hs +55/−83
• Pandora/Paradigm/Structure/Some/List.hs +39/−47
• Pandora/Paradigm/Structure/Some/Rose.hs +92/−42
• Pandora/Paradigm/Structure/Some/Splay.hs +38/−48
• Pandora/Paradigm/Structure/Some/Stream.hs +7/−6
• Pandora/Pattern/Category.hs +16/−20
• Pandora/Pattern/Functor/Adjoint.hs +23/−26
• Pandora/Pattern/Functor/Bindable.hs +8/−13
• Pandora/Pattern/Functor/Comonad.hs +2/−2
• Pandora/Pattern/Functor/Contravariant.hs +6/−8
• Pandora/Pattern/Functor/Covariant.hs +7/−9
• Pandora/Pattern/Functor/Distributive.hs +9/−13
• Pandora/Pattern/Functor/Extendable.hs +9/−12
• Pandora/Pattern/Functor/Invariant.hs +1/−1
• Pandora/Pattern/Functor/Monad.hs +1/−1
• Pandora/Pattern/Functor/Representable.hs +1/−1
• Pandora/Pattern/Functor/Traversable.hs +17/−20
• Pandora/Pattern/Object/Chain.hs +3/−1
• Pandora/Pattern/Object/Setoid.hs +3/−3
• pandora.cabal +14/−13

@@ -712,7 +712,7 @@ * Define `<-||-` length encoding operators in `Algebraic` module * Define `>-||-` length encoding operators in `Algebraic` module * Define `Horizontal` type and use it in binary tree zipper-* Define `?==` operator as replacemet for if statement+* Define `?=` operator as replacemet for if statement * Define `<:*:>`, `>:*:>`, `<:*:<`, `>:*:<` type synonyms * Define `<:+:>`, `>:+:>`, `<:+:<`, `>:+:<` type synonyms * Define `Functor` module in `Algebraic`@@ -720,3 +720,17 @@ * Change `Zipper` definition - tag it  # 0.5.3+* Move `Algebraic` module from `Primary` to `Paradigm`+* Define `<:*:>` infix operator+* Rename `Tail` constructor of `Segment` to `Rest`+* Remove 'twosome' in favor `<:*:>`+* Rename `?==` operator to `?=`+* Remove `Conditional` module+* Change operators' precedence, length of operators define precedence+* Remove `leaf`, `left`, `right`, `both` in `Binary` module+* Define `Zipper` instance of `Nonempty Rose` tree+* Change `Zipper` definition - add `structure` in tag+* Define `Roses` type synonymous+* Move `Tape` to `Structure.Modification.Tape` module++# 0.5.4

@@ -4,4 +4,5 @@ import Pandora.Paradigm.Inventory as Exports import Pandora.Paradigm.Controlflow as Exports import Pandora.Paradigm.Primary as Exports+import Pandora.Paradigm.Algebraic as Exports import Pandora.Paradigm.Schemes as Exports

@@ -0,0 +1,84 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+module Pandora.Paradigm.Algebraic (module Exports) where++import Pandora.Paradigm.Algebraic.Functor as Exports+import Pandora.Paradigm.Algebraic.Exponential as Exports+import Pandora.Paradigm.Algebraic.Product as Exports+import Pandora.Paradigm.Algebraic.Sum as Exports+import Pandora.Paradigm.Algebraic.Zero as Exports+import Pandora.Paradigm.Algebraic.One as Exports++import Pandora.Core.Functor (type (>))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((<--), (<---), identity)+import Pandora.Pattern.Kernel (constant)+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))+import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))+import Pandora.Pattern.Functor.Comonad (Comonad)+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))+import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted ((<~)))++instance (Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:*:> u) where+	mult = Flip <-- \(T_U lrxys) ->+		-- TODO: I need matrix transposing here+		let ((lxs :*: lys) :*: (rxs :*: rys)) = (mult @(<--) <~) <-||-- (mult @(<--) <~) <-|- lrxys in+		T_U (lxs :*: rxs) :*: T_U (lys :*: rys)++instance (Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <:*:> u) where+	mult = Straight <-- \(T_U (xls :*: xrs) :*: T_U (yls :*: yrs)) -> T_U <--- (mult @(-->) <~) (xls :*: yls) :*: (mult @(-->) <~) (xrs :*: yrs)++instance (Semimonoidal (-->) (:*:) (:+:) t, Semimonoidal (-->) (:*:) (:+:) u) => Semimonoidal (-->) (:*:) (:+:) (t <:*:> u) where+	mult = Straight <-- \(T_U (xls :*: xrs) :*: T_U (yls :*: yrs)) ->+		(mult @(-->) @(:*:) @(:+:) <~ (xls :*: yls)) <:*:> (mult @(-->) @(:*:) @(:+:) <~ (xrs :*: yrs))++instance (Monoidal (-->) (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) u)+	=> Monoidal (-->) (-->) (:*:) (:+:) (t <:*:> u) where+		unit _ = Straight <-- \_ -> empty <:*:> empty++instance Traversable (->) (->) ((:*:) s) where+	f <<- x = (attached x :*:) <-|- f (extract x)++instance Semimonoidal (-->) (:*:) (:*:) ((->) e) where+	mult :: ((e -> a) :*: (e -> b)) --> (e -> (a :*: b))+	mult = Straight <-- \(g :*: h) -> \x -> g x :*: h x++instance Monoidal (-->) (-->) (:*:) (:*:) ((->) e) where+	unit _ = Straight <-- constant . (<~ One)++instance Semimonoidal (<--) (:*:) (:*:) ((->) e) where+	mult :: ((e -> a) :*: (e -> b)) <-- (e -> a :*: b)+	mult = Flip <-- \f -> attached . f :*: extract . f++instance Semimonoidal (-->) (:*:) (:+:) ((:+:) e) where+	mult :: ((e :+: a) :*: (e :+: b)) --> (e :+: a :+: b)+	mult = Straight <-- \case+		Option _ :*: Option e' -> Option e'+		Option _ :*: Adoption y -> Adoption <-- Adoption y+		Adoption x :*: _ -> Adoption <-- Option x++instance Semimonoidal (-->) (:*:) (:*:) ((:+:) e) where+	mult = Straight <-- \case+		Adoption x :*: Adoption y -> Adoption <--- x :*: y+		Option e :*: _ -> Option e+		_ :*: Option e -> Option e++instance Monoidal (-->) (-->) (:*:) (:*:) ((:+:) e) where+	unit _ = Straight <-- Adoption . (<~ One)++instance Semimonoidal (<--) (:*:) (:*:) ((:*:) s) where+	mult = Flip <-- \(s :*: x :*: y) -> (s :*: x) :*: (s :*: y)++instance Monoidal (<--) (-->) (:*:) (:*:) ((:*:) s) where+	unit _ = Flip <-- \(_ :*: x) -> Straight (\_ -> x)++instance Comonad (->) ((:*:) s) where++instance Semimonoidal (<--) (:*:) (:*:) (Flip (:*:) a) where+	mult = Flip <-- \(Flip ((sx :*: sy) :*: r)) -> Flip (sx :*: r) :*: Flip (sy :*: r)++instance Monoidal (<--) (-->) (:*:) (:*:) (Flip (:*:) a) where+	unit _ = Flip <-- \(Flip (s :*: _)) -> Straight (\_ -> s)

@@ -0,0 +1,69 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+module Pandora.Paradigm.Algebraic.Exponential where++import Pandora.Pattern.Betwixt (Betwixt)+import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))+import Pandora.Pattern.Category (Category ((<--), identity))+import Pandora.Pattern.Kernel (Kernel (constant))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))+import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))+import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))+import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))+import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))++infixr 7 .:..+infixr 9 %+infixl 1 &++type instance Betwixt (->) (->) = (->)++instance Semigroupoid (->) where+	f . g = \x -> f (g x)++instance Category (->) where+	identity x = x++instance Kernel (->) where+	constant x _ = x++instance Covariant (->) (->) ((->) a) where+	(<-|-) = (.)++instance Distributive (->) (->) ((->) e) where+	f -<< g = \e -> f % e <-|- g++instance Bindable (->) ((->) e) where+	f =<< g = \x -> f <-- g x <-- x++instance Semigroup r => Semigroup (e -> r) where+	f + g = \e -> f e + g e++instance Ringoid r => Ringoid (e -> r) where+	f * g = \e -> f e * g e++type (<--) = Flip (->)++instance Contravariant (->) (->) ((<--) a) where+	f >-|- Flip g = Flip <-- g . f++type (-->) = Straight (->)++instance Covariant (->) (->) ((-->) b) where+	f <-|- Straight g = Straight <-- f . g++(.:..) :: (Covariant (->) target (v a), Semigroupoid v) => v c d -> target (v a (v b c)) (v a (v b d))+(.:..) f = (<-|-) (f .)++{-# INLINE (%) #-}+(%) :: (a -> b -> c) -> b -> a -> c+(%) f x y = f y x++{-# INLINE (&) #-}+(&) :: a -> (a -> b) -> b+x & f = f x++fix :: (a -> a) -> a+fix f = let x = f x in x

@@ -0,0 +1,141 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+module Pandora.Paradigm.Algebraic.Functor where++import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((<--))+import Pandora.Pattern.Kernel (constant)+import Pandora.Pattern.Morphism.Flip (Flip)+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|---), (<-|-|-)))+import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))+import Pandora.Pattern.Functor.Monoidal (Monoidal (unit), Unit)+import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-)))+import Pandora.Paradigm.Algebraic.Exponential (type (-->), type (<--), (&))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption))+import Pandora.Paradigm.Algebraic.Zero (Zero, absurd)+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Primary.Functor.Proxy (Proxy (Proxy))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted ((<~), (<~~~), (-#=)))++infixl 1 <-*------, .-*------, <-||-----, >-||-----+infixl 2 <-*-----, .-*-----, <-||----, >-||----+infixl 3 <-*----, .-*----, <-||---, >-||---+infixl 4 <-*---, .-*---, <-*-*-, <-||--, >-||--+infixl 5 <-*--, .-*--, .-*-*-, <-||-, >-||-+infixl 6 <-*-, .-*-, <-+-, .-+-++infixl 6 <-|-<-|-, <-|->-|-, >-|-<-|-, >-|->-|-++type instance Unit (:*:) = One+type instance Unit (:+:) = Zero++type Applicative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Monoidal (-->) (-->) (:*:) (:*:) t)+type Alternative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) t)+type Divisible t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Monoidal (-->) (<--) (:*:) (:*:) t)+type Decidable t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:+:) t, Monoidal (-->) (<--) (:*:) (:+:) t)++instance Adjoint (->) (->) ((:*:) s) ((->) s) where+	(-|) :: ((s :*: a) -> b) -> a -> (s -> b)+	f -| x = \s -> f (s :*: x)+	(|-) :: (a -> s -> b) -> (s :*: a) -> b+	f |- ~(s :*: x) = f x s++(<-*--------), (<-*-------), (<-*------), (<-*-----), (<-*----), (<-*---), (<-*--), (<-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b+f <-*-------- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*------- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*------ x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*----- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*---- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*--- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*-- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x+f <-*- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x++(.-*--------), (.-*-------), (.-*------), (.-*-----), (.-*----), (.-*---), (.-*--), (.-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b+y .-*-------- x = (\_ y' -> y') <-|- x <-*- y+y .-*------- x = (\_ y' -> y') <-|- x <-*- y+y .-*------ x = (\_ y' -> y') <-|- x <-*- y+y .-*----- x = (\_ y' -> y') <-|- x <-*- y+y .-*---- x = (\_ y' -> y') <-|- x <-*- y+y .-*--- x = (\_ y' -> y') <-|- x <-*- y+y .-*-- x = (\_ y' -> y') <-|- x <-*- y+y .-*- x = (\_ y' -> y') <-|- x <-*- y++(<-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u (a -> b)) -> t (u a) -> t (u b)+f <-*-*- x = (<-*-) <-|- f <-*- x++(.-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u b) -> t (u a) -> t (u b)+y .-*-*- x = (\_ y' -> y') <-|-|- x <-*-*- y++(<-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t b -> t a -> (a :+: b -> r) -> t r+y <-+- x = \f -> f <-|--- mult @(-->) <~~~ x :*: y++(.-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t a -> t a -> t a+y .-+- x = (\r -> case r of Option rx -> rx; Adoption ry -> ry) <-|--- mult @(-->) <~~~ x :*: y++loop :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t a -> t b+loop x = let r = r .-*- x in r++type Extractable t = Monoidal (<--) (-->) (:*:) (:*:) t+type Pointable t = Monoidal (-->) (-->) (:*:) (:*:) t+type Emptiable t = Monoidal (-->) (-->) (:*:) (:+:) t++extract :: Extractable t => t a -> a+extract j = unit @(<--) @(-->) Proxy <~ j <~ One++point :: Pointable t => a -> t a+point x = unit @(-->) Proxy <~~~ Straight <-- \One -> x++pass :: Pointable t => t ()+pass = point ()++empty :: Emptiable t => t a+empty = unit @(-->) Proxy <~ Straight absurd++(<-||-), (<-||--), (<-||---), (<-||----), (<-||-----), (<-||------), (<-||-------), (<-||--------)+	:: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c .+	(Covariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p a c) (p b c)+(<-||--------) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||-------) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||------) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||-----) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||----) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||---) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||--) f = (-#=) @m @(Flip p c) ((<-|-) f)+(<-||-) f = (-#=) @m @(Flip p c) ((<-|-) f)++(>-||-), (>-||--), (>-||---), (>-||----), (>-||-----), (>-||------), (>-||-------), (>-||--------)+	:: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c .+	(Contravariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p b c) (p a c)+(>-||--------) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||-------) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||------) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||-----) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||----) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||---) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||--) f = (-#=) @m @(Flip p c) ((>-|-) f)+(>-||-) f = (-#=) @m @(Flip p c) ((>-|-) f)++(<-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .+	(Covariant m m (p a), Covariant m m (Flip p d), Interpreted m (Flip p d))+	=> m a b :*: m c d -> m (p a c) (p b d)+(<-|-<-|-) (f :*: g) = (-#=) @m @(Flip p d) ((<-|-) f) . ((<-|-) g)++(<-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .+	(Covariant m m (Flip p c), Contravariant m m (p a), Interpreted m (Flip p c))+	=> m a b :*: m c d -> m (p a d) (p b c)+(<-|->-|-) (f :*: g) = (-#=) @m @(Flip p c) ((<-|-) f) . ((>-|-) g)++(>-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .+	(Contravariant m m (Flip p d), Covariant m m (p b), Interpreted m (Flip p d))+	=> m a b :*: m c d -> m (p b c) (p a d)+(>-|-<-|-) (f :*: g) = (-#=) @m @(Flip p d) ((>-|-) f) . ((<-|-) g)++(>-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .+	(Contravariant m m (p b), Contravariant m m (Flip p c), Interpreted m (Flip p c))+	=> m a b :*: m c d -> m (p b d) (p a c)+(>-|->-|-) (f :*: g) = (-#=) @m @(Flip p c) ((>-|-) f) . ((>-|-) g)++void :: Covariant (->) (->) t => t a -> t ()+void x = constant () <-|- x

@@ -0,0 +1,3 @@+module Pandora.Paradigm.Algebraic.One where++data One = One

@@ -0,0 +1,74 @@+module Pandora.Paradigm.Algebraic.Product where++import Pandora.Core.Functor (type (>))+import Pandora.Pattern.Category ((<---))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))+import Pandora.Pattern.Object.Setoid (Setoid ((==)))+import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))+import Pandora.Pattern.Object.Monoid (Monoid (zero))+import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))+import Pandora.Pattern.Object.Quasiring (Quasiring (one))+import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/)))+import Pandora.Pattern.Object.Lattice (Lattice)+import Pandora.Pattern.Object.Group (Group (invert))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Paradigm.Controlflow.Effect.Interpreted ()+import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>), type (>:.:>), type (<:.:<), type (>:.:<))++infixr 8 :*:+infixr 5 <:*:>++data (:*:) s a = s :*: a++instance Covariant (->) (->) ((:*:) s) where+	f <-|- ~(s :*: x) = s :*: f x++instance Covariant (->) (->) (Flip (:*:) a) where+	f <-|- Flip (x :*: y) = Flip (f x :*: y)++instance Extendable (->) ((:*:) s) where+	f <<= ~(s :*: x) = s :*: f (s :*: x)++instance (Setoid s, Setoid a) => Setoid (s :*: a) where+	~(sx :*: x) == ~(sy :*: y) = (sx == sy) * (x == y)++instance (Semigroup s, Semigroup a) => Semigroup (s :*: a) where+	~(sx :*: x) + ~(sy :*: y) = (sx + sy) :*: (x + y)++instance (Monoid s, Monoid a) => Monoid (s :*: a) where+	zero = zero :*: zero++instance (Ringoid s, Ringoid a) => Ringoid (s :*: a) where+	~(sx :*: x) * ~(sy :*: y) = (sx * sy) :*: (x * y)++instance (Quasiring s, Quasiring a) => Quasiring (s :*: a) where+	one = one :*: one++instance (Infimum s, Infimum a) => Infimum (s :*: a) where+	~(sx :*: x) /\ ~(sy :*: y) = sx /\ sy :*: x /\ y++instance (Supremum s, Supremum a) => Supremum (s :*: a) where+	~(sx :*: x) \/ ~(sy :*: y) = sx \/ sy :*: x \/ y++instance (Lattice s, Lattice a) => Lattice (s :*: a) where++instance (Group s, Group a) => Group (s :*: a) where+	invert ~(s :*: x) = invert s :*: invert x++delta :: a -> a :*: a+delta x = x :*: x++swap :: a :*: b -> b :*: a+swap ~(x :*: y) = y :*: x++attached :: a :*: b -> a+attached ~(x :*: _) = x++type (<:*:>) t u = t <:.:> u > (:*:)+type (>:*:>) t u = t >:.:> u > (:*:)+type (<:*:<) t u = t <:.:< u > (:*:)+type (>:*:<) t u = t >:.:< u > (:*:)++(<:*:>) :: t a -> u a -> t <:*:> u > a+(<:*:>) xs ys = T_U <--- xs :*: ys

@@ -0,0 +1,35 @@+module Pandora.Paradigm.Algebraic.Sum where++import Pandora.Core.Functor (type (>))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((<--))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Paradigm.Algebraic.Exponential ()+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Paradigm.Schemes.T_U (type (<:.:>), type (>:.:>), type (<:.:<), type (>:.:<))++infixr 7 :+:++data (:+:) o a = Option o | Adoption a++instance Covariant (->) (->) ((:+:) o) where+	_ <-|- Option s = Option s+	f <-|- Adoption x = Adoption <-- f x++instance Covariant (->) (->) (Flip (:+:) a) where+	_ <-|- Flip (Adoption x) = Flip . Adoption <-- x+	f <-|- Flip (Option y) = Flip . Option <-- f y++sum :: (e -> r) -> (a -> r) -> e :+: a -> r+sum f _ (Option x) = f x+sum _ s (Adoption x) = s x++-- TODO: keep it until we realize how to implement n-ary functors+bitraverse_sum :: Covariant (->) (->) t => (e -> t e') -> (a -> t a') -> (e :+: a) -> t (e' :+: a')+bitraverse_sum f _ (Option x) = Option <-|- f x+bitraverse_sum _ g (Adoption x) = Adoption <-|- g x++type (<:+:>) t u = t <:.:> u > (:+:)+type (>:+:>) t u = t >:.:> u > (:+:)+type (<:+:<) t u = t <:.:< u > (:+:)+type (>:+:<) t u = t >:.:< u > (:+:)

@@ -0,0 +1,8 @@+{-# LANGUAGE EmptyCase #-}++module Pandora.Paradigm.Algebraic.Zero where++data Zero++absurd :: Zero -> a+absurd x = case x of {}

@@ -1,6 +1,5 @@ module Pandora.Paradigm.Controlflow.Effect (module Exports) where  import Pandora.Paradigm.Controlflow.Effect.Transformer as Exports-import Pandora.Paradigm.Controlflow.Effect.Conditional as Exports import Pandora.Paradigm.Controlflow.Effect.Interpreted as Exports import Pandora.Paradigm.Controlflow.Effect.Adaptable as Exports

@@ -7,9 +7,9 @@ import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Transformer (Liftable (lift))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic (Pointable, extract, point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic (Pointable, extract, point) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly) import Pandora.Paradigm.Controlflow.Effect.Transformer (Monadic, wrap, (:>)) 

@@ -1,24 +0,0 @@-{-# LANGUAGE AllowAmbiguousTypes #-}-module Pandora.Paradigm.Controlflow.Effect.Conditional where--import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False))-import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))--class Conditional prompt clause where-	iff :: clause -> a -> a -> a--instance Conditional True Boolean where-	iff True x _ = x-	iff False _ y = y--instance Conditional False Boolean where-	iff False x _ = x-	iff True _ y = y--instance Conditional Just (Maybe a) where-	iff (Just _) x _ = x-	iff Nothing _ y = y--instance Conditional Nothing (Maybe a) where-	iff Nothing x _ = x-	iff (Just _) _ y = y

@@ -6,19 +6,18 @@ import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential ()  infixr 2 =#-, -#= -infixl 1 <~~~~~~~~~-infixl 2 <~~~~~~~~-infixl 3 <~~~~~~~-infixl 4 <~~~~~~-infixl 5 <~~~~~-infixl 6 <~~~~-infixl 7 <~~~-infixl 8 <~~-infixl 9 <~+infixl 1 <~~~~~~~~+infixl 2 <~~~~~~~+infixl 3 <~~~~~~+infixl 4 <~~~~~+infixl 5 <~~~~+infixl 6 <~~~+infixl 7 <~~+infixl 8 <~  type family Schematic (c :: (* -> * -> *) -> (* -> *) -> k) (t :: * -> *) = (r :: (* -> *) -> * -> *) | r -> t @@ -28,8 +27,7 @@ 	run :: m < t a < Primary t a 	unite :: m < Primary t a < t a -	(<~~~~~~~~~), (<~~~~~~~~), (<~~~~~~~), (<~~~~~~), (<~~~~~), (<~~~~), (<~~~), (<~~), (<~) :: m < t a < Primary t a-	(<~~~~~~~~~) = run+	(<~~~~~~~~), (<~~~~~~~), (<~~~~~~), (<~~~~~), (<~~~~), (<~~~), (<~~), (<~) :: m < t a < Primary t a 	(<~~~~~~~~) = run 	(<~~~~~~~) = run 	(<~~~~~~) = run

@@ -15,10 +15,10 @@ import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (Extractable, point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:)))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (Extractable, point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite, (<~~~)))  class Interpreted m t => Comonadic m t where@@ -29,7 +29,7 @@ newtype (:<) t u a = TC { tc :: Schematic Comonad t u a }  instance Covariant (->) (->) (Schematic Comonad t u) => Covariant (->) (->) (t :< u) where-	f <-|- TC x = TC <--- f <-|- x+	f <-|- TC x = TC <---- f <-|- x  instance Semimonoidal (-->) (:*:) (:*:) (Schematic Comonad t u) => Semimonoidal (-->) (:*:) (:*:) (t :< u) where 	mult = Straight <-- \(TC f :*: TC x) -> TC@@ -43,13 +43,13 @@ 	f <<- TC x = TC <-|- f <<- x  instance Distributive (->) (->) (Schematic Comonad t u) => Distributive (->) (->) (t :< u) where-	f -<< x = TC <--- tc . f --<< x+	f -<< x = TC <--- tc . f -<< x  instance Bindable (->) (Schematic Comonad t u) => Bindable (->) (t :< u) where-	f =<< TC x = TC <--- tc . f ==<< x+	f =<< TC x = TC <--- tc . f =<< x  instance Extendable (->) (Schematic Comonad t u) => Extendable (->) (t :< u) where-	f <<= TC x = TC <--- f . TC <<== x+	f <<= TC x = TC <--- f . TC <<= x  instance (Extractable (t :< u), Extendable (->) (t :< u)) => Comonad (->) (t :< u) where 

@@ -15,11 +15,11 @@ import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (Pointable, point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (Pointable, point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite, (<~~~)))  class Interpreted m t => Monadic m t where@@ -30,7 +30,7 @@ newtype (:>) t u a = TM { tm :: Schematic Monad t u a }  instance Covariant (->) (->) (Schematic Monad t u) => Covariant (->) (->) (t :> u) where-	f <-|- TM x = TM <--- f <-|- x+	f <-|- TM x = TM <---- f <-|- x  instance Semimonoidal (-->) (:*:) (:*:) (Schematic Monad t u) => Semimonoidal (-->) (:*:) (:*:) (t :> u) where 	mult = Straight <-- \(TM f :*: TM x) -> TM@@ -49,13 +49,13 @@ 	f <<- TM x = TM <-|- f <<- x  instance Distributive (->) (->) (Schematic Monad t u) => Distributive (->) (->) (t :> u) where-	f -<< x = TM <--- tm . f --<< x+	f -<< x = TM <--- tm . f -<< x  instance Bindable (->) (Schematic Monad t u) => Bindable (->) (t :> u) where-	f =<< TM x = TM <--- tm . f ==<< x+	f =<< TM x = TM <--- tm . f =<< x  instance Extendable (->) (Schematic Monad t u) => Extendable (->) (t :> u) where-	f <<= TM x = TM <--- f . TM <<== x+	f <<= TM x = TM <--- f . TM <<= x  instance (Covariant (->) (->) (Schematic Monad t u), Monoidal (-->) (-->) (:*:) (:*:) (Schematic Monad t u), Bindable (->) (t :> u)) => Monad (->) (t :> u) where 

@@ -4,7 +4,7 @@ import Pandora.Core.Functor (type (<)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--), (<---))-import Pandora.Paradigm.Primary.Algebraic (Applicative, loop)+import Pandora.Paradigm.Algebraic (Applicative, loop) import Pandora.Paradigm.Primary.Transformer.Continuation (Continuation (Continuation)) import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~~)) 

@@ -5,9 +5,9 @@ import Pandora.Pattern.Kernel (constant) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monoidal (Monoidal)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite)) import Pandora.Paradigm.Primary.Transformer.Continuation (Continuation (Continuation)) 

@@ -7,7 +7,7 @@  import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))+import Pandora.Pattern.Category ((<--), (<---), (<----)) import Pandora.Pattern.Kernel (constant) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--)))@@ -15,9 +15,9 @@ import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (--|), (|-), (|--))) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), type (<--))-import Pandora.Paradigm.Primary.Algebraic (Pointable, extract)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Exponential ((%), type (<--))+import Pandora.Paradigm.Algebraic (Pointable, extract) import Pandora.Paradigm.Primary (Simplification) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))@@ -44,7 +44,7 @@ 	zoom lens less = adapt . State <-- \source -> restruct |- run (lens <~ source) where  		restruct :: (Exactly ls -> bg) -> Exactly ls -> bg :*: result-		restruct to (Exactly target) = run <--- to . Exactly <-|- Flip (less <~ target)+		restruct to (Exactly target) = run <---- to . Exactly <-|- Flip (less <~ target)  instance Zoomable State Maybe where 	zoom :: forall bg ls t result . Stateful bg t => Obscure Lens bg ls -> State (Maybe ls) result -> t result

@@ -3,16 +3,16 @@  import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))+import Pandora.Pattern.Category ((<--), (<---), (<----)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Object.Monoid (Monoid) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))@@ -21,7 +21,7 @@ newtype Accumulator e a = Accumulator (e :*: a)  instance Covariant (->) (->) (Accumulator e) where-	f <-|- Accumulator x = Accumulator <--- f <-|- x+	f <-|- Accumulator x = Accumulator <---- f <-|- x  instance Semigroup e => Semimonoidal (-->) (:*:) (:*:) (Accumulator e) where 	mult = Straight <-- \(x :*: y) -> Accumulator <--- k <-- run x <-- run y where

@@ -2,13 +2,13 @@ module Pandora.Paradigm.Inventory.Some.Equipment (Equipment (..), retrieve) where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<---), (<-----))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Category ((<---), (<----))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Pattern.Functor.Extendable (Extendable ((<<=), (<<==)))+import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad)-import Pandora.Paradigm.Primary.Algebraic ()-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)+import Pandora.Paradigm.Algebraic ()+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), attached) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Inventory.Ability.Gettable (Gettable (Getting, get))@@ -17,13 +17,13 @@ newtype Equipment e a = Equipment (e :*: a)  instance Covariant (->) (->) (Equipment e) where-	f <-|- Equipment x = Equipment <--- f <-|- x+	f <-|- Equipment x = Equipment <---- f <-|- x  instance Traversable (->) (->) (Equipment e) where-	f <<- Equipment x = Equipment <-|- f <<- x+	f <<- Equipment x = Equipment <-|-- f <<- x  instance Extendable (->) (Equipment e) where-	f <<= Equipment (e :*: x) = Equipment . (:*:) e . f . Equipment <----- e :*: x+	f <<= Equipment (e :*: x) = Equipment . (:*:) e . f . Equipment <---- e :*: x  instance Interpreted (->) (Equipment e) where 	type Primary (Equipment e) a = e :*: a@@ -35,7 +35,7 @@ type Equipped e t = Adaptable (Equipment e) (->) t  instance {-# OVERLAPS #-} Extendable (->) u => Extendable (->) ((:*:) e <:.> u) where-	f <<= TU (e :*: x) = TU . (:*:) e <--- f . TU . (:*:) e <<== x+	f <<= TU (e :*: x) = TU . (:*:) e <--- f . TU . (:*:) e <<= x  retrieve :: Equipped e t => t a -> e retrieve = attached . run @(->) @(Equipment _) . adapt

@@ -2,14 +2,14 @@ module Pandora.Paradigm.Inventory.Some.Imprint (Imprint (..), Traceable) where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--))+import Pandora.Pattern.Category ((<--), (<---)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-))) import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Paradigm.Primary.Algebraic ()+import Pandora.Paradigm.Algebraic () import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable)@@ -24,7 +24,7 @@ 	f >-|- Flip (Imprint g) = Flip . Imprint <-- g . f  instance Distributive (->) (->) (Imprint e) where-	f -<< g = Imprint <-- (run @(->) <-|- f) -<< g+	f -<< g = Imprint <--- (run @(->) <-|- f) -<< g  instance Semigroup e => Extendable (->) (Imprint e) where 	f <<= Imprint x = Imprint <-- \e -> f . Imprint <-- x . (e +)@@ -37,6 +37,6 @@ type instance Schematic Comonad (Imprint e) = (<.:>) ((->) e)  instance {-# OVERLAPS #-} (Semigroup e, Extendable (->) u) => Extendable (->) ((->) e <.:> u) where-	f <<= UT x = UT <-- (\x' e -> f . UT . (<-|-) (. (e +)) <-- x') <<= x+	f <<= UT x = UT <--- (\x' e -> f . UT . (<-|-) (. (e +)) <-- x') <<= x  type Traceable e t = Adaptable t (->) (Imprint e)

@@ -4,20 +4,20 @@  import Pandora.Core.Impliable (Impliable (Arguments, imply)) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category (Category (identity, (<--), (<---), (<-----), (<-------)))+import Pandora.Pattern.Category (Category (identity, (<--), (<---), (<----), (<-----), (<-------))) import Pandora.Pattern.Kernel (Kernel (constant)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|-|-))) import Pandora.Pattern.Functor.Invariant (Invariant ((<!<))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Representable (Representable (Representation, (<#>), tabulate))-import Pandora.Pattern.Object.Setoid (Setoid ((?==)))+import Pandora.Pattern.Object.Setoid (Setoid ((?=))) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (run, (<~))) import Pandora.Paradigm.Inventory.Ability.Gettable (Gettable (Getting, get)) import Pandora.Paradigm.Inventory.Ability.Settable (Settable (Setting, set)) import Pandora.Paradigm.Inventory.Ability.Modifiable (Modifiable (Modification, modify))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), (%))-import Pandora.Paradigm.Primary.Algebraic (Pointable, point, extract, (>-||-----), (>-|-<-|-))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Exponential (type (-->), (%))+import Pandora.Paradigm.Algebraic (Pointable, point, extract, (>-||---)) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Pattern.Morphism.Flip (Flip (Flip))@@ -31,7 +31,7 @@ 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 Exactly@@ -86,7 +86,7 @@  -- | Representable based lens represent :: forall t a . (Representable t, Setoid (Representation t)) => Representation t -> Convex Lens (t a) a-represent r = imply @(Convex Lens (t a) a) (r <#>) (\source target -> tabulate <-- \r' -> r' ?== r <----- target <----- r' <#> source)+represent r = imply @(Convex Lens (t a) a) (r <#>) (\source target -> tabulate <-- \r' -> r' ?= r <----- target <----- r' <#> source)  class Lensic previous next where 	type Lensally previous next :: * -> *@@ -101,7 +101,7 @@ 	P_Q_T from >>> P_Q_T to = P_Q_T <-- \source -> case run <-- from source of 		Nothing :*: _ -> Store <--- Nothing :*: \_ -> source 		Just between :*: mbs -> case run <-- to between of-			Exactly target :*: itb -> Store <--- Just target :*: \mt -> mbs <--- itb . Exactly <-|- mt+			Exactly target :*: itb -> Store <--- Just target :*: \mt -> mbs <---- itb . Exactly <-|- mt  instance Lensic Exactly Maybe where 	type Lensally Exactly Maybe = Maybe

@@ -2,19 +2,19 @@ module Pandora.Paradigm.Inventory.Some.Provision where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category (identity, (<--), (<---))+import Pandora.Pattern.Category (identity, (<--), (<---), (<----), (<-----)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))-import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))+import Pandora.Pattern.Functor.Distributive (Distributive ((-<<), (---<<))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Monad (Monad)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), (%))-import Pandora.Paradigm.Primary.Algebraic ((<-||-))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->), (%))+import Pandora.Paradigm.Algebraic ((<-||-))+import Pandora.Paradigm.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite, (<~)))@@ -38,7 +38,7 @@ 	unit _ = Straight <-- \f -> Provision <-- \_ -> run f One  instance Distributive (->) (->) (Provision e) where-	f -<< g = Provision <-- (run @(->) <-|- f) -<< g+	f -<< g = Provision <--- (run @(->) <-|- f) -<< g  instance Bindable (->) (Provision e) where 	f =<< Provision x = Provision <-- \e -> (run % e) . f . x <-- e@@ -53,7 +53,7 @@ type instance Schematic Monad (Provision e) = (<:.>) ((->) e)  instance Monadic (->) (Provision e) where-	wrap x = TM . TU <--- point <-|- run x+	wrap x = TM . TU <---- point <-|- run x  type Provided e t = Adaptable t (->) (Provision e) 

@@ -5,26 +5,26 @@ import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), identity)+import Pandora.Pattern.Category ((<--), (<---), (<----), identity) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Invariant (Invariant ((<!<))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))-import Pandora.Pattern.Functor.Traversable (Traversable ((<<--)))-import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (===<<)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))+import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (==<<))) import Pandora.Pattern.Functor.Monad (Monad)-import Pandora.Pattern.Functor.Adjoint ((-|), (|--))+import Pandora.Pattern.Functor.Adjoint ((-|), (|-)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (=#-)), Schematic)+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, (<~), unite, (=#-)), Schematic) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Inventory.Ability.Gettable (Gettable (Getting, get)) import Pandora.Paradigm.Inventory.Ability.Settable (Settable (Setting, set)) import Pandora.Paradigm.Inventory.Ability.Modifiable (Modifiable (Modification, modify)) import Pandora.Paradigm.Schemes.TUT (TUT (TUT), type (<:<.>:>))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic ((:*:) ((:*:)), (.-*-), delta)-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (Pointable, point, (<-||-), (>-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic ((:*:) ((:*:)), (.-*-), delta)+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (Pointable, point, (<-||-), (>-||-))  -- | Effectful computation with a variable newtype State s a = State ((->) s :. (:*:) s > a)@@ -39,10 +39,10 @@ 		new :*: x :*: y  instance Monoidal (-->) (-->) (:*:) (:*:) (State s) where-	unit _ = Straight <--- State . (identity @(->) -|) . (<-- One) . run+	unit _ = Straight <-- State . (identity @(->) -|) . (<~ One)  instance Bindable (->) (State s) where-	f =<< x = State <--- (run . f |--) <-|- run x+	f =<< x = State <---- (run . f |-) <-|- run x  instance Monad (->) (State s) where @@ -57,17 +57,17 @@ 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 t = Adaptable t (->) (State s)  reconcile :: (Bindable (->) t, Stateful s t, Adaptable t (->) u) => (s -> u s) -> t s-reconcile f = adapt . set @State ===<< adapt . f  ===<< adapt <-- get @State+reconcile f = adapt . set @State ==<< adapt . f ==<< adapt <-- get @State  type Memorable s t = (Covariant (->) (->) t, Pointable t, Stateful s t)  fold :: (Traversable (->) (->) t, Memorable s u) => (a -> s -> s) -> t a -> u s-fold op struct = adapt <-- get @State .-*- (adapt . modify @State . op <<-- struct)+fold op struct = adapt <-- get @State .-*- (adapt . modify @State . op <<- struct)  instance Gettable State where 	type Getting State state ouput = State state state@@ -79,4 +79,4 @@  instance Modifiable State where 	type Modification State state output = (state -> state) -> State state state-	modify f = State <--- \s -> let r = f s in r :*: r+	modify f = State <--- \s -> f s :*: f s

@@ -3,18 +3,18 @@  import Pandora.Core (type (:.), type (>), type (<:=), type (~>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----), identity)+import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------), identity) import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)), (<-|-|-))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Invariant (Invariant ((<!<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Comonad (Comonad) import Pandora.Pattern.Functor.Adjoint ((-|), (|-))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%), (.:..))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic (extract, (<-||-), (>-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->), (%), (.:..))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), attached)+import Pandora.Paradigm.Algebraic (extract, (<-||-), (>-||-)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))@@ -39,7 +39,7 @@  -- TODO: Try to generalize (->) here instance Extendable (->) (Store s) where-	f <<= Store x = Store <---- f <-|-|- ((Store .:.. (identity @(->) -|)) <-|- x)+	f <<= Store x = Store <------ f <-|-|- ((Store .:.. (identity @(->) -|)) <-|-- x)  instance Comonad (->) (Store s) where 

@@ -1,114 +1,22 @@ {-# OPTIONS_GHC -fno-warn-orphans #-}-module Pandora.Paradigm.Primary (module Exports, Simplification, twosome) where+module Pandora.Paradigm.Primary (module Exports, Simplification) where  import Pandora.Paradigm.Primary.Linear as Exports import Pandora.Paradigm.Primary.Transformer as Exports import Pandora.Paradigm.Primary.Functor as Exports import Pandora.Paradigm.Primary.Object as Exports-import Pandora.Paradigm.Primary.Algebraic as Exports  import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category ((<--), (<---))-import Pandora.Pattern.Kernel (Kernel (constant))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))+import Pandora.Pattern.Category ((<---)) import Pandora.Pattern.Functor.Adjoint (Adjoint ((|-), (-|)))-import Pandora.Pattern.Transformer.Liftable (lift)-import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~))-import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Schemes (TU (TU), T_U (T_U), UT, TUT, 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 (Substance, substructure))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Schemes (TU, T_U, UT, TUT)  instance Adjoint (->) (->) (Flip (:*:) s) ((->) s) where 	f -| x = \s -> f . Flip <--- x :*: s 	f |- Flip (x :*: s) = f x s--instance Morphable (Into Maybe) (Conclusion e) where-	type Morphing (Into Maybe) (Conclusion e) = Maybe-	morphing = conclusion (constant Nothing) Just . premorph--instance Morphable (Into (Conclusion e)) Maybe where-	type Morphing (Into (Conclusion e)) Maybe = (->) e <:.> Conclusion e-	morphing (premorph -> Just x) = TU <-- \_ -> Success x-	morphing (premorph -> Nothing) = TU <-- \e -> Failure e--instance Morphable (Into (Flip Conclusion e)) Maybe where-	type Morphing (Into (Flip Conclusion e)) Maybe = (->) e <:.> Flip Conclusion e-	morphing (run . premorph -> Just x) = TU <-- \_ -> Flip <-- Failure x-	morphing (run . premorph -> Nothing) = TU <-- Flip . Success--instance Morphable (Into (Left Maybe)) Wye where-	type Morphing (Into (Left Maybe)) Wye = Maybe-	morphing (premorph -> Both ls _) = Just ls-	morphing (premorph -> Left ls) = Just ls-	morphing (premorph -> Right _) = Nothing-	morphing (premorph -> End) = Nothing--instance Morphable (Into (Right Maybe)) Wye where-	type Morphing (Into (Right Maybe)) Wye = Maybe-	morphing (premorph -> Both _ rs) = Just rs-	morphing (premorph -> Left _) = Nothing-	morphing (premorph -> Right rs) = Just rs-	morphing (premorph -> End) = Nothing--instance Morphable (Into (This Maybe)) (These e) where-	type Morphing (Into (This Maybe)) (These e) = Maybe-	morphing (premorph -> This x) = Just x-	morphing (premorph -> That _) = Nothing-	morphing (premorph -> These _ x) = Just x--instance Morphable (Into (That Maybe)) (Flip These a) where-	type Morphing (Into (That Maybe)) (Flip These a) = Maybe-	morphing (run . premorph -> This _) = Nothing-	morphing (run . premorph -> That x) = Just x-	morphing (run . premorph -> These y _) = Just y--instance Morphable (Into (Here Maybe)) (Flip Wedge a) where-	type Morphing (Into (Here Maybe)) (Flip Wedge a) = Maybe-	morphing (run . premorph -> Nowhere) = Nothing-	morphing (run . premorph -> Here x) = Just x-	morphing (run . premorph -> There _) = Nothing--instance Morphable (Into (There Maybe)) (Wedge e) where-	type Morphing (Into (There Maybe)) (Wedge e) = Maybe-	morphing (premorph -> Nowhere) = Nothing-	morphing (premorph -> Here _) = Nothing-	morphing (premorph -> There x) = Just x--instance Morphable (Into Wye) (Maybe <:.:> Maybe > (:*:)) where-	type Morphing (Into Wye) (Maybe <:.:> Maybe > (:*:)) = Wye-	morphing (run . premorph -> Just x :*: Just y) = Both x y-	morphing (run . premorph -> Nothing :*: Just y) = Right y-	morphing (run . premorph -> Just x :*: Nothing) = Left x-	morphing (run . premorph -> Nothing :*: Nothing) = End--instance Substructure Left Wye where-	type Substance Left Wye = Maybe-	substructure = P_Q_T <-- \new -> case lower new of-		End -> Store <--- Nothing :*: lift . resolve Left End-		Left x -> Store <--- Just x :*: lift . resolve Left End-		Right y -> Store <--- Nothing :*: lift . constant (Right y)-		Both x y -> Store <--- Just x :*: lift . resolve (Both % y) (Right y)--instance Substructure Right Wye where-	type Substance Right Wye = Maybe-	substructure = P_Q_T <-- \new -> case lower new of-		End -> Store <--- Nothing :*: lift . resolve Right End-		Left x -> Store <--- Nothing :*: lift . constant (Left x)-		Right y -> Store <--- Just y :*: lift . resolve Right End-		Both x y -> Store <--- Just y :*: lift . resolve (Both x) (Left x)--instance (Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => Semimonoidal (-->) (:*:) (:*:) (t <:.:> u > (:*:)) where-	mult = Straight <-- \(T_U (xls :*: xrs) :*: T_U (yls :*: yrs)) -> T_U <--- (mult @(-->) <~) (xls :*: yls) :*: (mult @(-->) <~) (xrs :*: yrs)--twosome :: t a -> u a -> (<:.:>) t u (:*:) a-twosome x y = T_U <--- x :*: y  type family Simplification (t :: * -> *) (a :: *) where 	Simplification Exactly a = a

@@ -1,73 +0,0 @@-{-# OPTIONS_GHC -fno-warn-orphans #-}-module Pandora.Paradigm.Primary.Algebraic (module Exports) where--import Pandora.Paradigm.Primary.Algebraic.Functor as Exports-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.Paradigm.Primary.Algebraic.Zero as Exports-import Pandora.Paradigm.Primary.Algebraic.One as Exports--import Pandora.Core.Functor (type (>))-import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Pattern.Morphism.Straight (Straight (Straight))-import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))-import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))-import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))-import Pandora.Pattern.Functor.Comonad (Comonad)-import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted ((<~)))--instance (Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:*:> u) where-	mult = Flip <-- \(T_U lrxys) ->-		-- TODO: I need matrix transposing here-		let ((lxs :*: lys) :*: (rxs :*: rys)) = (mult @(<--) <~) <-||-- (mult @(<--) <~) <-|- lrxys in-		T_U (lxs :*: rxs) :*: T_U (lys :*: rys)--instance Traversable (->) (->) ((:*:) s) where-	f <<- x = (attached x :*:) <-|- f (extract x)--instance Semimonoidal (-->) (:*:) (:*:) ((->) e) where-	mult :: ((e -> a) :*: (e -> b)) --> (e -> (a :*: b))-	mult = Straight <-- \(g :*: h) -> \x -> g x :*: h x--instance Monoidal (-->) (-->) (:*:) (:*:) ((->) e) where-	unit _ = Straight <-- constant . (<~ One)--instance Semimonoidal (<--) (:*:) (:*:) ((->) e) where-	mult :: ((e -> a) :*: (e -> b)) <-- (e -> a :*: b)-	mult = Flip <-- \f -> attached . f :*: extract . f--instance Semimonoidal (-->) (:*:) (:+:) ((:+:) e) where-	mult :: ((e :+: a) :*: (e :+: b)) --> (e :+: a :+: b)-	mult = Straight <-- \case-		Option _ :*: Option e' -> Option e'-		Option _ :*: Adoption y -> Adoption <-- Adoption y-		Adoption x :*: _ -> Adoption <-- Option x--instance Semimonoidal (-->) (:*:) (:*:) ((:+:) e) where-	mult = Straight <-- \case-		Adoption x :*: Adoption y -> Adoption <--- x :*: y-		Option e :*: _ -> Option e-		_ :*: Option e -> Option e--instance Monoidal (-->) (-->) (:*:) (:*:) ((:+:) e) where-	unit _ = Straight <-- Adoption . (<~ One)--instance Semimonoidal (<--) (:*:) (:*:) ((:*:) s) where-	mult = Flip <-- \(s :*: x :*: y) -> (s :*: x) :*: (s :*: y)--instance Monoidal (<--) (-->) (:*:) (:*:) ((:*:) s) where-	unit _ = Flip <-- \(_ :*: x) -> Straight (\_ -> x)--instance Comonad (->) ((:*:) s) where--instance Semimonoidal (<--) (:*:) (:*:) (Flip (:*:) a) where-	mult = Flip <-- \(Flip ((sx :*: sy) :*: r)) -> Flip (sx :*: r) :*: Flip (sy :*: r)--instance Monoidal (<--) (-->) (:*:) (:*:) (Flip (:*:) a) where-	unit _ = Flip <-- \(Flip (s :*: _)) -> Straight (\_ -> s)

@@ -1,69 +0,0 @@-{-# OPTIONS_GHC -fno-warn-orphans #-}-module Pandora.Paradigm.Primary.Algebraic.Exponential where--import Pandora.Pattern.Betwixt (Betwixt)-import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category (Category ((<--), identity))-import Pandora.Pattern.Kernel (Kernel (constant))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))-import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))-import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))-import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))-import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Pattern.Morphism.Straight (Straight (Straight))--infixr 7 .:..-infixr 9 %-infixl 1 &--type instance Betwixt (->) (->) = (->)--instance Semigroupoid (->) where-	f . g = \x -> f (g x)--instance Category (->) where-	identity x = x--instance Kernel (->) where-	constant x _ = x--instance Covariant (->) (->) ((->) a) where-	(<-|-) = (.)--instance Distributive (->) (->) ((->) e) where-	f -<< g = \e -> f % e <-|- g--instance Bindable (->) ((->) e) where-	f =<< g = \x -> f <-- g x <-- x--instance Semigroup r => Semigroup (e -> r) where-	f + g = \e -> f e + g e--instance Ringoid r => Ringoid (e -> r) where-	f * g = \e -> f e * g e--type (<--) = Flip (->)--instance Contravariant (->) (->) ((<--) a) where-	f >-|- Flip g = Flip <-- g . f--type (-->) = Straight (->)--instance Covariant (->) (->) ((-->) b) where-	f <-|- Straight g = Straight <-- f . g--(.:..) :: (Covariant (->) target (v a), Semigroupoid v) => v c d -> target (v a (v b c)) (v a (v b d))-(.:..) f = (<-|-) (f .)--{-# INLINE (%) #-}-(%) :: (a -> b -> c) -> b -> a -> c-(%) f x y = f y x--{-# INLINE (&) #-}-(&) :: a -> (a -> b) -> b-x & f = f x--fix :: (a -> a) -> a-fix f = let x = f x in x

@@ -1,143 +0,0 @@-{-# OPTIONS_GHC -fno-warn-orphans #-}-module Pandora.Paradigm.Primary.Algebraic.Functor where--import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--))-import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Morphism.Flip (Flip)-import Pandora.Pattern.Morphism.Straight (Straight (Straight))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|---), (<-|-|-)))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))-import Pandora.Pattern.Functor.Monoidal (Monoidal (unit), Unit)-import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-)))-import Pandora.Paradigm.Primary.Functor.Proxy (Proxy (Proxy))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), type (<--), (&))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.Zero (Zero, absurd)-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted ((<~), (<~~~), (-#=)))--infixl 1 <-*--------, .-*--------, <-||--------, >-||---------infixl 2 <-*-------, .-*-------, <-||-------, >-||--------infixl 3 <-*------, .-*------, <-||------, >-||-------infixl 4 <-*-----, .-*-----, <-||-----, >-||------infixl 5 <-*----, .-*----, <-||----, >-||-----infixl 6 <-*---, .-*---, <-||---, >-||----infixl 7 <-*--, .-*--, <-*-*-, .-*-*-, <-||--, >-||---infixl 8 <-*-, .-*-, <-+-, .-+-, <-||-, >-||---infixl 6 <-|-<-|-, <-|->-|-, >-|-<-|-, >-|->-|---type instance Unit (:*:) = One-type instance Unit (:+:) = Zero--type Applicative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t, Monoidal (-->) (-->) (:*:) (:*:) t)-type Alternative t = (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) t)-type Divisible t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Monoidal (-->) (<--) (:*:) (:*:) t)-type Decidable t = (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:+:) t, Monoidal (-->) (<--) (:*:) (:+:) t)--instance Adjoint (->) (->) ((:*:) s) ((->) s) where-	(-|) :: ((s :*: a) -> b) -> a -> (s -> b)-	f -| x = \s -> f (s :*: x)-	(|-) :: (a -> s -> b) -> (s :*: a) -> b-	f |- ~(s :*: x) = f x s--(<-*--------), (<-*-------), (<-*------), (<-*-----), (<-*----), (<-*---), (<-*--), (<-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t (a -> b) -> t a -> t b-f <-*-------- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*------- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*------ x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*----- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*---- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*--- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*-- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x-f <-*- x = (|-) @(->) @(->) (&) <-|--- mult @(-->) @_ @(:*:) <~~~ f :*: x--(.-*--------), (.-*-------), (.-*------), (.-*-----), (.-*----), (.-*---), (.-*--), (.-*-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t b -> t a -> t b-y .-*-------- x = (\_ y' -> y') <-|- x <-*- y-y .-*------- x = (\_ y' -> y') <-|- x <-*- y-y .-*------ x = (\_ y' -> y') <-|- x <-*- y-y .-*----- x = (\_ y' -> y') <-|- x <-*- y-y .-*---- x = (\_ y' -> y') <-|- x <-*- y-y .-*--- x = (\_ y' -> y') <-|- x <-*- y-y .-*-- x = (\_ y' -> y') <-|- x <-*- y-y .-*- x = (\_ y' -> y') <-|- x <-*- y--(<-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u (a -> b)) -> t (u a) -> t (u b)-f <-*-*- x = (<-*-) <-|- f <-*- x--(.-*-*-) :: (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:*:) u) => t (u b) -> t (u a) -> t (u b)-y .-*-*- x = (\_ y' -> y') <-|-|- x <-*-*- y--(<-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t b -> t a -> (a :+: b -> r) -> t r-y <-+- x = \f -> f <-|--- mult @(-->) <~~~ x :*: y--(.-+-) :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:+:) t) => t a -> t a -> t a-y .-+- x = (\r -> case r of Option rx -> rx; Adoption ry -> ry) <-|--- mult @(-->) <~~~ x :*: y--loop :: (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => t a -> t b-loop x = let r = r .-*- x in r--type Extractable t = Monoidal (<--) (-->) (:*:) (:*:) t-type Pointable t = Monoidal (-->) (-->) (:*:) (:*:) t-type Emptiable t = Monoidal (-->) (-->) (:*:) (:+:) t--extract :: Extractable t => t a -> a-extract j = unit @(<--) @(-->) Proxy <~ j <~ One--point :: Pointable t => a -> t a-point x = unit @(-->) Proxy <~~~ Straight <-- \One -> x--pass :: Pointable t => t ()-pass = point ()--empty :: Emptiable t => t a-empty = unit @(-->) Proxy <~ Straight absurd--(<-||-), (<-||--), (<-||---), (<-||----), (<-||-----), (<-||------), (<-||-------), (<-||--------)-	:: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c .-	(Covariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p a c) (p b c)-(<-||--------) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||-------) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||------) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||-----) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||----) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||---) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||--) f = (-#=) @m @(Flip p c) ((<-|-) f)-(<-||-) f = (-#=) @m @(Flip p c) ((<-|-) f)--(>-||-), (>-||--), (>-||---), (>-||----), (>-||-----), (>-||------), (>-||-------), (>-||--------)-	:: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c .-	(Contravariant m m (Flip p c), Interpreted m (Flip p c)) => m a b -> m (p b c) (p a c)-(>-||--------) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||-------) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||------) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||-----) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||----) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||---) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||--) f = (-#=) @m @(Flip p c) ((>-|-) f)-(>-||-) f = (-#=) @m @(Flip p c) ((>-|-) f)--(<-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .-	(Covariant m m (p a), Covariant m m (Flip p d), Interpreted m (Flip p d))-	=> m a b :*: m c d -> m (p a c) (p b d)-(<-|-<-|-) (f :*: g) = (-#=) @m @(Flip p d) ((<-|-) f) . ((<-|-) g)--(<-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .-	(Covariant m m (Flip p c), Contravariant m m (p a), Interpreted m (Flip p c))-	=> m a b :*: m c d -> m (p a d) (p b c)-(<-|->-|-) (f :*: g) = (-#=) @m @(Flip p c) ((<-|-) f) . ((>-|-) g)--(>-|-<-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .-	(Contravariant m m (Flip p d), Covariant m m (p b), Interpreted m (Flip p d))-	=> m a b :*: m c d -> m (p b c) (p a d)-(>-|-<-|-) (f :*: g) = (-#=) @m @(Flip p d) ((>-|-) f) . ((<-|-) g)--(>-|->-|-) :: forall (m :: * -> * -> *) (p :: * -> * -> *) a b c d .-	(Contravariant m m (p b), Contravariant m m (Flip p c), Interpreted m (Flip p c))-	=> m a b :*: m c d -> m (p b d) (p a c)-(>-|->-|-) (f :*: g) = (-#=) @m @(Flip p c) ((>-|-) f) . ((>-|-) g)--void :: Covariant (->) (->) t => t a -> t ()-void x = constant () <-|- x

@@ -1,3 +0,0 @@-module Pandora.Paradigm.Primary.Algebraic.One where--data One = One

@@ -1,69 +0,0 @@-module Pandora.Paradigm.Primary.Algebraic.Product where--import Pandora.Core.Functor (type (>))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))-import Pandora.Pattern.Object.Setoid (Setoid ((==)))-import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Pattern.Object.Ringoid (Ringoid ((*)))-import Pandora.Pattern.Object.Quasiring (Quasiring (one))-import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/)))-import Pandora.Pattern.Object.Lattice (Lattice)-import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Paradigm.Controlflow.Effect.Interpreted ()-import Pandora.Paradigm.Schemes.T_U (type (<:.:>), type (>:.:>), type (<:.:<), type (>:.:<))--infixr 8 :*:--data (:*:) s a = s :*: a--instance Covariant (->) (->) ((:*:) s) where-	f <-|- ~(s :*: x) = s :*: f x--instance Covariant (->) (->) (Flip (:*:) a) where-	f <-|- Flip (x :*: y) = Flip (f x :*: y)--instance Extendable (->) ((:*:) s) where-	f <<= ~(s :*: x) = s :*: f (s :*: x)--instance (Setoid s, Setoid a) => Setoid (s :*: a) where-	~(sx :*: x) == ~(sy :*: y) = (sx == sy) * (x == y)--instance (Semigroup s, Semigroup a) => Semigroup (s :*: a) where-	~(sx :*: x) + ~(sy :*: y) = (sx + sy) :*: (x + y)--instance (Monoid s, Monoid a) => Monoid (s :*: a) where-	zero = zero :*: zero--instance (Ringoid s, Ringoid a) => Ringoid (s :*: a) where-	~(sx :*: x) * ~(sy :*: y) = (sx * sy) :*: (x * y)--instance (Quasiring s, Quasiring a) => Quasiring (s :*: a) where-	one = one :*: one--instance (Infimum s, Infimum a) => Infimum (s :*: a) where-	~(sx :*: x) /\ ~(sy :*: y) = sx /\ sy :*: x /\ y--instance (Supremum s, Supremum a) => Supremum (s :*: a) where-	~(sx :*: x) \/ ~(sy :*: y) = sx \/ sy :*: x \/ y--instance (Lattice s, Lattice a) => Lattice (s :*: a) where--instance (Group s, Group a) => Group (s :*: a) where-	invert ~(s :*: x) = invert s :*: invert x--delta :: a -> a :*: a-delta x = x :*: x--swap :: a :*: b -> b :*: a-swap ~(x :*: y) = y :*: x--attached :: a :*: b -> a-attached ~(x :*: _) = x--type (<:*:>) t u = t <:.:> u > (:*:)-type (>:*:>) t u = t >:.:> u > (:*:)-type (<:*:<) t u = t <:.:< u > (:*:)-type (>:*:<) t u = t >:.:< u > (:*:)

@@ -1,35 +0,0 @@-module Pandora.Paradigm.Primary.Algebraic.Sum where--import Pandora.Core.Functor (type (>))-import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Paradigm.Schemes.T_U (type (<:.:>), type (>:.:>), type (<:.:<), type (>:.:<))--infixr 7 :+:--data (:+:) o a = Option o | Adoption a--instance Covariant (->) (->) ((:+:) o) where-	_ <-|- Option s = Option s-	f <-|- Adoption x = Adoption <-- f x--instance Covariant (->) (->) (Flip (:+:) a) where-	_ <-|- Flip (Adoption x) = Flip . Adoption <-- x-	f <-|- Flip (Option y) = Flip . Option <-- f y--sum :: (e -> r) -> (a -> r) -> e :+: a -> r-sum f _ (Option x) = f x-sum _ s (Adoption x) = s x---- TODO: keep it until we realize how to implement n-ary functors-bitraverse_sum :: Covariant (->) (->) t => (e -> t e') -> (a -> t a') -> (e :+: a) -> t (e' :+: a')-bitraverse_sum f _ (Option x) = Option <-|- f x-bitraverse_sum _ g (Adoption x) = Adoption <-|- g x--type (<:+:>) t u = t <:.:> u > (:+:)-type (>:+:>) t u = t >:.:> u > (:+:)-type (<:+:<) t u = t <:.:< u > (:+:)-type (>:+:<) t u = t >:.:< u > (:+:)

@@ -1,8 +0,0 @@-{-# LANGUAGE EmptyCase #-}--module Pandora.Paradigm.Primary.Algebraic.Zero where--data Zero--absurd :: Zero -> a-absurd x = case x of {}

@@ -15,16 +15,16 @@ import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) 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.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite, (<~))) import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM)) import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point)  data Conclusion e a = Failure e | Success a @@ -111,4 +111,4 @@  instance (Monoidal (-->) (-->) (:*:) (:*:) u, Bindable (->) u) => Catchable e (Conclusion e <.:> u) where 	catch (UT x) handle = let conclude = conclusion <-- run . handle <-- point . Success-		in UT <-- conclude =<< x+		in UT <--- conclude =<< x

@@ -14,7 +14,7 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential () import Pandora.Pattern.Morphism.Flip (Flip (Flip))  newtype Constant a b = Constant a

@@ -7,9 +7,9 @@ import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), type (<--))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))-import Pandora.Paradigm.Primary.Algebraic ()+import Pandora.Paradigm.Algebraic.Exponential (type (-->), type (<--))+import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:)))+import Pandora.Paradigm.Algebraic ()  data Convergence r a = Convergence (a -> a -> r) 

@@ -3,8 +3,8 @@ import Pandora.Pattern.Category ((<--)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic (point)  data Edges a = Empty | Leap a | Connect a | Overlay a 

@@ -6,9 +6,9 @@ import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (=#-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic ((>-|-<-|-))+import Pandora.Paradigm.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic ((>-|-<-|-))  newtype Endo a = Endo { endo :: a -> a } 

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Functor.Exactly where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))+import Pandora.Pattern.Category ((<--), (<---), (<----)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))@@ -23,10 +23,10 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (extract, (<-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (extract, (<-||-)) import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~))  newtype Exactly a = Exactly a@@ -66,7 +66,7 @@  instance Adjoint (->) (->) Exactly Exactly where 	f -| x = Exactly . f . Exactly <-- x-	g |- x = extract . extract <--- g <-|- x+	g |- x = extract . extract <---- g <-|- x  instance Setoid a => Setoid (Exactly a) where 	Exactly x == Exactly y = x == y

@@ -3,7 +3,7 @@ import Pandora.Core.Functor (type (<:=), type (:=>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential ()  newtype Fix t = Fix { unfix :: t (Fix t) } 

@@ -24,11 +24,11 @@ import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt)) import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point)  data Maybe a = Nothing | Just a 

@@ -10,9 +10,9 @@ import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Ringoid (Ringoid ((*))) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), bool)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:)(Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->), type (<--))+import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:)(Option, Adoption))+import Pandora.Paradigm.Algebraic.Exponential (type (-->), type (<--)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite))  newtype Predicate a = Predicate (a -> Boolean)

@@ -6,7 +6,7 @@ import Pandora.Pattern.Functor.Bindable (Bindable ((=<<))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) --import Pandora.Pattern.Functor.Monad (Monad)-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential ()  data Proxy a = Proxy 

@@ -2,7 +2,7 @@  import Pandora.Core.Functor (type (:=>), type (~>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))+import Pandora.Pattern.Category ((<--), (<---), (<----)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))@@ -23,10 +23,10 @@ import Pandora.Pattern.Object.Semilattice (Infimum ((/\)), Supremum ((\/))) import Pandora.Pattern.Object.Lattice (Lattice) import Pandora.Pattern.Object.Group (Group (invert))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (extract, (<-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (extract, (<-||-)) import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~))  newtype Tagged tag a = Tag a@@ -56,7 +56,7 @@ 	f <<- Tag x = Tag <-|- f x  instance Distributive (->) (->) (Tagged tag) where-	f -<< x = Tag <--- extract . f <-|- x+	f -<< x = Tag <---- extract . f <-|- x  instance Bindable (->) (Tagged tag) where 	f =<< Tag x = f x

@@ -4,8 +4,8 @@ import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic (point)  data These e a = This a | That e | These e a 

@@ -9,11 +9,11 @@ import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False))

@@ -3,8 +3,8 @@ import Pandora.Pattern.Category ((<--)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic (point)  data Wedge e a = Nowhere | Here e | There a 

@@ -6,8 +6,8 @@ import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))--- import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Exponential (type (<--))+-- import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:))) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce)) 

@@ -8,7 +8,7 @@ import Pandora.Pattern.Object.Quasiring (Quasiring (one)) import Pandora.Pattern.Object.Group (Group (invert)) import Pandora.Pattern.Object.Setoid (Setoid ((==)))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:))) import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))  data Vector r a where

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Primary.Transformer.Backwards where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---))+import Pandora.Pattern.Category ((<--), (<---), (<----)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))@@ -11,11 +11,11 @@ import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic ((<-*-))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point, extract, (<-||-))+import Pandora.Paradigm.Algebraic ((<-*-))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->), (%))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point, extract, (<-||-)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~)))@@ -23,11 +23,11 @@ newtype Backwards t a = Backwards (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Backwards t) where-	f <-|- Backwards x = Backwards <--- f <-|- x+	f <-|- Backwards x = Backwards <---- f <-|- x  -- TODO: check that effects evaluation goes in opposite order instance (Semimonoidal (-->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (-->) (:*:) (:*:) (Backwards t) where-	mult = Straight <-- \(Backwards x :*: Backwards y) -> Backwards <--- ((:*:) %) <-|- y <-*- x+	mult = Straight <-- \(Backwards x :*: Backwards y) -> Backwards <---- ((:*:) %) <-|- y <-*- x  instance (Covariant (->) (->) t, Monoidal (-->) (-->) (:*:) (:*:) t) => Monoidal (-->) (-->) (:*:) (:*:) (Backwards t) where 	unit _ = Straight <-- Backwards . point . (<~ One)@@ -42,10 +42,10 @@ 	f <<- Backwards x = Backwards <-|- f <<- x  instance Distributive (->) (->) t => Distributive (->) (->) (Backwards t) where-	f -<< x = Backwards <--- run . f --<< x+	f -<< x = Backwards <--- run . f -<< x  instance Contravariant (->) (->) t => Contravariant (->) (->) (Backwards t) where-	f >-|- Backwards x = Backwards <--- f >-|- x+	f >-|- Backwards x = Backwards <---- f >-|- x  instance Interpreted (->) (Backwards t) where 	type Primary (Backwards t) a = t a

@@ -3,8 +3,8 @@  import Pandora.Core.Functor (type (:.), type (>), type (:=>), type (~>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-)))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|----), (<-|-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-))@@ -16,32 +16,30 @@ import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Ringoid ((*)) import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Paradigm.Primary.Algebraic ((<-*--), extract)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (empty, (<-||-))+import Pandora.Paradigm.Algebraic ((<-*----), extract)+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (empty, (<-||-)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~), (<~~~))-import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))-import Pandora.Paradigm.Schemes (type (<::>))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~), (<~~~), (<~~~~))  infixr 7 .-+  data Construction t a = Construct a (t :. Construction t > a)  instance Covariant (->) (->) t => Covariant (->) (->) (Construction t) where-	f <-|- ~(Construct x xs) = Construct <---- f x <---- f <-|-|- xs+	f <-|- ~(Construct x xs) = Construct <------ f x <------ f <-|-|- xs  instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Semimonoidal (-->) (:*:) (:*:) (Construction t) where 	mult = Straight <-- \(Construct x xs :*: Construct y ys) -> Construct <----- x :*: y-		<----- (mult @(-->) <~) <-|--- mult @(-->) <~~~ xs :*: ys+		<----- (mult @(-->) <~) <-|-- mult @(-->) <~~~ xs :*: ys  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Semimonoidal (<--) (:*:) (:*:) (Construction t) where 	mult = Flip <-- \(Construct (x :*: y) xys) -> (Construct x <-||-) . (Construct y <-|-)-		<---- mult @(<--) <~~~ (mult @(<--) <~) <-|- xys+		<----- mult @(<--) <~~~~ (mult @(<--) <~) <-|- xys  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Monoidal (<--) (-->) (:*:) (:*:) (Construction t) where 	unit _ = Flip <-- \(Construct x _) -> Straight (\_ -> x)@@ -50,10 +48,10 @@ 	unit _ = Straight <-- \f -> Construct <-- run f One <-- empty  instance Traversable (->) (->) t => Traversable (->) (->) (Construction t) where-	f <<- ~(Construct x xs) = Construct <-|-- f x <-*-- f <<-<<- xs+	f <<- ~(Construct x xs) = Construct <-|---- f x <-*---- f <<-<<- xs  instance Covariant (->) (->) t => Extendable (->) (Construction t) where-	f <<= x = Construct <--- f x <--- (f <<=) <-|- deconstruct x+	f <<= x = Construct <---- f x <---- (f <<=) <-|- deconstruct x  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Comonad (->) (Construction t) where @@ -61,7 +59,7 @@ 	lower x = extract <-|- deconstruct x  instance (forall u . Semimonoidal (<--) (:*:) (:*:) u, forall u . Covariant (->) (->) u) => Hoistable (->) Construction where-	f /|\ x = Construct <--- extract x <--- (/|\) @(->) f <-|- f (deconstruct x)+	f /|\ x = Construct <---- extract x <---- (/|\) @(->) f <-|- f (deconstruct x)  instance (Setoid a, forall b . Setoid b => Setoid (t b), Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Setoid (Construction t a) where 	x == y = (extract x == extract y) * (deconstruct x == deconstruct y)@@ -72,18 +70,18 @@ instance (Monoid a, forall b . Semigroup b => Monoid (t b), Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t) => Monoid (Construction t a) where 	zero = Construct zero zero -instance Monotonic a (t :. Construction t > a) => Monotonic a (Construction t a) where-	reduce f r ~(Construct x xs) = f x <-- reduce f r xs--instance Monotonic a (t :. Construction t > a) => Monotonic a (t <::> Construction t > a) where-	reduce f r = reduce f r . run+-- instance Monotonic a (t :. Construction t > a) => Monotonic a (Construction t a) where+-- 	reduce f r ~(Construct x xs) = f x <-- reduce f r xs+--+-- instance Monotonic a (t :. Construction t > a) => Monotonic a (t <::> Construction t > a) where+-- 	reduce f r = reduce f r . run  deconstruct :: Construction t a -> t :. Construction t > a 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+f .-+ x = Construct x <---- (f .-+) <-|- f x  section :: (Comonad (->) t, Monoidal (<--) (-->) (:*:) (:*:) t) => t ~> Construction t section xs = Construct <--- extract xs <--- section <<= xs

@@ -11,9 +11,9 @@ import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential ((%), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic (point)  newtype Continuation r t a = Continuation ((->) ::|:. a :. t > r) 

@@ -7,7 +7,7 @@ import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((.:..))+import Pandora.Paradigm.Algebraic.Exponential ((.:..))  data Day t u a = forall b c . Day (t b) (u c) (b -> c -> a) 

@@ -3,7 +3,7 @@  import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))@@ -14,40 +14,40 @@ 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.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:)((:*:)))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~), (<~~~))  data Instruction t a = Enter a | Instruct (t :. Instruction t > a)  instance Covariant (->) (->) t => Covariant (->) (->) (Instruction t) where 	f <-|- Enter x = Enter <-- f x-	f <-|- Instruct xs = Instruct <---- f <-|-|- xs+	f <-|- Instruct xs = Instruct <------ f <-|-|- xs  instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Semimonoidal (-->) (:*:) (:*:) (Instruction t) where 	mult = Straight <-- \case 		Enter x :*: Enter y -> Enter <--- x :*: y 		Enter x :*: Instruct y -> (x :*:) <-|- Instruct y 		Instruct x :*: Enter y -> (:*: y) <-|- Instruct x-		Instruct x :*: Instruct y -> Instruct <----- (mult @(-->) <~) <-|--- mult @(-->) <~~~ x :*: y+		Instruct x :*: Instruct y -> Instruct <----- (mult @(-->) <~) <-|-- mult @(-->) <~~~ x :*: y  instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Monoidal (-->) (-->) (:*:) (:*:) (Instruction t) where 	unit _ = Straight <-- Enter . (<~ One)  instance Covariant (->) (->) t => Bindable (->) (Instruction t) where 	f =<< Enter x = f x-	f =<< Instruct xs = Instruct <--- (f =<<) <-|- xs+	f =<< Instruct xs = Instruct <---- (f =<<) <-|- xs  instance Monad (->) t => Monad (->) (Instruction t) where  instance Traversable (->) (->) t => Traversable (->) (->) (Instruction t) where 	f <<- Enter x = Enter <-|- f x-	f <<- Instruct xs = Instruct <-|-- f <<-<<- xs+	f <<- Instruct xs = Instruct <-|- (f <<-<<- xs)  instance Liftable (->) Instruction where-	lift x = Instruct <--- Enter <-|- x+	lift x = Instruct <---- Enter <-|- x  instance (forall t . Bindable (->) t, forall t . Monoidal (-->) (-->) (:*:) (:*:) t) => Lowerable (->) Instruction where 	lower (Enter x) = point x@@ -55,4 +55,4 @@  instance (forall v . Covariant (->) (->) v) => Hoistable (->) Instruction where 	_ /|\ Enter x = Enter x-	f /|\ Instruct xs = Instruct <--- (f /|\) <-|- f xs+	f /|\ Instruct xs = Instruct <---- (f /|\) <-|- f xs

@@ -2,7 +2,7 @@ module Pandora.Paradigm.Primary.Transformer.Jack where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), identity)+import Pandora.Pattern.Category ((<--), (<---), (<----), identity) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)), (<-|-)) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))@@ -12,9 +12,9 @@ import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic (point) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False)) import Pandora.Paradigm.Primary.Object.Ordering (Ordering (Less, Greater)) @@ -22,7 +22,7 @@  instance Covariant (->) (->) t => Covariant (->) (->) (Jack t) where 	f <-|- It x = It <-- f x-	f <-|- Other y = Other <--- f <-|- y+	f <-|- Other y = Other <---- f <-|- y  instance Traversable (->) (->) t => Traversable (->) (->) (Jack t) where 	f <<- It x = It <-|- f x@@ -30,11 +30,11 @@  instance (Monoidal (-->) (-->) (:*:) (:*:) t, Bindable (->) t) => Bindable (->) (Jack t) where 	f =<< It x = f x-	f =<< Other x = Other <--- jack point identity . f ==<< x+	f =<< Other x = Other <--- jack point identity . f =<< x  instance Extendable (->) t => Extendable (->) (Jack t) where 	f <<= It x = It . f <-- It x-	f <<= Other x = Other <--- f . Other <<== x+	f <<= Other x = Other <--- f . Other <<= x  instance Liftable (->) Jack where 	lift = Other

@@ -1,15 +1,17 @@ {-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Primary.Transformer.Jet where -import Pandora.Pattern.Category ((<----))+import Pandora.Pattern.Category ((<------)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|-|-), (<-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-))-import Pandora.Paradigm.Primary.Algebraic ((<-*--))+import Pandora.Paradigm.Algebraic ((<-*--))  data Jet t a = Jet a (Jet t (t a))  instance Covariant (->) (->) t => Covariant (->) (->) (Jet t) where-	f <-|- Jet x xs = Jet <---- f x <---- f <-|-|- xs+	f <-|- Jet x xs = Jet+		<------ f x+		<------ f <-|-|- xs  instance Traversable (->) (->) t => Traversable (->) (->) (Jet t) where-	f <<- Jet x xs = Jet <-|-- f x <-*-- f <<-<<- xs+	f <<- Jet x xs = Jet <-|-- f x <-*-- (f <<-<<- xs)

@@ -2,11 +2,11 @@ module Pandora.Paradigm.Primary.Transformer.Outline where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category (identity, (<--), (<---), (<------))+import Pandora.Pattern.Category (identity, (<--), (<----), (<------)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential ()  data Outline t a where 	Line :: a -> Outline t a@@ -14,7 +14,7 @@  instance Covariant (->) (->) (Outline t) where 	f <-|- Line a = Line (f a)-	f <-|- Outlined x y = Outlined x <--- (.) f <-|- y+	f <-|- Outlined x y = Outlined x <---- (.) f <-|- y  instance Liftable (->) Outline where 	lift t = Outlined t <-- Line identity

@@ -2,7 +2,7 @@ module Pandora.Paradigm.Primary.Transformer.Reverse where  import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))@@ -13,10 +13,11 @@ import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\))) import Pandora.Paradigm.Primary.Transformer.Backwards (Backwards (Backwards))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point, extract, (<-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point, extract, empty, (<-||-)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~)))@@ -24,7 +25,7 @@ newtype Reverse t a = Reverse (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Reverse t) where-	f <-|- Reverse x = Reverse <--- f <-|- x+	f <-|- Reverse x = Reverse <---- f <-|- x  instance (Semimonoidal (-->) (:*:) (:*:) t, Covariant (->) (->) t) => Semimonoidal (-->) (:*:) (:*:) (Reverse t) where 	mult = Straight <-- \(Reverse x :*: Reverse y) -> Reverse <---- mult @(-->) <~~~ x :*: y@@ -38,14 +39,20 @@ instance (Covariant (->) (->) t, Monoidal (<--) (-->) (:*:) (:*:) t) => Monoidal (<--) (-->) (:*:) (:*:) (Reverse t) where 	unit _ = Flip <-- \(Reverse x) -> Straight (\_ -> extract x) +instance (Semimonoidal (-->) (:*:) (:+:) t, Covariant (->) (->) t) => Semimonoidal (-->) (:*:) (:+:) (Reverse t) where+	mult = Straight <-- \(Reverse x :*: Reverse y) -> Reverse <---- mult @(-->)  @(:*:) @(:+:) <~~~ x :*: y++instance (Covariant (->) (->) t, Monoidal (-->) (-->) (:*:) (:+:) t) => Monoidal (-->) (-->) (:*:) (:+:) (Reverse t) where+	unit _ = Straight <-- \_ -> Reverse empty+ 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+	f -<< x = Reverse <--- run . f -<< x  instance Contravariant (->) (->) t => Contravariant (->) (->) (Reverse t) where-	f >-|- Reverse x = Reverse <--- f >-|- x+	f >-|- Reverse x = Reverse <---- f >-|- x  instance Interpreted (->) (Reverse t) where 	type Primary (Reverse t) a = t a

@@ -3,41 +3,32 @@  import Pandora.Core.Functor (type (>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<------))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|-))) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=), (<<==)))-import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower)) import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))-import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~~~), (-#=))-import Pandora.Paradigm.Primary.Algebraic ((<-*-), extract)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%))-import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))-import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))+import Pandora.Paradigm.Controlflow.Effect.Interpreted ((<~), (<~~~))+import Pandora.Paradigm.Algebraic ((<-*-), (<-||--), extract)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), (<:*:>))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))-import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))-import Pandora.Paradigm.Structure.Ability.Substructure-	(Substructure (Substance, substructure), Segment (Root))  data Tap t a = Tap a (t a)  instance Covariant (->) (->) t => Covariant (->) (->) (Tap t) where-	f <-|- Tap x xs = Tap <--- f x <--- f <-|- xs+	f <-|- Tap x xs = Tap <---- f x <---- f <-|- xs  instance Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap t) where-	mult = Straight <-- \(Tap x xs :*: Tap y ys) -> Tap -		<---- x :*: y-		<---- mult @(-->) <~~~ xs :*: ys+	mult = Straight <-- \(Tap x xs :*: Tap y ys) -> Tap <---- x :*: y <---- mult @(-->) <~~~ xs :*: ys  instance Semimonoidal (<--) (:*:) (:*:) t => Semimonoidal (<--) (:*:) (:*:) (Tap t) where-	mult = Flip <-- \(Tap (x :*: y) xys) -> ((-#=) @(->) @(Flip _ _) (Tap x <-|-) . (Tap y <-|-)) (mult @(<--) <~~~ xys)+	mult = Flip <-- \(Tap (x :*: y) xys) -> Tap x <-||-- Tap y <-|- mult @(<--) <~ xys  instance Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (-->) (:*:) (:*:) (Tap t) where 	unit _ = Flip <-- \(Tap x _) -> Straight (\_ -> x)@@ -46,7 +37,7 @@ 	f <<- Tap x xs = Tap <-|- f x <-*- f <<- xs  instance (Semimonoidal (<--) (:*:) (:*:) t, Extendable (->) t, Covariant (->) (->) t) => Extendable (->) (Tap t) where-	f <<= x = Tap <--- f x <--- f . Tap (extract x) <<== lower x+	f <<= x = Tap <--- f x <--- f . Tap (extract x) <<= lower x  instance Lowerable (->) Tap where 	lower (Tap _ xs) = xs@@ -56,19 +47,4 @@  instance {-# OVERLAPS #-} Semimonoidal (-->) (:*:) (:*:) t => Semimonoidal (-->) (:*:) (:*:) (Tap (t <:.:> t > (:*:))) where 	mult = Straight <-- \(Tap x (T_U (xls :*: xrs)) :*: Tap y (T_U (yls :*: yrs))) ->-		Tap (x :*: y) . T_U <--- (mult @(-->) <~~~ xls :*: yls) :*: (mult @(-->) <~~~ xrs :*: yrs)--instance (Covariant (->) (->) t) => Substructure Root (Tap (t <:.:> t > (:*:))) where-	type Substance Root (Tap (t <:.:> t > (:*:))) = Exactly-	substructure = P_Q_T <-- \zipper -> case lower zipper of-		Tap x xs -> Store <--- Exactly x :*: lift . (Tap % xs) . extract--instance (Covariant (->) (->) t) => Substructure Left (Tap (t <:.:> t > (:*:))) where-	type Substance Left (Tap (t <:.:> t > (:*:))) = t-	substructure = P_Q_T <-- \zipper -> case lower zipper of-		Tap x (T_U (future :*: past)) -> Store <--- future :*: lift . Tap x . T_U . (:*: past)--instance (Covariant (->) (->) t) => Substructure Right (Tap (t <:.:> t > (:*:))) where-	type Substance Right (Tap (t <:.:> t > (:*:))) = t-	substructure = P_Q_T <-- \zipper -> case lower zipper of-		Tap x (T_U (future :*: past)) -> Store <--- past :*: lift . Tap x . T_U . (future :*:)+		Tap (x :*: y) <------ (mult @(-->) <~~~ xls :*: yls) <:*:> (mult @(-->) <~~~ xrs :*: yrs)

@@ -6,7 +6,7 @@ import Pandora.Pattern.Category ((<--)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift))-import Pandora.Paradigm.Primary.Algebraic.Exponential ()+import Pandora.Paradigm.Algebraic.Exponential ()  newtype Yoneda t a = Yoneda 	{ yoneda :: forall b . (a -> b) -> t b }

@@ -17,31 +17,30 @@ import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--)) import Pandora.Pattern.Functor.Covariant (Covariant)-import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (--|), (|-), (|--)))+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)- 	=> Adjoint (->) (->) (v <:.> t) (u <:.> w) where-		g |- TU y = (run . g |--) |- y-		f -| x = TU <-- (f . TU --|) -| x+		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) 	=> Adjoint (->) (->) (v <:.> t) (w <.:> u) where-		g |- TU t = (run . g |--) |- t-		f -| x = UT <-- (f . TU --|) -| x+		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) 	=> Adjoint (->) (->) (t <.:> v) (w <.:> u) where-		g |- UT t =  (run . g |--) |- t-		f -| x = UT <-- (f . UT --|) -| x+		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) 	=> Adjoint (->) (->) (t <.:> v) (w <:.> u) where-		g |- UT x = (run . g |--) |- x-		f -| x = TU <-- (f . UT --|) -| x+		g |- UT x = (run . g |-) |- x+		f -| x = TU <-- (f . UT -|) -| x  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-		f -| x = TUT <--  ((f . TUT --|) -|) -| x+		g |- TUT x = ((run . g |-) |-) |- x+		f -| x = TUT <-- ((f . TUT -|) -|) -| x

@@ -11,17 +11,17 @@ import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-))-import Pandora.Pattern.Functor.Distributive (Distributive ((--<<)))+import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) 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 ((/|\)))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (=#-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:), bitraverse_sum)-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (empty, point, extract, (<-||-))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (<~~~~), (=#-)))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:), bitraverse_sum)+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (empty, point, extract, (<-||-), (<-||---)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) @@ -51,23 +51,23 @@ instance (Covariant (->) (->) t, Covariant (->) (->) t', Semimonoidal (-->) (:*:) (:+:) t) => Semimonoidal (-->) (:*:) (:+:) (t <::> t') where 	mult = Straight <-- \(TT x :*: TT y) -> TT 		<----- bitraverse_sum identity identity-			<-|--- mult @(-->) @(:*:) @(:+:)+			<-|-- mult @(-->) @(:*:) @(:+:) 				<~~~ x :*: y  instance (Covariant (->) (->) t, Covariant (->) (->) t', Semimonoidal (-->) (:*:) (:+:) t, Monoidal (-->) (-->) (:*:) (:+:) t) => Monoidal (-->) (-->) (:*:) (:+:) (t <::> t') where 	unit _ = Straight <-- \_ -> TT empty  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) t') => Semimonoidal (<--) (:*:) (:*:) (t <::> t') where-	mult = Flip <-- \(TT xys) -> (TT <-||-) . (TT <-|-) . (mult @(<--) <~) <--- (mult @(<--) <~) <-|- xys+	mult = Flip <-- \(TT xys) -> TT <-||--- TT <-|--- mult @(<--) <~~~~ (mult @(<--) <~) <-|- xys  instance (Covariant (->) (->) t, Monoidal (<--) (-->) (:*:) (:*:) t, Monoidal (<--) (-->) (:*:) (:*:) t') => Monoidal (<--) (-->) (:*:) (:*:) (t <::> t') where 	unit _ = Flip <-- \(TT x) -> Straight <---- constant <--- extract <-- extract x  instance (Traversable (->) (->) t, Traversable (->) (->) t') => Traversable (->) (->) (t <::> t') where-	f <<- x = TT <-|-- f <<-<<- run x+	f <<- x = TT <-|-- (f <<-<<- run x)  instance (Bindable (->) t, Distributive (->) (->) t, Covariant (->) (->) t', Bindable (->) t') => Bindable (->) (t <::> t') where-	f =<< TT x = TT <-- (\i -> (identity =<<) <-|-- run . f --<< i) =<< x+	f =<< TT x = TT <--- (\i -> (identity =<<) <-|- run . f -<< i) =<< x  instance Monoidal (-->) (-->) (:*:) (:*:) t => Liftable (->) (TT Covariant Covariant t) where 	lift :: Covariant (->) (->) t' => t' ~> t <::> t'@@ -79,4 +79,4 @@  instance Covariant (->) (->) t => Hoistable (->) (TT Covariant Covariant t) where 	(/|\) :: t' ~> v -> (t <::> t' ~> t <::> v)-	f /|\ TT x = TT <--- f <-|- x+	f /|\ TT x = TT <---- f <-|- x

@@ -4,23 +4,23 @@ import Pandora.Core.Functor (type (:.), type (>), type (~>)) import Pandora.Pattern.Betwixt (Betwixt) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category (identity, (<--), (<---), (<-----))+import Pandora.Pattern.Category (identity, (<--), (<---), (<----), (<-----)) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-))-import Pandora.Pattern.Functor.Distributive (Distributive ((--<<)))+import Pandora.Pattern.Functor.Distributive (Distributive ((-<<))) 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 ((/|\)))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (=#-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (empty, point, extract, (<-||-))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (<~~~~), (=#-)))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (empty, point, extract, (<-||-), (<-||---)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) @@ -50,23 +50,23 @@ instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:+:) u) => Semimonoidal (-->) (:*:) (:+:) (t <:.> u) where 	mult = Straight <-- \(TU x :*: TU y) -> TU 		<----- mult @(-->) @(:*:) @(:+:)-			<-|--- mult @(-->) @(:*:) @(:*:)+			<-|-- mult @(-->) @(:*:) @(:*:) 				<~~~ x :*: y  instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) t, Semimonoidal (-->) (:*:) (:+:) u, Monoidal (-->) (-->) (:*:) (:+:) t) => Monoidal (-->) (-->) (:*:) (:+:) (t <:.> u) where 	unit _ = Straight <-- \_ -> TU empty  instance (Covariant (->) (->) t, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <:.> u) where-	mult = Flip <-- \(TU xys) -> (TU <-||-) <----- TU <-|--- mult @(<--) <~~~ (mult @(<--) <~) <-|- xys+	mult = Flip <-- \(TU xys) -> TU <-||--- TU <-|--- mult @(<--) <~~~~ (mult @(<--) <~) <-|- xys  instance (Covariant (->) (->) t, Monoidal (<--) (-->) (:*:) (:*:) t, Monoidal (<--) (-->) (:*:) (:*:) u) => Monoidal (<--) (-->) (:*:) (:*:) (t <:.> u) where 	unit _ = Flip <-- \(TU x) -> Straight (\_ -> extract <-- extract x)  instance (Traversable (->) (->) t, Traversable (->) (->) u) => Traversable (->) (->) (t <:.> u) where-	f <<- x = TU <-|-- f <<-<<- run x+	f <<- x = TU <-|-- (f <<-<<- run x)  instance (Bindable (->) t, Distributive (->) (->) t, Covariant (->) (->) u, Bindable (->) u) => Bindable (->) (t <:.> u) where-	f =<< TU x = TU <-- (\i -> (identity =<<) <-|-- run . f --<< i) =<< x+	f =<< TU x = TU <--- (\i -> (identity =<<) <-|- run . f -<< i) =<< x  instance Monoidal (-->) (-->) (:*:) (:*:) t => Liftable (->) (TU Covariant Covariant t) where 	lift :: Covariant (->) (->) u => u ~> t <:.> u@@ -78,4 +78,4 @@  instance Covariant (->) (->) t => Hoistable (->) (TU Covariant Covariant t) where 	(/|\) :: u ~> v -> (t <:.> u ~> t <:.> v)-	f /|\ TU x = TU <--- f <-|- x+	f /|\ TU x = TU <---- f <-|- x

@@ -4,8 +4,8 @@ import Pandora.Core.Functor (type (:.), type (>), type (~>)) import Pandora.Pattern.Betwixt (Betwixt) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category (identity, (<--), (<---), (<------))-import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<-|-), (<-|---), (<-|-|-), (<-|-|---), (<-|-|-|-)))+import Pandora.Pattern.Category (identity, (<--), (<---), (<----), (<------))+import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-), (<-|-|---), (<-|-|-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))@@ -15,11 +15,11 @@ import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (--|), (|-), (|--))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point, extract, (<-||-))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point, extract, (<-||-)) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Pattern.Morphism.Straight (Straight (Straight)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (=#-)))@@ -58,8 +58,8 @@ instance {-# OVERLAPS #-} (Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:+:) u) => Semimonoidal (-->) (:*:) (:+:) ((->) s <:<.>:> (:*:) s > u) where  mult = Straight <-- \(TUT x :*: TUT y) -> TUT 	<------ product_over_sum-		<-|-|--- mult @(-->) @(:*:) @(:+:)-			<-|--- mult @(-->) @(:*:) @(:*:) +		<-|-|- mult @(-->) @(:*:) @(:+:)+			<-|-- mult @(-->) @(:*:) @(:*:) 				<~~~ x :*: y  product_over_sum :: s :*: a :+: s :*: b -> s :*: (a :+: b)@@ -67,13 +67,13 @@ product_over_sum (Adoption (s :*: y)) = s :*: Adoption y  instance (Covariant (->) (->) t, Covariant (->) (->) t', Adjoint (->) (->) t' t, Bindable (->) u) => Bindable (->) (t <:<.>:> t' > u) where-	f =<< x = TUT <--- ((run . f |--) =<<) <-|- run x+	f =<< x = TUT <---- ((run . f |--) =<<) <-|- run x  instance (Bindable (->) u, Monoidal (-->) (-->) (:*:) (:*:) u, Adjoint (->) (->) t' t) => Monoidal (-->) (-->) (:*:) (:*:) (t <:<.>:> t' > u) where 	unit _ = Straight <-- unite . (point -|) . (<~ One)  instance (Adjoint (->) (->) t' t, Extendable (->) u) => Extendable (->) (t' <:<.>:> t > u) where-	f <<= x = TUT <--- ((f . unite --|) <<=) <-|- run x+	f <<= x = TUT <---- ((f . unite --|) <<=) <-|- run x  instance (Adjoint (->) (->) t' t, Distributive (->) (->) t) => Liftable (->) (t <:<.>:> t') where 	lift :: Covariant (->) (->) u => u ~> t <:<.>:> t' > u

@@ -6,7 +6,7 @@ import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) import Pandora.Pattern.Category (identity, (<--), (<---), (<----), (<-----)) import Pandora.Pattern.Morphism.Straight (Straight (Straight))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|---), (<-|-|-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---), (<-|-|-))) import Pandora.Pattern.Functor.Contravariant (Contravariant) import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))@@ -14,12 +14,12 @@ import Pandora.Pattern.Functor.Traversable (Traversable ((<<--))) import Pandora.Pattern.Transformer.Liftable (Liftable (lift)) import Pandora.Pattern.Transformer.Lowerable (Lowerable (lower))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (=#-)))-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))-import Pandora.Paradigm.Primary.Algebraic.One (One (One))-import Pandora.Paradigm.Primary.Algebraic (point, extract, (<-||-))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (<~), (<~~~), (<~~~~), (=#-)))+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic.One (One (One))+import Pandora.Paradigm.Algebraic (point, extract, (<-||-), (<-||---)) import Pandora.Pattern.Morphism.Flip (Flip (Flip))  newtype UT ct cu t u a = UT (u :. t > a)@@ -45,7 +45,7 @@ instance (Covariant (->) (->) u, Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) u, Semimonoidal (-->) (:*:) (:+:) t) => Semimonoidal (-->) (:*:) (:+:) (t <.:> u) where 	mult = Straight <-- \(UT x :*: UT y) -> UT 		<----- mult @(-->) @(:*:) @(:+:)-			<-|--- mult @(-->) @(:*:) @(:*:)+			<-|-- mult @(-->) @(:*:) @(:*:) 				<~~~ x :*: y  instance (Covariant (->) (->) t, Covariant (->) (->) u, Semimonoidal (-->) (:*:) (:*:) u, Monoidal (-->) (-->) (:*:) (:*:) t, Monoidal (-->) (-->) (:*:) (:*:) u) => Monoidal (-->) (-->) (:*:) (:*:) (t <.:> u) where@@ -55,14 +55,14 @@ 	f =<< UT x = UT <---- ((identity =<<) <-|-) . (run . f <<--) ==<< x  instance (Covariant (->) (->) u, Semimonoidal (<--) (:*:) (:*:) t, Semimonoidal (<--) (:*:) (:*:) u) => Semimonoidal (<--) (:*:) (:*:) (t <.:> u) where-	mult = Flip <-- \(UT xys) -> (UT <-||-) <----- UT <-|--- mult @(<--) <~~~ (mult @(<--) <~) <-|- xys+	mult = Flip <-- \(UT xys) -> UT <-||--- UT <-|--- mult @(<--) <~~~~ (mult @(<--) <~) <-|- xys  instance (Covariant (->) (->) u, Monoidal (<--) (-->) (:*:) (:*:) t, Monoidal (<--) (-->) (:*:) (:*:) u) => Monoidal (<--) (-->) (:*:) (:*:) (t <.:> u) where 	unit _ = Flip <-- \(UT x) -> Straight (\_ -> extract <-- extract x)  instance Monoidal (-->) (-->) (:*:) (:*:) t => Liftable (->) (UT Covariant Covariant t) where 	lift :: Covariant (->) (->) u => u ~> t <.:> u-	lift x = UT <--- point <-|- x+	lift x = UT <---- point <-|- x  instance Monoidal (<--) (-->) (:*:) (:*:) t => Lowerable (->) (UT Covariant Covariant t) where 	lower :: Covariant (->) (->) u => t <.:> u ~> u

@@ -7,38 +7,114 @@ import Pandora.Paradigm.Structure.Modification as Exports import Pandora.Paradigm.Structure.Some as Exports -import Pandora.Core.Functor (type (>)) import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--), (<---), identity)+import Pandora.Pattern.Kernel (constant) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Semigroup ((+))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (=#-), (<~))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~)) import Pandora.Paradigm.Inventory.Some.Optics () import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:) (Option, Adoption))-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))-import Pandora.Paradigm.Primary.Algebraic (extract)+import Pandora.Paradigm.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), attached)+import Pandora.Paradigm.Algebraic.Sum ((:+:) (Option, Adoption))+import Pandora.Paradigm.Algebraic (extract) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))+import Pandora.Paradigm.Primary.Functor.Conclusion (Conclusion (Failure, Success), conclusion) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Both, Left, Right, End))+import Pandora.Paradigm.Primary.Functor.Wedge (Wedge (Nowhere, Here, There))+import Pandora.Paradigm.Primary.Functor.These (These (This, That, These)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Primary.Linear.Vector (Vector (Scalar, Vector))-import Pandora.Paradigm.Primary (twosome) import Pandora.Pattern.Morphism.Flip (Flip (Flip)) import Pandora.Paradigm.Primary.Transformer.Tap (Tap (Tap))-import Pandora.Paradigm.Schemes.TU (type (<:.>)) import Pandora.Paradigm.Schemes.TT (TT (TT))-import Pandora.Paradigm.Schemes.T_U ( type (<:.:>))+import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>)) import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))  instance Monotonic s a => Monotonic s (s :*: a) where 	reduce f r x = reduce f <-- f (attached x) r <-- extract x -instance (Covariant (->) (->) t) => Substructure Tail (Tap t) where-	type Substance Tail (Tap t) = t+instance Morphable (Into Maybe) (Conclusion e) where+	type Morphing (Into Maybe) (Conclusion e) = Maybe+	morphing = conclusion (constant Nothing) Just . premorph++instance Morphable (Into (Conclusion e)) Maybe where+	type Morphing (Into (Conclusion e)) Maybe = (->) e <:.> Conclusion e+	morphing (premorph -> Just x) = TU <-- \_ -> Success x+	morphing (premorph -> Nothing) = TU <-- \e -> Failure e++instance Morphable (Into (Flip Conclusion e)) Maybe where+	type Morphing (Into (Flip Conclusion e)) Maybe = (->) e <:.> Flip Conclusion e+	morphing (run . premorph -> Just x) = TU <-- \_ -> Flip <-- Failure x+	morphing (run . premorph -> Nothing) = TU <-- Flip . Success++instance Morphable (Into (Left Maybe)) Wye where+	type Morphing (Into (Left Maybe)) Wye = Maybe+	morphing (premorph -> Both ls _) = Just ls+	morphing (premorph -> Left ls) = Just ls+	morphing (premorph -> Right _) = Nothing+	morphing (premorph -> End) = Nothing++instance Morphable (Into (Right Maybe)) Wye where+	type Morphing (Into (Right Maybe)) Wye = Maybe+	morphing (premorph -> Both _ rs) = Just rs+	morphing (premorph -> Left _) = Nothing+	morphing (premorph -> Right rs) = Just rs+	morphing (premorph -> End) = Nothing++instance Morphable (Into (This Maybe)) (These e) where+	type Morphing (Into (This Maybe)) (These e) = Maybe+	morphing (premorph -> This x) = Just x+	morphing (premorph -> That _) = Nothing+	morphing (premorph -> These _ x) = Just x++instance Morphable (Into (That Maybe)) (Flip These a) where+	type Morphing (Into (That Maybe)) (Flip These a) = Maybe+	morphing (run . premorph -> This _) = Nothing+	morphing (run . premorph -> That x) = Just x+	morphing (run . premorph -> These y _) = Just y++instance Morphable (Into (Here Maybe)) (Flip Wedge a) where+	type Morphing (Into (Here Maybe)) (Flip Wedge a) = Maybe+	morphing (run . premorph -> Nowhere) = Nothing+	morphing (run . premorph -> Here x) = Just x+	morphing (run . premorph -> There _) = Nothing++instance Morphable (Into (There Maybe)) (Wedge e) where+	type Morphing (Into (There Maybe)) (Wedge e) = Maybe+	morphing (premorph -> Nowhere) = Nothing+	morphing (premorph -> Here _) = Nothing+	morphing (premorph -> There x) = Just x++instance Morphable (Into Wye) (Maybe <:*:> Maybe) where+	type Morphing (Into Wye) (Maybe <:*:> Maybe) = Wye+	morphing (run . premorph -> Just x :*: Just y) = Both x y+	morphing (run . premorph -> Nothing :*: Just y) = Right y+	morphing (run . premorph -> Just x :*: Nothing) = Left x+	morphing (run . premorph -> Nothing :*: Nothing) = End++instance Substructure Left Wye where+	type Substance Left Wye = Maybe+	substructure = P_Q_T <-- \new -> case lower new of+		End -> Store <--- Nothing :*: lift . resolve Left End+		Left x -> Store <--- Just x :*: lift . resolve Left End+		Right y -> Store <--- Nothing :*: lift . constant (Right y)+		Both x y -> Store <--- Just x :*: lift . resolve (Both % y) (Right y)++instance Substructure Right Wye where+	type Substance Right Wye = Maybe+	substructure = P_Q_T <-- \new -> case lower new of+		End -> Store <--- Nothing :*: lift . resolve Right End+		Left x -> Store <--- Nothing :*: lift . constant (Left x)+		Right y -> Store <--- Just y :*: lift . resolve Right End+		Both x y -> Store <--- Just y :*: lift . resolve (Both x) (Left x)++instance (Covariant (->) (->) t) => Substructure Rest (Tap t) where+	type Substance Rest (Tap t) = t 	substructure = P_Q_T <-- \tap -> case extract <-- run tap of 		Tap x xs -> Store <--- xs :*: lift . Tap x 

@@ -1,7 +1,6 @@ module Pandora.Paradigm.Structure.Ability (module Exports) where  import Pandora.Paradigm.Structure.Ability.Monotonic as Exports-import Pandora.Paradigm.Structure.Ability.Zipper as Exports import Pandora.Paradigm.Structure.Ability.Substructure as Exports import Pandora.Paradigm.Structure.Ability.Morphable as Exports import Pandora.Paradigm.Structure.Ability.Possible as Exports

@@ -2,7 +2,7 @@  import Pandora.Pattern.Category ((<----)) import Pandora.Pattern.Kernel (constant)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((.:..))+import Pandora.Paradigm.Algebraic.Exponential ((.:..))  class Monotonic a e where 	{-# MINIMAL reduce #-}

@@ -6,8 +6,8 @@ import Pandora.Pattern.Category ((<--)) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Setoid (Setoid)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic (extract)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic (extract) import Pandora.Paradigm.Primary.Functor (Comparison) import Pandora.Paradigm.Primary.Functor.Convergence (Convergence (Convergence)) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))@@ -18,7 +18,8 @@ import Pandora.Paradigm.Schemes.TT (TT (TT), type (<::>)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>)) -class Morphable mod struct | mod struct -> struct where+-- type Morphable :: k -> (* -> *) -> Constraint+class Morphable (mod :: k) struct | mod struct -> struct where 	type Morphing (mod :: k) (struct :: * -> *) :: * -> * 	morphing :: Tagged mod <::> struct ~> Morphing mod struct 

@@ -2,26 +2,25 @@ {-# LANGUAGE UndecidableInstances #-} module Pandora.Paradigm.Structure.Ability.Substructure where -import Pandora.Core.Functor (type (>)) import Pandora.Pattern.Semigroupoid (Semigroupoid ((.)))-import Pandora.Pattern.Category (identity, (<--), (<---), (<-----))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))+import Pandora.Pattern.Category ((<--), (<---), (<----))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-|-))) 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, unite, (=#-)) import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Inventory.Some.Optics (Lens, Convex, type (#=@), type (@>>>))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), type (<:*:>))-import Pandora.Paradigm.Primary.Algebraic ((>-|-<-|-))-import Pandora.Paradigm.Primary.Functor.Exactly (Exactly)+import Pandora.Paradigm.Inventory.Some.Optics (type (@>>>), view, replace)+import Pandora.Paradigm.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>))+import Pandora.Paradigm.Algebraic ((>-||-), extract)+import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly)) import Pandora.Paradigm.Primary.Functor.Tagged (Tagged) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))+import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Schemes.TU (type (<:.>))-import Pandora.Paradigm.Schemes.T_U (T_U (T_U))+import Pandora.Paradigm.Schemes.TT (type (<::>)) import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T)) -data Segment a = Root a | Tail a- type Substructured segment source target = (Substructure segment source, Substance segment source ~ target)  class Substructure segment (structure :: * -> *) where@@ -29,24 +28,36 @@ 	substructure :: (Tagged segment <:.> structure) @>>> Substance segment structure  	sub :: (Covariant (->) (->) structure) => structure @>>> Substance segment structure-	sub = ((lift :*: (lower @(->) <-|-)) >-|-<-|-) =#- substructure @segment @structure---- TODO: generalize `available` and then rename to `singleton`--- The main problem is that we should handle (Maybe target -> sourse)--- For Convex Lens: we can ignore Exactly cause we can wrap/unwrap its value--- For Obscure Lens: if we got nothing -> nothing should change---only :: forall segment structure element . (Covariant (->) (->) structure, Substructured segment structure Exactly Exactly) => Convex Lens (structure element) element---only = inner . ((sub @segment) :: Convex Lens (structure element) (Exactly element)) where+	sub = (lift >-||-) . (lower @(->) <-|-|-) =#- substructure @segment @structure ---	inner :: Convex Lens (Exactly element) element---	inner = P_Q_T <-- \x -> Store <--- x :*: identity+tagstruct :: Covariant (->) (->) structure => (Tagged segment <:.> structure) @>>> structure+tagstruct = P_Q_T <-- \ts -> case lower ts of+	struct -> Store <--- struct :*: lift  instance (Covariant (->) (->) t, Covariant (->) (->) u) => Substructure Left (t <:*:> u) where 	type Substance Left (t <:*:> u) = t 	substructure = P_Q_T <-- \x -> case run <-- lower x of-		ls :*: rs -> Store <--- ls :*: lift . (T_U . (:*: rs))+		ls :*: rs -> Store <--- ls :*: lift . (<:*:> rs)  instance (Covariant (->) (->) t, Covariant (->) (->) u) => Substructure Right (t <:*:> u) where 	type Substance Right (t <:*:> u) = u 	substructure = P_Q_T <-- \x -> case run <-- lower x of-		ls :*: rs -> Store <--- rs :*: lift . (T_U . (ls :*:))+		ls :*: rs -> Store <--- rs :*: lift . (ls <:*:>)++data Segment a = Root a | Rest a | Branch a | Ancestors a | Forest a++instance Covariant (->) (->) t => Substructure Root (Construction t) where+	type Substance Root (Construction t) = Exactly+	substructure = P_Q_T <-- \source -> case lower source of+		Construct x xs -> Store <--- Exactly x :*: lift . (Construct % xs) . extract++instance Covariant (->) (->) t => Substructure Rest (Construction t) where+	type Substance Rest (Construction t) = t <::> Construction t+	substructure = P_Q_T <-- \source -> case lower source of+		Construct x xs -> Store <--- unite xs :*: lift . Construct x . run++instance (Covariant (->) (->) t, Substructure i t) => Substructure (i Branch) (Construction t) where+	type Substance (i Branch) (Construction t) = Substance i t <::> Construction t+	substructure = P_Q_T <-- \source -> case lower source of+		Construct x xs -> Store <--- unite (view <-- sub @i <-- xs) :*: \target ->+			lift <---- Construct x <--- replace <-- run target <-- sub @i <-- xs

@@ -1,107 +0,0 @@-{-# OPTIONS_GHC -fno-warn-orphans #-}-{-# LANGUAGE UndecidableInstances #-}-{-# LANGUAGE TypeSynonymInstances #-}-module Pandora.Paradigm.Structure.Ability.Zipper where--import Pandora.Core.Functor (type (>), type (<), type (:.), type (:::))-import Pandora.Core.Impliable (Impliable (Arguments, imply))-import Pandora.Pattern.Morphism.Flip (Flip (Flip))-import Pandora.Pattern.Morphism.Straight (Straight (Straight))-import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----))-import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--)))-import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))-import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))-import Pandora.Pattern.Transformer.Liftable (lift)-import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Paradigm.Primary.Algebraic (extract)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--), type (-->), (%))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), type (<:*:>))-import Pandora.Paradigm.Primary.Algebraic ((<-*-), (<-*--), point)-import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))-import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))-import Pandora.Paradigm.Primary.Functor.Tagged (Tagged)-import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse (Reverse))-import Pandora.Paradigm.Primary (twosome)-import Pandora.Paradigm.Schemes.TT (TT (TT), type (<::>))-import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>))-import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))-import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))-import Pandora.Paradigm.Structure.Ability.Morphable (Morphable, Morph (Rotate), Vertical (Up, Down), Occurrence (All))-import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure), Segment (Root), sub)-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~), (=#-))-import Pandora.Paradigm.Inventory.Ability.Gettable (get)-import Pandora.Paradigm.Inventory.Ability.Settable (set)-import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Inventory.Some.Optics (Lens, Convex, view, replace, mutate)--class Zippable (structure :: * -> *) where-	type Breadcrumbs structure :: * -> *--type Zipper (structure :: * -> *) = Tagged Zippable <:.> (Exactly <:*:> Breadcrumbs structure)--type Breadcrumbed structure t = (Zippable structure, Breadcrumbs structure ~ t)--instance {-# OVERLAPS #-} Semimonoidal (<--) (:*:) (:*:) t-	=> Semimonoidal (<--) (:*:) (:*:) (Exactly <:.:> t > (:*:)) where-	mult = Flip <-- \(T_U (Exactly (x :*: y) :*: xys)) ->-		let xs :*: ys = mult @(<--) <~ xys in-			T_U (Exactly x :*: xs) :*: T_U (Exactly y :*: ys)--instance {-# OVERLAPS #-} Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (-->) (:*:) (:*:) (Exactly <:.:> t > (:*:)) where-	unit _ = Flip <-- \(T_U (Exactly x :*: _)) -> Straight (\_ -> x)--type family Fastenable structure rs where-	Fastenable structure (r ::: rs) = (Morphable < Rotate r < structure, Fastenable structure rs)-	Fastenable structure r = Morphable < Rotate r < structure--type Tape t = Tagged Zippable <:.> (Exactly <:*:> (Reverse t <:*:> t))--instance Covariant (->) (->) t => Impliable (Tape t a) where-	type Arguments (Tape t a) = a -> t a -> t a -> Tape t a-	imply focused left right = lift-		<---- twosome <-- Exactly focused -			<--- twosome <-- Reverse left <-- right---- TODO: Isn't too fragile to define such an instance without any hints about zippers?-instance Covariant (->) (->) t => Substructure Root (Tape t) where-	type Substance Root (Tape t) = Exactly-	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of-		 Exactly x :*: xs -> Store <--- Exactly x :*: lift . lift . T_U . (:*: xs)--instance Covariant (->) (->) t => Substructure Left (Tape t) where-	type Substance Left (Tape t) = Reverse t-	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of-		Exactly x :*: T_U (ls :*: rs) -> Store <--- ls :*: lift . (imply @(Tape t _) x % rs) . run--instance Covariant (->) (->) t => Substructure Right (Tape t) where-	type Substance Right (Tape t) = t-	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of-		Exactly x :*: T_U (Reverse ls :*: rs) -> Store <--- rs :*: lift . imply @(Tape t _) x ls--instance Covariant (->) (->) t => Substructure Up (Tape t <::> Tape t) where-	type Substance Up (Tape t <::> Tape t) = t <::> Tape t-	substructure = P_Q_T <-- \x -> case run . lower . run . lower <-- x of-		Exactly focused :*: T_U (Reverse d :*: u) ->-			Store <--- TT u :*: lift . TT . imply @(Tape t _) focused d . run--instance Covariant (->) (->) t => Substructure Down (Tape t <::> Tape t) where-	type Substance Down (Tape t <::> Tape t) = Reverse t <::> Tape t-	substructure = P_Q_T <-- \ii -> case run . lower . run . lower <-- ii of-		Exactly focused :*: T_U (d :*: u) ->-			Store <--- TT d :*: lift . TT . (imply @(Tape t _) focused % u) . run . run--instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure (All Left) (Tape t <::> Tape t) where-	type Substance (All Left) (Tape t <::> Tape t) = Tape t <::> Reverse t-	substructure = P_Q_T <-- \source ->-		let target = (view (sub @Left) <-|-) =#- lower source in-		let updated new = replace % sub @Left <-|-- new <-*-- run <-- lower source in-		Store <--- target :*: lift . (updated =#-)--instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure (All Right) (Tape t <::> Tape t) where-	type Substance (All Right) (Tape t <::> Tape t) = Tape t <::> t-	substructure = P_Q_T <-- \source ->-		let target = (view (sub @Right) <-|-) =#- lower source in-		let updated new = replace % sub @Right <-|-- new <-*-- run <-- lower source in-			Store <--- target :*: lift . (updated =#-)

@@ -1,5 +1,6 @@ module Pandora.Paradigm.Structure.Interface (module Exports) where +import Pandora.Paradigm.Structure.Interface.Zipper as Exports import Pandora.Paradigm.Structure.Interface.Stack as Exports import Pandora.Paradigm.Structure.Interface.Dictionary as Exports import Pandora.Paradigm.Structure.Interface.Set as Exports

@@ -5,13 +5,13 @@ import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--), (<---)) import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Functor.Traversable (Traversable ((<<-), (<<--)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Object.Setoid (Setoid ((!=))) import Pandora.Pattern.Object.Semigroup ((+)) import Pandora.Pattern.Object.Quasiring (one)-import Pandora.Paradigm.Primary.Algebraic ()-import Pandora.Paradigm.Primary.Algebraic.Product (attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic ()+import Pandora.Paradigm.Algebraic.Product (attached)+import Pandora.Paradigm.Algebraic.Exponential ((%)) import Pandora.Paradigm.Primary.Functor.Convergence (Convergence (Convergence)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Nothing)) import Pandora.Paradigm.Primary.Functor.Predicate (Predicate, equate)@@ -26,7 +26,7 @@ type Set t f a = (Traversable (->) (->) t, Setoid a, Setoid (t a), Morphable (Find f) t)  subset :: forall t f a . (Set t f a, Morphing (Find f) t ~ (Predicate <:.:> Maybe > (->))) => Convergence Boolean > t a-subset = Convergence <-- \s ss -> Nothing != (find @f @t @Maybe % s) . equate <<-- ss+subset = Convergence <-- \s ss -> Nothing != ((find @f @t @Maybe % s) . equate <<- ss)  cardinality :: Traversable (->) (->) t => t a -> Numerator cardinality s = attached <--- constant (modify @State (+ one)) <<- s <~~ Zero

@@ -15,5 +15,6 @@ 	type Popping t :: * -> * 	type Pushing t :: * -> * 	top :: Lens (Topping t) (t e) e+	-- TODO: In case of nonempty list we know that we return an element 	pop :: State ((Popping t) e) (Maybe e) 	push :: e -> State ((Pushing t) e) e

@@ -0,0 +1,55 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE TypeSynonymInstances #-}+module Pandora.Paradigm.Structure.Interface.Zipper where++import Pandora.Core.Functor (type (>), type (<), type (:.), type (:::))+import Pandora.Core.Impliable (Impliable (Arguments, imply))+import Pandora.Pattern.Morphism.Flip (Flip (Flip))+import Pandora.Pattern.Morphism.Straight (Straight (Straight))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<------))+import Pandora.Pattern.Kernel (constant)+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-), (<<---)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))+import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))+import Pandora.Pattern.Transformer.Liftable (lift)+import Pandora.Pattern.Transformer.Lowerable (lower)+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->), (%))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>))+import Pandora.Paradigm.Algebraic ((<-*-), (<-*--), (<-*---), (.-*-), extract, point)+import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))+import Pandora.Paradigm.Primary.Functor.Tagged (Tagged)+import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>))+import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))+import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))+import Pandora.Paradigm.Inventory.Some.Store (Store (Store))+import Pandora.Paradigm.Structure.Ability.Morphable (Morphable, Morph (Rotate))+import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure, sub), Segment (Root, Rest))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, unite, (<~), (=#-))++class Zippable (structure :: * -> *) where+	type Breadcrumbs structure :: * -> *++type Zipper (structure :: * -> *) = Tagged (Zippable structure) <:.> (Exactly <:*:> Breadcrumbs structure)++type Breadcrumbed structure t = (Zippable structure, Breadcrumbs structure ~ t)++instance {-# OVERLAPS #-} Semimonoidal (<--) (:*:) (:*:) t+	=> Semimonoidal (<--) (:*:) (:*:) (Exactly <:*:> t) where+	mult = Flip <-- \(T_U (Exactly (x :*: y) :*: xys)) ->+		let xs :*: ys = mult @(<--) <~ xys in+			(Exactly x <:*:> xs) :*: (Exactly y <:*:> ys)++instance {-# OVERLAPS #-} Semimonoidal (<--) (:*:) (:*:) t => Monoidal (<--) (-->) (:*:) (:*:) (Exactly <:*:> t) where+	unit _ = Flip <-- \(T_U (Exactly x :*: _)) -> Straight (\_ -> x)++instance Covariant (->) (->) t => Substructure Root (Tagged (Zippable structure) <:.> (Exactly <:*:> t)) where+	type Substance Root (Tagged (Zippable structure) <:.> (Exactly <:*:> t)) = Exactly+	substructure = P_Q_T <-- \source -> case lower . lower <-- source of+		T_U (Exactly x :*: xs) -> Store <--- Exactly x :*: lift . lift . (<:*:> xs)++type family Fastenable structure rs where+	Fastenable structure (r ::: rs) = (Morphable < Rotate r < structure, Fastenable structure rs)+	Fastenable structure r = Morphable < Rotate r < structure

@@ -1,6 +1,7 @@ module Pandora.Paradigm.Structure.Modification (module Exports) where  import Pandora.Paradigm.Structure.Modification.Turnover as Exports+import Pandora.Paradigm.Structure.Modification.Tape as Exports import Pandora.Paradigm.Structure.Modification.Prefixed as Exports import Pandora.Paradigm.Structure.Modification.Comprehension as Exports import Pandora.Paradigm.Structure.Modification.Combinative as Exports

@@ -10,7 +10,7 @@ import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult)) import Pandora.Pattern.Functor.Monoidal (Monoidal (unit)) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (===<<)))+import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (==<<))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))@@ -21,10 +21,10 @@ import Pandora.Paradigm.Schemes.TT (TT (TT), 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.Primary.Algebraic.Exponential (type (-->))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic.Sum ((:+:))-import Pandora.Paradigm.Primary.Algebraic (empty, (<-|-<-|-))+import Pandora.Paradigm.Algebraic.Exponential (type (-->))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic.Sum ((:+:))+import Pandora.Paradigm.Algebraic (empty, (<-|-<-|-))  newtype Comprehension t a = Comprehension (t <::> Construction t > a) @@ -34,7 +34,7 @@ 	unite = Comprehension  instance Covariant (->) (->) (t <::> Construction t) => Covariant (->) (->) (Comprehension t) where-	f <-|- Comprehension x = Comprehension <--- f <-|- x+	f <-|- Comprehension x = Comprehension <---- f <-|- x  instance Traversable (->) (->) (t <::> Construction t) => Traversable (->) (->) (Comprehension t) where 	f <<- Comprehension x = Comprehension <-|- f <<- x@@ -46,7 +46,7 @@ 	unit _ = Straight <-- \_ -> Comprehension empty  instance (forall a . Semigroup (t <::> Construction t > a), Bindable (->) t) => Bindable (->) (Comprehension t) where-	f =<< Comprehension (TT t) = Comprehension . TT <-- (\(Construct x xs) -> run . run @(->) <---- f x + (f ===<< Comprehension <-- TT xs)) =<< t+	f =<< Comprehension (TT t) = Comprehension . TT <--- (\(Construct x xs) -> run . run @(->) <-- f x + (f ==<< Comprehension <-- TT xs)) =<< t  instance Setoid (t <::> Construction t > a) => Setoid (Comprehension t a) where 	Comprehension ls == Comprehension rs = ls == rs

@@ -4,10 +4,10 @@  import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|-|-)))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|----), (<-|-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)), (<<-<<-))-import Pandora.Paradigm.Primary.Algebraic (extract)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic (extract)+import Pandora.Paradigm.Algebraic.Product ((:*:)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (=#-))) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Into), premorph) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)@@ -24,7 +24,7 @@ 	(<-|-) f = (=#-) (f <-|-|-)  instance Traversable (->) (->) t => Traversable (->) (->) (Prefixed t k) where-	f <<- Prefixed x = Prefixed <-|-- f <<-<<- x+	f <<- Prefixed x = Prefixed <-|---- f <<-<<- x  instance Covariant (->) (->) t => Morphable (Into t) (Prefixed t k) where 	type Morphing (Into t) (Prefixed t k) = t

@@ -0,0 +1,78 @@+{-# OPTIONS_GHC -fno-warn-orphans #-}+module Pandora.Paradigm.Structure.Modification.Tape where++import Pandora.Core.Impliable (Impliable (Arguments, imply))+import Pandora.Pattern.Semigroupoid ((.))+import Pandora.Pattern.Category ((<--), (<---), (<----), (<------))+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|---)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-), (<<---)))+import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))+import Pandora.Pattern.Functor.Monoidal (Monoidal (unit))+import Pandora.Pattern.Transformer.Liftable (lift)+import Pandora.Pattern.Transformer.Lowerable (lower)+import Pandora.Paradigm.Algebraic.Exponential (type (<--), type (-->), (%))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>))+import Pandora.Paradigm.Algebraic ((<-*-), (<-*--), (<-*---), (.-*-), extract, point)+import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>))+import Pandora.Paradigm.Schemes.TT (TT (TT), type (<::>))+import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))+import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T))+import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))+import Pandora.Paradigm.Primary.Functor.Tagged (Tagged)+import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))+import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse (Reverse))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, unite, (<~), (=#-))+import Pandora.Paradigm.Structure.Ability.Morphable (Morphable, Morph (Rotate), Vertical (Up, Down), Occurrence (All))+import Pandora.Paradigm.Structure.Interface.Zipper (Zippable)+import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure), Segment (Root), sub)+import Pandora.Paradigm.Inventory.Some.Store (Store (Store))+import Pandora.Paradigm.Inventory.Some.Optics (Lens, Convex, view, replace, mutate)++type Tape structure = Tagged (Zippable structure)+	<:.> (Exactly <:*:> Reverse structure <:*:> structure)++instance {-# OVERLAPS #-} Traversable (->) (->) t => Traversable (->) (->) (Tape t) where+	f <<- z = (\ls x rs -> lift <------ x <:*:> ls <:*:> rs)+		<-|--- f <<--- view <-- sub @Left <-- z+		<-*--- f <<--- view <-- sub @Root <-- z+		<-*--- f <<--- view <-- sub @Right <-- z++instance Covariant (->) (->) t => Impliable (Tape t a) where+	type Arguments (Tape t a) = a -> t a -> t a -> Tape t a+	imply focused left right = lift <------ Exactly focused <:*:> Reverse left <:*:> right++instance Covariant (->) (->) t => Substructure Left (Tape t) where+	type Substance Left (Tape t) = Reverse t+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (ls :*: rs) -> Store <--- ls :*: lift . (imply @(Tape t _) x % rs) . run++instance Covariant (->) (->) t => Substructure Right (Tape t) where+	type Substance Right (Tape t) = t+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (Reverse ls :*: rs) -> Store <--- rs :*: lift . imply @(Tape t _) x ls++instance Covariant (->) (->) t => Substructure Up (Tape t <::> Tape t) where+	type Substance Up (Tape t <::> Tape t) = t <::> Tape t+	substructure = P_Q_T <-- \x -> case run . lower . run . lower <-- x of+		Exactly focused :*: T_U (Reverse d :*: u) ->+			Store <--- TT u :*: lift . TT . imply @(Tape t _) focused d . run++instance Covariant (->) (->) t => Substructure Down (Tape t <::> Tape t) where+	type Substance Down (Tape t <::> Tape t) = Reverse t <::> Tape t+	substructure = P_Q_T <-- \ii -> case run . lower . run . lower <-- ii of+		Exactly focused :*: T_U (d :*: u) ->+			Store <--- TT d :*: lift . TT . (imply @(Tape t _) focused % u) . run . run++instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure (All Left) (Tape t <::> Tape t) where+	type Substance (All Left) (Tape t <::> Tape t) = Tape t <::> Reverse t+	substructure = P_Q_T <-- \source ->+		let target = (view (sub @Left) <-|-) =#- lower source in+		let updated new = replace % sub @Left <-|-- new <-*-- run <-- lower source in+		Store <--- target :*: lift . (updated =#-)++instance (Covariant (->) (->) t, Semimonoidal (-->) (:*:) (:*:) t) => Substructure (All Right) (Tape t <::> Tape t) where+	type Substance (All Right) (Tape t <::> Tape t) = Tape t <::> t+	substructure = P_Q_T <-- \source ->+		let target = (view (sub @Right) <-|-) =#- lower source in+		let updated new = replace % sub @Right <-|-- new <-*-- run <-- lower source in+			Store <--- target :*: lift . (updated =#-)

@@ -3,8 +3,8 @@  import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-))) import Pandora.Pattern.Transformer.Hoistable ((/|\))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic ((>-|-<-|-))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))+import Pandora.Paradigm.Algebraic ((>-|-<-|-)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (Interpreted (Primary, run, unite, (=#-))) import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure)) 

@@ -7,13 +7,13 @@ import Pandora.Pattern.Kernel (constant) import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--), (<-|-|-))) import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))-import Pandora.Pattern.Functor.Bindable (Bindable ((===<<)))+import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (==<<))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower) import Pandora.Pattern.Object.Chain (Chain ((<=>)))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), type (:*:), type (<:*:>), attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%), (&), (.:..))-import Pandora.Paradigm.Primary.Algebraic ((<-*-), (<-*--), (<-*-*-), extract, point, empty)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>), attached)+import Pandora.Paradigm.Algebraic.Exponential ((%), (&), (.:..))+import Pandora.Paradigm.Algebraic ((<-*-), (<-*--), (<-*-*-), extract, point, empty) import Pandora.Paradigm.Primary.Object.Ordering (order) import Pandora.Paradigm.Primary.Functor (Comparison) import Pandora.Paradigm.Primary.Functor.Convergence (Convergence (Convergence))@@ -21,7 +21,6 @@ import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct))-import Pandora.Paradigm.Primary (twosome) import Pandora.Paradigm.Schemes (TT (TT), T_U (T_U), P_Q_T (P_Q_T), type (<::>), type (<:.:>)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~)) import Pandora.Paradigm.Inventory.Ability.Gettable (get)@@ -33,26 +32,12 @@ import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (resolve)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), morph, premorph 	, Morph (Rotate, Into, Insert, Lookup, Key), Vertical (Up, Down), Horizontal (Leftward, Rightward), lookup)-import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure), Segment (Root), sub)-import Pandora.Paradigm.Structure.Ability.Zipper (Zippable (Breadcrumbs))+import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure), Segment (Root, Branch), sub)+import Pandora.Paradigm.Structure.Interface.Zipper (Zippable (Breadcrumbs)) import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed (Prefixed))  type Binary = Maybe <::> Construction (Maybe <:*:> Maybe) --- instance {-# OVERLAPS #-} Traversable (->) (->) (Construction Wye) where-	-- f <<- Construct x (Left l) = Construct <-|-- f x <-*-- Left <-|- f <<- l-	-- f <<- Construct x (Right r) = Construct <-|-- f x <-*-- Right <-|- f <<- r-	-- f <<- Construct x (Both l r) = Construct <-|-- f x <-*-- Both <-|- f <<- l <-*- f <<- r-	-- f <<- Construct x End = Construct % End <-|- f x---- instance {-# OVERLAPS #-} Traversable (->) (->) (Construction (Maybe <:*:> Maybe)) where-	-- f <<- Construct x branches = Construct <-|- f x <-*- (f <<- branches :: _)--	-- f <<- Construct x (Left l) = Construct <-|-- f x <-*-- Left <-|- f <<- l-	-- f <<- Construct x (Right r) = Construct <-|-- f x <-*-- Right <-|- f <<- r-	-- f <<- Construct x (Both l r) = Construct <-|-- f x <-*-- Both <-|- f <<- l <-*- f <<- r-	-- f <<- Construct x (Nothing <:*:> Nothing) = Construct % (Nothing <:*:> Nothing) <-|- f x- --rebalance :: Chain a => (Wye :. Construction Wye > a) -> Nonempty Binary a --rebalance (Both x y) = extract x <=> extract y & order --	# Construct (extract x) (Both # rebalance (deconstruct x) # rebalance (deconstruct y))@@ -62,65 +47,60 @@ -- instance Morphable Insert Binary where 	-- type Morphing Insert Binary = (Exactly <:.:> Comparison > (:*:)) <:.:> Binary > (->) 	-- morphing struct = case run ---> premorph struct of-		-- Nothing -> T_U <-- \(T_U (Exactly x :*: _)) -> lift <-- leaf x+		-- Nothing -> T_U <-- \(T_U (Exactly x :*: _)) -> lift <-- point x 		-- Just binary -> T_U <-- \(T_U (Exactly x :*: Convergence f)) -> 			-- let continue xs = run <-- morph @Insert @(Nonempty Binary) xs <--- twosome <-- Exactly x <-- Convergence f in-			-- let step = iff @Just <-|-|- get @(Obscure Lens) <-*-*- modify @(Obscure Lens) continue <-*-*- set @(Obscure Lens) <-- leaf x in+			-- let step = iff @Just <-|-|- get @(Obscure Lens) <-*-*- modify @(Obscure Lens) continue <-*-*- set @(Obscure Lens) <-- point x in 			-- lift <---- order binary 				-- <--- step <-- sub @Left <-- binary 				-- <--- step <-- sub @Right <-- binary 				-- <--- f x <-- extract binary -instance Substructure Left Binary where-	type Substance Left Binary = Binary+instance Substructure (Left Branch) Binary where+	type Substance (Left Branch) Binary = Binary 	substructure = P_Q_T <-- \struct -> case run <-- lower struct of 		Nothing -> Store <--- empty :*: lift . constant empty-		Just tree -> lift . lift @(->) <-|- sub @Left <~ tree+		Just tree -> lift . lift @(->) <-|- sub @(Left Branch) <~ tree -instance Substructure Right Binary where-	type Substance Right Binary = Binary+instance Substructure (Right Branch) Binary where+	type Substance (Right Branch) Binary = Binary 	substructure = P_Q_T <-- \struct -> case run . extract . run ---> struct of 		Nothing -> Store <--- empty :*: lift . constant empty-		Just tree -> lift . lift @(->) <-|- sub @Right <~ tree+		Just tree -> lift . lift @(->) <-|- sub @(Right Branch) <~ tree  -------------------------------------- Non-empty binary tree --------------------------------------- -type instance Nonempty Binary = Construction (Maybe <:*:> Maybe)+type instance Nonempty Binary = Construction > Maybe <:*:> Maybe -instance Morphable (Into Binary) (Construction (Maybe <:*:> Maybe)) where-	type Morphing (Into Binary) (Construction (Maybe <:*:> Maybe)) = Binary+instance Morphable (Into Binary) (Construction > Maybe <:*:> Maybe) where+	type Morphing (Into Binary) (Construction > Maybe <:*:> Maybe) = Binary 	morphing = lift . premorph  -- instance Morphable Insert (Construction Wye) where 	-- type Morphing Insert (Construction Wye) = (Exactly <:.:> Comparison > (:*:)) <:.:> Construction Wye > (->) 	-- morphing (premorph -> struct) = T_U <-- \(T_U (Exactly x :*: Convergence f)) -> 		-- let continue xs = run <--- morph @Insert @(Nonempty Binary) xs <---- twosome <--- Exactly x <--- Convergence f in-		-- let step = iff @Just <-|-|- (run .:.. view) <-*-*- mutate continue <-*-*- replace (leaf x) in+		-- let step = iff @Just <-|-|- (run .:.. view) <-*-*- mutate continue <-*-*- replace (point x) in 		-- order struct 			-- <---- step <--- sub @Left <--- struct 			-- <---- step <--- sub @Right <--- struct 			-- <---- f x <--- extract struct -instance Substructure Root (Construction (Maybe <:*:> Maybe)) where-	type Substance Root (Construction (Maybe <:*:> Maybe)) = Exactly-	substructure = P_Q_T <-- \struct -> case lower struct of-		Construct x xs -> Store <--- Exactly x :*: lift . (Construct % xs) . extract--instance Substructure Left (Construction (Maybe <:*:> Maybe)) where-	type Substance Left (Construction (Maybe <:*:> Maybe)) = Binary-	substructure = P_Q_T <-- \struct -> case extract ---> run struct of-		Construct x (T_U (Nothing :*: Nothing)) -> Store <--- TT Nothing :*: lift . resolve (Construct x . left) (leaf x) . run-		Construct x (T_U (Just lst :*: Nothing)) -> Store <--- TT (Just lst) :*: lift . Construct x . resolve left end . run-		Construct x (T_U (Nothing :*: Just rst)) -> Store <--- TT Nothing :*: lift . Construct x . resolve (both % rst) (right rst) . run-		Construct x (T_U (Just lst :*: Just rst)) -> Store <--- TT (Just lst) :*: lift . Construct x . resolve (both % rst) (right rst) . run--instance Substructure Right (Construction (Maybe <:*:> Maybe)) where-	type Substance Right (Construction (Maybe <:*:> Maybe)) = Binary-	substructure = P_Q_T <-- \struct -> case extract <-- run struct of-		Construct x (T_U (Nothing :*: Nothing)) -> Store <--- TT Nothing :*: lift . resolve (Construct x . right) (leaf x) . run-		Construct x (T_U (Just lst :*: Nothing)) -> Store <--- TT Nothing :*: lift . Construct x . resolve (both lst) (left lst) . run-		Construct x (T_U (Nothing :*: Just rst)) -> Store <--- TT (Just rst) :*: lift . Construct x . resolve right end . run-		Construct x (T_U (Just lst :*: Just rst)) -> Store <--- TT (Just rst) :*: lift . Construct x . resolve (both lst) (left lst) . run+-- instance Substructure Left (Construction (Maybe <:*:> Maybe)) where+-- 	type Substance Left (Construction (Maybe <:*:> Maybe)) = Binary+-- 	substructure = P_Q_T <-- \struct -> case extract ---> run struct of+-- 		Construct x (T_U (Nothing :*: Nothing)) -> Store <--- TT Nothing :*: lift . resolve (Construct x . left) (point x) . run+-- 		Construct x (T_U (Just lst :*: Nothing)) -> Store <--- TT (Just lst) :*: lift . Construct x . resolve left end . run+-- 		Construct x (T_U (Nothing :*: Just rst)) -> Store <--- TT Nothing :*: lift . Construct x . resolve (both % rst) (right rst) . run+-- 		Construct x (T_U (Just lst :*: Just rst)) -> Store <--- TT (Just lst) :*: lift . Construct x . resolve (both % rst) (right rst) . run+--+-- instance Substructure Right (Construction (Maybe <:*:> Maybe)) where+-- 	type Substance Right (Construction (Maybe <:*:> Maybe)) = Binary+-- 	substructure = P_Q_T <-- \struct -> case extract <-- run struct of+-- 		Construct x (T_U (Nothing :*: Nothing)) -> Store <--- TT Nothing :*: lift . resolve (Construct x . right) (point x) . run+-- 		Construct x (T_U (Just lst :*: Nothing)) -> Store <--- TT Nothing :*: lift . Construct x . resolve (both lst) (left lst) . run+-- 		Construct x (T_U (Nothing :*: Just rst)) -> Store <--- TT (Just rst) :*: lift . Construct x . resolve right end . run+-- 		Construct x (T_U (Just lst :*: Just rst)) -> Store <--- TT (Just rst) :*: lift . Construct x . resolve (both lst) (left lst) . run  -------------------------------------- Prefixed binary tree ---------------------------------------- @@ -129,15 +109,15 @@ 	morphing struct = case run . run . premorph <-- struct of 		Nothing -> TT <-- \_ -> Nothing 		Just tree -> TT <-- \key ->-			key <=> attached <-- extract tree & order-				<---- Just --> extract --> extract tree-				<---- lookup @Key key . Prefixed ===<< run (view <-- sub @Left <-- tree)-				<---- lookup @Key key . Prefixed ===<< run (view <-- sub @Right <-- tree)+			key <=> attached (extract tree) & order+				<--- Just --> extract --> extract tree+				<--- lookup @Key key . Prefixed =<< run (view <-- sub @(Left Branch) <-- tree)+				<--- lookup @Key key . Prefixed =<< run (view <-- sub @(Right Branch) <-- tree)  -- instance Chain k => Morphable (Vary Element) (Prefixed Binary k) where 	-- type Morphing (Vary Element) (Prefixed Binary k) = ((:*:) k <::> Exactly) <:.:> Prefixed Binary k > (->) 	-- morphing struct = case run . run . premorph ! struct of-		-- Nothing -> T_U ! \(TT (key :*: Exactly value)) -> Prefixed . lift . leaf ! key :*: value+		-- Nothing -> T_U ! \(TT (key :*: Exactly value)) -> Prefixed . lift . point ! key :*: value 		-- Just tree -> T_U ! \(TT (key :*: Exactly value)) -> 			-- let continue = ((vary @Element @k @_ @(Prefixed Binary _) key value -#=) -#=) in 			-- Prefixed . lift ! key <=> attached (extract tree) & order@@ -152,8 +132,8 @@ 	morphing (run . premorph -> Construct x xs) = TT <-- \key -> 		key <=> attached x & order 			<---- Just <-- extract x-			<---- lookup @Key key . Prefixed ===<< get @(Obscure Lens) <-- sub @Left <-- xs-			<---- lookup @Key key . Prefixed ===<< get @(Obscure Lens) <-- sub @Left <-- xs+			<---- lookup @Key key . Prefixed ==<< get @(Obscure Lens) <-- sub @Left <-- xs+			<---- lookup @Key key . Prefixed ==<< get @(Obscure Lens) <-- sub @Left <-- xs  -------------------------------------- Zipper of binary tree --------------------------------------- 	{-@@ -184,34 +164,34 @@ 		= Maybe <::> ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> Bifurcation <::> Bicursor > (:*:)) 	morphing struct = case run ---> premorph struct of 		focused :*: TT (TT (Horizontal (Rightward (Construct (T_U (Exactly parent :*: rest)) next)))) ->-			lift . (twosome % TT (TT next)) . twosome (Exactly parent) . TT <---- resolve+			lift . ((<:*:>) % TT (TT next)) . (<:*:>) (Exactly parent) . TT <---- resolve 				<--- Both <-- _focused_part_to_nonempty_binary_tree focused 				<--- Left <-- _focused_part_to_nonempty_binary_tree focused 				<--- run rest 		focused :*: TT (TT (Horizontal (Leftward (Construct (T_U (Exactly parent :*: rest)) next)))) ->-			lift . (twosome % TT (TT next)) . twosome (Exactly parent) . TT <---- resolve+			lift . ((<:*:>) % TT (TT next)) . (<:*:>) (Exactly parent) . TT <---- resolve 				<--- Both % _focused_part_to_nonempty_binary_tree focused 				<--- Right <-- _focused_part_to_nonempty_binary_tree focused 				<--- run rest 		_ -> TT Nothing  _nonempty_binary_tree_to_focused_part :: Construction Wye ~> Exactly <:.:> Wye <::> Construction Wye > (:*:)-_nonempty_binary_tree_to_focused_part (Construct x xs) = twosome <--- Exactly x <--- TT xs+_nonempty_binary_tree_to_focused_part (Construct x xs) = Exactly x <:*:> TT xs  instance Morphable (Rotate > Down Left) ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> (Bifurcation <::> Bicursor) > (:*:)) where 	type Morphing (Rotate > Down Left) ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> (Bifurcation <::> Bicursor) > (:*:)) 		= Maybe <::> ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> Bifurcation <::> Bicursor > (:*:)) 	morphing struct = case run ---> premorph struct of 		T_U (Exactly x :*: TT (Left lst)) :*: TT (TT next) ->-			lift . twosome (_nonempty_binary_tree_to_focused_part lst)-				. TT . TT . Horizontal . Leftward <---- Construct -					<--- twosome <-- Exactly x <-- TT Nothing -					<--- next+			lift . (<:*:>) (_nonempty_binary_tree_to_focused_part lst)+				. TT . TT . Horizontal . Leftward <------- Construct+					<------ Exactly x <:*:> TT Nothing+					<------ next 		T_U (Exactly x :*: TT (Both lst rst)) :*: TT (TT next) ->-			lift . twosome (_nonempty_binary_tree_to_focused_part lst)-				. TT . TT . Horizontal . Leftward <---- Construct-					<--- twosome <-- Exactly x <-- lift rst -					<--- next+			lift . (<:*:>) (_nonempty_binary_tree_to_focused_part lst)+				. TT . TT . Horizontal . Leftward <------- Construct+					<------ Exactly x <:*:> lift rst+					<------ next 		_ -> TT Nothing  instance Morphable (Rotate > Down Right) ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> (Bifurcation <::> Bicursor) > (:*:)) where@@ -219,18 +199,10 @@ 		= Maybe <::> ((Exactly <:.:> Wye <::> Construction Wye > (:*:)) <:.:> Bifurcation <::> Bicursor > (:*:)) 	morphing struct = case run ---> premorph struct of 		T_U (Exactly x :*: TT (Right rst)) :*: TT (TT next) ->-			lift . twosome (_nonempty_binary_tree_to_focused_part rst)-				. TT . TT . Horizontal . Rightward <---- Construct (twosome <--- Exactly x <--- TT Nothing) next+			lift . (<:*:>) (_nonempty_binary_tree_to_focused_part rst)+				. TT . TT . Horizontal . Rightward <---- Construct (Exactly x <:*:> TT Nothing) next 		T_U (Exactly x :*: TT (Both lst rst)) :*: TT (TT next) ->-			lift . twosome (_nonempty_binary_tree_to_focused_part rst)-				. TT . TT . Horizontal . Rightward <---- Construct (twosome <--- Exactly x <--- lift lst) next+			lift . (<:*:>) (_nonempty_binary_tree_to_focused_part rst)+				. TT . TT . Horizontal . Rightward <---- Construct (Exactly x <:*:> lift lst) next 		_ -> TT Nothing -}--leaf :: a :=> Nonempty Binary-leaf x = Construct x end--left x = T_U <--- Just x :*: Nothing-right x = T_U <--- Nothing :*: Just x-both x y = T_U <--- Just x :*: Just y-end = T_U <--- Nothing :*: Nothing

@@ -4,22 +4,22 @@ import Pandora.Core.Functor (type (:.), type (<), type (>)) import Pandora.Core.Impliable (imply) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (-->), (--->), (---->), identity)+import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------), (-->), (--->), (---->), identity) import Pandora.Pattern.Kernel (constant) import Pandora.Pattern.Functor.Covariant (Covariant, Covariant ((<-|-), (<-|--), (<-|-|-)))-import Pandora.Pattern.Functor.Traversable (Traversable ((<<-), (<<--)))+import Pandora.Pattern.Functor.Traversable (Traversable ((<<-))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (==<<), (===<<), (====<<))) import Pandora.Pattern.Functor.Adjoint (Adjoint ((|-))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Pattern.Object.Setoid (Setoid ((==), (?==)))+import Pandora.Pattern.Object.Setoid (Setoid ((==), (?=))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))-import Pandora.Paradigm.Primary.Algebraic ((<-*-), (<-*--), (.-*-), (.-+-), (.:..), extract, point, empty, void)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))-import Pandora.Paradigm.Primary.Algebraic ((<-|-<-|-))+import Pandora.Paradigm.Algebraic ((<-*-), (<-*--), (.-*-), (.-+-), (.:..), extract, point, empty, void)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>), attached)+import Pandora.Paradigm.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic ((<-|-<-|-)) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly))@@ -28,29 +28,30 @@ import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct, (.-+)) import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse (Reverse))-import Pandora.Paradigm.Primary (twosome)+import Pandora.Paradigm.Primary () import Pandora.Paradigm.Inventory.Ability.Gettable (get) import Pandora.Paradigm.Inventory.Ability.Settable (set) import Pandora.Paradigm.Inventory.Ability.Modifiable (modify) import Pandora.Paradigm.Inventory.Some.State (State, fold) import Pandora.Paradigm.Inventory.Some.Store (Store (Store)) import Pandora.Paradigm.Inventory.Some.Optics (Convex, Obscure, Lens)-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~), (=#-))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, (<~), (<~~~), (=#-)) import Pandora.Paradigm.Schemes.TT (TT (TT), type (<::>)) import Pandora.Paradigm.Schemes.TU (TU (TU)) import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>)) import Pandora.Paradigm.Schemes.P_Q_T (P_Q_T (P_Q_T)) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)-import Pandora.Paradigm.Structure.Ability.Zipper (Zippable (Breadcrumbs), Zipper, Tape)+import Pandora.Paradigm.Structure.Interface.Zipper (Zippable (Breadcrumbs), Zipper) import Pandora.Paradigm.Structure.Ability.Monotonic (resolve) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing) 	, Morph (Rotate, Into, Push, Pop, Delete, Find, Lookup, Element, Key) 	, Occurrence (All, First), premorph, rotate, item, filter, find, lookup, into)-import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure, sub), Segment (Root, Tail))+import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure, sub), Segment (Root, Rest)) import Pandora.Paradigm.Structure.Interface.Stack (Stack (Popping, Pushing, Topping, push, pop, top)) import Pandora.Paradigm.Structure.Modification.Combinative (Combinative) import Pandora.Paradigm.Structure.Modification.Comprehension (Comprehension (Comprehension)) import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed (Prefixed))+import Pandora.Paradigm.Structure.Modification.Tape (Tape) import Pandora.Paradigm.Structure.Modification.Turnover (Turnover (Turnover))  -- | Linear data structure that serves as a collection of elements@@ -80,24 +81,24 @@ 	morphing list = case run --> premorph list of 		Nothing -> T_U <-- \_ -> Nothing 		Just (Construct x xs) -> T_U <-- \p ->-			p <~ x ?== True <----- Just x-				<----- find @Element @List @Maybe <-- p <-- TT xs+			(p <~ x) ?= True <---- Just x+				<---- find @Element @List @Maybe <-- p <-- TT xs  instance Morphable (Delete First) List where 	type Morphing (Delete First) List = Predicate <:.:> List > (->) 	morphing list = case run --> premorph list of 		Nothing -> T_U <-- constant empty-		Just (Construct x xs) -> T_U <-- \p -> -			p <~ x ?== True <----- TT xs-				<----- lift . Construct x . run . filter @First @List p <-- TT xs+		Just (Construct x xs) -> T_U <-- \p ->+			(p <~ x) ?= True <--- TT xs+				<--- lift . Construct x . run . filter @First @List p <-- TT xs  instance Morphable (Delete All) List where 	type Morphing (Delete All) List = Predicate <:.:> List > (->) 	morphing list = case run <--- premorph list of 		Nothing -> T_U <-- constant empty-		Just (Construct x xs) -> T_U <-- \p -> p <~ x ?== True-				<----- filter @All @List p <-- TT xs-				<----- lift . Construct x . run . filter @All @List p <-- TT xs+		Just (Construct x xs) -> T_U <-- \p -> (p <~ x) ?= True+				<--- filter @All @List p <-- TT xs+				<--- lift . Construct x . run . filter @All @List p <-- TT xs  instance Stack List where 	type Topping List = Maybe@@ -107,7 +108,7 @@ 		TT Nothing -> Store <--- Nothing :*: constant empty 		TT (Just xs) -> Store <--- Just (extract xs) :*: \new -> case new of 			Nothing -> TT <-- deconstruct xs-			Just x -> TT <--- Construct x . Just <-|- deconstruct xs+			Just x -> TT <---- Construct x . Just <-|- deconstruct xs 	pop = resolve @(Nonempty List _) (\(Construct x xs) -> constant (Just x) <-|- set @State (TT xs)) (point Nothing) . run ==<< get @State 	push x = point x .-*- modify @State (item @Push x) @@ -117,10 +118,10 @@ 		Just (Construct x xs) -> Store <--- Just x :*: lift . resolve (lift . (Construct % xs)) zero 		Nothing -> Store <--- Nothing :*: lift . resolve (lift . point) zero -instance Substructure Tail List where-	type Substance Tail List = List+instance Substructure Rest List where+	type Substance Rest List = List 	substructure = P_Q_T <-- \source -> case run . lower <-- source of-		Just ns -> lift . lift @(->) <-|- run (sub @Tail) ns+		Just ns -> lift . lift @(->) <-|- run (sub @Rest) ns 		Nothing -> Store <--- zero :*: lift . identity  -- | Transform any traversable structure into a list@@ -137,7 +138,7 @@  instance Morphable (Find Element) (Construction Maybe) where 	type Morphing (Find Element) (Construction Maybe) = Predicate <:.:> Maybe > (->)-	morphing (premorph -> Construct x xs) = T_U <-- \p -> p <~ x ?== True <----- Just x+	morphing (premorph -> Construct x xs) = T_U <-- \p -> (p <~ x) ?= True <----- Just x 		<----- find @Element @(Nonempty List) @Maybe <-- p ===<< xs  instance Morphable (Into List) (Construction Maybe) where@@ -156,16 +157,6 @@ 	type Morphing Push (Construction Maybe) = Exactly <:.:> Construction Maybe > (->) 	morphing (premorph -> xs) = T_U <-- \(Exactly x) -> Construct x <-- Just xs -instance Substructure Root (Construction Maybe) where-	type Substance Root (Construction Maybe) = Exactly-	substructure = P_Q_T <-- \source -> case lower source of-		Construct x xs -> Store <--- Exactly x :*: lift . (Construct % xs) . extract--instance Substructure Tail (Construction Maybe) where-	type Substance Tail (Construction Maybe) = List-	substructure = P_Q_T <-- \source -> case lower source of-		Construct x xs -> Store <--- TT xs :*: lift . Construct x . run- instance Stack (Construction Maybe) where 	type Topping (Construction Maybe) = Exactly 	type Popping (Construction Maybe) = Construction Maybe@@ -182,11 +173,11 @@ ----------------------------------------- Zipper of list -------------------------------------------  instance Zippable List where-	type Breadcrumbs List = Reverse List <:.:> List > (:*:)+	type Breadcrumbs List = Reverse List <:*:> List  instance {-# OVERLAPS #-} Traversable (->) (->) (Tape List) where-	f <<- TU (Tag (T_U (Exactly x :*: T_U (left :*: right)))) = -		(\past' x' left' -> lift <---- twosome <-- Exactly x' <--- twosome <-- left' <-- run past')+	f <<- TU (Tag (T_U (Exactly x :*: T_U (left :*: right)))) =+		(\past' x' left' -> lift <------ Exactly x' <:*:> left' <:*:> run past') 			<-|- f <<- Reverse right <-*- f x <-*- f <<- left  -- instance {-# OVERLAPS #-} Extendable (->) (Tape List) where@@ -206,7 +197,7 @@ 		rotate_left focused rs (Construct lx lxs) = imply @(Tape List _) <-- lx <-- TT lxs <-- item @Push focused rs  		rotate_over :: a -> Nonempty List a -> Tape List a-		rotate_over focused rs = let new_left = attached <--- run <-- put_over <<- rs <-- point focused in+		rotate_over focused rs = let new_left = attached <--- (put_over <<- rs <~~~ point focused) in 			imply @(Tape List _) <--- extract new_left <--- TT <-- deconstruct new_left <--- empty  		put_over :: a -> State (Nonempty List a) ()@@ -222,7 +213,7 @@ 		rotate_right focused ls (Construct rx rxs) = imply @(Tape List _) <-- rx <-- item @Push focused ls <-- TT rxs  		rotate_over :: a -> Nonempty List a -> Tape List a-		rotate_over focused ls = let new_right = attached (run <-- put_over <<- ls <-- point focused) in+		rotate_over focused ls = let new_right = attached (put_over <<- ls <~~~ point focused) in 			imply @(Tape List _) <--- extract new_right <--- empty <--- TT <-- deconstruct new_right  		put_over :: a -> State (Nonempty List a) ()@@ -235,19 +226,19 @@ instance Morphable (Into List) (Tape List) where 	type Morphing (Into List) (Tape List) = List 	morphing (lower . premorph -> T_U (Exactly x :*: T_U (Reverse left :*: right))) = attached <---- run @(->) @(State _)-		<--- modify @State . item @Push @List <<-- right+		<--- modify @State . item @Push @List <<- right 		<--- item @Push x left  instance Morphable (Into > Comprehension Maybe) (Tape List) where 	type Morphing (Into > Comprehension Maybe) (Tape List) = Comprehension Maybe 	morphing (lower . premorph -> T_U (Exactly x :*: T_U (Reverse left :*: right))) = attached <---- run @(->) @(State _)-		<--- modify @State . item @Push @(Comprehension Maybe) <<-- right+		<--- modify @State . item @Push @(Comprehension Maybe) <<- right 		<--- item @Push x <-- Comprehension left  ------------------------------------- Zipper of non-empty list -------------------------------------  instance Zippable (Construction Maybe) where-	type Breadcrumbs (Construction Maybe) = Reverse > Construction Maybe <:.:> Construction Maybe > (:*:)+	type Breadcrumbs (Construction Maybe) = Reverse > Construction Maybe <:*:> Construction Maybe  instance Morphable (Rotate Left) (Tape > Construction Maybe) where 	type Morphing (Rotate Left) (Tape > Construction Maybe) = Maybe <::> (Tape > Construction Maybe)@@ -282,19 +273,19 @@ instance Morphable (Into > Construction Maybe) (Tape > Construction Maybe) where 	type Morphing (Into > Construction Maybe) (Tape > Construction Maybe) = Construction Maybe 	morphing (lower . premorph -> T_U (Exactly x :*: T_U (Reverse left :*: right))) = attached <---- run @(->) @(State _)-		<--- modify @State . item @Push @(Nonempty List) <<-- right+		<--- modify @State . item @Push @(Nonempty List) <<- right 		<--- item @Push x left  instance Morphable (Into List) (Tape > Construction Maybe) where 	type Morphing (Into List) (Tape > Construction Maybe) = List 	morphing (lower . premorph -> T_U (Exactly x :*: T_U (Reverse left :*: right))) = attached <---- run @(->) @(State _)-		<--- modify @State . item @Push @List <<-- right+		<--- modify @State . item @Push @List <<- right 		<--- item @Push x <-- lift left  ------------------------------------ Zipper of combinative list ------------------------------------  instance Zippable (Comprehension Maybe) where-	type Breadcrumbs (Comprehension Maybe) = Comprehension Maybe <:.:> Comprehension Maybe > (:*:)+	type Breadcrumbs (Comprehension Maybe) = Comprehension Maybe <:*:> Comprehension Maybe  ----------------------------------------- Prefixed list -------------------------------------------- @@ -307,5 +298,6 @@ 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) = TT <-- \key -> extract <-|- search key where-		search key = key ?== attached x <----- Just x -			<----- find @Element <--- Predicate <-- (key ==) . attached ====<< xs+		search key = key ?= attached x+			<----- Just x+			<----- find @Element <--- Predicate <-- (key ==) . attached ===<< xs

@@ -5,64 +5,50 @@ import Pandora.Pattern.Semigroupoid ((.)) import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----)) import Pandora.Pattern.Kernel (constant)-import Pandora.Pattern.Functor.Contravariant ((>-|--))+import Pandora.Pattern.Functor.Covariant ((<-|-), (<-|-|-))+import Pandora.Pattern.Functor.Contravariant ((>-|-)) 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.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))-import Pandora.Paradigm.Primary.Algebraic (extract)+import Pandora.Pattern.Transformer.Hoistable ((/|\))+import Pandora.Pattern.Object.Setoid (Setoid ((==), (!=), (?=)))+import Pandora.Pattern.Object.Semigroup ((+))+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), attached)+import Pandora.Paradigm.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic (extract, empty, (>-||-)) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)), attached)-import Pandora.Paradigm.Primary.Algebraic.Exponential ((%))-import Pandora.Paradigm.Primary.Algebraic (extract)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>), (<:*:>), attached)+import Pandora.Paradigm.Algebraic.Exponential ((%))+import Pandora.Paradigm.Algebraic (extract, point) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True)) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Predicate (equate)+import Pandora.Paradigm.Primary.Functor.Tagged (Tagged)+import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct)-import Pandora.Paradigm.Schemes (TU (TU), P_Q_T (P_Q_T), type (<:.>))-import Pandora.Paradigm.Controlflow.Effect.Interpreted (run)+import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse)+import Pandora.Paradigm.Schemes (TU (TU), TT (TT), T_U (T_U), P_Q_T (P_Q_T),  type (<::>), type (<:.>))+import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, unite, (<~), (=#-), (<~~~~)) import Pandora.Paradigm.Inventory.Some.Store (Store (Store))-import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Lookup, Element, Key), premorph, find)+import Pandora.Paradigm.Inventory.Some.Optics (view)+import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing)+	, Morph (Into, Rotate, Lookup, Element, Key), Vertical (Up, Down), premorph, find) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)-import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure), Segment (Root, Tail))+import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substance, substructure)+	, Segment (Root, Rest, Forest), sub, tagstruct)+import Pandora.Paradigm.Structure.Interface.Zipper (Zippable (Breadcrumbs))+import Pandora.Paradigm.Structure.Interface.Stack (Stack (pop, push)) import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed)+import Pandora.Paradigm.Structure.Modification.Tape (Tape) import Pandora.Paradigm.Structure.Some.List (List)  type Rose = Maybe <:.> Construction List --- 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 = Exactly---	substructure = P_Q_T <-- \rose -> case run # lower rose of---		Nothing -> Store <--- Nothing :*: TU . Tag . TU . ((Construct % empty) . extract <-|-)---		Just nonempty_rose -> Store <--- Just (Exactly # extract nonempty_rose) :*: \case---			Just (Exactly new) -> lift . TU . Just . Construct new <-- deconstruct nonempty_rose---			Nothing -> lift empty----instance Substructure Just Rose where---	type Available Just Rose = Exactly---	type Substance Just Rose = List <:.> Construction List---	substructure = P_Q_T <-- \rose -> case run . extract . run # rose of---		Nothing -> Store <--- Exactly empty :*: constant (lift empty)---		Just (Construct x xs) -> Store <--- Exactly (TU xs) :*: lift . lift . Construct x . run . extract- --------------------------------------- Non-empty rose tree ----------------------------------------  type instance Nonempty Rose = Construction List -instance Substructure Root (Construction List) where-	type Substance Root (Construction List) = Exactly-	--substructure = P_Q_T <-- \rose -> Store <--- Exactly (Exactly <-- extract (lower rose)) :*: lift . (Construct % deconstruct (lower rose)) . extract . extract--instance Substructure Tail (Construction List) where-	type Substance Tail (Construction List) = List <:.> Construction List-	--substructure = P_Q_T <-- \rose -> case extract <-- run rose of-	--	Construct x xs -> Store <--- Exactly (TU xs) :*: lift . Construct x . run . extract- --------------------------------------- Prefixed rose tree -----------------------------------------  instance Setoid k => Morphable (Lookup Key) (Prefixed Rose k) where@@ -96,8 +82,72 @@ --			! 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 <----- find_rose_sub_tree ks =<< subtree <----- Nothing where +find_rose_sub_tree (Construct k ks) tree = k ?= attached (extract tree)+	<----- case ks of+		Just keys -> find_rose_sub_tree keys =<< subtree keys+		Nothing -> Just <--- extract <-- extract tree+	<----- Nothing where -	subtree :: Maybe :. Nonempty Rose > k :*: a-	subtree = find @Element <---- attached . extract >-|-- equate <-- extract ks <---- deconstruct tree+	subtree :: Nonempty List k -> Maybe :. Nonempty Rose > k :*: a+	subtree keys = find @Element+		<---- attached . extract+			>-|- equate <-- extract keys+		<---- deconstruct tree++------------------------------ Non-empty rose tree zipper -----------------------------++type Roses = List <::> Construction List++instance Zippable (Construction List) where+	type Breadcrumbs (Construction List) = Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)++-- TODO: Try to use substructure @Right . substructure @Right . substructure @Right . substructure @Right here+instance Substructure (Up Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) where+	type Substance (Up Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) = List <::> Tape Roses+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (down :*: T_U (left :*: T_U (right :*: up))) ->+			Store <--- up :*: lift . lift . (Exactly x <:*:>) . (down <:*:>) . (left <:*:>) . (right <:*:>)++-- TODO: Try to use substructure @Left . substructure @Right here+instance Substructure (Down Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) where+	type Substance (Down Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) = Roses+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (down :*: rest) ->+			Store <--- down :*: lift . lift . (Exactly x <:*:>) . (<:*:> rest)++-- TODO: Try to use substructure @Left . substructure @Right . substructure @Right here+instance Substructure (Left Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) where+	type Substance (Left Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) = Reverse Roses+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (down :*: T_U (left :*: rest)) ->+			Store <--- left :*: lift . lift . (Exactly x <:*:>) . (down <:*:>) . (<:*:> rest)++-- TODO: Try to use substructure @Left . substructure @Right . substructure @Right . substructure @Right here+instance Substructure (Right Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) where+	type Substance (Right Forest) (Tagged (Zippable structure) <:.> Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)) = Roses+	substructure = P_Q_T <-- \zipper -> case run . lower <-- lower zipper of+		Exactly x :*: T_U (down :*: T_U (left :*: T_U (right :*: rest))) ->+			Store <--- right :*: lift . lift . (Exactly x <:*:>) . (down <:*:>) . (left <:*:>) . (<:*:> rest)++instance Morphable (Into (Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)))) (Construction List) where+	type Morphing (Into (Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)))) (Construction List) =+		Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses))+	morphing nonempty_rose_tree = case premorph nonempty_rose_tree of+		Construct x xs -> lift <----- Exactly x <:*:> unite xs <:*:> empty <:*:> empty <:*:> empty++instance Morphable (Rotate Up) (Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses))) where+	type Morphing (Rotate Up) (Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses))) =+		Maybe <::> (Tagged (Zippable structure) <:.> (Exactly <:*:> Roses <:*:> Reverse Roses <:*:> Roses <:*:> (List <::> Tape Roses)))+	morphing (premorph -> nonempty_rose_tree) = case pop @List <~ run (view <-- sub @(Up Forest) <-- nonempty_rose_tree) of+		-- TODO: Traversable for Maybe up over Product+		parents :*: Just parent ->+			let child_node = extract <--- view <-- sub @Root <-- nonempty_rose_tree in+			let central_children = run <--- view <-- sub @(Down Forest) <-- nonempty_rose_tree in+			let left_children = run @(->) <---- run <--- view <-- sub @(Left Forest) <-- nonempty_rose_tree in+			let right_children = run <--- view <-- sub @(Right Forest) <-- nonempty_rose_tree in+			lift . lift <----- view <-- sub @Root <-- parent+				<:*:> unite <-- left_children + point (Construct child_node central_children) + right_children+				<:*:> view <-- sub @Left <-- parent+				<:*:> view <-- sub @Right <-- parent+				<:*:> unite parents+		_ :*: Nothing -> empty

@@ -2,26 +2,23 @@ {-# LANGUAGE AllowAmbiguousTypes #-} module Pandora.Paradigm.Structure.Some.Splay where -import Pandora.Core.Functor (type (~>), type (:.), type (>))+import Pandora.Core.Functor (type (~>), type (>)) import Pandora.Pattern.Semigroupoid ((.))-import Pandora.Pattern.Category ((<--), (<---), (<----), (<-----), (<------), identity)-import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|--)))-import Pandora.Pattern.Functor.Bindable (Bindable ((==<<), (===<<)))+import Pandora.Pattern.Category ((<--), (<---), (<----), identity)+import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-), (<-|---)))+import Pandora.Pattern.Functor.Bindable (Bindable ((=<<), (==<<), (===<<))) import Pandora.Pattern.Transformer.Hoistable ((/|\))-import Pandora.Paradigm.Primary ()-import Pandora.Paradigm.Primary.Algebraic ((<-*-), extract)-import Pandora.Paradigm.Primary.Algebraic.Product (type (<:*:>))+import Pandora.Paradigm.Algebraic ((<-*-), extract)+import Pandora.Paradigm.Algebraic.Product (type (<:*:>), (<:*:>)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just))-import Pandora.Paradigm.Primary.Functor.Tagged (type (:#)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))-import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct)-import Pandora.Paradigm.Primary (twosome)+import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Inventory.Some.Optics (view, mutate) import Pandora.Paradigm.Schemes (TT (TT), type (<::>)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morphed, Morph (Rotate), premorph, rotate) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)-import Pandora.Paradigm.Structure.Ability.Substructure (sub)+import Pandora.Paradigm.Structure.Ability.Substructure (Segment (Root, Branch), sub) import Pandora.Paradigm.Structure.Ability.Monotonic (resolve) import Pandora.Paradigm.Structure.Some.Binary (Binary) @@ -29,82 +26,75 @@  instance Morphable (Rotate > Left Zig) Binary where 	type Morphing (Rotate > Left Zig) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Left Zig) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Left Zig) =<< run binary  instance Morphable (Rotate > Right Zig) Binary where 	type Morphing (Rotate > Right Zig) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Right Zig) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Right Zig) =<< run binary  instance Morphable (Rotate > Left > Zig Zig) Binary where 	type Morphing (Rotate > Left > Zig Zig) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Left > Zig Zig) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Left > Zig Zig) =<< run binary  instance Morphable (Rotate > Right > Zig Zig) Binary where 	type Morphing (Rotate > Right > Zig Zig) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Right > Zig Zig) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Right > Zig Zig) =<< run binary  instance Morphable (Rotate > Left > Zig Zag) Binary where 	type Morphing (Rotate > Left > Zig Zag) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Left > Zig Zag) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Left > Zig Zag) =<< run binary  instance Morphable (Rotate > Right > Zig Zag) Binary where 	type Morphing (Rotate > Right > Zig Zag) Binary = Binary-	morphing (premorph -> binary) = TT <--- run . rotate @(Right > Zig Zag) ==<< run binary+	morphing (premorph -> binary) = TT <--- run . rotate @(Right > Zig Zag) =<< run binary  -------------------------------------- Non-empty Splay tree ---------------------------------------- --- TODO: refactor so that there is only one expression instance Morphable (Rotate > Left Zig) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Left Zig) (Construction (Maybe <:*:> Maybe)) = Binary-	morphing :: forall a . (:#) (Rotate > Left Zig) <::> Construction (Maybe <:*:> Maybe) > a -> Binary a-	morphing (premorph -> Construct x xs) = TT <--- Construct <-|- parent <-*- Just nodes where--		nodes :: (Maybe <:*:> Maybe) :. Nonempty Binary > a-		nodes = twosome-			<------ view <-- sub @Left <-- xs-			<------ Just . Construct x-				<----- twosome-					<---- view (sub @Left) ===<< deconstruct <-|- view (sub @Right) xs-					<---- view (sub @Right) ===<< deconstruct <-|- view (sub @Right) xs--		parent :: Maybe a-		parent = extract <-|-- view <-- sub @Right <-- xs+	morphing (premorph -> tree) = TT <---- Construct+		<-|- (extract <-|--- run <--- view <-- sub @(Right Branch) <-- tree)+		<-*- Just (+			(<:*:>)+				(run <--- view <-- sub @(Left Branch) <-- tree)+				(Just . Construct (extract <--- view <-- sub @Root <-- tree) <-- (<:*:>)+					(run . view (sub @(Left Branch)) ===<< run <--- view <-- sub @(Right Branch) <-- tree)+					(run . view (sub @(Right Branch)) ===<< run <--- view <-- sub @(Right Branch) <-- tree)+				)+			)  instance Morphable (Rotate > Right Zig) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Right Zig) (Construction (Maybe <:*:> Maybe)) = Binary-	morphing :: forall a . (:#) (Rotate > Right Zig) <::> Construction (Maybe <:*:> Maybe) > a -> Binary a-	morphing (premorph -> Construct x xs) = TT <--- Construct <-|- parent <-*- Just nodes where--		nodes :: (Maybe <:*:> Maybe) :. Nonempty Binary > a-		nodes = twosome-			<------ view (sub @Left) ===<< deconstruct <-|- view (sub @Left) xs-			<------ Just . Construct x-				<----- twosome-					<---- view (sub @Right) ===<< deconstruct <-|- view (sub @Left) xs-					<---- view (sub @Right) xs--		parent :: Maybe a-		parent = extract <-|-- view <-- sub @Left <-- xs+	morphing (premorph -> tree) = TT <---- Construct+		<-|- (extract <-|--- run <--- view <-- sub @(Left Branch) <-- tree)+		<-*- Just (+			(<:*:>)+				(run . view (sub @(Left Branch)) ===<< run <--- view <-- sub @(Left Branch) <-- tree)+				(Just . Construct (extract <--- view <-- sub @Root <-- tree) <-- (<:*:>)+					(run . view (sub @(Left Branch)) ===<< run <--- view <-- sub @(Left Branch) <-- tree)+					(run <--- view <-- sub @(Right Branch) <-- tree)+				)+			)  -- TODO: Morphing ... = Conclussion Error <::> Nonempty Binary instance Morphable (Rotate > Left > Zig Zig) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Left > Zig Zig) (Construction (Maybe <:*:> Maybe)) = Maybe <::> Construction (Maybe <:*:> Maybe)-	morphing (premorph -> tree) = TT <---- run . rotate @(Left Zig) ===<< run <-- rotate @(Left Zig) tree+	morphing (premorph -> tree) = TT <---- run . rotate @(Left Zig) ==<< run <-- rotate @(Left Zig) tree  -- TODO: Morphing ... = Conclussion Error <::> Nonempty Binary instance Morphable (Rotate > Right > Zig Zig) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Right > Zig Zig) (Construction (Maybe <:*:> Maybe)) = Maybe <::> Construction (Maybe <:*:> Maybe)-	morphing (premorph -> tree) = TT <---- run . rotate @(Right Zig) ===<< run <-- rotate @(Right Zig) tree+	morphing (premorph -> tree) = TT <---- run . rotate @(Right Zig) ==<< run <-- rotate @(Right Zig) tree  -- TODO: Morphing ... = Conclussion Error <::> Nonempty Binary instance Morphable (Rotate > Left > Zig Zag) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Left > Zig Zag) (Construction (Maybe <:*:> Maybe)) = Maybe <::> Construction (Maybe <:*:> Maybe)-	morphing (premorph -> struct) = rotate @(Left Zig) <--- mutate <-- (try_to_rotate @(Right Zig) /|\) <-- sub @Left <-- struct+	morphing (premorph -> struct) = rotate @(Left Zig) <--- mutate <-- (try_to_rotate @(Right Zig) /|\) <-- sub @(Left Branch) <-- struct  -- TODO: Morphing ... = Conclussion Error <::> Nonempty Binary instance Morphable (Rotate > Right > Zig Zag) (Construction (Maybe <:*:> Maybe)) where 	type Morphing (Rotate > Right > Zig Zag) (Construction (Maybe <:*:> Maybe)) = Maybe <::> Construction (Maybe <:*:> Maybe)-	morphing (premorph -> struct) = rotate @(Right Zig) <--- mutate <-- (try_to_rotate @(Left Zig) /|\) <-- sub @Right <-- struct+	morphing (premorph -> struct) = rotate @(Right Zig) <--- mutate <-- (try_to_rotate @(Left Zig) /|\) <-- sub @(Right Branch) <-- struct  -- TODO: Include error instead of returning empty tree try_to_rotate :: forall direction . Morphed (Rotate direction) (Nonempty Binary) Binary => Nonempty Binary ~> Nonempty Binary

@@ -8,22 +8,23 @@ import Pandora.Pattern.Functor.Covariant (Covariant ((<-|--))) import Pandora.Pattern.Functor.Extendable (Extendable ((<<=))) import Pandora.Pattern.Transformer.Lowerable (lower)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))-import Pandora.Paradigm.Primary.Algebraic (extract)+import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)), type (<:*:>))+import Pandora.Paradigm.Algebraic (extract) import Pandora.Paradigm.Primary.Functor.Exactly (Exactly (Exactly)) import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct, (.-+)) import Pandora.Paradigm.Primary.Transformer.Reverse (Reverse (Reverse)) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Rotate), premorph, rotate)-import Pandora.Paradigm.Structure.Ability.Zipper (Zippable (Breadcrumbs), Tape)-import Pandora.Paradigm.Schemes.T_U (T_U (T_U), type (<:.:>))-import Pandora.Paradigm.Primary.Algebraic (point)+import Pandora.Paradigm.Structure.Interface.Zipper (Zippable (Breadcrumbs))+import Pandora.Paradigm.Structure.Modification.Tape (Tape)+import Pandora.Paradigm.Schemes.T_U (T_U (T_U))+import Pandora.Paradigm.Algebraic (point) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run)  type Stream = Construction Exactly  instance Zippable (Construction Exactly) where-	type Breadcrumbs (Construction Exactly) = Reverse Stream <:.:> Stream > (:*:)+	type Breadcrumbs (Construction Exactly) = Reverse Stream <:*:> Stream  instance Morphable (Rotate Left) (Tape Stream) where 	type Morphing (Rotate Left) (Tape Stream) = Tape Stream

@@ -2,23 +2,21 @@  import Pandora.Pattern.Semigroupoid (Semigroupoid ((.))) -infixl 1 <----------infixl 2 <---------infixl 3 <--------infixl 4 <-------infixl 5 <------infixl 6 <-----infixl 7 <----infixl 8 <--+infixl 1 <--------+infixl 2 <-------+infixl 3 <------+infixl 4 <-----+infixl 5 <----+infixl 6 <---+infixl 7 <-- -infixr 1 --------->-infixr 2 -------->-infixr 3 ------->-infixr 4 ------>-infixr 5 ----->-infixr 6 ---->-infixr 7 --->-infixr 8 -->+infixr 1 -------->+infixr 2 ------->+infixr 3 ------>+infixr 4 ----->+infixr 5 ---->+infixr 6 --->+infixr 7 -->  {- | > When providing a new instance, you should ensure it satisfies:@@ -29,8 +27,7 @@ class Semigroupoid m => Category m where 	identity :: m a a -	(<---------), (<--------), (<-------), (<------), (<-----), (<----), (<---), (<--) :: m (m a b) (m a b)-	(<---------) = identity . identity+	(<--------), (<-------), (<------), (<-----), (<----), (<---), (<--) :: m (m a b) (m a b) 	(<--------) = identity . identity 	(<-------) = identity . identity 	(<------) = identity . identity@@ -39,8 +36,7 @@ 	(<---) = identity . identity 	(<--) = identity . identity -	(--------->), (-------->), (------->), (------>), (----->), (---->), (--->), (-->) :: m (m a b) (m a b)-	(--------->) = identity . identity+	(-------->), (------->), (------>), (----->), (---->), (--->), (-->) :: m (m a b) (m a b) 	(-------->) = identity . identity 	(------->) = identity . identity 	(------>) = identity . identity

@@ -4,15 +4,14 @@  type (-|) = Adjoint -infixl 1 ---------|, |----------infixl 2 --------|, |---------infixl 3 -------|, |--------infixl 4 ------|, |-------infixl 5 -----|, |------infixl 6 ----|, |-----infixl 7 ---|, |----infixl 8 --|, |---infixl 9 -|, |-+infixl 1 --------|, |--------+infixl 2 -------|, |-------+infixl 3 ------|, |------+infixl 4 -----|, |-----+infixl 5 ----|, |----+infixl 6 ---|, |---+infixl 7 --|, |--+infixl 8 -|, |-  {- | > When providing a new instance, you should ensure it satisfies:@@ -26,22 +25,20 @@ 	(-|) :: source (t a) b -> target a (u b) 	(|-) :: target a (u b) -> source (t a) b -	(|--), (|---), (|----), (|-----), (|------), (|-------), (|--------), (|---------)  :: target a (u b) -> source (t a) b-	(|--) = (|-)-	(|---) = (|-)-	(|----) = (|-)-	(|-----) = (|-)-	(|------) = (|-)-	(|-------) = (|-)+	(|--------), (|-------), (|------),  (|-----),  (|----), (|---), (|--) :: target a (u b) -> source (t a) b 	(|--------) = (|-)-	(|---------) = (|--)-	-	(--|), (---|), (----|), (-----|), (------|), (-------|), (--------|), (---------|)  :: source (t a) b -> target a (u b)-	(--|) = (-|)-	(---|) = (-|)-	(----|) = (-|)-	(-----|) = (-|)-	(------|) = (-|)-	(-------|) = (-|)+	(|-------) = (|-)+	(|------) = (|-)+	(|-----) = (|-)+	(|----) = (|-)+	(|---) = (|-)+	(|--) = (|-)++	(--------|), (-------|), (------|), (-----|), (----|), (---|), (--|) :: source (t a) b -> target a (u b) 	(--------|) = (-|)-	(---------|) = (-|)+	(-------|) = (-|)+	(------|) = (-|)+	(-----|) = (-|)+	(----|) = (-|)+	(---|) = (-|)+	(--|) = (-|)

@@ -2,15 +2,13 @@  import Pandora.Pattern.Functor.Covariant (Covariant) -infixr 1 =========<<-infixr 2 ========<<-infixr 3 =======<<-infixr 4 ======<<-infixr 5 =====<<-infixr 6 ====<<-infixr 7 ===<<-infixr 8 ==<<-infixr 9 =<<+infixr 1 =======<<+infixr 2 ======<<+infixr 3 =====<<+infixr 4 ====<<+infixr 5 ===<<+infixr 6 ==<<+infixr 7 =<<  {- | > When providing a new instance, you should ensure it satisfies :@@ -20,13 +18,10 @@ class Covariant source source t => Bindable source t where 	(=<<) :: source a (t b) -> source (t a) (t b) -	(==<<), (===<<), (====<<), (=====<<), (======<<),-		(=======<<), (========<<), (=========<<)  :: source a (t b) -> source (t a) (t b)+	(==<<), (===<<), (====<<), (=====<<), (======<<), (=======<<)  :: source a (t b) -> source (t a) (t b) 	(==<<) = (=<<) 	(===<<) = (=<<) 	(====<<) = (=<<) 	(=====<<) = (=<<) 	(======<<) = (=<<) 	(=======<<) = (=<<)-	(========<<) = (=<<)-	(=========<<) = (=<<)

@@ -3,8 +3,8 @@ import Pandora.Pattern.Morphism.Straight (Straight) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Functor.Extendable (Extendable)-import Pandora.Paradigm.Primary.Algebraic.Exponential (type (<--))-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic.Exponential (type (<--))+import Pandora.Paradigm.Algebraic.Product ((:*:))  {- | > Let f :: (Extendable t, Extractable t) => t a -> b

@@ -3,14 +3,12 @@ import Pandora.Pattern.Category (Category) import Pandora.Pattern.Betwixt (Betwixt) -infixl 1 >-|---------infixl 2 >-|--------infixl 3 >-|------, >-|-|-, >$$<-infixl 4 >-|------infixl 5 >-|-----infixl 6 >-|----infixl 7 >-|---infixl 8 >-|-+infixl 1 >-|------+infixl 2 >-|-----+infixl 3 >-|----+infixl 4 >-|---, >-|-|-+infixl 5 >-|--+infixl 6 >-|-  {- | > When providing a new instance, you should ensure it satisfies:

@@ -4,14 +4,12 @@ import Pandora.Pattern.Betwixt (Betwixt) import Pandora.Pattern.Semigroupoid (Semigroupoid) -infixl 1 <-|--------, <-|-|--------infixl 2 <-|-------, <-|-|-------infixl 3 <-|------, <-|-|-----, <$$>-infixl 4 <-|-----, <-|-|----, <$$$>-infixl 5 <-|----, <-|-|----infixl 6 <-|---, <-|-|--, <-|-|-|--infixl 7 <-|--, <-|-|--infixl 8 <-|-+infixl 1 <-|------, <-|-|----+infixl 2 <-|-----, <-|-|-|-, <-|-|---+infixl 3 <-|----, <-|-|--+infixl 4 <-|---, <-|-|-+infixl 5 <-|--+infixl 6 <-|-  {- | > When providing a new instance, you should ensure it satisfies:@@ -21,7 +19,7 @@  class (Semigroupoid source, Semigroupoid target) => Covariant source target t where 	(<-|-) :: source a b -> target (t a) (t b)-	+ 	(<-|--), (<-|---), (<-|----), (<-|-----), (<-|------), 		(<-|-------), (<-|--------) :: source a b -> target (t a) (t b) 	(<-|--) = (<-|-)

@@ -10,25 +10,21 @@ > * Interchange collection: (f -<<) ≡ (identity -<<) . (f <-|-) -} -infixl 1 ---------<<-infixl 2 --------<<-infixl 3 -------<<-infixl 4 ------<<-infixl 5 -----<<-infixl 6 ----<<-infixl 7 ---<<-infixl 8 --<<-infixl 9 -<<+infixl 1 -------<<+infixl 2 ------<<+infixl 3 -----<<+infixl 4 ----<<+infixl 5 ---<<+infixl 6 --<<+infixl 7 -<<  class Covariant source target t => Distributive source target t where 	(-<<) :: Covariant source target u => source a (t b) -> target (u a) (t (u b))-	-	(--<<), (---<<), (----<<), (-----<<), (------<<), (-------<<), (--------<<), (---------<<) :: Covariant source target u => source a (t b) -> target (u a) (t (u b))++	(--<<), (---<<), (----<<), (-----<<), (------<<), (-------<<) :: Covariant source target u => source a (t b) -> target (u a) (t (u b)) 	(--<<) = (-<<) 	(---<<) = (-<<) 	(----<<) = (-<<) 	(-----<<) = (-<<) 	(------<<) = (-<<) 	(-------<<) = (-<<)-	(--------<<) = (-<<)-	(---------<<) = (-<<)

@@ -2,15 +2,13 @@  import Pandora.Pattern.Functor.Covariant (Covariant) -infixr 1 <<=========-infixr 2 <<========-infixr 3 <<=======-infixr 4 <<======-infixr 5 <<=====-infixr 6 <<====-infixr 7 <<===-infixr 8 <<==-infixr 9 <<=+infixr 1 <<=======+infixr 2 <<======+infixr 3 <<=====+infixr 4 <<====+infixr 5 <<===+infixr 6 <<==+infixr 7 <<=  {- | > When providing a new instance, you should ensure it satisfies:@@ -20,9 +18,8 @@  class Covariant source source t => Extendable source t where 	(<<=) :: source (t a) b -> source (t a) (t b)-	-	(<<==), (<<===), (<<====), (<<=====), (<<======), (<<=======), (<<========), (<<=========)  :: source (t a) b -> source (t a) (t b)-	(<<=========) = (<<=)++	(<<==), (<<===), (<<====), (<<=====), (<<======), (<<=======), (<<========)  :: source (t a) b -> source (t a) (t b) 	(<<========) = (<<=) 	(<<=======) = (<<=) 	(<<======) = (<<=)

@@ -6,7 +6,7 @@ > Interpreted of morphisms: invmap g j . invmap f h = invmap (g . f) (h . j) -} -infixl 4 <!<+infixl 7 <!<  class Invariant (t :: * -> *) where 	{-# MINIMAL (<!<) #-}

@@ -4,7 +4,7 @@ import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Bindable (Bindable) import Pandora.Pattern.Functor.Monoidal (Monoidal)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic.Product ((:*:))  {- | > Let f :: (Monoidal t (->) (->) (:*:) (:*:), Bindable t) => a -> t a

@@ -10,7 +10,7 @@ > * Interchange tabulation: comap f . tabulate ≡ tabulate . comap f -} -infixr 6 <#>+infixr 7 <#>  class Representable t where 	{-# MINIMAL (<#>), tabulate #-}

@@ -3,7 +3,7 @@ import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Monoidal (Monoidal) import Pandora.Pattern.Morphism.Straight (Straight)-import Pandora.Paradigm.Primary.Algebraic.Product ((:*:))+import Pandora.Paradigm.Algebraic.Product ((:*:))  {- | > Let f :: (Applicative t, Applicative g) => t a -> u a@@ -16,31 +16,28 @@ > * Preserving apply: f (x <.-*- y) ≡ f x <.-*- f y -} -infixl 8 <<-<<-+infixl 4 <<-<<- -infixl 1 <<----------infixl 2 <<---------infixl 3 <<--------infixl 4 <<-------infixl 5 <<------infixl 6 <<-----infixl 7 <<----infixl 8 <<---infixl 9 <<-+infixl 1 <<-------+infixl 2 <<------+infixl 3 <<-----+infixl 4 <<----+infixl 5 <<---+infixl 6 <<--+infixl 7 <<-  class Covariant source target t => Traversable source target t where 	(<<-) :: (Covariant source target u, Monoidal (Straight source) (Straight target) (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b)) -	(<<--), (<<---), (<<----), (<<-----), (<<------),-		(<<-------), (<<--------), (<<---------) :: (Covariant source target u, Monoidal (Straight source) (Straight target) (:*:) (:*:) u) => source a (u b) -> target (t a) (u (t b))-	(<<--) = (<<-)-	(<<---) = (<<-)-	(<<----) = (<<-)-	(<<-----) = (<<-)-	(<<------) = (<<-)+	(<<-------), (<<------), (<<-----), (<<----), (<<---), (<<--)+		:: (Covariant source target u, Monoidal (Straight source) (Straight target) (:*:) (:*:) u)+		=> source a (u b) -> target (t a) (u (t b)) 	(<<-------) = (<<-)-	(<<--------) = (<<-)-	(<<---------) = (<<-)+	(<<------) = (<<-)+	(<<-----) = (<<-)+	(<<----) = (<<-)+	(<<---) = (<<-)+	(<<--) = (<<-)  (<<-<<-) :: forall t u v category a b . 	(Traversable category category t, Covariant category category u, Monoidal (Straight category) (Straight category) (:*:) (:*:) u, Traversable category category v)

@@ -4,7 +4,9 @@ import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False)) import Pandora.Paradigm.Primary.Object.Ordering (Ordering, order) -infixl 4 <=>, <, <=, >=, >+infixl 7 <=>+infixl 8 <=, >=+infixl 9 <, >  {- | > When providing a new instance, you should ensure it satisfies:

@@ -2,7 +2,7 @@  import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False, True)) -infix 6 ==, !=, ?==+infix 8 ==, !=, ?=  {- | > When providing a new instance, you should ensure it satisfies:@@ -21,7 +21,7 @@ 		True -> False 		False -> True -	(?==) :: a -> a -> r -> r -> r-	(?==) x y xc yc = case x == y of+	(?=) :: a -> a -> r -> r -> r+	(?=) x y xc yc = case x == y of 		True -> xc 		False -> yc

@@ -1,5 +1,5 @@ name:                pandora-version:             0.5.2+version:             0.5.3 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@@ -26,15 +26,15 @@      Pandora.Paradigm     -- Basic constructions+    Pandora.Paradigm.Algebraic+    Pandora.Paradigm.Algebraic.Functor+    Pandora.Paradigm.Algebraic.Exponential+    Pandora.Paradigm.Algebraic.Product+    Pandora.Paradigm.Algebraic.Sum+    Pandora.Paradigm.Algebraic.Zero+    Pandora.Paradigm.Algebraic.One     Pandora.Paradigm.Primary     Pandora.Paradigm.Primary.Object-    Pandora.Paradigm.Primary.Algebraic-    Pandora.Paradigm.Primary.Algebraic.Functor-    Pandora.Paradigm.Primary.Algebraic.Exponential-    Pandora.Paradigm.Primary.Algebraic.Product-    Pandora.Paradigm.Primary.Algebraic.Sum-    Pandora.Paradigm.Primary.Algebraic.Zero-    Pandora.Paradigm.Primary.Algebraic.One     Pandora.Paradigm.Primary.Object.Boolean     Pandora.Paradigm.Primary.Object.Ordering     Pandora.Paradigm.Primary.Object.Numerator@@ -58,8 +58,6 @@     Pandora.Paradigm.Primary.Transformer     Pandora.Paradigm.Primary.Transformer.Backwards     Pandora.Paradigm.Primary.Transformer.Reverse-    Pandora.Pattern.Morphism.Flip-    Pandora.Pattern.Morphism.Straight     Pandora.Paradigm.Primary.Transformer.Continuation     Pandora.Paradigm.Primary.Transformer.Construction     Pandora.Paradigm.Primary.Transformer.Instruction@@ -89,7 +87,6 @@     -- Typeclassess about functor junctions     Pandora.Paradigm.Controlflow.Effect     Pandora.Paradigm.Controlflow.Effect.Interpreted-    Pandora.Paradigm.Controlflow.Effect.Conditional     Pandora.Paradigm.Controlflow.Effect.Transformer     Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic     Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic@@ -118,17 +115,18 @@     Pandora.Paradigm.Structure.Ability.Possible     Pandora.Paradigm.Structure.Ability.Substructure     Pandora.Paradigm.Structure.Ability.Nonempty-    Pandora.Paradigm.Structure.Ability.Zipper     Pandora.Paradigm.Structure.Ability.Monotonic     Pandora.Paradigm.Structure.Modification     Pandora.Paradigm.Structure.Modification.Combinative     Pandora.Paradigm.Structure.Modification.Comprehension     Pandora.Paradigm.Structure.Modification.Prefixed     Pandora.Paradigm.Structure.Modification.Turnover+    Pandora.Paradigm.Structure.Modification.Tape     Pandora.Paradigm.Structure.Interface     Pandora.Paradigm.Structure.Interface.Set     Pandora.Paradigm.Structure.Interface.Dictionary     Pandora.Paradigm.Structure.Interface.Stack+    Pandora.Paradigm.Structure.Interface.Zipper     Pandora.Paradigm.Structure.Some     Pandora.Paradigm.Structure.Some.Stream     Pandora.Paradigm.Structure.Some.List@@ -142,6 +140,9 @@      Pandora.Pattern     Pandora.Pattern.Betwixt+    -- Different morphisms+    Pandora.Pattern.Morphism.Flip+    Pandora.Pattern.Morphism.Straight     -- Algebra typeclasses     Pandora.Pattern.Semigroupoid     Pandora.Pattern.Category@@ -183,7 +184,7 @@     Pandora.Pattern.Transformer.Liftable     Pandora.Pattern.Transformer.Lowerable   default-extensions:-    DataKinds, ConstraintKinds, ExistentialQuantification, GADTs, QuantifiedConstraints, InstanceSigs+    DataKinds, ConstraintKinds, ExistentialQuantification, GADTs, QuantifiedConstraints, InstanceSigs, StandaloneKindSignatures     FlexibleContexts, FlexibleInstances, KindSignatures, StandaloneKindSignatures, LiberalTypeSynonyms, LambdaCase, FunctionalDependencies     MultiParamTypeClasses, NoImplicitPrelude, PackageImports, PolyKinds, RankNTypes, ViewPatterns     ScopedTypeVariables, TypeApplications, TypeFamilies, TypeFamilyDependencies, TypeOperators