Rose

Rose Trees are trees with an unbounded number of branches per node. Each node contains a value and zero or more subtrees.

Documentation

data Rose a

A Rose tree. This type can be produced and consumed using the Rose pattern.

Instances

Monad Rose

Defined in Rose

Methods

(>>=) :: Rose a -> (a -> Rose b) -> Rose b

(>>) :: Rose a -> Rose b -> Rose b

return :: a -> Rose a

Functor Rose

Defined in Rose

Methods

fmap :: (a -> b) -> Rose a -> Rose b

(<$) :: a -> Rose b -> Rose a

Applicative Rose

Defined in Rose

Methods

pure :: a -> Rose a

(<*>) :: Rose (a -> b) -> Rose a -> Rose b

liftA2 :: (a -> b -> c) -> Rose a -> Rose b -> Rose c

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

(<*) :: Rose a -> Rose b -> Rose a

Foldable Rose

Defined in Rose

Methods

fold :: Monoid m => Rose m -> m

foldMap :: Monoid m => (a -> m) -> Rose a -> m

foldMap' :: Monoid m => (a -> m) -> Rose a -> m

foldr :: (a -> b -> b) -> b -> Rose a -> b

foldr' :: (a -> b -> b) -> b -> Rose a -> b

foldl :: (b -> a -> b) -> b -> Rose a -> b

foldl' :: (b -> a -> b) -> b -> Rose a -> b

foldr1 :: (a -> a -> a) -> Rose a -> a

foldl1 :: (a -> a -> a) -> Rose a -> a

toList :: Rose a -> [a]

null :: Rose a -> Bool

length :: Rose a -> Int

elem :: Eq a => a -> Rose a -> Bool

maximum :: Ord a => Rose a -> a

minimum :: Ord a => Rose a -> a

sum :: Num a => Rose a -> a

product :: Num a => Rose a -> a

Traversable Rose

Defined in Rose

Methods

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

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

mapM :: Monad m => (a -> m b) -> Rose a -> m (Rose b)

sequence :: Monad m => Rose (m a) -> m (Rose a)

Eq1 Rose

Defined in Rose

Methods

liftEq :: (a -> b -> Bool) -> Rose a -> Rose b -> Bool

Ord1 Rose

Defined in Rose

Methods

liftCompare :: (a -> b -> Ordering) -> Rose a -> Rose b -> Ordering

Read1 Rose

Defined in Rose

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Rose a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Rose a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Rose a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Rose a]

Show1 Rose

Defined in Rose

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Rose a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Rose a] -> ShowS

MonadZip Rose

Defined in Rose

Methods

mzip :: Rose a -> Rose b -> Rose (a, b)

mzipWith :: (a -> b -> c) -> Rose a -> Rose b -> Rose c

munzip :: Rose (a, b) -> (Rose a, Rose b)

Comonad Rose

Defined in Rose

Methods

extract :: Rose a -> a

duplicate :: Rose a -> Rose (Rose a)

extend :: (Rose a -> b) -> Rose a -> Rose b

ComonadCofree [] Rose

Defined in Rose

Methods

unwrap :: Rose a -> [Rose a]

Eq a => Eq (Rose a)

Defined in Rose

Methods

(==) :: Rose a -> Rose a -> Bool

(/=) :: Rose a -> Rose a -> Bool

Ord a => Ord (Rose a)

Defined in Rose

Methods

compare :: Rose a -> Rose a -> Ordering

(<) :: Rose a -> Rose a -> Bool

(<=) :: Rose a -> Rose a -> Bool

(>) :: Rose a -> Rose a -> Bool

(>=) :: Rose a -> Rose a -> Bool

max :: Rose a -> Rose a -> Rose a

min :: Rose a -> Rose a -> Rose a

Read a => Read (Rose a)

Defined in Rose

Methods

readsPrec :: Int -> ReadS (Rose a)

readList :: ReadS [Rose a]

readPrec :: ReadPrec (Rose a)

readListPrec :: ReadPrec [Rose a]

Show a => Show (Rose a)

Defined in Rose

Methods

showsPrec :: Int -> Rose a -> ShowS

show :: Rose a -> String

showList :: [Rose a] -> ShowS

Generic (Rose a)

Defined in Rose

Associated Types

type Rep (Rose a) :: Type -> Type

Methods

from :: Rose a -> Rep (Rose a) x

to :: Rep (Rose a) x -> Rose a

Generic1 Rose

Defined in Rose

Associated Types

type Rep1 Rose :: k -> Type

Methods

from1 :: forall (a :: k). Rose a -> Rep1 Rose a

to1 :: forall (a :: k). Rep1 Rose a -> Rose a

type Rep (Rose a)

Defined in Rose

type Rep (Rose a) = D1 ('MetaData "Rose" "Rose" "rose-0.1-FMRjGtAL9Q8GbehzqQkGtO" 'True) (C1 ('MetaCons "MkRose" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Cofree [] a))))

type Rep1 Rose

Defined in Rose

type Rep1 Rose = D1 ('MetaData "Rose" "Rose" "rose-0.1-FMRjGtAL9Q8GbehzqQkGtO" 'True) (C1 ('MetaCons "MkRose" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (Cofree []))))

pattern Rose :: a -> [Rose a] -> Rose a

singleton :: a -> Rose a

Generate a singleton rose tree. It has no leaves and one shoot.

>>> singleton @Int 3
Rose 3 []

coiter :: (a -> [a]) -> a -> Rose a

Use coiteration to generate a rose tree from a seed.

The coiteration terminates when the generating function returns an empty list:

>>> 'coiter' (\i -> if i > 3 then [] else [i + 1]) 0
Rose 0 [Rose 1 [Rose 2 [Rose 3 [Rose 4 []]]]]

An infinite, lazy generator for the fibonacci sequence:

>>> take 10 $ map fst $ 'Data.Foldable.toList' $ 'coiter' (\(a, b) -> [(b, a + b)]) (0, 1)

coiterW :: Comonad w => (w a -> [w a]) -> w a -> Rose a

Like coiter for comonadic values.

unfold :: (b -> (a, [b])) -> b -> Rose a

Unfold a rose tree from a seed.

unfoldM :: Monad m => (b -> m (a, [b])) -> b -> m (Rose a)

Unfold a rose tree from a seed, monadically.

telescoped :: Functor f => [(Rose a -> f (Rose a)) -> [Rose a] -> f [Rose a]] -> (a -> f a) -> Rose a -> f (Rose a)

Construct an Lens into a rose tree given a list of lenses into the base functor.

When the input list is empty, this is equivalent to _extract. When the input list is non-empty, this composes the input lenses with _unwrap to walk through the rose tree before using _extract to get the element at the final location.

For more on lenses see the lens package on hackage.

telescoped :: [Lens' [Rose a] (Rose a)]      -> Lens' (Rose a) a

telescoped :: [Traversal' [Rose a] (Rose a)] -> Traversal' (Rose a) a

telescoped :: [Getter [Rose a] (Rose a)]     -> Getter (Rose a) a

telescoped :: [Fold [Rose a] (Rose a)]       -> Fold (Rose a) a

telescoped :: [Setter' [Rose a] (Rose a)]    -> Setter' (Rose a) a

telescoped_ :: Functor f => [(Rose a -> f (Rose a)) -> [Rose a] -> f [Rose a]] -> (Rose a -> f (Rose a)) -> Rose a -> f (Rose a)

Construct an Lens into a rose tree given a list of lenses into the base functor.

The only difference between this and telescoped is that telescoped focuses on a single value, but this focuses on the entire remaining subtree. When the input list is empty, this is equivalent to id. When the input list is non-empty, this composes the input lenses with _unwrap to walk through the rose tree.

For more on lenses see the lens package on hackage.

telescoped :: [Lens' [Rose a] (Rose a)]      -> Lens' (Rose a) (Rose a)

telescoped :: [Traversal' [Rose a] (Rose a)] -> Traversal' (Rose a) (Rose a)

telescoped :: [Getter [Rose a] (Rose a)]     -> Getter (Rose a) (Rose a)

telescoped :: [Fold [Rose a] (Rose a)]       -> Fold (Rose a) (Rose a)

telescoped :: [Setter' [Rose a] (Rose a)]    -> Setter' (Rose a) (Rose a)

shoots :: Applicative f => (a -> f a) -> Rose a -> f (Rose a)

A Traversal' that gives access to all non-leaf elements of a rose tree, where non-leaf is defined as x from Rose x xs where null xs is False.

Because this doesn't give access to all values in the rose tree, it cannot be used to change types (use traverse for that).

leaves :: Applicative f => (a -> f a) -> Rose a -> f (Rose a)

A Traversal' that gives access to all leaf elements of a rose tree, where leaf is defined as x from Rose x xs where null xs is True.

Because this doesn't give access to all values in the rose tree, it cannot be used to change types (use traverse for that).