module Algebra.Monoid where
import qualified Algebra.Additive as Additive
import qualified Algebra.Ring as Ring
import Data.Monoid as Mn
class C a where
idt :: a
(<*>) :: a -> a -> a
cumulate :: [a] -> a
cumulate = foldr (<*>) idt
instance C All where
idt = mempty
(<*>) = mappend
cumulate = mconcat
instance C Any where
idt = mempty
(<*>) = mappend
cumulate = mconcat
instance C a => C (Dual a) where
idt = Mn.Dual idt
(Mn.Dual x) <*> (Mn.Dual y) = Mn.Dual (y <*> x)
cumulate = Mn.Dual . cumulate . reverse . map Mn.getDual
instance C (Endo a) where
idt = mempty
(<*>) = mappend
cumulate = mconcat
instance C (First a) where
idt = mempty
(<*>) = mappend
cumulate = mconcat
instance C (Last a) where
idt = mempty
(<*>) = mappend
cumulate = mconcat
instance Ring.C a => C (Product a) where
idt = Mn.Product Ring.one
(Mn.Product x) <*> (Mn.Product y) = Mn.Product (x Ring.* y)
cumulate = Mn.Product . Ring.product . map Mn.getProduct
instance Additive.C a => C (Sum a) where
idt = Mn.Sum Additive.zero
(Mn.Sum x) <*> (Mn.Sum y) = Mn.Sum (x Additive.+ y)
cumulate = Mn.Sum . Additive.sum . map Mn.getSum