pandora 0.1.9 → 0.2.0

raw patch · 36 files changed

+243/−481 lines, 36 filesPVP ok

version bump matches the API change (PVP)

API changes (from Hackage documentation)

Files

• CHANGELOG.md +11/−0
• Pandora/Core/Functor.hs +12/−7
• Pandora/Paradigm/Basis/Conclusion.hs +7/−6
• Pandora/Paradigm/Basis/Continuation.hs +2/−1
• Pandora/Paradigm/Basis/Free.hs +2/−2
• Pandora/Paradigm/Basis/Identity.hs +3/−3
• Pandora/Paradigm/Basis/Maybe.hs +7/−6
• Pandora/Paradigm/Basis/Product.hs +3/−3
• Pandora/Paradigm/Basis/Twister.hs +3/−3
• Pandora/Paradigm/Inventory/Optics.hs +9/−2
• Pandora/Paradigm/Inventory/Stateful.hs +9/−9
• Pandora/Paradigm/Inventory/Storage.hs +3/−3
• Pandora/Paradigm/Structure/Graph.hs +17/−5
• Pandora/Paradigm/Structure/Stack.hs +3/−3
• Pandora/Pattern.hs +1/−0
• Pandora/Pattern/Functor.hs +2/−0
• Pandora/Pattern/Functor/Adjoint.hs +18/−8
• Pandora/Pattern/Functor/Applicative.hs +11/−8
• Pandora/Pattern/Functor/Bindable.hs +5/−2
• Pandora/Pattern/Functor/Contravariant.hs +7/−7
• Pandora/Pattern/Functor/Covariant.hs +7/−7
• Pandora/Pattern/Functor/Distributive.hs +8/−8
• Pandora/Pattern/Functor/Divariant.hs +25/−0
• Pandora/Pattern/Functor/Extendable.hs +2/−2
• Pandora/Pattern/Functor/Pointable.hs +4/−0
• Pandora/Pattern/Functor/Representable.hs +28/−0
• Pandora/Pattern/Functor/Traversable.hs +7/−7
• Pandora/Pattern/Junction.hs +1/−5
• Pandora/Pattern/Junction/Schemes.hs +7/−0
• Pandora/Pattern/Junction/Schemes/TU.hs +3/−53
• Pandora/Pattern/Junction/Schemes/TUV.hs +3/−81
• Pandora/Pattern/Junction/Schemes/TUVW.hs +3/−113
• Pandora/Pattern/Junction/Schemes/UT.hs +3/−60
• Pandora/Pattern/Junction/Schemes/UTU.hs +3/−60
• README.md +0/−6
• pandora.cabal +4/−1

@@ -99,3 +99,14 @@ * Rename `equip` to `wrap` and `Layout` to `Schema` in `Transformer` typeclass * Make `Composition` a superclass for `Transformer` typeclass * Move all `Junction` modules to `Pattern` submodule except `Kan`++# 0.2.0+* Define `Representable` functor typeclass+* Define `Pointable`, `Applicative`, `Bindable` and `Representable` instances for `->`+* Define infix `Adjoint` operators - `-|` and `|-`+* Define `Adjoint` instance for `Stateful` and `Storage` datatypes+* Change `Graph` definition: from type synonymous to newtype+* Rename `><` to `>`, `:.:` to `.:`, `.:.` to `:.`+* Remove all instances for `Junction` schemes+* Define type operators for profunctorish types: `::|:.`, `::|.:` and `::|::`+* Define `Divariant` (also known as `Profunctor`) `Functor` typeclass

@@ -1,12 +1,17 @@-module Pandora.Core.Functor (Variant (..), type (:.:), type (.:.), type (><)) where+module Pandora.Core.Functor where  data Variant = Co | Contra -infixr 1 :.:-type (:.:) t u a = t (u a)+infixr 1 :.+type (:.) t u a = t (u a) -infixr 1 .:.-type (.:.) t u a = u (t a)+infixr 1 .:+type (.:) t u a = u (t a) -infixr 0 ><-type (><) t a = t a+infixr 0 >+type (>) t a = t a++infixr 2 ::|:., ::|.:, ::|::+type (::|:.) p a b = p (p a b) b+type (::|.:) p a b = p a (p a b)+type (::|::) p a b = p (p a b) (p a b)

@@ -1,5 +1,6 @@ module Pandora.Paradigm.Basis.Conclusion (Conclusion (..), conclusion, fail) where +import Pandora.Core.Functor (Variant (Co)) import Pandora.Core.Morphism ((.), ($)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap)) import Pandora.Pattern.Junction.Transformer (Transformer (Schema, lay, wrap))@@ -47,23 +48,23 @@ 	unwrap x = x  instance Transformer (Conclusion e) where-	type Schema (Conclusion e) u = UT (Conclusion e) () (Conclusion e) u+	type Schema (Conclusion e) u = UT 'Co 'Co (Conclusion e) u 	lay x = UT $ Success <$> x 	wrap x = UT . point $ x -instance Covariant u => Covariant (UT (Conclusion e) () (Conclusion e) u) where+instance Covariant u => Covariant (UT 'Co 'Co (Conclusion e) u) where 	f <$> UT x = UT $ f <$$> x -instance Applicative u => Applicative (UT (Conclusion e) () (Conclusion e) u) where+instance Applicative u => Applicative (UT 'Co 'Co (Conclusion e) u) where 	UT f <*> UT x = UT $ apply <$> f <*> x -instance Pointable u => Pointable (UT (Conclusion e) () (Conclusion e) u) where+instance Pointable u => Pointable (UT 'Co 'Co (Conclusion e) u) where 	point = UT . point . point -instance (Pointable u, Bindable u) => Bindable (UT (Conclusion e) () (Conclusion e) u) where+instance (Pointable u, Bindable u) => Bindable (UT 'Co 'Co (Conclusion e) u) where 	UT x >>= f = UT $ x >>= conclusion (point . Failure) (unwrap . f) -instance Monad u => Monad (UT (Conclusion e) () (Conclusion e) u) where+instance Monad u => Monad (UT 'Co 'Co (Conclusion e) u) where  instance (Setoid e, Setoid a) => Setoid (Conclusion e a) where 	Success x == Success y = x == y

@@ -1,5 +1,6 @@ module Pandora.Paradigm.Basis.Continuation (Continuation (..), oblige, cwcc, reset, shift) where +import Pandora.Core.Functor (type (:.), type (>), type (::|:.)) import Pandora.Core.Morphism ((.), ($), (!), (?)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Pointable (Pointable (point))@@ -7,7 +8,7 @@ import Pandora.Pattern.Functor.Bindable (Bindable ((>>=))) import Pandora.Pattern.Functor.Monad (Monad) -newtype Continuation r t a = Continuation { continue :: (a -> t r) -> t r }+newtype Continuation r t a = Continuation { continue :: (->) ::|:. a :. t > r }  instance Covariant t => Covariant (Continuation r t) where 	f <$> Continuation continuation = Continuation $ continuation . (. f)

@@ -1,6 +1,6 @@ module Pandora.Paradigm.Basis.Free (Free (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>))) import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))@@ -10,7 +10,7 @@ import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>))) import Pandora.Pattern.Functor.Bindable (Bindable ((>>=))) -data Free t a = Pure a | Impure (t :.: Free t >< a)+data Free t a = Pure a | Impure (t :. Free t > a)  instance Covariant t => Covariant (Free t) where 	f <$> Pure x = Pure $ f x

@@ -11,7 +11,7 @@ import Pandora.Pattern.Functor.Extendable (Extendable ((=>>))) import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Functor.Comonad (Comonad)-import Pandora.Pattern.Functor.Adjoint (Adjoint (phi, psi))+import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))@@ -52,8 +52,8 @@ instance Comonad Identity  instance Adjoint Identity Identity where-	phi f = Identity . f . Identity-	psi f = extract . extract . comap f+	x -| f = Identity . f . Identity $ x+	x |- g = extract . extract . comap g $ x  instance Setoid a => Setoid (Identity a) where 	Identity x == Identity y = x == y

@@ -1,5 +1,6 @@ module Pandora.Paradigm.Basis.Maybe (Maybe (..), maybe) where +import Pandora.Core.Functor (Variant (Co)) import Pandora.Core.Morphism ((.), ($)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap)) import Pandora.Pattern.Junction.Transformer (Transformer (Schema, lay, wrap))@@ -54,23 +55,23 @@ 	unwrap x = x  instance Transformer Maybe where-	type Schema Maybe u = UT Maybe () Maybe u+	type Schema Maybe u = UT 'Co 'Co Maybe u 	lay x = UT $ Just <$> x 	wrap x = UT . point $ x -instance Covariant u => Covariant (UT Maybe () Maybe u) where+instance Covariant u => Covariant (UT 'Co 'Co Maybe u) where 	f <$> UT x = UT $ f <$$> x -instance Applicative u => Applicative (UT Maybe () Maybe u) where+instance Applicative u => Applicative (UT 'Co 'Co Maybe u) where 	UT f <*> UT x = UT $ apply <$> f <*> x -instance Pointable u => Pointable (UT Maybe () Maybe u) where+instance Pointable u => Pointable (UT 'Co 'Co Maybe u) where 	point = UT . point . point -instance (Pointable u, Bindable u) => Bindable (UT Maybe () Maybe u) where+instance (Pointable u, Bindable u) => Bindable (UT 'Co 'Co Maybe u) where 	UT x >>= f = UT $ x >>= maybe (point Nothing) (unwrap . f) -instance Monad u => Monad (UT Maybe () Maybe u) where+instance Monad u => Monad (UT 'Co 'Co Maybe u) where  instance Setoid a => Setoid (Maybe a) where 	Just x == Just y = x == y

@@ -7,7 +7,7 @@ import Pandora.Pattern.Functor.Traversable (Traversable ((->>))) import Pandora.Pattern.Functor.Extendable (Extendable ((=>>))) import Pandora.Pattern.Functor.Comonad (Comonad)-import Pandora.Pattern.Functor.Adjoint (Adjoint (phi, psi))+import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-))) import Pandora.Pattern.Object.Setoid (Setoid ((==)), (&&)) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.Pattern.Object.Monoid (Monoid (zero))@@ -37,8 +37,8 @@ instance Comonad (Product a) where  instance Adjoint (Product a) ((->) a) where-	phi f x y = f $ y :*: x-	psi f (y :*: x) = f x y+	x -| f = \y -> f $ y :*: x+	(y :*: x) |- f = f x y  instance (Setoid a, Setoid b) => Setoid (Product a b) where 	(x :*: y) == (x' :*: y') = x == x' && y == y'

@@ -1,6 +1,6 @@ module Pandora.Paradigm.Basis.Twister (Twister (..), untwist, coiterate, section) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Transformation (type (~>)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), comap)) import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))@@ -19,7 +19,7 @@  infixr 5 :< -data Twister t a = a :< (t :.: Twister t >< a)+data Twister t a = a :< (t :. Twister t > a)  instance Covariant t => Covariant (Twister t) where 	f <$> (x :< xs) = f x :< (f <$$> xs)@@ -56,7 +56,7 @@ instance (Monoid a, forall b . Semigroup b => Monoid (t b)) => Monoid (Twister t a) where 	zero = zero :< zero -untwist :: Twister t a -> (t :.: Twister t) a+untwist :: Twister t a -> (t :. Twister t) a untwist (_ :< xs) = xs  coiterate :: Covariant t => (a -> t a) -> a -> Twister t a

@@ -1,10 +1,17 @@ module Pandora.Paradigm.Inventory.Optics 	(Lens, type (:-.), (|>), view, set, over, (^.), (.~), (%~)) where -import Pandora.Core.Morphism ((.), ($))-import Pandora.Paradigm.Inventory.Storage (Storage, access, position, retrofit)+import Pandora.Core.Morphism ((.), ($), (!))+import Pandora.Paradigm.Basis.Product (Product ((:*:)))+import Pandora.Paradigm.Inventory.Stateful (Stateful (Stateful), statefully)+import Pandora.Paradigm.Inventory.Storage (Storage (Storage), access, position, retrofit) import Pandora.Pattern.Functor.Covariant (Covariant ((<$))) import Pandora.Pattern.Functor.Extractable (Extractable (extract))+import Pandora.Pattern.Functor.Adjoint (Adjoint ((-|), (|-)))++instance Adjoint (Storage s) (Stateful s) where+	v -| f = Stateful $ \s -> (:*:) s . f . Storage $ s :*: (v !)+	Storage (s :*: f) |- g = extract . statefully s . g $ f s  infixr 0 :-. type (:-.) src tgt = Lens src tgt

@@ -1,7 +1,7 @@ module Pandora.Paradigm.Inventory.Stateful 	(Stateful (..), statefully, get, modify, put, fold, find) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (Variant (Co), type (:.), type (>)) import Pandora.Core.Morphism ((.), ($)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap)) import Pandora.Pattern.Junction.Transformer (Transformer (Schema, lay, wrap))@@ -19,7 +19,7 @@ import Pandora.Pattern.Functor.Monad (Monad) import Pandora.Pattern.Object.Setoid (bool) -newtype Stateful s a = Stateful ((->) s :.: (:*:) s >< a)+newtype Stateful s a = Stateful ((->) s :. (:*:) s > a)  statefully :: s -> Stateful s a -> s :*: a statefully initial (Stateful state) = state initial@@ -58,24 +58,24 @@ find p struct = fold empty (\x s -> (<+>) s . bool empty (point x) . predicate p $ x) struct  instance Composition (Stateful s) where-	type Primary (Stateful s) a = (->) s :.: (:*:) s >< a+	type Primary (Stateful s) a = (->) s :. (:*:) s > a 	unwrap (Stateful x) = x  instance Transformer (Stateful s) where-	type Schema (Stateful s) u = TUV Stateful () Stateful ((->) s) u ((:*:) s)+	type Schema (Stateful s) u = TUV 'Co 'Co 'Co ((->) s) u ((:*:) s) 	lay x = TUV $ \s -> (s :*:) <$> x 	wrap x = TUV $ point <$> unwrap x -instance Covariant u => Covariant (TUV Stateful () Stateful ((->) s) u ((:*:) s)) where+instance Covariant u => Covariant (TUV 'Co 'Co 'Co ((->) s) u ((:*:) s)) where 	f <$> TUV x = TUV $ \old -> f <$$> x old -instance Bindable u => Applicative (TUV Stateful () Stateful ((->) s) u ((:*:) s)) where+instance Bindable u => Applicative (TUV 'Co 'Co 'Co ((->) s) u ((:*:) s)) where 	TUV f <*> TUV x = TUV $ \old -> f old >>= \(new :*: g) -> g <$$> x new -instance Pointable u => Pointable (TUV Stateful () Stateful ((->) s) u ((:*:) s)) where+instance Pointable u => Pointable (TUV 'Co 'Co 'Co ((->) s) u ((:*:) s)) where 	point x = TUV $ \s -> point $ s :*: x -instance Bindable u => Bindable (TUV Stateful () Stateful ((->) s) u ((:*:) s)) where+instance Bindable u => Bindable (TUV 'Co 'Co 'Co ((->) s) u ((:*:) s)) where 	TUV x >>= f = TUV $ \old -> x old >>= \(new :*: y) -> ($ new) . unwrap . f $ y -instance Monad u => Monad (TUV Stateful () Stateful ((->) s) u ((:*:) s)) where+instance Monad u => Monad (TUV 'Co 'Co 'Co ((->) s) u ((:*:) s)) where

@@ -1,6 +1,6 @@ module Pandora.Paradigm.Inventory.Storage (Storage (..), position, access, retrofit) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism ((.), ($), (?)) import Pandora.Paradigm.Basis.Product (Product ((:*:)), type (:*:)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))@@ -8,13 +8,13 @@ import Pandora.Pattern.Functor.Extendable (Extendable ((=>>))) import Pandora.Pattern.Functor.Comonad (Comonad) -newtype Storage p a = Storage { stored :: (:*:) p :.: (->) p >< a }+newtype Storage p a = Storage { stored :: (:*:) p :. (->) p > a }  instance Covariant (Storage p) where 	g <$> Storage (p :*: f) = Storage . (:*:) p $ (g .) f  instance Extractable (Storage p) where-	extract (Storage (p :*: x)) = x p+	extract (Storage (p :*: f)) = f p  instance Extendable (Storage p) where 	Storage (old :*: f) =>> g = Storage . (:*:) old

@@ -1,15 +1,27 @@ module Pandora.Paradigm.Structure.Graph (Graph, loose) where -import Pandora.Core.Functor (type (:.:), type (><))-import Pandora.Core.Morphism ((.))+import Pandora.Core.Functor (type (:.), type (>))+import Pandora.Core.Morphism ((.), ($)) import Pandora.Paradigm.Basis.Edges (Edges (Empty, Overlay)) import Pandora.Paradigm.Basis.Twister (Twister ((:<))) import Pandora.Paradigm.Inventory.Stateful (fold)-import Pandora.Pattern.Functor.Traversable (Traversable)+import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>)))+import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>)))+import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))  -- | Acyclic graph structure without loops-type Graph a = Edges :.: Twister Edges >< a+newtype Graph a = Graph (Edges :. Twister Edges > a) +instance Covariant Graph where+	f <$> Graph stack = Graph $ f <$$> stack++instance Traversable Graph where+	Graph stack ->> f = Graph <$> stack ->>> f++instance Composition Graph where+	type Primary Graph a = Edges :. Twister Edges > a+	unwrap (Graph stack) = stack+ -- | Transform any traversable structure into all loose edges graph loose :: Traversable t => t a -> Graph a-loose = fold Empty (\x -> Overlay . (:<) x)+loose = Graph . fold Empty (\x -> Overlay . (:<) x)

@@ -1,6 +1,6 @@ module Pandora.Paradigm.Structure.Stack (Stack, push, top, pop, filter, linearize) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism ((.), ($)) import Pandora.Core.Transformation (type (~>)) import Pandora.Paradigm.Basis.Maybe (Maybe (Just, Nothing))@@ -19,7 +19,7 @@ import Pandora.Pattern.Object.Setoid (bool)  -- | Linear data structure that serves as a collection of elements-newtype Stack a = Stack (Maybe :.: Twister Maybe >< a)+newtype Stack a = Stack (Maybe :. Twister Maybe > a)  instance Covariant Stack where 	f <$> Stack stack = Stack $ f <$$> stack@@ -40,7 +40,7 @@ 	Stack stack ->> f = Stack <$> stack ->>> f  instance Composition Stack where-	type Primary Stack a = Maybe :.: Twister Maybe >< a+	type Primary Stack a = Maybe :. Twister Maybe > a 	unwrap (Stack stack) = stack  push :: a -> Stack a -> Stack a

@@ -1,4 +1,5 @@ module Pandora.Pattern (module Exports) where  import Pandora.Pattern.Object as Exports+import Pandora.Pattern.Junction as Exports import Pandora.Pattern.Functor as Exports

@@ -1,9 +1,11 @@ module Pandora.Pattern.Functor (module Exports) where +import Pandora.Pattern.Functor.Divariant as Exports import Pandora.Pattern.Functor.Lowerable as Exports import Pandora.Pattern.Functor.Liftable as Exports import Pandora.Pattern.Functor.Comonad as Exports import Pandora.Pattern.Functor.Monad as Exports+import Pandora.Pattern.Functor.Representable as Exports import Pandora.Pattern.Functor.Adjoint as Exports import Pandora.Pattern.Functor.Extendable as Exports import Pandora.Pattern.Functor.Bindable as Exports

@@ -1,9 +1,13 @@ module Pandora.Pattern.Functor.Adjoint (Adjoint (..), type (-|)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism (identity) import Pandora.Pattern.Functor.Covariant (Covariant) +type (-|) = Adjoint++infixl 4 -|, |-+ {- | > When providing a new instance, you should ensure it satisfies the four laws: > * Left adjunction identity: phi cozero ≡ identity@@ -13,15 +17,21 @@ -}  class (Covariant t, Covariant u) => Adjoint t u where-	{-# MINIMAL phi, psi #-}+	{-# MINIMAL (-|), (|-) #-} 	-- | Left adjunction-	phi :: (t a -> b) -> a -> u b+	(-|) :: a -> (t a -> b) -> u b 	-- | Right adjunction-	psi :: (a -> u b) -> t a -> b+	(|-) :: t a -> (a -> u b) -> b -	eta :: a -> u :.: t >< a+	-- | Prefix and flipped version of '-|'+	phi :: (t a -> b) -> a -> u b+	phi f x = x -| f+	-- | Prefix and flipped version of '|-'+	psi :: (a -> u b) -> t a -> b+	psi g x = x |- g+	-- | Also known as 'unit'+	eta :: a -> u :. t > a 	eta = phi identity-	epsilon :: t :.: u >< a -> a+	-- | Also known as 'counit'+	epsilon :: t :. u > a -> a 	epsilon = psi identity--type (-|) = Adjoint

@@ -1,7 +1,7 @@ module Pandora.Pattern.Functor.Applicative (Applicative (..)) where -import Pandora.Core.Functor (type (:.:), type (><))-import Pandora.Core.Morphism (identity)+import Pandora.Core.Functor (type (:.), type (>))+import Pandora.Core.Morphism (identity, ($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$)))  infixl 4 <*>, <*, *>@@ -32,13 +32,16 @@ 	forever x = x *> forever x  	-- | Infix versions of `apply` with various nesting levels-	(<**>) :: Applicative u => t :.: u >< (a -> b) -> t :.: u >< a -> t :.: u >< b+	(<**>) :: Applicative u => t :. u > (a -> b) -> t :. u > a -> t :. u > b 	f <**> x = (<*>) <$> f <*> x-	(<***>) :: (Applicative u, Applicative v) => t :.: u :.: v >< (a -> b)-		-> t :.: u :.: v >< a -> t :.: u :.: v >< b+	(<***>) :: (Applicative u, Applicative v) => t :. u :. v > (a -> b)+		-> t :. u :. v > a -> t :. u :. v > b 	f <***> x = (<**>) <$> f <*> x 	(<****>) :: (Applicative u, Applicative v, Applicative w)-		=> t :.: u :.: v :.: w >< (a -> b)-		-> t :.: u :.: v :.: w >< a-		-> t :.: u :.: v :.: w >< b+		=> t :. u :. v :. w > (a -> b)+		-> t :. u :. v :. w > a+		-> t :. u :. v :. w > b 	f <****> x = (<***>) <$> f <*> x++instance Applicative ((->) e) where+	(<*>) f g x = f x $ g x

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Bindable (Bindable (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism ((?), identity) import Pandora.Pattern.Functor.Covariant (Covariant) @@ -24,7 +24,7 @@ 	bind :: (a -> t b) -> t a -> t b 	bind f t = t >>= f 	-- | Merge effects/contexts, the dual of 'duplicate'-	join :: t :.: t >< a -> t a+	join :: t :. t > a -> t a 	join t = t >>= identity 	-- | Left-to-right Kleisli composition 	(>=>) :: (a -> t b) -> (b -> t c) -> (a -> t c)@@ -32,3 +32,6 @@ 	-- | Right-to-left Kleisli composition 	(<=<) :: (b -> t c) -> (a -> t b) -> (a -> t c) 	(<=<) = (?) (>=>)++instance Bindable ((->) e) where+	f >>= g = \x -> g (f x) x

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Contravariant (Contravariant (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism ((.), (!), (?))  infixl 4 >$<, $<, >$@@ -33,21 +33,21 @@ 	x >&< f = f >$< x  	-- | Infix versions of `contramap` with various nesting levels-	(>$$<) :: Contravariant u => (a -> b) -> t :.: u >< a -> t :.: u >< b+	(>$$<) :: Contravariant u => (a -> b) -> t :. u > a -> t :. u > b 	(>$$<) = (>$<) . (>$<) 	(>$$$<) :: (Contravariant u, Contravariant v)-		=> (a -> b) -> t :.: u :.: v >< b -> t :.: u :.: v >< a+		=> (a -> b) -> t :. u :. v > b -> t :. u :. v > a 	(>$$$<) = (>$<) . (>$<) . (>$<) 	(>$$$$<) :: (Contravariant u, Contravariant v, Contravariant w)-		=> (a -> b) -> t :.: u :.: v :.: w >< a -> t :.: u :.: v :.: w >< b+		=> (a -> b) -> t :. u :. v :. w > a -> t :. u :. v :. w > b 	(>$$$$<) = (>$<) . (>$<) . (>$<) . (>$<)  	-- | Infix flipped versions of `contramap` with various nesting levels-	(>&&<) :: Contravariant u => t :.: u >< a -> (a -> b) -> t :.: u >< b+	(>&&<) :: Contravariant u => t :. u > a -> (a -> b) -> t :. u > b 	x >&&< f = f >$$< x 	(>&&&<) :: (Contravariant u, Contravariant v)-		=> t :.: u :.: v >< b -> (a -> b) -> t :.: u :.: v >< a+		=> t :. u :. v > b -> (a -> b) -> t :. u :. v > a 	x >&&&< f = f >$$$< x 	(>&&&&<) :: (Contravariant u, Contravariant v, Contravariant w)-		=> t :.: u :.: v :.: w >< a -> (a -> b) -> t :.: u :.: v :.: w >< b+		=> t :. u :. v :. w > a -> (a -> b) -> t :. u :. v :. w > b 	x >&&&&< f = f >$$$$< x

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Covariant (Covariant (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism (fix, (.), ($), (!), (?))  infixl 4 <$>, <$, $>@@ -36,23 +36,23 @@ 	x <&> f = f <$> x  	-- | Infix versions of `comap` with various nesting levels-	(<$$>) :: Covariant u => (a -> b) -> t :.: u >< a -> t :.: u >< b+	(<$$>) :: Covariant u => (a -> b) -> t :. u > a -> t :. u > b 	(<$$>) = (<$>) . (<$>) 	(<$$$>) :: (Covariant u, Covariant v)-		=> (a -> b) -> t :.: u :.: v >< a -> t :.: u :.: v >< b+		=> (a -> b) -> t :. u :. v > a -> t :. u :. v > b 	(<$$$>) = (<$>) . (<$>) . (<$>) 	(<$$$$>) :: (Covariant u, Covariant v, Covariant w)-		=> (a -> b) -> t :.: u :.: v :.: w >< a -> t :.: u :.: v :.: w >< b+		=> (a -> b) -> t :. u :. v :. w > a -> t :. u :. v :. w > b 	(<$$$$>) = (<$>) . (<$>) . (<$>) . (<$>)  	-- | Infix flipped versions of `comap` with various nesting levels-	(<&&>) :: Covariant u => t :.: u >< a -> (a -> b) -> t :.: u >< b+	(<&&>) :: Covariant u => t :. u > a -> (a -> b) -> t :. u > b 	x <&&> f = f <$$> x 	(<&&&>) :: (Covariant u, Covariant v)-		=> t :.: u :.: v >< a -> (a -> b) -> t :.: u :.: v >< b+		=> t :. u :. v > a -> (a -> b) -> t :. u :. v > b 	x <&&&> f = f <$$$> x 	(<&&&&>) :: (Covariant u, Covariant v, Covariant w)-		=> t :.: u :.: v :.: w >< a -> (a -> b) -> t :.: u :.: v :.: w >< b+		=> t :. u :. v :. w > a -> (a -> b) -> t :. u :. v :. w > b 	x <&&&&> f = f <$$$$> x  instance Covariant ((->) a) where

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Distributive (Distributive (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism (identity, (.), (?)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) @@ -16,25 +16,25 @@  class Covariant u => Distributive u where 	{-# MINIMAL (>>-) #-}-	-- | Infix version of 'collect'-	(>>-) :: Covariant t => t a -> (a -> u b) -> u :.: t >< b+	-- | Infix and flipped version of 'collect'+	(>>-) :: Covariant t => t a -> (a -> u b) -> u :. t > b  	-- | Prefix version of '>>-'-	collect :: Covariant t => (a -> u b) -> t a -> u :.: t >< b+	collect :: Covariant t => (a -> u b) -> t a -> u :. t > b 	collect f t = t >>- f 	-- | The dual of 'sequence'-	distribute :: Covariant t => t :.: u >< a -> u :.: t >< a+	distribute :: Covariant t => t :. u > a -> u :. t > a 	distribute t = t >>- identity  	-- | Infix versions of `collect` with various nesting levels 	(>>>-) :: (Covariant t, Covariant v)-		=> t :.: v >< a -> (a -> u b) -> u :.: t :.: v >< b+		=> t :. v > a -> (a -> u b) -> u :. t :. v > b 	x >>>- f = (collect . collect) f x 	(>>>>-) :: (Covariant t, Covariant v, Covariant w)-		=> t :.: v :.: w >< a -> (a -> u b) -> u :.: t :.: v :.: w >< b+		=> t :. v :. w > a -> (a -> u b) -> u :. t :. v :. w > b 	x >>>>- f = (collect . collect . collect) f x 	(>>>>>-) :: (Covariant t, Covariant v, Covariant w, Covariant j)-		=> t :.: v :.: w :.: j >< a -> (a -> u b) -> u :.: t :.: v :.: w :.: j >< b+		=> t :. v :. w :. j > a -> (a -> u b) -> u :. t :. v :. w :. j > b 	x >>>>>- f = (collect . collect . collect . collect) f x  instance Distributive ((->) e) where

@@ -0,0 +1,25 @@+module Pandora.Pattern.Functor.Divariant (Divariant (..)) where++import Pandora.Pattern.Functor.Covariant (Covariant)++import Pandora.Core.Morphism ((.), ($))++infixl 4 >->++{- |+> When providing a new instance, you should ensure it satisfies the two laws:+> * Identity: dimap identity identity ≡ identity+> * Composition: dimap (f . g) (h . i) ≡ dimap g h . dimap f i+-}++class (forall a . Covariant (t a)) => Divariant (t :: * -> * -> *) where+	{-# MINIMAL (>->) #-}+	-- | Infix version of 'comap'+	(>->) :: (a -> b) -> (c -> d) -> t b c -> t a d++	-- | Prefix version of '>->'+	dimap :: (a -> b) -> (c -> d) -> t b c -> t a d+	dimap f g x = f >-> g $ x++instance Divariant ((->)) where+	(>->) ab cd bc = cd . bc . ab

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Extendable (Extendable (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism ((.), (?), identity) import Pandora.Pattern.Functor.Covariant (Covariant) @@ -25,7 +25,7 @@ 	extend :: (t a -> b) -> t a -> t b 	extend f t = t =>> f 	-- | Clone existing structure, the dual of 'join'-	duplicate :: t a -> t :.: t >< a+	duplicate :: t a -> t :. t > a 	duplicate t = t =>> identity 	-- | Right-to-left Cokleisli composition 	(=<=) :: (t b -> c) -> (t a -> b) -> t a -> c

@@ -1,6 +1,10 @@ module Pandora.Pattern.Functor.Pointable (Pointable (..)) where +import Pandora.Core.Morphism ((!)) import Pandora.Pattern.Functor.Covariant (Covariant)  class Covariant t => Pointable t where 	point :: a -> t a++instance Pointable ((->) e) where+	point = (!)

@@ -0,0 +1,28 @@+module Pandora.Pattern.Functor.Representable (Representable (..)) where++import Pandora.Core.Morphism (identity, (?))+import Pandora.Pattern.Functor.Pointable (Pointable)++{- |+> When providing a new instance, you should ensure it satisfies the three laws:+> * Isomorphism (to): tabulate . index ≡ identity+> * Isomorphism (from): index . tabulate ≡ identity+> * Right adjoint: tabulate . point ≡ point+> * Interchange tabulation: comap f . tabulate ≡ tabulate . comap f+-}++class Pointable t => Representable t where+	{-# MINIMAL (<#>), tabulate #-}+	type Representation t :: *+	-- | Infix and flipped version of 'index'+	(<#>) :: Representation t -> t a -> a+	-- Build with a function which describes value+	tabulate :: (Representation t -> a) -> t a+	-- | Prefix and flipped version of '<#>'+	index :: t a -> Representation t -> a+	index x f = f <#> x++instance Representable ((->) e) where+	type Representation ((->) e) = e+	(<#>) = (identity ?)+	tabulate = identity

@@ -1,6 +1,6 @@ module Pandora.Pattern.Functor.Traversable (Traversable (..)) where -import Pandora.Core.Functor (type (:.:), type (><))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Core.Morphism (identity, (.)) import Pandora.Pattern.Functor.Covariant (Covariant) import Pandora.Pattern.Functor.Applicative (Applicative)@@ -22,22 +22,22 @@ class Covariant t => Traversable t where 	{-# MINIMAL (->>) #-} 	-- | Infix version of 'traverse'-	(->>) :: (Pointable u, Applicative u) => t a -> (a -> u b) -> u :.: t >< b+	(->>) :: (Pointable u, Applicative u) => t a -> (a -> u b) -> u :. t > b  	-- | Prefix version of '->>'-	traverse :: (Pointable u, Applicative u) => (a -> u b) -> t a -> u :.: t >< b+	traverse :: (Pointable u, Applicative u) => (a -> u b) -> t a -> u :. t > b 	traverse f t = t ->> f 	-- | The dual of 'distribute'-	sequence :: (Pointable u, Applicative u) => (t :.: u) a -> u :.: t >< a+	sequence :: (Pointable u, Applicative u) => (t :. u) a -> u :. t > a 	sequence t = t ->> identity  	-- | Infix versions of `traverse` with various nesting levels 	(->>>) :: (Pointable u, Applicative u, Traversable v)-		=> v :.: t >< a -> (a -> u b) -> u :.: v :.: t >< b+		=> v :. t > a -> (a -> u b) -> u :. v :. t > b 	x ->>> f = (traverse . traverse) f x 	(->>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w)-		=> w :.: v :.: t >< a -> (a -> u b) -> u :.: w :.: v :.: t >< b+		=> w :. v :. t > a -> (a -> u b) -> u :. w :. v :. t > b 	x ->>>> f = (traverse . traverse . traverse) f x 	(->>>>>) :: (Pointable u, Applicative u, Traversable v, Traversable w, Traversable j)-		=> j :.: w :.: v :.: t >< a -> (a -> u b) -> u :.: j :.: w :.: v :.: t >< b+		=> j :. w :. v :. t > a -> (a -> u b) -> u :. j :. w :. v :. t > b 	x ->>>>> f = (traverse . traverse . traverse . traverse) f x

@@ -1,9 +1,5 @@ module Pandora.Pattern.Junction (module Exports) where -import Pandora.Pattern.Junction.Schemes.UTU as Exports-import Pandora.Pattern.Junction.Schemes.UT as Exports-import Pandora.Pattern.Junction.Schemes.TUVW as Exports-import Pandora.Pattern.Junction.Schemes.TUV as Exports-import Pandora.Pattern.Junction.Schemes.TU as Exports+import Pandora.Pattern.Junction.Schemes as Exports import Pandora.Pattern.Junction.Transformer as Exports import Pandora.Pattern.Junction.Composition as Exports

@@ -0,0 +1,7 @@+module Pandora.Pattern.Junction.Schemes (module Exports) where++import Pandora.Pattern.Junction.Schemes.UTU as Exports+import Pandora.Pattern.Junction.Schemes.UT as Exports+import Pandora.Pattern.Junction.Schemes.TUVW as Exports+import Pandora.Pattern.Junction.Schemes.TUV as Exports+import Pandora.Pattern.Junction.Schemes.TU as Exports

@@ -1,60 +1,10 @@ module Pandora.Pattern.Junction.Schemes.TU (TU (..)) where -import Pandora.Core.Functor (Variant (Co, Contra), type (:.:), type (><))-import Pandora.Core.Morphism ((.), ($))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), comap))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<), (>$$<)))-import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), apply))-import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>)))-import Pandora.Pattern.Functor.Distributive (Distributive ((>>-), distribute))-import Pandora.Pattern.Functor.Adjoint (Adjoint (phi, psi)) -newtype TU ct cu t u a = TU (t :.: u >< a)+newtype TU ct cu t u a = TU (t :. u > a)  instance Composition (TU ct cu t u) where-	type Primary (TU ct cu t u) a = t :.: u >< a+	type Primary (TU ct cu t u) a = t :. u > a 	unwrap (TU x) = x--instance (Covariant t, Covariant u) => Covariant (TU 'Co 'Co t u) where-	f <$> TU x = TU $ f <$$> x--instance (Covariant t, Contravariant u) => Contravariant (TU 'Co 'Contra t u) where-	f >$< TU x = TU $ (f >$<) <$> x--instance (Contravariant t, Covariant u) => Contravariant (TU 'Contra 'Co t u) where-	f >$< TU x = TU $ (f <$>) >$< x--instance (Contravariant t, Contravariant u) => Covariant (TU 'Contra 'Contra t u) where-	f <$> TU x = TU $ f >$$< x--instance (Pointable t, Pointable u) => Pointable (TU 'Co 'Co t u) where-	point = TU . point . point--instance (Extractable t, Extractable u) => Extractable (TU 'Co 'Co t u) where-	extract = extract . extract . unwrap--instance (Avoidable t, Covariant u) => Avoidable (TU 'Co 'Co t u) where-	empty = TU empty--instance (Applicative t, Applicative u) => Applicative (TU 'Co 'Co t u) where-	TU f <*> TU x = TU $ apply <$> f <*> x--instance (Alternative t, Covariant u) => Alternative (TU 'Co 'Co t u) where-	TU x <+> TU y = TU $ x <+> y--instance (Traversable t, Traversable u) => Traversable (TU 'Co 'Co t u) where-	TU x ->> f = TU <$> x ->>> f--instance (Distributive t, Distributive u) => Distributive (TU 'Co 'Co t u) where-	x >>- f = TU . comap distribute . distribute $ unwrap . f <$> x--type (:-|:) t u = (Extractable t, Pointable t, Extractable u, Pointable u, Adjoint t u)--instance (t :-|: u, v :-|: w) => Adjoint (TU 'Co 'Co t v) (TU 'Co 'Co u w) where-	phi f = point . f . point-	psi f = extract . extract . comap f

@@ -1,88 +1,10 @@ module Pandora.Pattern.Junction.Schemes.TUV (TUV (..)) where -import Pandora.Core.Functor (Variant (Co, Contra), type (:.:), type (><))-import Pandora.Core.Morphism ((.), ($))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), (<$$$>), comap))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<), (>$$<), (>$$$<)), contramap)-import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), apply))-import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>>)))-import Pandora.Pattern.Functor.Distributive (Distributive ((>>-), distribute))-import Pandora.Pattern.Functor.Adjoint (Adjoint (phi, psi)) -newtype TUV ct cu cv t u v a = TUV (t :.: u :.: v >< a)+newtype TUV ct cu cv t u v a = TUV (t :. u :. v > a)  instance Composition (TUV ct cu cv t u v) where-	type Primary (TUV ct cu cv t u v) a = t :.: u :.: v >< a+	type Primary (TUV ct cu cv t u v) a = t :. u :. v > a 	unwrap (TUV x) = x--instance (Covariant t, Covariant u, Covariant v)-	=> Covariant (TUV 'Co 'Co 'Co t u v) where-	f <$> TUV x = TUV $ f <$$$> x--instance (Covariant t, Covariant u, Contravariant v)-	=> Contravariant (TUV 'Co 'Co 'Contra t u v) where-	f >$< TUV x = TUV $ (f >$<) <$$> x--instance (Covariant t, Contravariant u, Covariant v)-	=> Contravariant (TUV 'Co 'Contra 'Co t u v) where-	f >$< TUV x = TUV $ contramap (comap f) <$> x--instance (Contravariant t, Covariant u, Covariant v)-	=> Contravariant (TUV 'Contra 'Co 'Co t u v) where-	f >$< TUV x = TUV $ (f <$$>) >$< x--instance (Contravariant t, Contravariant u, Covariant v)-	=> Covariant (TUV 'Contra 'Contra 'Co t u v) where-	f <$> TUV x = TUV $ contramap (comap f) >$< x--instance (Covariant t, Contravariant u, Contravariant v)-	=> Covariant (TUV 'Co 'Contra 'Contra t u v) where-	f <$> TUV x = TUV $ (f >$$<) <$> x--instance (Contravariant t, Covariant u, Contravariant v)-	=> Covariant (TUV 'Contra 'Co 'Contra t u v) where-	f <$> TUV x = TUV $ comap (contramap f) >$< x--instance (Contravariant t, Contravariant u, Contravariant v)-	=> Contravariant (TUV 'Contra 'Contra 'Contra t u v) where-	f >$< TUV x = TUV $ f >$$$< x--instance (Pointable t, Pointable u, Pointable v)-	=> Pointable (TUV 'Co 'Co 'Co t u v) where-	point = TUV . point . point . point--instance (Extractable t, Extractable u, Extractable v)-	=> Extractable (TUV 'Co 'Co 'Co t u v) where-	extract = extract . extract . extract . unwrap--instance (Avoidable t, Covariant u, Covariant v)-	=> Avoidable (TUV 'Co 'Co 'Co t u v) where-	empty = TUV empty--instance (Applicative t, Applicative u, Applicative v)-	=> Applicative (TUV 'Co 'Co 'Co t u v) where-	TUV f <*> TUV x = TUV $ ((apply <$>) . (apply <$$>) $ f) <*> x--instance (Alternative t, Covariant u, Covariant v)-	=> Alternative (TUV 'Co 'Co 'Co t u v) where-	TUV x <+> TUV y = TUV $ x <+> y--instance (Traversable t, Traversable u, Traversable v)-	=> Traversable (TUV 'Co 'Co 'Co t u v) where-	TUV x ->> f = TUV <$> x ->>>> f--instance (Distributive t, Distributive u, Distributive v)-	=> Distributive (TUV 'Co 'Co 'Co t u v) where-	x >>- f = TUV . (distribute <$$>) . (distribute <$>) . distribute $ unwrap . f <$> x--type (:-|:) t u = (Extractable t, Pointable t, Extractable u, Pointable u, Adjoint t u)--instance (t :-|: w, v :-|: x, u :-|: y)-	=> Adjoint (TUV 'Co 'Co 'Co t v u) (TUV 'Co 'Co 'Co w x y) where-	phi f = point . f . point-	psi f = extract . extract . comap f

@@ -1,120 +1,10 @@ module Pandora.Pattern.Junction.Schemes.TUVW (TUVW (..)) where -import Pandora.Core.Functor (Variant (Co, Contra), type (:.:), type (><))-import Pandora.Core.Morphism ((.), ($))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), (<$$$>), (<$$$$>), comap))-import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<), (>$$<), (>$$$<), (>$$$$<), contramap))-import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), apply))-import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>>>)))-import Pandora.Pattern.Functor.Distributive (Distributive ((>>-), distribute))-import Pandora.Pattern.Functor.Adjoint (Adjoint (phi, psi)) -newtype TUVW ct cu cv cw t u v w a = TUVW (t :.: u :.: v :.: w >< a)+newtype TUVW ct cu cv cw t u v w a = TUVW (t :. u :. v :. w > a)  instance Composition (TUVW ct cu cv cw t u v w) where-	type Primary (TUVW ct cu cv cw t u v w) a = t :.: u :.: v :.: w >< a+	type Primary (TUVW ct cu cv cw t u v w) a = t :. u :. v :. w > a 	unwrap (TUVW x) = x--instance (Covariant t, Covariant u, Covariant v, Covariant w)-	=> Covariant (TUVW 'Co 'Co 'Co 'Co t u v w) where-	f <$> TUVW x = TUVW $ f <$$$$> x--instance (Covariant t, Covariant u, Covariant v, Contravariant w)-	=> Contravariant (TUVW 'Co 'Co 'Co 'Contra t u v w) where-	f >$< TUVW x = TUVW $ (f >$<) <$$$> x--instance (Covariant t, Covariant u, Contravariant v, Covariant w)-	=> Contravariant (TUVW 'Co 'Co 'Contra 'Co t u v w) where-	f >$< TUVW x = TUVW $ (contramap (comap f)) <$$> x--instance (Covariant t, Contravariant u, Covariant v, Covariant w)-	=> Contravariant (TUVW 'Co 'Contra 'Co 'Co t u v w) where-	f >$< TUVW x = TUVW $ (contramap (comap (comap f))) <$> x--instance (Contravariant t, Covariant u, Covariant v, Covariant w)-	=> Contravariant (TUVW 'Contra 'Co 'Co 'Co t u v w) where-	f >$< TUVW x = TUVW $ (f <$$$>) >$< x--instance (Contravariant t, Contravariant u, Covariant v, Covariant w)-	=> Covariant (TUVW 'Contra 'Contra 'Co 'Co t u v w) where-	f <$> TUVW x = TUVW $ (contramap . contramap . comap . comap $ f) x--instance (Covariant t, Contravariant u, Contravariant v, Covariant w)-	=> Covariant (TUVW 'Co 'Contra 'Contra 'Co t u v w) where-	f <$> TUVW x = TUVW $ (comap . contramap . contramap . comap $ f) x--instance (Covariant t, Covariant u, Contravariant v, Contravariant w)-	=> Covariant (TUVW 'Co 'Co 'Contra 'Contra t u v w) where-	f <$> TUVW x = TUVW $ (f >$$<) <$$> x--instance (Covariant t, Contravariant u, Covariant v, Contravariant w)-	=> Covariant (TUVW 'Co 'Contra 'Co 'Contra t u v w) where-	f <$> TUVW x = TUVW $ (comap . contramap . comap . contramap $ f) x--instance (Contravariant t, Covariant u, Contravariant v, Covariant w)-	=> Covariant (TUVW 'Contra 'Co 'Contra 'Co t u v w) where-	f <$> TUVW x = TUVW $ (contramap . comap . contramap . comap $ f) x--instance (Contravariant t, Covariant u, Covariant v, Contravariant w)-	=> Covariant (TUVW 'Contra 'Co 'Co 'Contra t u v w) where-	f <$> TUVW x = TUVW $ (contramap . comap . comap . contramap $ f) x--instance (Contravariant t, Contravariant u, Contravariant v, Covariant w)-	=> Contravariant (TUVW 'Contra 'Contra 'Contra 'Co t u v w) where-	f >$< TUVW x = TUVW $ (f <$>) >$$$< x--instance (Covariant t, Contravariant u, Contravariant v, Contravariant w)-	=> Contravariant (TUVW 'Co 'Contra 'Contra 'Contra t u v w) where-	f >$< TUVW x = TUVW $ (f >$$$<) <$> x--instance (Contravariant t, Covariant u, Contravariant v, Contravariant w)-	=> Contravariant (TUVW 'Contra 'Co 'Contra 'Contra t u v w) where-	f >$< TUVW x = TUVW $ (contramap . comap . contramap . contramap) f x--instance (Contravariant t, Contravariant u, Covariant v, Contravariant w)-	=> Contravariant (TUVW 'Contra 'Contra 'Co 'Contra t u v w) where-	f >$< TUVW x = TUVW $ (contramap . contramap . comap . contramap) f x--instance (Contravariant t, Contravariant u, Contravariant v, Contravariant w)-	=> Covariant (TUVW 'Contra 'Contra 'Contra 'Contra t u v w) where-	f <$> TUVW x = TUVW $ f >$$$$< x--instance (Pointable t, Pointable u, Pointable v, Pointable w)-	=> Pointable (TUVW 'Co 'Co 'Co 'Co t u v w) where-	point = TUVW . point . point . point . point--instance (Extractable t, Extractable u, Extractable v, Extractable w)-	=> Extractable (TUVW 'Co 'Co 'Co 'Co t u v w) where-	extract = extract . extract . extract . extract . unwrap--instance (Avoidable t, Covariant u, Covariant v, Covariant w)-	=> Avoidable (TUVW 'Co 'Co 'Co 'Co t u v w) where-	empty = TUVW empty--instance (Applicative t, Applicative u, Applicative v, Applicative w)-	=> Applicative (TUVW 'Co 'Co 'Co 'Co t u v w) where-	TUVW f <*> TUVW x = TUVW $ ((apply <$>) . (apply <$$>) . (apply <$$$>) $ f) <*> x--instance (Alternative t, Covariant u, Covariant v, Covariant w)-	=> Alternative (TUVW 'Co 'Co 'Co 'Co t u v w) where-	TUVW x <+> TUVW y = TUVW $ x <+> y--instance (Traversable t, Traversable u, Traversable v, Traversable w)-	=> Traversable (TUVW 'Co 'Co 'Co 'Co t u v w) where-	TUVW x ->> f = TUVW <$> x ->>>>> f--instance (Distributive t, Distributive u, Distributive v, Distributive w)-	=> Distributive (TUVW 'Co 'Co 'Co 'Co t u v w) where-	x >>- f = TUVW . (distribute <$$$>) . (distribute <$$>) . (distribute <$>) . distribute $ unwrap . f <$> x--type (:-|:) t u = (Extractable t, Pointable t, Extractable u, Pointable u, Adjoint t u)--instance (t :-|: u, v :-|: w, q :-|: q, r :-|: s)-	=> Adjoint (TUVW 'Co 'Co 'Co 'Co t v q r) (TUVW 'Co 'Co 'Co 'Co u w q s) where-	phi f = point . f . point-	psi f = extract . extract . comap f

@@ -1,67 +1,10 @@ module Pandora.Pattern.Junction.Schemes.UT (UT (..)) where -import Pandora.Core.Functor (Variant (Co), type (:.:), type (><))-import Pandora.Core.Morphism ((.), ($))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), comap))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), apply))-import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>)))-import Pandora.Pattern.Functor.Distributive (Distributive ((>>-), distribute))-import Pandora.Pattern.Functor.Liftable (Liftable (lift))-import Pandora.Pattern.Functor.Lowerable (Lowerable (lower))-import Pandora.Pattern.Object.Setoid (Setoid ((==)))-import Pandora.Pattern.Object.Chain (Chain ((<=>)))-import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Pattern.Object.Monoid (Monoid (zero)) -newtype UT ct cu t u a = UT (u :.: t >< a)+newtype UT ct cu t u a = UT (u :. t > a)  instance Composition (UT ct cu t u) where-	type Primary (UT ct cu t u) a = u :.: t >< a+	type Primary (UT ct cu t u) a = u :. t > a 	unwrap (UT x) = x--instance (Covariant t, Covariant u) => Covariant (UT 'Co 'Co t u) where-	f <$> UT x = UT $ f <$$> x--instance (Pointable t, Pointable u) => Pointable (UT 'Co 'Co t u) where-	point = UT . point . point--instance (Extractable t, Extractable u) => Extractable (UT 'Co 'Co t u) where-	extract = extract . extract . unwrap--instance (Covariant t, Avoidable u) => Avoidable (UT 'Co 'Co t u) where-	empty = UT empty--instance (Covariant t, Alternative u) => Alternative (UT 'Co 'Co t u) where-	UT x <+> UT y = UT $ x <+> y--instance (Applicative t, Applicative u) => Applicative (UT 'Co 'Co t u) where-	UT f <*> UT x = UT $ apply <$> f <*> x--instance Pointable t => Liftable (UT 'Co 'Co t) where-	lift x = UT $ point <$> x--instance Extractable t => Lowerable (UT 'Co 'Co t) where-	lower (UT x) = extract <$> x--instance (Traversable t, Traversable u) => Traversable (UT 'Co 'Co t u) where-	UT x ->> f = UT <$> x ->>> f--instance (Distributive t, Distributive u) => Distributive (UT 'Co 'Co t u) where-	x >>- f = UT . comap distribute . distribute $ unwrap . f <$> x--instance Setoid (u :.: t >< a) => Setoid (UT 'Co 'Co t u a) where-	UT x == UT y = x == y--instance Chain (u :.: t >< a) => Chain (UT 'Co 'Co t u a) where-	UT x <=> UT y = x <=> y--instance Semigroup (u :.: t >< a) => Semigroup (UT 'Co 'Co t u a) where-	UT x + UT y = UT $ x + y--instance Monoid (u :.: t >< a) => Monoid (UT 'Co 'Co t u a) where-	zero = UT zero

@@ -1,67 +1,10 @@ module Pandora.Pattern.Junction.Schemes.UTU (UTU (..)) where -import Pandora.Core.Functor (Variant (Co), type (:.:), type (><))-import Pandora.Core.Morphism ((.), ($))+import Pandora.Core.Functor (type (:.), type (>)) import Pandora.Pattern.Junction.Composition (Composition (Primary, unwrap))-import Pandora.Pattern.Functor.Covariant (Covariant ((<$>), (<$$>), comap))-import Pandora.Pattern.Functor.Pointable (Pointable (point))-import Pandora.Pattern.Functor.Extractable (Extractable (extract))-import Pandora.Pattern.Functor.Avoidable (Avoidable (empty))-import Pandora.Pattern.Functor.Alternative (Alternative ((<+>)))-import Pandora.Pattern.Functor.Applicative (Applicative ((<*>), apply))-import Pandora.Pattern.Functor.Traversable (Traversable ((->>), (->>>)))-import Pandora.Pattern.Functor.Distributive (Distributive ((>>-), distribute))-import Pandora.Pattern.Functor.Liftable (Liftable (lift))-import Pandora.Pattern.Functor.Lowerable (Lowerable (lower))-import Pandora.Pattern.Object.Setoid (Setoid ((==)))-import Pandora.Pattern.Object.Chain (Chain ((<=>)))-import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))-import Pandora.Pattern.Object.Monoid (Monoid (zero)) -newtype UTU ct cu t u a = UTU (u :.: t u >< a)+newtype UTU ct cu t u a = UTU (u :. t u > a)  instance Composition (UTU ct cu t u) where-	type Primary (UTU ct cu t u) a = u :.: t u >< a+	type Primary (UTU ct cu t u) a = u :. t u > a 	unwrap (UTU x) = x--instance (Covariant (t u), Covariant u) => Covariant (UTU 'Co 'Co t u) where-	f <$> UTU x = UTU $ f <$$> x--instance (Pointable (t u), Pointable u) => Pointable (UTU 'Co 'Co t u) where-	point = UTU . point . point--instance (Extractable (t u), Extractable u) => Extractable (UTU 'Co 'Co t u) where-	extract = extract . extract . unwrap--instance (Covariant (t u), Avoidable u) => Avoidable (UTU 'Co 'Co t u) where-	empty = UTU empty--instance (Covariant (t u), Alternative u) => Alternative (UTU 'Co 'Co t u) where-	UTU x <+> UTU y = UTU $ x <+> y--instance (Applicative (t u), Applicative u) => Applicative (UTU 'Co 'Co t u) where-	UTU f <*> UTU x = UTU $ apply <$> f <*> x--instance (Traversable (t u), Traversable u) => Traversable (UTU 'Co 'Co t u) where-	UTU x ->> f = UTU <$> x ->>> f--instance (Distributive (t u), Distributive u) => Distributive (UTU 'Co 'Co t u) where-	x >>- f = UTU . comap distribute . distribute $ unwrap . f <$> x--instance (forall u' . Pointable u', Liftable t) => Liftable (UTU 'Co 'Co t) where-	lift = UTU . point . lift--instance (forall u' . Extractable u', Lowerable t) => Lowerable (UTU 'Co 'Co t) where-	lower = lower . extract . unwrap--instance (forall u' . Setoid (u' :.: t u' >< a)) => Setoid (UTU 'Co 'Co t u a) where-	UTU x == UTU y = x == y--instance (forall u' . Chain (u' :.: t u' >< a)) => Chain (UTU 'Co 'Co t u a) where-	UTU x <=> UTU y = x <=> y--instance (forall u' . Semigroup (u' :.: t u' >< a)) => Semigroup (UTU 'Co 'Co t u a) where-	UTU x + UTU y = UTU $ x + y--instance (forall u' . Monoid (u' :.: t u' >< a)) => Monoid (UTU 'Co 'Co t u a) where-	zero = UTU zero

@@ -14,9 +14,3 @@ * Library: http://hackage.haskell.org/package/semigroupoids * Library: http://hackage.haskell.org/package/transformers * Library: http://hackage.haskell.org/package/invariant--## Diagram of functor patterns:-![Functors diagram](/Diagrams/Functors.png)--## Diagram of object patterns:-![Objects diagram](/Diagrams/Objects.png)

@@ -1,5 +1,5 @@ name:                pandora-version:             0.1.9+version:             0.2.0 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@@ -85,11 +85,14 @@     Pandora.Pattern.Functor.Lowerable     Pandora.Pattern.Functor.Monad     Pandora.Pattern.Functor.Pointable+    Pandora.Pattern.Functor.Representable     Pandora.Pattern.Functor.Traversable+    Pandora.Pattern.Functor.Divariant     -- Typeclassess about functor junctions     Pandora.Pattern.Junction     Pandora.Pattern.Junction.Composition     Pandora.Pattern.Junction.Transformer+    Pandora.Pattern.Junction.Schemes     Pandora.Pattern.Junction.Schemes.TU     Pandora.Pattern.Junction.Schemes.TUV     Pandora.Pattern.Junction.Schemes.TUVW