module Pandora.Paradigm.Primary.Functor.Constant where import Pandora.Pattern.Category (($)) import Pandora.Pattern.Functor.Covariant (Covariant ((<$>))) import Pandora.Pattern.Functor.Contravariant (Contravariant ((>$<))) import Pandora.Pattern.Functor.Invariant (Invariant ((>-<))) import Pandora.Pattern.Functor.Pointable (Pointable (point)) import Pandora.Pattern.Functor.Traversable (Traversable ((->>))) import Pandora.Pattern.Functor.Bivariant (Bivariant ((<->))) import Pandora.Pattern.Object.Setoid (Setoid ((==))) import Pandora.Pattern.Object.Chain (Chain ((<=>))) import Pandora.Pattern.Object.Semigroup (Semigroup ((+))) import Pandora.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)) newtype Constant a b = Constant a instance Covariant (Constant a) where a -> b _ <$> :: (a -> b) -> Constant a a -> Constant a b <$> Constant a x = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant a x instance Contravariant (Constant a) where a -> b _ >$< :: (a -> b) -> Constant a b -> Constant a a >$< Constant a x = a -> Constant a a forall k a (b :: k). a -> Constant a b Constant a x instance Invariant (Constant a) where a -> b _ >-< :: (a -> b) -> (b -> a) -> Constant a a -> Constant a b >-< b -> a _ = \(Constant a x) -> a -> Constant a b forall k a (b :: k). a -> Constant a b Constant a x instance Traversable (Constant a) where Constant a x ->> :: Constant a a -> (a -> u b) -> (u :. Constant a) := b ->> a -> u b _ = Constant a b :=> u forall (t :: * -> *) a. Pointable t => a :=> t point (a -> Constant a b forall k a (b :: k). a -> Constant a b Constant a x) instance Bivariant Constant where a -> b f <-> :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d <-> c -> d _ = \(Constant a x) -> b -> Constant b d forall k a (b :: k). a -> Constant a b Constant (b -> Constant b d) -> b -> Constant b d forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a -> b f a x instance Setoid a => Setoid (Constant a b) where Constant a x == :: Constant a b -> Constant a b -> Boolean == Constant a y = a x a -> a -> Boolean forall a. Setoid a => a -> a -> Boolean == a y instance Chain a => Chain (Constant a b) where Constant a x <=> :: Constant a b -> Constant a b -> Ordering <=> Constant a y = a x a -> a -> Ordering forall a. Chain a => a -> a -> Ordering <=> a y instance Semigroup a => Semigroup (Constant a b) where Constant a x + :: Constant a b -> Constant a b -> Constant a b + Constant a y = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant (a -> Constant a b) -> a -> Constant a b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a x a -> a -> a forall a. Semigroup a => a -> a -> a + a y instance Monoid a => Monoid (Constant a b) where zero :: Constant a b zero = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant a forall a. Monoid a => a zero instance Ringoid a => Ringoid (Constant a b) where Constant a x * :: Constant a b -> Constant a b -> Constant a b * Constant a y = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant (a -> Constant a b) -> a -> Constant a b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a x a -> a -> a forall a. Ringoid a => a -> a -> a * a y instance Quasiring a => Quasiring (Constant a b) where one :: Constant a b one = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant a forall a. Quasiring a => a one instance Infimum a => Infimum (Constant a b) where Constant a x /\ :: Constant a b -> Constant a b -> Constant a b /\ Constant a y = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant (a -> Constant a b) -> a -> Constant a b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a x a -> a -> a forall a. Infimum a => a -> a -> a /\ a y instance Supremum a => Supremum (Constant a b) where Constant a x \/ :: Constant a b -> Constant a b -> Constant a b \/ Constant a y = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant (a -> Constant a b) -> a -> Constant a b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a x a -> a -> a forall a. Supremum a => a -> a -> a \/ a y instance Lattice a => Lattice (Constant a b) where instance Group a => Group (Constant a b) where invert :: Constant a b -> Constant a b invert (Constant a x) = a -> Constant a b forall k a (b :: k). a -> Constant a b Constant (a -> Constant a b) -> a -> Constant a b forall (m :: * -> * -> *) a b. Category m => m a b -> m a b $ a -> a forall a. Group a => a -> a invert a x