Data.Monoid.Abelian

Documentation

newtype FreeAbelianMonoid a

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

Constructors

FreeAbelianMonoid (Map a Natural)

Instances

FreeAlgebra FreeAbelianMonoid

Defined in Data.Monoid.Abelian

Methods

returnFree :: a -> FreeAbelianMonoid a

foldMapFree :: (AlgebraType FreeAbelianMonoid d, AlgebraType0 FreeAbelianMonoid a) => (a -> d) -> FreeAbelianMonoid a -> d

proof :: AlgebraType0 FreeAbelianMonoid a => Proof (AlgebraType FreeAbelianMonoid (FreeAbelianMonoid a)) (FreeAbelianMonoid a)

forget :: AlgebraType FreeAbelianMonoid a => Proof (AlgebraType0 FreeAbelianMonoid a) (FreeAbelianMonoid a)

Eq a => Eq (FreeAbelianMonoid a)

Defined in Data.Monoid.Abelian

Methods

(==) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool

(/=) :: FreeAbelianMonoid a -> FreeAbelianMonoid a -> Bool

Ord a => Ord (FreeAbelianMonoid a)

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)

Defined in Data.Monoid.Abelian

Methods

showsPrec :: Int -> FreeAbelianMonoid a -> ShowS

show :: FreeAbelianMonoid a -> String

showList :: [FreeAbelianMonoid a] -> ShowS

Ord a => Semigroup (FreeAbelianMonoid a)

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)

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)

Defined in Data.Monoid.Abelian

type AlgebraType0 FreeAbelianMonoid (a :: *)

Defined in Data.Monoid.Abelian

type AlgebraType0 FreeAbelianMonoid (a :: *) = Ord a

type AlgebraType FreeAbelianMonoid (m :: *)

Defined in Data.Monoid.Abelian

type AlgebraType FreeAbelianMonoid (m :: *) = (Ord m, Monoid m, AbelianSemigroup m)