Graphics.Implicit.SaneOperators

Num is too big a class and doesn't make sense for, say, vectors.

class Additive a b c | a b -> c where

Methods

(+) :: a -> b -> c

Instances

Additive ℕ ℕ ℕ

Additive ℕ ℝ ℝ

Additive ℝ3 ℝ3 ℝ3

Additive ℝ2 ℝ2 ℝ2

Additive ℝ ℕ ℝ

Additive ℝ ℝ ℝ

Additive a b c => Additive (d -> a) (d -> b) (d -> c)

class Multiplicative a b c | a b -> c where

Methods

(*) :: a -> b -> c

Instances

Multiplicative ℕ ℕ ℕ

Multiplicative ℕ ℝ ℝ

Multiplicative ℝ ℕ ℝ

Multiplicative ℝ ℝ3 ℝ3

Multiplicative ℝ ℝ2 ℝ2

Multiplicative ℝ ℝ ℝ

Multiplicative a b c => Multiplicative (d -> a) (d -> b) (d -> c)

class AdditiveInvertable a where

Methods

additiveInverse :: a -> a

Instances

AdditiveInvertable ℕ

AdditiveInvertable ℝ3

AdditiveInvertable ℝ2

AdditiveInvertable ℝ

class MultiplicativeInvertable a where

Methods

multiplicativeInverse :: a -> a

Instances

MultiplicativeInvertable ℝ

class Normable a where

Methods

norm :: a -> ℝ

Instances

Normable ℝ3

Normable ℝ2

Normable ℝ

class InnerProductSpace a where

Methods

(⋅) :: a -> a -> ℝ

Instances

InnerProductSpace ℝ3

InnerProductSpace ℝ2

InnerProductSpace ℝ

I should be able to create instances for all Num instances,

(-) :: Additive a b c => AdditiveInvertable b => a -> b -> c

(/) :: Multiplicative a b c => MultiplicativeInvertable b => a -> b -> c