120
правок
Изменения
→Algebra
==Algebra==
class Monoid a where mempty :: a mappend :: a -> a -> a
class Monoid a => Group a where ginv :: a -> a mconcat :: (Monoid a) => List a -> a mconcat = foldr mappend mempty instance Monoid Unit where mempty = Unit mappend _ _ = Unit instance Group Unit where ginv _ = Unit instance (Monoid a, Monoid b) => Monoid (Pair a b) where mempty = Pair mempty mempty mappend a b = Pair {fst = fst a `mappend` fst b, snd = snd b `mappend` snd b} instance (Monoid a) => Monoid (Maybe a) where mempty = Just mempty mappend (Just a) (Just b) = Just $ mappend a b mappend _ _ = Nothing newtype First a = First { getFirst :: Maybe a} instance Monoid (First a) where mempty = First Nothing mappend (First Nothing) x = x mappend x _ = x newtype Last a = Last { getLast :: Maybe a} instance Monoid (Last a) where mempty = Last Nothing mappend x (Last Nothing) = x mappend _ x = x newtype Any = Any { getAny :: Bool } instance Monoid Any where mempty = Any False mappend (Any a) (Any b) = Any $ a || b newtype All = All { getAll :: Bool } instance Monoid All where mempty = All True mappend (All a) (All b) = All $ a && b -- Лексикографическое сравнение instance Monoid Tri where mempty = EQ mappend LT _ = LT mappend EQ a = a mappend GT _ = GT newtype Sum a = Sum { getSum :: a } instance Monoid (Sum Nat) where mempty = Sum natZero mappend (Sum a) (Sum b) = Sum $ a +. b newtype Product a = Product { getProduct :: a } instance Monoid (Product Nat ) where mempty = Product natOne mappend (Product a) (Product b) = Product $ a *. b instance Monoid (Sum Int) where mempty = Sum intZero mappend (Sum a) (Sum b) = Sum $ a .+. b instance Group (Sum Int) where ginv = Sum . intNeg . getSum instance Monoid (Product Int) where mempty = Product intOne mappend (Product a) (Product b) = Product $ a .*. b instance Monoid (Sum Rat) where mempty = Sum ratZero mappend (Sum a) (Sum b) = Sum $ a %+ b instance Group (Sum Rat) where ginv = Sum . ratNeg . getSum instance Monoid (Product Rat) where mempty = Product ratOne mappend (Product a) (Product b) = Product $ a %* b instance Group (Product Rat) where ginv = Product . ratInv . getProduct instance Monoid (List a) where mempty = Nil mappend = (++)
==Categories==
