Safe Haskell	None
Language	Haskell2010

Data.Monoid.Abelian

Synopsis

newtype FreeAbelianMonoid a = FreeAbelianMonoid (Map a Natural)

Documentation

newtype FreeAbelianMonoid a Source #

Free abelian monoid. Note that `FreeAbelianMonoid () ≅ Natural` as expected.

Constructors

FreeAbelianMonoid (Map a Natural)

Instances

FreeAlgebra FreeAbelianMonoid Source #
Instance details Defined in Data.Monoid.Abelian Methods returnFree :: a -> FreeAbelianMonoid a Source # foldMapFree :: (AlgebraType FreeAbelianMonoid d, AlgebraType0 FreeAbelianMonoid a) => (a -> d) -> FreeAbelianMonoid a -> d Source # codom :: AlgebraType0 FreeAbelianMonoid a => Proof (AlgebraType FreeAbelianMonoid (FreeAbelianMonoid a)) (FreeAbelianMonoid a) Source # forget :: AlgebraType FreeAbelianMonoid a => Proof (AlgebraType0 FreeAbelianMonoid a) (FreeAbelianMonoid a) Source #
Eq a => Eq (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian Methods (==) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool # (/=) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool #
Ord a => Ord (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian Methods compare :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Ordering # (<) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool # (<=) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool # (>) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool # (>=) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool # max :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> FreeAbelianMonoid a # min :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> FreeAbelianMonoid a #
Show a => Show (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian Methods showsPrec :: Int -> FreeAbelianMonoid a -> ShowS # show :: FreeAbelianMonoid a -> String # showList :: [FreeAbelianMonoid a] -> ShowS #
Ord a => Semigroup (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian Methods (<>) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> FreeAbelianMonoid a # sconcat :: NonEmpty (FreeAbelianMonoid a) -> FreeAbelianMonoid a # stimes :: Integral b => b -> FreeAbelianMonoid a -> FreeAbelianMonoid a #
Ord a => Monoid (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian Methods mempty :: FreeAbelianMonoid a # mappend :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> FreeAbelianMonoid a # mconcat :: [FreeAbelianMonoid a] -> FreeAbelianMonoid a #
Ord a => AbelianSemigroup (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian
type AlgebraType0 FreeAbelianMonoid (a :: Type) Source #
Instance details Defined in Data.Monoid.Abelian type AlgebraType0 FreeAbelianMonoid (a :: Type) = Ord a
type AlgebraType FreeAbelianMonoid (m :: Type) Source #
Instance details Defined in Data.Monoid.Abelian type AlgebraType FreeAbelianMonoid (m :: Type) = (Ord m, Monoid m, AbelianSemigroup m)