Linear.Covector

Operations on affine spaces.

Documentation

newtype Covector r a

Linear functionals from elements of an (infinite) free module to a scalar

Constructors

Covector

Fields

• runCovector :: (a -> r) -> r

Instances

Num r => Alternative (Covector r)

Defined in Linear.Covector

Methods

empty :: Covector r a

(<|>) :: Covector r a -> Covector r a -> Covector r a

some :: Covector r a -> Covector r [a]

many :: Covector r a -> Covector r [a]

Applicative (Covector r)

Defined in Linear.Covector

Methods

pure :: a -> Covector r a

(<*>) :: Covector r (a -> b) -> Covector r a -> Covector r b

liftA2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c

(*>) :: Covector r a -> Covector r b -> Covector r b

(<*) :: Covector r a -> Covector r b -> Covector r a

Functor (Covector r)

Defined in Linear.Covector

Methods

fmap :: (a -> b) -> Covector r a -> Covector r b

(<$) :: a -> Covector r b -> Covector r a

Monad (Covector r)

Defined in Linear.Covector

Methods

(>>=) :: Covector r a -> (a -> Covector r b) -> Covector r b

(>>) :: Covector r a -> Covector r b -> Covector r b

return :: a -> Covector r a

Num r => MonadPlus (Covector r)

Defined in Linear.Covector

Methods

mzero :: Covector r a

mplus :: Covector r a -> Covector r a -> Covector r a

Num r => Alt (Covector r)

Defined in Linear.Covector

Methods

(<!>) :: Covector r a -> Covector r a -> Covector r a

some :: Applicative (Covector r) => Covector r a -> Covector r [a]

many :: Applicative (Covector r) => Covector r a -> Covector r [a]

Apply (Covector r)

Defined in Linear.Covector

Methods

(<.>) :: Covector r (a -> b) -> Covector r a -> Covector r b

(.>) :: Covector r a -> Covector r b -> Covector r b

(<.) :: Covector r a -> Covector r b -> Covector r a

liftF2 :: (a -> b -> c) -> Covector r a -> Covector r b -> Covector r c

Bind (Covector r)

Defined in Linear.Covector

Methods

(>>-) :: Covector r a -> (a -> Covector r b) -> Covector r b

join :: Covector r (Covector r a) -> Covector r a

Num r => Plus (Covector r)

Defined in Linear.Covector

Methods

zero :: Covector r a

Coalgebra r m => Num (Covector r m)

Defined in Linear.Covector

Methods

(+) :: Covector r m -> Covector r m -> Covector r m

(-) :: Covector r m -> Covector r m -> Covector r m

(*) :: Covector r m -> Covector r m -> Covector r m

negate :: Covector r m -> Covector r m

abs :: Covector r m -> Covector r m

signum :: Covector r m -> Covector r m

fromInteger :: Integer -> Covector r m

($*) :: Representable f => Covector r (Rep f) -> f r -> r infixr 0