Data.Semigroup.Abelian

Documentation

class Semigroup m => AbelianSemigroup m

Class of commutative monoids, e.g. with additional law: a <> b = b <> a

Instances

AbelianSemigroup ()

Defined in Data.Semigroup.Abelian

AbelianSemigroup Void

Defined in Data.Semigroup.Abelian

AbelianSemigroup All

Defined in Data.Semigroup.Abelian

AbelianSemigroup Any

Defined in Data.Semigroup.Abelian

AbelianSemigroup IntSet

Defined in Data.Semigroup.Abelian

Ord a => AbelianSemigroup (Min a)

Defined in Data.Semigroup.Abelian

Ord a => AbelianSemigroup (Max a)

Defined in Data.Semigroup.Abelian

AbelianSemigroup a => AbelianSemigroup (Option a)

Defined in Data.Semigroup.Abelian

AbelianSemigroup a => AbelianSemigroup (Dual a)

Defined in Data.Semigroup.Abelian

Num a => AbelianSemigroup (Sum a)

Defined in Data.Semigroup.Abelian

Num a => AbelianSemigroup (Product a)

Defined in Data.Semigroup.Abelian

Ord a => AbelianSemigroup (Set a)

Defined in Data.Semigroup.Abelian

Ord a => AbelianSemigroup (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

Ord a => AbelianSemigroup (FreeAbelianMonoid a)

Defined in Data.Monoid.Abelian

Ord a => AbelianSemigroup (FreeSemilattice a)

Defined in Data.Semigroup.Semilattice

data FreeAbelianSemigroup a

Free abelian semigroup is isomorphic to a non empty map with keys a and values positive natural numbers.

It is a monad on the full subcategory which satisfies the Ord constraint, but base does not allow to define a functor / applicative / monad instances which are constraint by a class.

Instances

FreeAlgebra FreeAbelianSemigroup

Defined in Data.Semigroup.Abelian

Methods

returnFree :: a -> FreeAbelianSemigroup a

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

codom :: AlgebraType0 FreeAbelianSemigroup a => Proof (AlgebraType FreeAbelianSemigroup (FreeAbelianSemigroup a)) (FreeAbelianSemigroup a)

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

Eq a => Eq (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

Methods

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

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

Ord a => Ord (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

Methods

compare :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Ordering

(<) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Bool

(<=) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Bool

(>) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Bool

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

max :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> FreeAbelianSemigroup a

min :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> FreeAbelianSemigroup a

Show a => Show (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

Methods

showsPrec :: Int -> FreeAbelianSemigroup a -> ShowS

show :: FreeAbelianSemigroup a -> String

showList :: [FreeAbelianSemigroup a] -> ShowS

Ord a => Semigroup (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

Methods

(<>) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> FreeAbelianSemigroup a

sconcat :: NonEmpty (FreeAbelianSemigroup a) -> FreeAbelianSemigroup a

stimes :: Integral b => b -> FreeAbelianSemigroup a -> FreeAbelianSemigroup a

Ord a => AbelianSemigroup (FreeAbelianSemigroup a)

Defined in Data.Semigroup.Abelian

type AlgebraType0 FreeAbelianSemigroup (a :: Type)

Defined in Data.Semigroup.Abelian

type AlgebraType0 FreeAbelianSemigroup (a :: Type) = Ord a

type AlgebraType FreeAbelianSemigroup (a :: Type)

Defined in Data.Semigroup.Abelian

type AlgebraType FreeAbelianSemigroup (a :: Type) = (Ord a, AbelianSemigroup a)

toNonEmpty :: FreeAbelianSemigroup a -> NonEmpty (a, Natural)

fromNonEmpty :: Ord a => NonEmpty (a, Natural) -> Maybe (FreeAbelianSemigroup a)

Smart constructor which creates FreeAbelianSemigroup from a non empty list of pairs (a, n) :: (a, Natural) where n > 0.