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 #