Control.Algebra.Properties

absorbtion :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> Boolean

leftAlternativeIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

rightAlternativeIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

alternativeIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

anticommutative :: forall b a. Eq b => (a -> a -> b) -> a -> a -> Boolean

antireflexive :: forall b a. HeytingAlgebra b => Eq b => (a -> a -> b) -> a -> b

asymmetric :: forall a. Eq a => (a -> a -> Boolean) -> a -> a -> Boolean

antisymmetric :: forall a. Eq a => (a -> a -> Boolean) -> a -> a -> Boolean

antitransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

associative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

leftCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightCancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

cancellative :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

commutative :: forall b a. Eq b => (a -> a -> b) -> a -> a -> Boolean

congruent :: forall a. Eq a => (a -> a) -> a -> a -> Boolean

elasticIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

leftDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

rightDistributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

distributive :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Boolean

falsehoodPreserving :: forall a. HeytingAlgebra a => Eq a => (a -> a -> a) -> a -> a -> a

flexibleIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

idempotent :: forall a. Eq a => (a -> a) -> a -> Boolean

idempotent' :: forall a. Eq a => (a -> a -> a) -> a -> Boolean

identity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

intransitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

involution :: forall a. Eq a => (a -> a) -> a -> Boolean

jacobiIdentity :: forall a. Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> a -> Boolean

jordanIdentity :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

medial :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> a -> Boolean

monotonic :: forall a. HeytingAlgebra a => Eq a => (a -> a -> a) -> a -> a -> a -> a

powerAssociative :: forall a. Eq a => (a -> a -> a) -> a -> Boolean

A magma M is power-associative if the subalgebra generated by any element is associative.

∀ m n. m,n ∈ ℤ+ x^m • x^n = x^(m + n) where x^m • x^n is defined recursively via x^1 = x, x^(n + 1) = x^n • x

reflexive :: forall b a. HeytingAlgebra b => Eq b => (a -> a -> b) -> a -> b

leftSemimedial :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> a -> Boolean

rightSemimedial :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> a -> Boolean

semimedial :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> a -> Boolean

transitive :: forall b a. HeytingAlgebra b => (a -> a -> b) -> a -> a -> a -> b

truthPreserving :: forall a. HeytingAlgebra a => Eq a => (a -> a -> a) -> a -> a -> a

leftUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

rightUnar :: forall a. Eq a => (a -> a -> a) -> a -> a -> a -> Boolean

unipotent :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean

zeropotent :: forall a. Eq a => (a -> a -> a) -> a -> a -> Boolean