Numeric.AD.Jet

Documentation

data Jet f a

A Jet is a tower of all (higher order) partial derivatives of a function

At each step, a Jet f is wrapped in another layer worth of f.

a :- f a :- f (f a) :- f (f (f a)) :- ...

Constructors

a :- (Jet f (f a)) infixl 3

Instances

Functor f => Functor (Jet f)

Methods

fmap :: (a -> b) -> Jet f a -> Jet f b

(<$) :: a -> Jet f b -> Jet f a

Foldable f => Foldable (Jet f)

Methods

fold :: Monoid m => Jet f m -> m

foldMap :: Monoid m => (a -> m) -> Jet f a -> m

foldr :: (a -> b -> b) -> b -> Jet f a -> b

foldr' :: (a -> b -> b) -> b -> Jet f a -> b

foldl :: (b -> a -> b) -> b -> Jet f a -> b

foldl' :: (b -> a -> b) -> b -> Jet f a -> b

foldr1 :: (a -> a -> a) -> Jet f a -> a

foldl1 :: (a -> a -> a) -> Jet f a -> a

toList :: Jet f a -> [a]

null :: Jet f a -> Bool

length :: Jet f a -> Int

elem :: Eq a => a -> Jet f a -> Bool

maximum :: Ord a => Jet f a -> a

minimum :: Ord a => Jet f a -> a

sum :: Num a => Jet f a -> a

product :: Num a => Jet f a -> a

Traversable f => Traversable (Jet f)

Methods

traverse :: Applicative f => (a -> f b) -> Jet f a -> f (Jet f b)

sequenceA :: Applicative f => Jet f (f a) -> f (Jet f a)

mapM :: Monad m => (a -> m b) -> Jet f a -> m (Jet f b)

sequence :: Monad m => Jet f (m a) -> m (Jet f a)

(Functor f, Show (f Showable), Show a) => Show (Jet f a)

Methods

showsPrec :: Int -> Jet f a -> ShowS

show :: Jet f a -> String

showList :: [Jet f a] -> ShowS

headJet :: Jet f a -> a

Take the head of a Jet.

tailJet :: Jet f a -> Jet f (f a)

Take the tail of a Jet.

jet :: Functor f => Cofree f a -> Jet f a

Construct a Jet by unzipping the layers of a Cofree Comonad.