AERN2.Interval

Intervals for use as function domains

Documentation

data Interval l r

Constructors

Interval l r

Instances

ConvertibleExactly Integer DyadicInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: Integer -> ConvertResult DyadicInterval

ConvertibleExactly Rational DyadicInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: Rational -> ConvertResult DyadicInterval

ConvertibleExactly MPBall DyadicInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: MPBall -> ConvertResult DyadicInterval

ConvertibleExactly Dyadic DyadicInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: Dyadic -> ConvertResult DyadicInterval

ConvertibleExactly DyadicInterval MPBall

Defined in AERN2.Interval

Methods

safeConvertExactly :: DyadicInterval -> ConvertResult MPBall

(Eq l, Eq r) => Eq (Interval l r)

Defined in AERN2.Interval

Methods

(==) :: Interval l r -> Interval l r -> Bool

(/=) :: Interval l r -> Interval l r -> Bool

(Read l, Read r) => Read (Interval l r)

Defined in AERN2.Interval

Methods

readsPrec :: Int -> ReadS (Interval l r)

readList :: ReadS [Interval l r]

readPrec :: ReadPrec (Interval l r)

readListPrec :: ReadPrec [Interval l r]

(Show l, Show r) => Show (Interval l r)

Defined in AERN2.Interval

Methods

showsPrec :: Int -> Interval l r -> ShowS

show :: Interval l r -> String

showList :: [Interval l r] -> ShowS

Generic (Interval l r)

Defined in AERN2.Interval

Associated Types

type Rep (Interval l r) :: Type -> Type

Methods

from :: Interval l r -> Rep (Interval l r) x

to :: Rep (Interval l r) x -> Interval l r

(Arbitrary l, Arbitrary r, HasOrderCertainlyAsymmetric l r) => Arbitrary (Interval l r)

Defined in AERN2.Interval

Methods

arbitrary :: Gen (Interval l r)

shrink :: Interval l r -> [Interval l r]

IsInterval (Interval e e)

Defined in AERN2.Interval

Associated Types

type IntervalEndpoint (Interval e e)

Methods

endpoints :: Interval e e -> (IntervalEndpoint (Interval e e), IntervalEndpoint (Interval e e))

fromEndpoints :: IntervalEndpoint (Interval e e) -> IntervalEndpoint (Interval e e) -> Interval e e

(HasOrderAsymmetric l Integer, OrderCompareType l Integer ~ Bool, HasOrderAsymmetric Integer r, OrderCompareType Integer r ~ Bool) => CanTestContains (Interval l r) Integer

Defined in AERN2.Interval

Methods

contains :: Interval l r -> Integer -> Bool

(HasOrderAsymmetric l Int, OrderCompareType l Int ~ Bool, HasOrderAsymmetric Int r, OrderCompareType Int r ~ Bool) => CanTestContains (Interval l r) Int

Defined in AERN2.Interval

Methods

contains :: Interval l r -> Int -> Bool

(HasOrderAsymmetric l Rational, OrderCompareType l Rational ~ Bool, HasOrderAsymmetric Rational r, OrderCompareType Rational r ~ Bool) => CanTestContains (Interval l r) Rational

Defined in AERN2.Interval

Methods

contains :: Interval l r -> Rational -> Bool

(HasOrderAsymmetric l Dyadic, OrderCompareType l Dyadic ~ Bool, HasOrderAsymmetric Dyadic r, OrderCompareType Dyadic r ~ Bool) => CanTestContains (Interval l r) Dyadic

Defined in AERN2.Interval

Methods

contains :: Interval l r -> Dyadic -> Bool

(CanSubSameType e, CanAddSubMulBy t e, HasIntegerBounds t, CanSubThis t Integer, CanDivBy t Integer) => CanMapInside (Interval e e) t

Defined in AERN2.Interval

Methods

mapInside :: Interval e e -> t -> t

(CanBeCReal l, CanBeCReal r, HasOrderCertainly l r, Show l, Show r, Typeable l, Typeable r) => ConvertibleExactly (l, r) RealInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: (l, r) -> ConvertResult RealInterval

(CanBeDyadic l, CanBeDyadic r, HasOrderCertainly l r, Show l, Show r, Typeable l, Typeable r) => ConvertibleExactly (l, r) DyadicInterval

Defined in AERN2.Interval

Methods

safeConvertExactly :: (l, r) -> ConvertResult DyadicInterval

(HasOrderAsymmetric l l', OrderCompareType l l' ~ Bool, HasOrderAsymmetric r' r, OrderCompareType r' r ~ Bool) => CanTestContains (Interval l r) (Interval l' r')

Defined in AERN2.Interval

Methods

contains :: Interval l r -> Interval l' r' -> Bool

(CanMinMaxSameType l, CanMinMaxSameType r, HasOrderCertainly l r) => CanIntersectAsymmetric (Interval l r) (Interval l r)

Defined in AERN2.Interval

Associated Types

type IntersectionType (Interval l r) (Interval l r)

Methods

intersect :: Interval l r -> Interval l r -> IntersectionType (Interval l r) (Interval l r)

(HasEqAsymmetric l1 l2, HasEqAsymmetric r1 r2, EqCompareType l1 l2 ~ EqCompareType r1 r2, CanAndOrSameType (EqCompareType l1 l2)) => HasEqAsymmetric (Interval l1 r1) (Interval l2 r2)

Defined in AERN2.Interval

Associated Types

type EqCompareType (Interval l1 r1) (Interval l2 r2)

Methods

equalTo :: Interval l1 r1 -> Interval l2 r2 -> EqCompareType (Interval l1 r1) (Interval l2 r2)

notEqualTo :: Interval l1 r1 -> Interval l2 r2 -> EqCompareType (Interval l1 r1) (Interval l2 r2)

type Rep (Interval l r)

Defined in AERN2.Interval

type Rep (Interval l r) = D1 ('MetaData "Interval" "AERN2.Interval" "aern2-fun-0.2.9.0-4AlMbXgmPZtHbHcHCnPDza" 'False) (C1 ('MetaCons "Interval" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 l) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 r)))

type IntervalEndpoint (Interval e e)

Defined in AERN2.Interval

type IntervalEndpoint (Interval e e) = e

type IntersectionType (Interval l r) (Interval l r)

Defined in AERN2.Interval

type IntersectionType (Interval l r) (Interval l r) = CN (Interval l r)

type EqCompareType (Interval l1 r1) (Interval l2 r2)

Defined in AERN2.Interval

type EqCompareType (Interval l1 r1) (Interval l2 r2) = EqCompareType l1 l2

singleton :: a -> Interval a a

width :: CanSub r l => Interval l r -> SubType r l

split :: (CanAddSameType t, CanMulBy t Dyadic) => Interval t t -> (Interval t t, Interval t t)

arbitraryNonEmptyInterval :: (Arbitrary l, Arbitrary r, HasOrderCertainlyAsymmetric l r) => Gen (Interval l r)

arbitraryNonEmptySmallInterval :: (Arbitrary e, CanAddThis e Integer) => Gen (Interval e e)

intersect :: CanIntersectAsymmetric e1 e2 => e1 -> e2 -> IntersectionType e1 e2

intersects :: (CanMinMaxSameType l, CanMinMaxSameType r, HasOrderCertainly l r) => Interval l r -> Interval l r -> Bool

type DyadicInterval = Interval Dyadic Dyadic

type CanBeDyadicInterval t = ConvertibleExactly t DyadicInterval

dyadicInterval :: CanBeDyadicInterval t => t -> DyadicInterval

type RealInterval = Interval CReal CReal

type CanBeRealInterval t = ConvertibleExactly t RealInterval

realInterval :: CanBeRealInterval t => t -> RealInterval