NumHask.Laws

Documentation

data LawArity a

unification of law equations

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

unification of law equations with 2 types

Constructors

Unary10 (a -> Bool)

Unary01 (b -> Bool)

Binary11 (a -> b -> Bool)

Binary20 (a -> a -> Bool)

Ternary21 (a -> a -> b -> Bool)

Ternary12 (a -> b -> b -> Bool)

Ternary30 (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]

additive

additiveLaws_ :: Epsilon a => [Law a]

additive with approximate association equality

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

additive laws with a failure on association

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) => [Law a]

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

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

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

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

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

rationalLaws :: (Eq a, FromRatio a, ToRatio a) => [Law a]

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

normedLaws :: forall a b. (Ord b, AdditiveUnital a, AdditiveUnital b, MultiplicativeUnital b, Normed a b) => [Law2 a b]

normedBoundedLaws :: forall a b. (Eq a, Bounded a, Ord b, AdditiveUnital a, AdditiveUnital b, MultiplicativeUnital b, Normed a b) => [Law2 a b]

metricIntegralLaws :: forall a b. (FromInteger b, Ord b, Signed b, Epsilon b, Metric a b) => [Law2 a b]

metricIntegralBoundedLaws :: forall a b. (FromInteger b, Bounded b, Ord b, Signed b, Epsilon b, Metric a b) => [Law2 a b]

metricRationalLaws :: forall a b. (FromRatio b, Ord b, Signed b, Epsilon b, Metric a b, Normed a b) => [Law2 a b]

upperBoundedFieldLaws :: forall a. (Eq a, UpperBoundedField a) => [Law a]

lowerBoundedFieldLaws :: forall a. (Eq a, LowerBoundedField a) => [Law a]

quotientFieldLaws :: (Field a, QuotientField a Integer, FromInteger a) => [Law2 a Integer]

expFieldLaws :: forall a b. (FromInteger b, AdditiveUnital b, ExpField a, Normed a b, Epsilon a, Ord a, Ord b) => [Law2 a b]

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

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

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

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

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

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

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

banachLaws :: (Foldable r, Epsilon (r a), Banach r a, Singleton r, Signed a, FromRatio a, Ord a) => [Law2 (r a) a]

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

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

semiring

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

ring

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

starsemiring

involutiveRingLaws :: forall a. (Eq a, MultiplicativeUnital a, InvolutiveRing a) => [Law a]

involutive ring

integralsLaws :: (Eq a, AdditiveGroup a, Integral a, Signed a, ToInteger a, FromInteger a, Multiplicative a) => [Law a]