-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Laws and tests for numhask
--   
--   Laws and tests for numhask.
@package numhask-hedgehog
@version 0.3

module NumHask.Hedgehog.Gen

-- | a rational-style random variate
rational :: (ToRatio a, FromRatio a, MonadGen m) => Range a -> m a

-- | a rational style random variate utilising Bounds
rational_ :: (Additive a, Bounded a, ToRatio a, FromRatio a, MonadGen m) => m a

-- | an integral-stype random variate
integral :: (ToInteger a, FromInteger a, MonadGen m) => Range a -> m a

-- | an integral-style random variate utilising Bounds
integral_ :: (Additive a, Bounded a, ToInteger a, FromInteger a, MonadGen m) => m a

-- | a uniform distribution between zero and one
uniform :: (Field a, ToRatio a, FromRatio a, MonadGen m) => m a

-- | a uniform distribution between -1 and 1
negUniform :: (Field a, ToRatio a, FromRatio a, Subtractive a, MonadGen m) => m a

-- | a pair
genPair :: Monad m => m a -> m (Pair a)

-- | Space
genRange :: forall a m. (JoinSemiLattice a, MeetSemiLattice a, MonadGen m) => m a -> m (Range a)
genRangePos :: forall a m. (JoinSemiLattice a, MeetSemiLattice a, MonadGen m) => m a -> m (Range a)

-- | a complex random variate
genComplex :: Monad m => m a -> m (Complex a)

module NumHask.Hedgehog.Prop

-- | running tests in parallel
assertProps :: GroupName -> TestLimit -> Gen a -> (Gen a -> [(PropertyName, Property)]) -> IO Bool

-- | run tests sequentially
assertPropsSeq :: GroupName -> TestLimit -> Gen a -> (Gen a -> [(PropertyName, Property)]) -> IO Bool

-- | Combinator for a property of involving a single element
unary :: Show a => Gen a -> (a -> Bool) -> Property

-- | Combinator for a property involving two elements
binary :: Show a => Gen a -> (a -> a -> Bool) -> Property

-- | Combinator for a property involving three elements
ternary :: Show a => Gen a -> (a -> a -> a -> Bool) -> Property
isIdempotent :: (Eq a, Show a) => (a -> a -> a) -> Gen a -> Property
isCommutative :: (Eq a, Show a) => (a -> a -> a) -> Gen a -> Property
isUnital :: (Eq a, Show a) => a -> (a -> a -> a) -> Gen a -> Property
isAssociative :: (Eq a, Show a) => (a -> a -> a) -> Gen a -> Property
isAdditive :: (Eq a, Show a, Additive a) => Gen a -> [(PropertyName, Property)]
isGroup :: (Eq a, Show a) => a -> (a -> a -> a) -> (a -> a -> a) -> (a -> a) -> Gen a -> Property
isSubtractive :: (Eq a, Show a, Subtractive a) => Gen a -> [(PropertyName, Property)]
isMultiplicative :: (Eq a, Show a, Multiplicative a) => Gen a -> [(PropertyName, Property)]
isDivisive :: (Eq a, Show a, Divisive a) => Gen a -> [(PropertyName, Property)]
isDistributive :: (Eq a, Show a) => a -> (a -> a -> a) -> (a -> a -> a) -> Gen a -> Property
isAbsorbativeUnit :: (Eq a, Show a) => a -> (a -> a -> a) -> Gen a -> Property
isAbsorbative :: (Eq a, Show a) => (a -> a -> a) -> (a -> a -> a) -> Gen a -> Property
isIntegral :: (Eq a, Show a, Integral a) => Gen a -> Property
isFromIntegral :: (Eq a, Show a, FromInteger a, ToInteger a) => Gen a -> Property
isRational :: (Eq a, Show a, FromRatio a, ToRatio a) => Gen a -> Property
isSigned :: (Eq a, Show a, Signed a) => Gen a -> Property
isNormed :: forall a b. (JoinSemiLattice b, Show a, Normed a b) => [b] -> Gen a -> Property
isNormedBounded :: forall a. (JoinSemiLattice a, Bounded a, Show a, Normed a a) => Gen a -> Property
isNormedUnbounded :: forall a. (JoinSemiLattice a, Show a, Normed a a) => Gen a -> Property
isMetricBounded :: forall a. (JoinSemiLattice a, Bounded a, Additive a, Show a, Metric a a) => Gen a -> Property
isMetricUnbounded :: forall a. (JoinSemiLattice a, Additive a, Show a, Metric a a) => Gen a -> Property
isUpperBoundedField :: forall a. (Eq a, UpperBoundedField a, Show a) => Gen a -> Property
isLowerBoundedField :: forall a. (Eq a, LowerBoundedField a, Show a) => Gen a -> Property
isQuotientIntegerField :: forall a. (JoinSemiLattice a, FromInteger a, QuotientField a Integer, Show a) => Gen a -> Property
isExpField :: forall a. (Ord a, Epsilon a, ExpField a, Show a, Normed a a) => Gen a -> Property
isSemiring :: (Eq a, Show a, Distributive a) => Gen a -> [(PropertyName, Property)]
isRing :: (Eq a, Show a, Distributive a, Subtractive a) => Gen a -> [(PropertyName, Property)]
isStarSemiring :: (Eq a, Show a, StarSemiring a) => Gen a -> Property
isInvolutive :: forall a. (Eq a, Show a, InvolutiveRing a) => Gen a -> Property

module NumHask.Hedgehog.Prop.Space
type CanMeasure a = (Lattice a, Multiplicative a, Show a, Epsilon a)
isIdempotent :: forall a. CanMeasure a => (Range a -> Range a -> Range a) -> a -> Gen a -> Property
isCommutative :: forall a. CanMeasure a => (a -> a -> a) -> (Range a -> Range a -> Range a) -> a -> Gen a -> Property
isUnital :: forall a. CanMeasure a => a -> (a -> a -> a) -> a -> Gen a -> Property
isAssociative :: forall a. CanMeasure a => (a -> a -> a) -> (Range a -> Range a -> Range a) -> a -> Gen a -> Property
isAdditive :: forall a. CanMeasure a => a -> Gen a -> [(PropertyName, Property)]
isSubtractive :: forall a. CanMeasure a => a -> Gen a -> Property
isMultiplicative :: forall a. CanMeasure a => a -> Gen a -> [(PropertyName, Property)]
isDivisive :: forall a. (CanMeasure a, BoundedLattice a, Divisive a) => a -> Gen a -> Property
isDistributiveTimesPlus :: forall a. CanMeasure a => a -> Gen a -> Property
isDistributiveJoinMeet :: forall a. CanMeasure a => a -> Gen a -> Property
isZeroAbsorbative :: forall a. CanMeasure a => (a -> a -> a) -> a -> Gen a -> Property
isAbsorbative :: forall a. CanMeasure a => (a -> a -> a) -> (a -> a -> a) -> (Range a -> Range a -> Range a) -> (Range a -> Range a -> Range a) -> a -> Gen a -> Property
isSigned :: forall a. (CanMeasure a, Signed a) => a -> Gen a -> Property
isNormedUnbounded :: forall a. (CanMeasure a, Normed a a) => a -> Gen a -> Property
isMetricUnbounded :: forall a. (CanMeasure a, Metric a a) => a -> Gen a -> Property
isExpField :: forall a. (CanMeasure a, ExpField a, Signed a) => a -> Gen a -> Property
isCommutativeSpace :: forall s. (Epsilon (Element s), Multiplicative (Element s), Show s, Space s) => (s -> s -> s) -> Element s -> Gen s -> Property
isAssociativeSpace :: forall s. (Epsilon (Element s), Multiplicative (Element s), Show s, Space s) => (s -> s -> s) -> Element s -> Gen s -> Property
isUnitalSpace :: forall s. (Epsilon (Element s), Multiplicative (Element s), Show s, Space s) => s -> (s -> s -> s) -> Element s -> Gen s -> Property
isLatticeSpace :: forall s. (Show s, Space s) => Gen s -> Property
isSubtractiveSpace :: forall s. (Space s, Subtractive s, Eq s, CanMeasure (Element s), Show s) => Gen s -> Property
isDivisiveSpace :: forall s. (Space s, Divisive s, Eq s, CanMeasure (Element s), Show s) => Gen s -> Property
isContainedUnion :: forall s. (Epsilon (Element s), Multiplicative (Element s), Show s, Space s) => Element s -> Gen s -> Property
isProjectiveLower :: forall s. (FieldSpace s, Epsilon (Element s), Show s) => Element s -> Gen s -> Property
isProjectiveUpper :: forall s. (FieldSpace s, Epsilon (Element s), Show s) => Gen s -> Property

module NumHask.Hedgehog.Props
integralProps :: forall a. (Show a, Distributive a, Subtractive a, Integral a, FromInteger a, ToInteger a, Signed a, Bounded a, Normed a a, Metric a a, JoinSemiLattice a) => Gen a -> [(PropertyName, Property)]
integralUnboundedProps :: forall a. (Show a, Distributive a, Subtractive a, Integral a, FromInteger a, ToInteger a, Signed a, Normed a a, Metric a a, JoinSemiLattice a) => Gen a -> [(PropertyName, Property)]
naturalProps :: forall a. (Show a, Distributive a, Integral a, FromInteger a, ToInteger a, Signed a, Normed a a, JoinSemiLattice a) => Gen a -> [(PropertyName, Property)]
boolProps :: forall a. (Show a, Ord a, Distributive a) => Gen a -> [(PropertyName, Property)]
rationalProps :: forall a. (Show a, Ord a, Distributive a, Subtractive a, Divisive a, FromRatio a, ToRatio a, Signed a, Normed a a, Metric a a, JoinSemiLattice a) => Gen a -> [(PropertyName, Property)]

-- | field laws
fieldProps :: forall a. (CanMeasure a, BoundedLattice a, LowerBoundedField a, UpperBoundedField a, Signed a, Normed a a, Metric a a) => Gen a -> [(PropertyName, Property)]

-- | quotient field laws
quotientFieldProps :: forall a. (CanMeasure a, FromInteger a, QuotientField a Integer) => Gen a -> [(PropertyName, Property)]
complexFieldProps :: forall a. (CanMeasure (Complex a), Epsilon a, BoundedLattice (Complex a), Divisive a, FromRatio a) => Complex a -> Gen (Complex a) -> [(PropertyName, Property)]

-- | field laws
logFieldProps :: forall a. (CanMeasure a, BoundedLattice a, Divisive a) => Gen a -> [(PropertyName, Property)]

-- | lattice laws
latticeProps :: forall a. CanMeasure a => Gen a -> [(PropertyName, Property)]

-- | space laws
spaceProps :: forall s. (Show s, Space s, Monoid s, Eq s, Epsilon (Element s), LowerBoundedField (Element s), UpperBoundedField (Element s), BoundedJoinSemiLattice (Element s), BoundedMeetSemiLattice (Element s)) => Gen s -> [(PropertyName, Property)]

-- | space laws
fieldSpaceProps :: forall s. (Show s, FieldSpace s, Epsilon (Element s)) => Gen s -> [(PropertyName, Property)]

-- | Interval algebra is not distributive
spaceAlgebraProps :: forall s. (Eq s, Show s, Space s, Subtractive s, Divisive s, CanMeasure (Element s)) => Gen s -> [(PropertyName, Property)]

module NumHask.Hedgehog