Copyright	(c) Michal Konecny
License	BSD3
Maintainer	mikkonecny@gmail.com
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell98

AERN2.Sequence.Comparison

Contents

Orphan instances

Description

Comparison operations on convergent sequences.

Synopsis

Documentation

type SeqBoolP = SequenceP (Maybe Bool) #

type SeqBoolA to = SequenceA to (Maybe Bool) #

type SeqBool = SeqBoolA (->) #

pBool :: SeqBoolP #

data SequenceAtAccuracy a #

SequenceAtAccuracy exists only so that we can QuickCheck that Sequence satisfies properties whose statement relies on an instance of HasEqCertainly. Sequence is not an instance but SequenceAtAccuracy is.

Constructors

SequenceAtAccuracy (Sequence a) AccuracySG

Instances

Show a => Show (SequenceAtAccuracy a) #
Methods showsPrec :: Int -> SequenceAtAccuracy a -> ShowS # show :: SequenceAtAccuracy a -> String # showList :: [SequenceAtAccuracy a] -> ShowS #
(HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Associated Types type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * # Methods equalTo :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # notEqualTo :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
(HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
Associated Types type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * # Methods lessThan :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # greaterThan :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # leq :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # geq :: SequenceAtAccuracy a -> SequenceAtAccuracy b -> OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) = EqCompareType a b
type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) #
type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) = OrderCompareType a b

Orphan instances

(CanMinMaxAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MinMaxType MPBall b)) => CanMinMaxAsymmetric MPBall (Sequence b) #
Associated Types type MinMaxType MPBall (Sequence b) :: * # Methods min :: MPBall -> Sequence b -> MinMaxType MPBall (Sequence b) # max :: MPBall -> Sequence b -> MinMaxType MPBall (Sequence b) #
(QAArrow to, CanMinMaxAsymmetric Int b, SuitableForSeq b, SuitableForSeq (MinMaxType Int b)) => CanMinMaxAsymmetric Int (SequenceA to b) #
Associated Types type MinMaxType Int (SequenceA to b) :: * # Methods min :: Int -> SequenceA to b -> MinMaxType Int (SequenceA to b) # max :: Int -> SequenceA to b -> MinMaxType Int (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Integer b, SuitableForSeq b, SuitableForSeq (MinMaxType Integer b)) => CanMinMaxAsymmetric Integer (SequenceA to b) #
Associated Types type MinMaxType Integer (SequenceA to b) :: * # Methods min :: Integer -> SequenceA to b -> MinMaxType Integer (SequenceA to b) # max :: Integer -> SequenceA to b -> MinMaxType Integer (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Rational b, SuitableForSeq b, SuitableForSeq (MinMaxType Rational b)) => CanMinMaxAsymmetric Rational (SequenceA to b) #
Associated Types type MinMaxType Rational (SequenceA to b) :: * # Methods min :: Rational -> SequenceA to b -> MinMaxType Rational (SequenceA to b) # max :: Rational -> SequenceA to b -> MinMaxType Rational (SequenceA to b) #
(QAArrow to, CanMinMaxAsymmetric Dyadic b, SuitableForSeq b, SuitableForSeq (MinMaxType Dyadic b)) => CanMinMaxAsymmetric Dyadic (SequenceA to b) #
Associated Types type MinMaxType Dyadic (SequenceA to b) :: * # Methods min :: Dyadic -> SequenceA to b -> MinMaxType Dyadic (SequenceA to b) # max :: Dyadic -> SequenceA to b -> MinMaxType Dyadic (SequenceA to b) #
(QAArrow to, HasEqAsymmetric Int a, SuitableForSeq a, SuitableForSeq (EqCompareType Int a)) => HasEqAsymmetric Int (SequenceA to a) #
Associated Types type EqCompareType Int (SequenceA to a) :: * # Methods equalTo :: Int -> SequenceA to a -> EqCompareType Int (SequenceA to a) # notEqualTo :: Int -> SequenceA to a -> EqCompareType Int (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (EqCompareType Integer a)) => HasEqAsymmetric Integer (SequenceA to a) #
Associated Types type EqCompareType Integer (SequenceA to a) :: * # Methods equalTo :: Integer -> SequenceA to a -> EqCompareType Integer (SequenceA to a) # notEqualTo :: Integer -> SequenceA to a -> EqCompareType Integer (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (EqCompareType Rational a)) => HasEqAsymmetric Rational (SequenceA to a) #
Associated Types type EqCompareType Rational (SequenceA to a) :: * # Methods equalTo :: Rational -> SequenceA to a -> EqCompareType Rational (SequenceA to a) # notEqualTo :: Rational -> SequenceA to a -> EqCompareType Rational (SequenceA to a) #
(QAArrow to, HasEqAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (EqCompareType Dyadic a)) => HasEqAsymmetric Dyadic (SequenceA to a) #
Associated Types type EqCompareType Dyadic (SequenceA to a) :: * # Methods equalTo :: Dyadic -> SequenceA to a -> EqCompareType Dyadic (SequenceA to a) # notEqualTo :: Dyadic -> SequenceA to a -> EqCompareType Dyadic (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Int a, SuitableForSeq a, SuitableForSeq (OrderCompareType Int a)) => HasOrderAsymmetric Int (SequenceA to a) #
Associated Types type OrderCompareType Int (SequenceA to a) :: * # Methods lessThan :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # greaterThan :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # leq :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) # geq :: Int -> SequenceA to a -> OrderCompareType Int (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (OrderCompareType Integer a)) => HasOrderAsymmetric Integer (SequenceA to a) #
Associated Types type OrderCompareType Integer (SequenceA to a) :: * # Methods lessThan :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # greaterThan :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # leq :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) # geq :: Integer -> SequenceA to a -> OrderCompareType Integer (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (OrderCompareType Rational a)) => HasOrderAsymmetric Rational (SequenceA to a) #
Associated Types type OrderCompareType Rational (SequenceA to a) :: * # Methods lessThan :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # greaterThan :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # leq :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) # geq :: Rational -> SequenceA to a -> OrderCompareType Rational (SequenceA to a) #
(QAArrow to, HasOrderAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (OrderCompareType Dyadic a)) => HasOrderAsymmetric Dyadic (SequenceA to a) #
Associated Types type OrderCompareType Dyadic (SequenceA to a) :: * # Methods lessThan :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # greaterThan :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # leq :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) # geq :: Dyadic -> SequenceA to a -> OrderCompareType Dyadic (SequenceA to a) #
(QAArrow to, HasBools b, SuitableForSeq b) => ConvertibleExactly Bool (SequenceA to b) #
Methods safeConvertExactly :: Bool -> ConvertResult (SequenceA to b) #
(CanMinMaxAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MinMaxType a MPBall)) => CanMinMaxAsymmetric (Sequence a) MPBall #
Associated Types type MinMaxType (Sequence a) MPBall :: * # Methods min :: Sequence a -> MPBall -> MinMaxType (Sequence a) MPBall # max :: Sequence a -> MPBall -> MinMaxType (Sequence a) MPBall #
(QAArrow to, CanAbs a, SuitableForSeq a, SuitableForSeq (AbsType a)) => CanAbs (SequenceA to a) #
Associated Types type AbsType (SequenceA to a) :: * # Methods abs :: SequenceA to a -> AbsType (SequenceA to a) #
(QAArrow to, CanNeg a, SuitableForSeq a, SuitableForSeq (NegType a)) => CanNeg (SequenceA to a) #
Associated Types type NegType (SequenceA to a) :: * # Methods negate :: SequenceA to a -> NegType (SequenceA to a) #
(QAArrow to, CanMinMaxAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (MinMaxType a Integer)) => CanMinMaxAsymmetric (SequenceA to a) Integer #
Associated Types type MinMaxType (SequenceA to a) Integer :: * # Methods min :: SequenceA to a -> Integer -> MinMaxType (SequenceA to a) Integer # max :: SequenceA to a -> Integer -> MinMaxType (SequenceA to a) Integer #
(QAArrow to, CanMinMaxAsymmetric a Int, SuitableForSeq a, SuitableForSeq (MinMaxType a Int)) => CanMinMaxAsymmetric (SequenceA to a) Int #
Associated Types type MinMaxType (SequenceA to a) Int :: * # Methods min :: SequenceA to a -> Int -> MinMaxType (SequenceA to a) Int # max :: SequenceA to a -> Int -> MinMaxType (SequenceA to a) Int #
(QAArrow to, CanMinMaxAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (MinMaxType a Rational)) => CanMinMaxAsymmetric (SequenceA to a) Rational #
Associated Types type MinMaxType (SequenceA to a) Rational :: * # Methods min :: SequenceA to a -> Rational -> MinMaxType (SequenceA to a) Rational # max :: SequenceA to a -> Rational -> MinMaxType (SequenceA to a) Rational #
(QAArrow to, CanMinMaxAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (MinMaxType a Dyadic)) => CanMinMaxAsymmetric (SequenceA to a) Dyadic #
Associated Types type MinMaxType (SequenceA to a) Dyadic :: * # Methods min :: SequenceA to a -> Dyadic -> MinMaxType (SequenceA to a) Dyadic # max :: SequenceA to a -> Dyadic -> MinMaxType (SequenceA to a) Dyadic #
(QAArrow to, HasEqAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (EqCompareType a Integer)) => HasEqAsymmetric (SequenceA to a) Integer #
Associated Types type EqCompareType (SequenceA to a) Integer :: * # Methods equalTo :: SequenceA to a -> Integer -> EqCompareType (SequenceA to a) Integer # notEqualTo :: SequenceA to a -> Integer -> EqCompareType (SequenceA to a) Integer #
(QAArrow to, HasEqAsymmetric a Int, SuitableForSeq a, SuitableForSeq (EqCompareType a Int)) => HasEqAsymmetric (SequenceA to a) Int #
Associated Types type EqCompareType (SequenceA to a) Int :: * # Methods equalTo :: SequenceA to a -> Int -> EqCompareType (SequenceA to a) Int # notEqualTo :: SequenceA to a -> Int -> EqCompareType (SequenceA to a) Int #
(QAArrow to, HasEqAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (EqCompareType a Rational)) => HasEqAsymmetric (SequenceA to a) Rational #
Associated Types type EqCompareType (SequenceA to a) Rational :: * # Methods equalTo :: SequenceA to a -> Rational -> EqCompareType (SequenceA to a) Rational # notEqualTo :: SequenceA to a -> Rational -> EqCompareType (SequenceA to a) Rational #
(QAArrow to, HasEqAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (EqCompareType a Dyadic)) => HasEqAsymmetric (SequenceA to a) Dyadic #
Associated Types type EqCompareType (SequenceA to a) Dyadic :: * # Methods equalTo :: SequenceA to a -> Dyadic -> EqCompareType (SequenceA to a) Dyadic # notEqualTo :: SequenceA to a -> Dyadic -> EqCompareType (SequenceA to a) Dyadic #
(QAArrow to, HasOrderAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (OrderCompareType a Integer)) => HasOrderAsymmetric (SequenceA to a) Integer #
Associated Types type OrderCompareType (SequenceA to a) Integer :: * # Methods lessThan :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # greaterThan :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # leq :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer # geq :: SequenceA to a -> Integer -> OrderCompareType (SequenceA to a) Integer #
(QAArrow to, HasOrderAsymmetric a Int, SuitableForSeq a, SuitableForSeq (OrderCompareType a Int)) => HasOrderAsymmetric (SequenceA to a) Int #
Associated Types type OrderCompareType (SequenceA to a) Int :: * # Methods lessThan :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # greaterThan :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # leq :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int # geq :: SequenceA to a -> Int -> OrderCompareType (SequenceA to a) Int #
(QAArrow to, HasOrderAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (OrderCompareType a Rational)) => HasOrderAsymmetric (SequenceA to a) Rational #
Associated Types type OrderCompareType (SequenceA to a) Rational :: * # Methods lessThan :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # greaterThan :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # leq :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational # geq :: SequenceA to a -> Rational -> OrderCompareType (SequenceA to a) Rational #
(QAArrow to, HasOrderAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (OrderCompareType a Dyadic)) => HasOrderAsymmetric (SequenceA to a) Dyadic #
Associated Types type OrderCompareType (SequenceA to a) Dyadic :: * # Methods lessThan :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # greaterThan :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # leq :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic # geq :: SequenceA to a -> Dyadic -> OrderCompareType (SequenceA to a) Dyadic #
(CanMinMaxAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (MinMaxType a (SequenceA to b)), SuitableForCE es) => CanMinMaxAsymmetric (CollectErrors es a) (SequenceA to b) #
Associated Types type MinMaxType (CollectErrors es a) (SequenceA to b) :: * # Methods min :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) # max :: CollectErrors es a -> SequenceA to b -> MinMaxType (CollectErrors es a) (SequenceA to b) #
(CanMinMaxAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (MinMaxType (SequenceA to a) b), SuitableForCE es) => CanMinMaxAsymmetric (SequenceA to a) (CollectErrors es b) #
Associated Types type MinMaxType (SequenceA to a) (CollectErrors es b) :: * # Methods min :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) # max :: SequenceA to a -> CollectErrors es b -> MinMaxType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, CanMinMaxAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (MinMaxType a b)) => CanMinMaxAsymmetric (SequenceA to a) (SequenceA to b) #
Associated Types type MinMaxType (SequenceA to a) (SequenceA to b) :: * # Methods min :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) # max :: SequenceA to a -> SequenceA to b -> MinMaxType (SequenceA to a) (SequenceA to b) #
(HasEqAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (EqCompareType a (SequenceA to b)), IsBool (EnsureCE es (EqCompareType a (SequenceA to b))), SuitableForCE es) => HasEqAsymmetric (CollectErrors es a) (SequenceA to b) #
Associated Types type EqCompareType (CollectErrors es a) (SequenceA to b) :: * # Methods equalTo :: CollectErrors es a -> SequenceA to b -> EqCompareType (CollectErrors es a) (SequenceA to b) # notEqualTo :: CollectErrors es a -> SequenceA to b -> EqCompareType (CollectErrors es a) (SequenceA to b) #
(HasEqAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (EqCompareType (SequenceA to a) b), IsBool (EnsureCE es (EqCompareType (SequenceA to a) b)), SuitableForCE es) => HasEqAsymmetric (SequenceA to a) (CollectErrors es b) #
Associated Types type EqCompareType (SequenceA to a) (CollectErrors es b) :: * # Methods equalTo :: SequenceA to a -> CollectErrors es b -> EqCompareType (SequenceA to a) (CollectErrors es b) # notEqualTo :: SequenceA to a -> CollectErrors es b -> EqCompareType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceA to a) (SequenceA to b) #
Associated Types type EqCompareType (SequenceA to a) (SequenceA to b) :: * # Methods equalTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) # notEqualTo :: SequenceA to a -> SequenceA to b -> EqCompareType (SequenceA to a) (SequenceA to b) #
(HasOrderAsymmetric a (SequenceA to b), CanEnsureCE es a, CanEnsureCE es (OrderCompareType a (SequenceA to b)), IsBool (EnsureCE es (OrderCompareType a (SequenceA to b))), SuitableForCE es) => HasOrderAsymmetric (CollectErrors es a) (SequenceA to b) #
Associated Types type OrderCompareType (CollectErrors es a) (SequenceA to b) :: * # Methods lessThan :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # greaterThan :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # leq :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) # geq :: CollectErrors es a -> SequenceA to b -> OrderCompareType (CollectErrors es a) (SequenceA to b) #
(HasOrderAsymmetric (SequenceA to a) b, CanEnsureCE es b, CanEnsureCE es (OrderCompareType (SequenceA to a) b), IsBool (EnsureCE es (OrderCompareType (SequenceA to a) b)), SuitableForCE es) => HasOrderAsymmetric (SequenceA to a) (CollectErrors es b) #
Associated Types type OrderCompareType (SequenceA to a) (CollectErrors es b) :: * # Methods lessThan :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # greaterThan :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # leq :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) # geq :: SequenceA to a -> CollectErrors es b -> OrderCompareType (SequenceA to a) (CollectErrors es b) #
(QAArrow to, HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceA to a) (SequenceA to b) #
Associated Types type OrderCompareType (SequenceA to a) (SequenceA to b) :: * # Methods lessThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # greaterThan :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # leq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) # geq :: SequenceA to a -> SequenceA to b -> OrderCompareType (SequenceA to a) (SequenceA to b) #
(QAArrow to, CanAndOrAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (AndOrType a b)) => CanAndOrAsymmetric (SequenceA to a) (SequenceA to b) #
Associated Types type AndOrType (SequenceA to a) (SequenceA to b) :: * # Methods and2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) # or2 :: SequenceA to a -> SequenceA to b -> AndOrType (SequenceA to a) (SequenceA to b) #