Safe Haskell	Safe-Inferred
Language	Haskell2010

PlutusTx.Numeric

Contents

Type classes
Helper newtypes
Helper functions
Orphan instances

Synopsis

class AdditiveSemigroup a where
- (+) :: a -> a -> a
class AdditiveSemigroup a => AdditiveMonoid a where
- zero :: a
class AdditiveMonoid a => AdditiveGroup a where
- (-) :: a -> a -> a
class MultiplicativeSemigroup a where
- (*) :: a -> a -> a
class MultiplicativeSemigroup a => MultiplicativeMonoid a where
- one :: a
type Semiring a = (AdditiveMonoid a, MultiplicativeMonoid a)
type Ring a = (AdditiveGroup a, MultiplicativeMonoid a)
class (Ring s, AdditiveGroup v) => Module s v | v -> s where
- scale :: s -> v -> v
newtype Additive a = Additive a
newtype Multiplicative a = Multiplicative a
negate :: AdditiveGroup a => a -> a
divMod :: Integer -> Integer -> (Integer, Integer)
quotRem :: Integer -> Integer -> (Integer, Integer)
abs :: (Ord n, AdditiveGroup n) => n -> n

Type classes

class AdditiveSemigroup a where Source #

A Semigroup that it is sensible to describe using addition.

Methods

(+) :: a -> a -> a infixl 6 Source #

Instances

Instances details

AdditiveSemigroup Rational Source #
Instance details Defined in PlutusTx.Ratio Methods (+) :: Rational -> Rational -> Rational Source #
AdditiveSemigroup Integer Source #
Instance details Defined in PlutusTx.Numeric Methods (+) :: Integer -> Integer -> Integer Source #
AdditiveSemigroup Bool Source #
Instance details Defined in PlutusTx.Numeric Methods (+) :: Bool -> Bool -> Bool Source #
Semigroup a => AdditiveSemigroup (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods (+) :: Additive a -> Additive a -> Additive a Source #

class AdditiveSemigroup a => AdditiveMonoid a where Source #

A Monoid that it is sensible to describe using addition and zero.

Methods

zero :: a Source #

Instances

Instances details

AdditiveMonoid Rational Source #
Instance details Defined in PlutusTx.Ratio Methods zero :: Rational Source #
AdditiveMonoid Integer Source #
Instance details Defined in PlutusTx.Numeric Methods zero :: Integer Source #
AdditiveMonoid Bool Source #
Instance details Defined in PlutusTx.Numeric Methods zero :: Bool Source #
Monoid a => AdditiveMonoid (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods zero :: Additive a Source #

class AdditiveMonoid a => AdditiveGroup a where Source #

A Group that it is sensible to describe using addition, zero, and subtraction.

Methods

(-) :: a -> a -> a infixl 6 Source #

Instances

Instances details

AdditiveGroup Rational Source #
Instance details Defined in PlutusTx.Ratio Methods (-) :: Rational -> Rational -> Rational Source #
AdditiveGroup Integer Source #
Instance details Defined in PlutusTx.Numeric Methods (-) :: Integer -> Integer -> Integer Source #
Group a => AdditiveGroup (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods (-) :: Additive a -> Additive a -> Additive a Source #

class MultiplicativeSemigroup a where Source #

A Semigroup that it is sensible to describe using multiplication.

Methods

(*) :: a -> a -> a infixl 7 Source #

Instances

Instances details

MultiplicativeSemigroup Rational Source #
Instance details Defined in PlutusTx.Ratio Methods (*) :: Rational -> Rational -> Rational Source #
MultiplicativeSemigroup Integer Source #
Instance details Defined in PlutusTx.Numeric Methods (*) :: Integer -> Integer -> Integer Source #
MultiplicativeSemigroup Bool Source #
Instance details Defined in PlutusTx.Numeric Methods (*) :: Bool -> Bool -> Bool Source #
Semigroup a => MultiplicativeSemigroup (Multiplicative a) Source #
Instance details Defined in PlutusTx.Numeric Methods (*) :: Multiplicative a -> Multiplicative a -> Multiplicative a Source #

class MultiplicativeSemigroup a => MultiplicativeMonoid a where Source #

A Semigroup that it is sensible to describe using multiplication and one.

Methods

one :: a Source #

Instances

Instances details

MultiplicativeMonoid Rational Source #
Instance details Defined in PlutusTx.Ratio Methods one :: Rational Source #
MultiplicativeMonoid Integer Source #
Instance details Defined in PlutusTx.Numeric Methods one :: Integer Source #
MultiplicativeMonoid Bool Source #
Instance details Defined in PlutusTx.Numeric Methods one :: Bool Source #
Monoid a => MultiplicativeMonoid (Multiplicative a) Source #
Instance details Defined in PlutusTx.Numeric Methods one :: Multiplicative a Source #

type Semiring a = (AdditiveMonoid a, MultiplicativeMonoid a) Source #

A semiring.

type Ring a = (AdditiveGroup a, MultiplicativeMonoid a) Source #

A ring.

class (Ring s, AdditiveGroup v) => Module s v | v -> s where Source #

A module, with a type of scalars which can be used to scale the values.

Methods

scale :: s -> v -> v Source #

Instances

Instances details

Module Integer Rational Source #
Instance details Defined in PlutusTx.Ratio Methods scale :: Integer -> Rational -> Rational Source #

Helper newtypes

newtype Additive a Source #

A newtype wrapper to derive Additive classes via.

Constructors

Additive a

Instances

Instances details

Group a => AdditiveGroup (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods (-) :: Additive a -> Additive a -> Additive a Source #
Monoid a => AdditiveMonoid (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods zero :: Additive a Source #
Semigroup a => AdditiveSemigroup (Additive a) Source #
Instance details Defined in PlutusTx.Numeric Methods (+) :: Additive a -> Additive a -> Additive a Source #

newtype Multiplicative a Source #

A newtype wrapper to derive Multiplicative classes via.

Constructors

Multiplicative a

Instances

Instances details

Monoid a => MultiplicativeMonoid (Multiplicative a) Source #
Instance details Defined in PlutusTx.Numeric Methods one :: Multiplicative a Source #
Semigroup a => MultiplicativeSemigroup (Multiplicative a) Source #
Instance details Defined in PlutusTx.Numeric Methods (*) :: Multiplicative a -> Multiplicative a -> Multiplicative a Source #

Helper functions

negate :: AdditiveGroup a => a -> a Source #

divMod :: Integer -> Integer -> (Integer, Integer) Source #

Simultaneous div and mod.

quotRem :: Integer -> Integer -> (Integer, Integer) Source #

Simultaneous quot and rem.

abs :: (Ord n, AdditiveGroup n) => n -> n Source #

Absolute value for any AdditiveGroup.

Orphan instances

MultiplicativeMonoid a => Monoid (Product a) Source #
Instance details Methods mempty :: Product a Source #
AdditiveMonoid a => Monoid (Sum a) Source #
Instance details Methods mempty :: Sum a Source #
MultiplicativeSemigroup a => Semigroup (Product a) Source #
Instance details Methods (<>) :: Product a -> Product a -> Product a Source #
AdditiveSemigroup a => Semigroup (Sum a) Source #
Instance details Methods (<>) :: Sum a -> Sum a -> Sum a Source #