numhask-0.12.0.0: A numeric class hierarchy.
Safe HaskellSafe-Inferred
LanguageGHC2021

NumHask.Data.Positive

Description

Field classes

Synopsis

Documentation

newtype Positive a Source #

zero is positive

>>> 1 :: Positive Int
UnsafePositive {unPositive = 1}

>>> positive 0 == zero
True

>>> positive (-1)
UnsafePositive {unPositive = 0}

>>> maybePositive (-1)
Nothing

Constructors

UnsafePositive 

Fields

Instances

Instances details
Show a => Show (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

showsPrec :: Int -> Positive a -> ShowS #

show :: Positive a -> String #

showList :: [Positive a] -> ShowS #

Eq a => Eq (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(==) :: Positive a -> Positive a -> Bool #

(/=) :: Positive a -> Positive a -> Bool #

Ord a => Ord (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

compare :: Positive a -> Positive a -> Ordering #

(<) :: Positive a -> Positive a -> Bool #

(<=) :: Positive a -> Positive a -> Bool #

(>) :: Positive a -> Positive a -> Bool #

(>=) :: Positive a -> Positive a -> Bool #

max :: Positive a -> Positive a -> Positive a #

min :: Positive a -> Positive a -> Positive a #

AdditiveAction a => AdditiveAction (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type AdditiveScalar (Positive a) Source #

Methods

(|+) :: Positive a -> AdditiveScalar (Positive a) -> Positive a Source #

DivisiveAction a => DivisiveAction (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(|/) :: Positive a -> Scalar (Positive a) -> Positive a Source #

MultiplicativeAction a => MultiplicativeAction (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type Scalar (Positive a) Source #

Methods

(|*) :: Positive a -> Scalar (Positive a) -> Positive a Source #

SubtractiveAction a => SubtractiveAction (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(|-) :: Positive a -> AdditiveScalar (Positive a) -> Positive a Source #

Additive a => Additive (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(+) :: Positive a -> Positive a -> Positive a Source #

zero :: Positive a Source #

QuotientField (Positive Double) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type Whole (Positive Double) Source #

Methods

properFraction :: Positive Double -> (Whole (Positive Double), Positive Double) Source #

round :: Positive Double -> Whole (Positive Double) Source #

ceiling :: Positive Double -> Whole (Positive Double) Source #

floor :: Positive Double -> Whole (Positive Double) Source #

truncate :: Positive Double -> Whole (Positive Double) Source #

(Additive a, JoinSemiLattice a) => BoundedJoinSemiLattice (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

bottom :: Positive a Source #

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

top :: Positive a Source #

JoinSemiLattice a => JoinSemiLattice (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(\/) :: Positive a -> Positive a -> Positive a Source #

MeetSemiLattice a => MeetSemiLattice (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(/\) :: Positive a -> Positive a -> Positive a Source #

Basis a => Basis (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type Mag (Positive a) Source #

type Base (Positive a) Source #

Methods

magnitude :: Positive a -> Mag (Positive a) Source #

basis :: Positive a -> Base (Positive a) Source #

Direction a => Direction (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Associated Types

type Dir (Positive a) Source #

Methods

angle :: Positive a -> Dir (Positive a) Source #

ray :: Dir (Positive a) -> Positive a Source #

Epsilon a => Epsilon (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

epsilon :: Positive a Source #

Divisive a => Divisive (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

recip :: Positive a -> Positive a Source #

(/) :: Positive a -> Positive a -> Positive a Source #

Multiplicative a => Multiplicative (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(*) :: Positive a -> Positive a -> Positive a Source #

one :: Positive a Source #

FromInteger a => FromInteger (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

fromInteger :: Integer -> Positive a Source #

Integral a => Integral (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

div :: Positive a -> Positive a -> Positive a Source #

mod :: Positive a -> Positive a -> Positive a Source #

divMod :: Positive a -> Positive a -> (Positive a, Positive a) Source #

quot :: Positive a -> Positive a -> Positive a Source #

rem :: Positive a -> Positive a -> Positive a Source #

quotRem :: Positive a -> Positive a -> (Positive a, Positive a) Source #

(Subtractive a, MeetSemiLattice a) => Monus (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(∸) :: Positive a -> Positive a -> Positive a Source #

FromRational a => FromRational (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

fromRational :: Rational -> Positive a Source #

(MeetSemiLattice a, Integral a) => FromIntegral (Positive a) a Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

fromIntegral :: a -> Positive a Source #

FromIntegral a b => FromIntegral (Positive a) b Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

fromIntegral :: b -> Positive a Source #

ToIntegral a b => ToIntegral (Positive a) b Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

toIntegral :: Positive a -> b Source #

FromRatio a b => FromRatio (Positive a) b Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

fromRatio :: Ratio b -> Positive a Source #

ToRatio a b => ToRatio (Positive a) b Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

toRatio :: Positive a -> Ratio b Source #

type AdditiveScalar (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

type AdditiveScalar (Positive a) = AdditiveScalar (Wrapped a)
type Scalar (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

type Scalar (Positive a) = Scalar (Wrapped a)
type Whole (Positive Double) Source # 
Instance details

Defined in NumHask.Data.Positive

type Whole (Positive Double) = Positive Int
type Base (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

type Base (Positive a) = Base (Wrapped a)
type Dir (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

type Dir (Positive a) = Dir (Wrapped a)
type Mag (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

type Mag (Positive a) = Mag (Wrapped a)

positive :: (Additive a, MeetSemiLattice a) => a -> Positive a Source #

Constructor which returns zero for a negative input.

>>> positive (-1)
UnsafePositive {unPositive = 0}

maybePositive :: (Additive a, MeetSemiLattice a) => a -> Maybe (Positive a) Source #

Constructor which returns Nothing for a negative number. >>> maybePositive (-one) Nothing

positive_ :: a -> Positive a Source #

Unsafe constructors.

>>> positive_ (-one)
UnsafePositive {unPositive = -1}

class Monus a where Source #

Monus or truncated subtraction.

>>> positive 4 ∸ positive 7
UnsafePositive {unPositive = 0}

>>> 4 ∸ 7 :: Positive Int
UnsafePositive {unPositive = 0}

Minimal complete definition

(∸)

Methods

(∸) :: a -> a -> a infixl 6 Source #

default (∸) :: (BoundedJoinSemiLattice a, MeetSemiLattice a, Subtractive a) => a -> a -> a Source #

Instances

Instances details
(Subtractive a, MeetSemiLattice a) => Monus (Positive a) Source # 
Instance details

Defined in NumHask.Data.Positive

Methods

(∸) :: Positive a -> Positive a -> Positive a Source #

class Addus a where Source #

Truncated addition

Minimal complete definition

(∔)

Methods

(∔) :: a -> a -> a infixl 6 Source #

default (∔) :: (BoundedMeetSemiLattice a, JoinSemiLattice a, Additive a) => a -> a -> a Source #

type MonusSemiField a = (Monus a, Distributive a, Divisive a) Source #

A field but with truncated subtraction.