Numeric.AD.Jet

Description

Synopsis

Documentation

data Jet f a Source #

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) Source #
Methods fmap :: (a -> b) -> Jet f a -> Jet f b # (<$) :: a -> Jet f b -> Jet f a #
Foldable f => Foldable (Jet f) Source #
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) Source #
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) Source #
Methods showsPrec :: Int -> Jet f a -> ShowS # show :: Jet f a -> String # showList :: [Jet f a] -> ShowS #

Take the head of a Jet.

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

Take the tail of a Jet.

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