free-algebras-0.0.8.1: Free algebras

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LanguageHaskell2010

Data.Semigroup.Abelian

Synopsis

Documentation

class Semigroup m => AbelianSemigroup m Source #

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

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

Ord a => AbelianSemigroup (FreeSemilattice a) Source # 
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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 # 
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Eq a => Eq (FreeAbelianSemigroup a) Source # 
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Ord a => Ord (FreeAbelianSemigroup a) Source # 
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Show a => Show (FreeAbelianSemigroup a) Source # 
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Ord a => Semigroup (FreeAbelianSemigroup a) Source # 
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Ord a => AbelianSemigroup (FreeAbelianSemigroup a) Source # 
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type AlgebraType0 FreeAbelianSemigroup (a :: Type) Source # 
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type AlgebraType FreeAbelianSemigroup (a :: Type) Source # 
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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.