algebra-3.1: Constructive abstract algebra

Safe Haskell | None

Numeric.Module.Representable

Contents

- Representable Additive
- Representable Monoidal
- Representable Group
- Representable Multiplicative (via Algebra)
- Representable Unital (via UnitalAlgebra)
- Representable Rig (via Algebra)
- Representable Ring (via Algebra)

Synopsis

- addRep :: (Zip m, Additive r) => m r -> m r -> m r
- sinnum1pRep :: (Whole n, Functor m, Additive r) => n -> m r -> m r
- zeroRep :: (Applicative m, Monoidal r) => m r
- sinnumRep :: (Whole n, Functor m, Monoidal r) => n -> m r -> m r
- negateRep :: (Functor m, Group r) => m r -> m r
- minusRep :: (Zip m, Group r) => m r -> m r -> m r
- subtractRep :: (Zip m, Group r) => m r -> m r -> m r
- timesRep :: (Integral n, Functor m, Group r) => n -> m r -> m r
- mulRep :: (Representable m, Algebra r (Key m)) => m r -> m r -> m r
- oneRep :: (Representable m, Unital r, UnitalAlgebra r (Key m)) => m r
- fromNaturalRep :: (UnitalAlgebra r (Key m), Representable m, Rig r) => Natural -> m r
- fromIntegerRep :: (UnitalAlgebra r (Key m), Representable m, Ring r) => Integer -> m r

# Representable Additive

addRep :: (Zip m, Additive r) => m r -> m r -> m rSource

`Additive.(+)` default definition

sinnum1pRep :: (Whole n, Functor m, Additive r) => n -> m r -> m rSource

`sinnum1p` default definition

# Representable Monoidal

zeroRep :: (Applicative m, Monoidal r) => m rSource

`zero` default definition

sinnumRep :: (Whole n, Functor m, Monoidal r) => n -> m r -> m rSource

`sinnum` default definition

# Representable Group

negateRep :: (Functor m, Group r) => m r -> m rSource

`negate` default definition

minusRep :: (Zip m, Group r) => m r -> m r -> m rSource

`Group.(-)` default definition

subtractRep :: (Zip m, Group r) => m r -> m r -> m rSource

`subtract` default definition

timesRep :: (Integral n, Functor m, Group r) => n -> m r -> m rSource

`times` default definition

# Representable Multiplicative (via Algebra)

mulRep :: (Representable m, Algebra r (Key m)) => m r -> m r -> m rSource

`Multiplicative.(*)` default definition

# Representable Unital (via UnitalAlgebra)

oneRep :: (Representable m, Unital r, UnitalAlgebra r (Key m)) => m rSource

`one` default definition

# Representable Rig (via Algebra)

fromNaturalRep :: (UnitalAlgebra r (Key m), Representable m, Rig r) => Natural -> m rSource

`fromNatural` default definition

# Representable Ring (via Algebra)

fromIntegerRep :: (UnitalAlgebra r (Key m), Representable m, Ring r) => Integer -> m rSource

`fromInteger` default definition