aern2-real-0.1.1.0: Exact real numbers via Cauchy sequences and MPFR

Copyright(c) Michal Konecny
LicenseBSD3
Maintainermikkonecny@gmail.com
Stabilityexperimental
Portabilityportable
Safe HaskellNone
LanguageHaskell98

AERN2.Sequence.Comparison

Contents

Description

Comparison operations on convergent sequences.

Synopsis

Documentation

type SeqBoolA to = SequenceA to (Maybe Bool) #

type SeqBool = SeqBoolA (->) #

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.

Instances
Arbitrary CauchyRealAtAccuracy # 
Instance details

Defined in AERN2.Real.Tests

Show a => Show (SequenceAtAccuracy a) # 
Instance details

Defined in AERN2.Sequence.Comparison

(HasEqAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (EqCompareType a b)) => HasEqAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) # 
Instance details

Defined in AERN2.Sequence.Comparison

Associated Types

type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * #

(HasOrderAsymmetric a b, SuitableForSeq a, SuitableForSeq b, SuitableForSeq (OrderCompareType a b)) => HasOrderAsymmetric (SequenceAtAccuracy a) (SequenceAtAccuracy b) # 
Instance details

Defined in AERN2.Sequence.Comparison

Associated Types

type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) :: * #

type EqCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # 
Instance details

Defined in AERN2.Sequence.Comparison

type OrderCompareType (SequenceAtAccuracy a) (SequenceAtAccuracy b) # 
Instance details

Defined in AERN2.Sequence.Comparison

Orphan instances

(CanMinMaxAsymmetric MPBall b, SuitableForSeq b, CanSetPrecision (MinMaxType MPBall b)) => CanMinMaxAsymmetric MPBall (Sequence b) # 
Instance details

Associated Types

type MinMaxType MPBall (Sequence b) :: * #

(QAArrow to, CanMinMaxAsymmetric Int b, SuitableForSeq b, SuitableForSeq (MinMaxType Int b)) => CanMinMaxAsymmetric Int (SequenceA to b) # 
Instance details

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) # 
Instance details

Associated Types

type MinMaxType Integer (SequenceA to b) :: * #

(QAArrow to, CanMinMaxAsymmetric Rational b, SuitableForSeq b, SuitableForSeq (MinMaxType Rational b)) => CanMinMaxAsymmetric Rational (SequenceA to b) # 
Instance details

Associated Types

type MinMaxType Rational (SequenceA to b) :: * #

(QAArrow to, CanMinMaxAsymmetric Dyadic b, SuitableForSeq b, SuitableForSeq (MinMaxType Dyadic b)) => CanMinMaxAsymmetric Dyadic (SequenceA to b) # 
Instance details

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) # 
Instance details

Associated Types

type EqCompareType Int (SequenceA to a) :: * #

(QAArrow to, HasEqAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (EqCompareType Integer a)) => HasEqAsymmetric Integer (SequenceA to a) # 
Instance details

Associated Types

type EqCompareType Integer (SequenceA to a) :: * #

(QAArrow to, HasEqAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (EqCompareType Rational a)) => HasEqAsymmetric Rational (SequenceA to a) # 
Instance details

Associated Types

type EqCompareType Rational (SequenceA to a) :: * #

(QAArrow to, HasEqAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (EqCompareType Dyadic a)) => HasEqAsymmetric Dyadic (SequenceA to a) # 
Instance details

Associated Types

type EqCompareType Dyadic (SequenceA to a) :: * #

(QAArrow to, HasOrderAsymmetric Int a, SuitableForSeq a, SuitableForSeq (OrderCompareType Int a)) => HasOrderAsymmetric Int (SequenceA to a) # 
Instance details

Associated Types

type OrderCompareType Int (SequenceA to a) :: * #

(QAArrow to, HasOrderAsymmetric Integer a, SuitableForSeq a, SuitableForSeq (OrderCompareType Integer a)) => HasOrderAsymmetric Integer (SequenceA to a) # 
Instance details

Associated Types

type OrderCompareType Integer (SequenceA to a) :: * #

(QAArrow to, HasOrderAsymmetric Rational a, SuitableForSeq a, SuitableForSeq (OrderCompareType Rational a)) => HasOrderAsymmetric Rational (SequenceA to a) # 
Instance details

Associated Types

type OrderCompareType Rational (SequenceA to a) :: * #

(QAArrow to, HasOrderAsymmetric Dyadic a, SuitableForSeq a, SuitableForSeq (OrderCompareType Dyadic a)) => HasOrderAsymmetric Dyadic (SequenceA to a) # 
Instance details

Associated Types

type OrderCompareType Dyadic (SequenceA to a) :: * #

(QAArrow to, HasBools b, SuitableForSeq b) => ConvertibleExactly Bool (SequenceA to b) # 
Instance details

(CanMinMaxAsymmetric a MPBall, SuitableForSeq a, CanSetPrecision (MinMaxType a MPBall)) => CanMinMaxAsymmetric (Sequence a) MPBall # 
Instance details

Associated Types

type MinMaxType (Sequence a) MPBall :: * #

(QAArrow to, CanAbs a, SuitableForSeq a, SuitableForSeq (AbsType a)) => CanAbs (SequenceA to a) # 
Instance details

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) # 
Instance details

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 # 
Instance details

Associated Types

type MinMaxType (SequenceA to a) Integer :: * #

(QAArrow to, CanMinMaxAsymmetric a Int, SuitableForSeq a, SuitableForSeq (MinMaxType a Int)) => CanMinMaxAsymmetric (SequenceA to a) Int # 
Instance details

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 # 
Instance details

Associated Types

type MinMaxType (SequenceA to a) Rational :: * #

(QAArrow to, CanMinMaxAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (MinMaxType a Dyadic)) => CanMinMaxAsymmetric (SequenceA to a) Dyadic # 
Instance details

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 # 
Instance details

Associated Types

type EqCompareType (SequenceA to a) Integer :: * #

(QAArrow to, HasEqAsymmetric a Int, SuitableForSeq a, SuitableForSeq (EqCompareType a Int)) => HasEqAsymmetric (SequenceA to a) Int # 
Instance details

Associated Types

type EqCompareType (SequenceA to a) Int :: * #

(QAArrow to, HasEqAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (EqCompareType a Rational)) => HasEqAsymmetric (SequenceA to a) Rational # 
Instance details

Associated Types

type EqCompareType (SequenceA to a) Rational :: * #

(QAArrow to, HasEqAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (EqCompareType a Dyadic)) => HasEqAsymmetric (SequenceA to a) Dyadic # 
Instance details

Associated Types

type EqCompareType (SequenceA to a) Dyadic :: * #

(QAArrow to, HasOrderAsymmetric a Integer, SuitableForSeq a, SuitableForSeq (OrderCompareType a Integer)) => HasOrderAsymmetric (SequenceA to a) Integer # 
Instance details

Associated Types

type OrderCompareType (SequenceA to a) Integer :: * #

(QAArrow to, HasOrderAsymmetric a Int, SuitableForSeq a, SuitableForSeq (OrderCompareType a Int)) => HasOrderAsymmetric (SequenceA to a) Int # 
Instance details

Associated Types

type OrderCompareType (SequenceA to a) Int :: * #

(QAArrow to, HasOrderAsymmetric a Rational, SuitableForSeq a, SuitableForSeq (OrderCompareType a Rational)) => HasOrderAsymmetric (SequenceA to a) Rational # 
Instance details

Associated Types

type OrderCompareType (SequenceA to a) Rational :: * #

(QAArrow to, HasOrderAsymmetric a Dyadic, SuitableForSeq a, SuitableForSeq (OrderCompareType a Dyadic)) => HasOrderAsymmetric (SequenceA to a) Dyadic # 
Instance details

Associated Types

type 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) # 
Instance details

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) # 
Instance details

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) # 
Instance details

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) # 
Instance details

Associated Types

type 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) # 
Instance details

Associated Types

type 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) # 
Instance details

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) # 
Instance details

Associated Types

type 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) # 
Instance details

Associated Types

type 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) # 
Instance details

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) # 
Instance details

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) #