Safe Haskell	Safe
Language	Haskell2010

Data.Semigroup.Abelian

Synopsis

class Semigroup m => AbelianSemigroup m
data FreeAbelianSemigroup a
toNonEmpty :: FreeAbelianSemigroup a -> NonEmpty (a, Natural)
fromNonEmpty :: Ord a => NonEmpty (a, Natural) -> Maybe (FreeAbelianSemigroup a)

Documentation

class Semigroup m => AbelianSemigroup m Source #

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

Instances

AbelianSemigroup () Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup Void Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup All Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup Any Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup IntSet Source #
Instance details Defined in Data.Semigroup.Abelian
Ord a => AbelianSemigroup (Min a) Source #
Instance details Defined in Data.Semigroup.Abelian
Ord a => AbelianSemigroup (Max a) Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup a => AbelianSemigroup (Option a) Source #
Instance details Defined in Data.Semigroup.Abelian
AbelianSemigroup a => AbelianSemigroup (Dual a) Source #
Instance details Defined in Data.Semigroup.Abelian
Num a => AbelianSemigroup (Sum a) Source #
Instance details Defined in Data.Semigroup.Abelian
Num a => AbelianSemigroup (Product a) Source #
Instance details Defined in Data.Semigroup.Abelian
Ord a => AbelianSemigroup (Set a) Source #
Instance details Defined in Data.Semigroup.Abelian
Ord a => AbelianSemigroup (FreeAbelianSemigroup a) Source #
Instance details Defined in Data.Semigroup.Abelian
Ord a => AbelianSemigroup (FreeAbelianMonoid a) Source #
Instance details Defined in Data.Monoid.Abelian
Ord a => AbelianSemigroup (FreeSemilattice a) Source #
Instance details Defined in Data.Semigroup.Semilattice

data FreeAbelianSemigroup a Source #

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 Source #
Instance details Defined in Data.Semigroup.Abelian Methods returnFree :: a -> FreeAbelianSemigroup a Source # foldMapFree :: (AlgebraType FreeAbelianSemigroup d, AlgebraType0 FreeAbelianSemigroup a) => (a -> d) -> FreeAbelianSemigroup a -> d Source # codom :: AlgebraType0 FreeAbelianSemigroup a => Proof (AlgebraType FreeAbelianSemigroup (FreeAbelianSemigroup a)) (FreeAbelianSemigroup a) Source # forget :: AlgebraType FreeAbelianSemigroup a => Proof (AlgebraType0 FreeAbelianSemigroup a) (FreeAbelianSemigroup a) Source #
Eq a => Eq (FreeAbelianSemigroup a) Source #
Instance details Defined in Data.Semigroup.Abelian Methods (==) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Bool # (/=) :: FreeAbelianSemigroup a -> FreeAbelianSemigroup a -> Bool #
Ord a => Ord (FreeAbelianSemigroup a) Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Abelian Methods showsPrec :: Int -> FreeAbelianSemigroup a -> ShowS # show :: FreeAbelianSemigroup a -> String # showList :: [FreeAbelianSemigroup a] -> ShowS #
Ord a => Semigroup (FreeAbelianSemigroup a) Source #
Instance details 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) Source #
Instance details Defined in Data.Semigroup.Abelian
type AlgebraType0 FreeAbelianSemigroup (a :: Type) Source #
Instance details Defined in Data.Semigroup.Abelian type AlgebraType0 FreeAbelianSemigroup (a :: Type) = Ord a
type AlgebraType FreeAbelianSemigroup (a :: Type) Source #
Instance details Defined in Data.Semigroup.Abelian type AlgebraType FreeAbelianSemigroup (a :: Type) = (Ord a, AbelianSemigroup a)

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

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

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