NumHask.Laws

Documentation

data LawArity a

Constructors

Nonary Bool

Unary (a -> Bool)

Binary (a -> a -> Bool)

Ternary (a -> a -> a -> Bool)

Ornary (a -> a -> a -> a -> Bool)

Failiary (a -> Property)

data LawArity2 a b

Constructors

Unary2 (a -> Bool)

Binary2 (a -> b -> Bool)

Ternary2 (a -> a -> b -> Bool)

Ternary2' (a -> b -> b -> Bool)

Ternary2'' (a -> a -> a -> Bool)

Quad31 (a -> a -> a -> b -> Bool)

Quad22 (a -> a -> b -> b -> Bool)

Failiary2 (a -> Property)

type Law a = (TestName, LawArity a)

type Law2 a b = (TestName, LawArity2 a b)

testLawOf :: (Arbitrary a, Show a) => [a] -> Law a -> TestTree

testLawOf2 :: (Arbitrary a, Show a, Arbitrary b, Show b) => [(a, b)] -> Law2 a b -> TestTree

idempotentLaws :: (Eq a, Additive a, Multiplicative a) => [Law a]

additiveLaws :: (Eq a, Additive a) => [Law a]

additiveLawsFail :: (Eq a, Additive a, Show a, Arbitrary a) => [Law a]

additiveGroupLaws :: (Eq a, AdditiveGroup a) => [Law a]

multiplicativeLaws :: (Eq a, Multiplicative a) => [Law a]

multiplicativeLawsFail :: (Eq a, Show a, Arbitrary a, Multiplicative a) => [Law a]

multiplicativeMonoidalLaws :: (Eq a, MultiplicativeUnital a, MultiplicativeAssociative a) => [Law a]

multiplicativeGroupLaws :: (Epsilon a, Eq a, MultiplicativeGroup a) => [Law a]

distributionLaws :: (Eq a, Distribution a) => [Law a]

distributionLawsFail :: (Show a, Arbitrary a, Epsilon a, Eq a, Distribution a) => [Law a]

integralLaws :: (Eq a, Integral a, FromInteger a, ToInteger a) => [Law a]

signedLaws :: (Eq a, Signed a) => [Law a]

metricFloatLaws :: [Law Float]

metricComplexFloatLaws :: [Law (Complex Float)]

boundedFieldFloatLaws :: [Law Float]

quotientFieldLaws :: (Ord a, Field a, QuotientField a, FromInteger a) => [Law a]

expFieldLaws :: (ExpField a, Signed a, Epsilon a, Fractional a, Ord a) => [Law a]

expFieldComplexLooseLaws :: Float -> [Law (Complex Float)]

additiveBasisLaws :: (Eq (r a), Epsilon (r a), AdditiveBasis r a) => [Law (r a)]

additiveGroupBasisLaws :: (Eq (r a), Singleton r, AdditiveGroupBasis r a) => [Law (r a)]

multiplicativeBasisLaws :: (Eq (r a), Singleton r, MultiplicativeBasis r a) => [Law (r a)]

multiplicativeGroupBasisLaws :: (Eq (r a), Epsilon a, Epsilon (r a), Singleton r, MultiplicativeGroupBasis r a) => [Law (r a)]

additiveModuleLaws :: (Eq (r a), Epsilon a, Epsilon (r a), AdditiveModule r a) => [Law2 (r a) a]

additiveGroupModuleLaws :: (Eq (r a), Epsilon a, Epsilon (r a), AdditiveGroupModule r a) => [Law2 (r a) a]

multiplicativeModuleLaws :: (Eq (r a), Epsilon a, Epsilon (r a), MultiplicativeModule r a) => [Law2 (r a) a]

multiplicativeGroupModuleLawsFail :: (Eq a, Show a, Arbitrary a, Eq (r a), Show (r a), Arbitrary (r a), Epsilon a, Epsilon (r a), MultiplicativeGroupModule r a) => [Law2 (r a) a]

expFieldNaperianLaws :: (ExpField (r a), Foldable r, ExpField a, Epsilon a, Signed a, Epsilon (r a), Fractional a, Ord a) => [Law (r a)]

metricNaperianFloatLaws :: Metric (r Float) Float => [Law (r Float)]

tensorProductLaws :: (Eq (r (r a)), Additive (r (r a)), Eq (r a), Eq a, TensorProduct (r a), Epsilon a, Epsilon (r a)) => [Law2 (r a) a]

banachLaws :: (Ord a, Fractional a, Signed a, Foldable r, Fractional b, Eq (r a), Epsilon b, Epsilon (r a), Metric (r a) b, MultiplicativeGroup b, Banach r a, Normed (r a) b, Singleton r) => [Law2 (r a) b]

hilbertLaws :: (Eq (r a), Eq a, Multiplicative a, MultiplicativeModule r a, Epsilon a, Epsilon (r a), Hilbert r a) => [Law2 (r a) a]

semiringLaws :: (Eq a, Semiring a) => [Law a]

semiring

ringLaws :: (Eq a, Ring a) => [Law a]

ring

starSemiringLaws :: (Eq a, StarSemiring a) => [Law a]

starsemiring