Safe Haskell	Safe-Inferred
Language	GHC2021

NumHask.Algebra.Action

Description

Algebra for Actions

Convention: the |'s in the operators point towards the higher-kinded number, representing an operator or action into a structure.

Synopsis

class Additive (AdditiveScalar m) => AdditiveAction m where
- type AdditiveScalar m :: Type
- (|+) :: m -> AdditiveScalar m -> m
(+|) :: AdditiveAction m => AdditiveScalar m -> m -> m
class (AdditiveAction m, Subtractive (AdditiveScalar m)) => SubtractiveAction m where
- (|-) :: m -> AdditiveScalar m -> m
(-|) :: (AdditiveAction m, Subtractive m) => AdditiveScalar m -> m -> m
class Multiplicative (Scalar m) => MultiplicativeAction m where
- type Scalar m :: Type
- (|*) :: m -> Scalar m -> m
(*|) :: MultiplicativeAction m => Scalar m -> m -> m
class (Divisive (Scalar m), MultiplicativeAction m) => DivisiveAction m where
- (|/) :: m -> Scalar m -> m
(/|) :: (MultiplicativeAction m, Divisive m) => Scalar m -> m -> m
type Module m = (Distributive (Scalar m), MultiplicativeAction m)

Documentation

class Additive (AdditiveScalar m) => AdditiveAction m where Source #

Additive Action

m |+ zero == m

Associated Types

type AdditiveScalar m :: Type Source #

Methods

(|+) :: m -> AdditiveScalar m -> m infixl 6 Source #

Instances

Instances details

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 #
AdditiveAction a => AdditiveAction (Wrapped a) Source #
Instance details Defined in NumHask.Data.Wrapped Associated Types type AdditiveScalar (Wrapped a) Source # Methods (\|+) :: Wrapped a -> AdditiveScalar (Wrapped a) -> Wrapped a Source #

(+|) :: AdditiveAction m => AdditiveScalar m -> m -> m infixl 6 Source #

flipped additive action

(+|) == flip (|+)
zero +| m = m

class (AdditiveAction m, Subtractive (AdditiveScalar m)) => SubtractiveAction m where Source #

Subtractive Action

m |- zero = m

Methods

(|-) :: m -> AdditiveScalar m -> m infixl 6 Source #

Instances

Instances details

SubtractiveAction a => SubtractiveAction (Positive a) Source #
Instance details Defined in NumHask.Data.Positive Methods (\|-) :: Positive a -> AdditiveScalar (Positive a) -> Positive a Source #
SubtractiveAction a => SubtractiveAction (Wrapped a) Source #
Instance details Defined in NumHask.Data.Wrapped Methods (\|-) :: Wrapped a -> AdditiveScalar (Wrapped a) -> Wrapped a Source #

(-|) :: (AdditiveAction m, Subtractive m) => AdditiveScalar m -> m -> m infixl 6 Source #

Subtraction with the scalar on the left

(-|) == (+|) . negate
zero -| m = negate m

class Multiplicative (Scalar m) => MultiplicativeAction m where Source #

Multiplicative Action

m |* one = m
m |* zero = zero

Associated Types

type Scalar m :: Type Source #

Methods

(|*) :: m -> Scalar m -> m infixl 7 Source #

Instances

Instances details

Multiplicative a => MultiplicativeAction (EuclideanPair a) Source #
Instance details Defined in NumHask.Algebra.Metric Associated Types type Scalar (EuclideanPair a) Source # Methods (\|*) :: EuclideanPair a -> Scalar (EuclideanPair a) -> EuclideanPair 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 #
MultiplicativeAction a => MultiplicativeAction (Wrapped a) Source #
Instance details Defined in NumHask.Data.Wrapped Associated Types type Scalar (Wrapped a) Source # Methods (\|*) :: Wrapped a -> Scalar (Wrapped a) -> Wrapped a Source #

(*|) :: MultiplicativeAction m => Scalar m -> m -> m infixl 7 Source #

flipped multiplicative action

(*|) == flip (|*)
one *| m = one
zero *| m = zero

class (Divisive (Scalar m), MultiplicativeAction m) => DivisiveAction m where Source #

Divisive Action

m |/ one = m

Methods

(|/) :: m -> Scalar m -> m infixl 7 Source #

Instances

Instances details

Divisive a => DivisiveAction (EuclideanPair a) Source #
Instance details Defined in NumHask.Algebra.Metric Methods (\|/) :: EuclideanPair a -> Scalar (EuclideanPair a) -> EuclideanPair a Source #
DivisiveAction a => DivisiveAction (Positive a) Source #
Instance details Defined in NumHask.Data.Positive Methods (\|/) :: Positive a -> Scalar (Positive a) -> Positive a Source #
DivisiveAction a => DivisiveAction (Wrapped a) Source #
Instance details Defined in NumHask.Data.Wrapped Methods (\|/) :: Wrapped a -> Scalar (Wrapped a) -> Wrapped a Source #

(/|) :: (MultiplicativeAction m, Divisive m) => Scalar m -> m -> m Source #

left scalar division

(/|) == (*|) . recip
one |/ m = recip m

type Module m = (Distributive (Scalar m), MultiplicativeAction m) Source #

A Module

a *| one == a
(a + b) *| c == (a *| c) + (b *| c)
c |* (a + b) == (c |* a) + (c |* b)
a *| zero == zero
a *| b == b |* a