Safe Haskell	Safe
Language	Haskell2010

Data.RAVec.Tree

Contents

Construction
Conversions
Indexing
Folds
Special folds
Mapping
Zipping
Universe
QuickCheck

Description

Depth indexed perfect binary tree.

Synopsis

data Tree (n :: Nat) a where
- Leaf :: a -> Tree 'Z a
- Node :: Tree n a -> Tree n a -> Tree ('S n) a
singleton :: a -> Tree 'Z a
toList :: Tree n a -> [a]
reverse :: Tree n a -> Tree n a
(!) :: Tree n a -> Wrd n -> a
tabulate :: forall n a. SNatI n => (Wrd n -> a) -> Tree n a
leftmost :: Tree n a -> a
rightmost :: Tree n a -> a
foldMap :: Monoid m => (a -> m) -> Tree n a -> m
foldMap1 :: Semigroup s => (a -> s) -> Tree n a -> s
ifoldMap :: Monoid m => (Wrd n -> a -> m) -> Tree n a -> m
ifoldMap1 :: Semigroup s => (Wrd n -> a -> s) -> Tree n a -> s
foldr :: (a -> b -> b) -> b -> Tree n a -> b
ifoldr :: (Wrd n -> a -> b -> b) -> b -> Tree n a -> b
foldr1Map :: (a -> b -> b) -> (a -> b) -> Tree n a -> b
ifoldr1Map :: (Wrd n -> a -> b -> b) -> (Wrd n -> a -> b) -> Tree n a -> b
foldl :: (b -> a -> b) -> b -> Tree n a -> b
ifoldl :: (Wrd n -> b -> a -> b) -> b -> Tree n a -> b
length :: Tree n a -> Int
null :: Tree n a -> Bool
sum :: Num a => Tree n a -> a
product :: Num a => Tree n a -> a
map :: (a -> b) -> Tree n a -> Tree n b
imap :: (Wrd n -> a -> b) -> Tree n a -> Tree n b
traverse :: Applicative f => (a -> f b) -> Tree n a -> f (Tree n b)
itraverse :: Applicative f => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b)
traverse1 :: Apply f => (a -> f b) -> Tree n a -> f (Tree n b)
itraverse1 :: Apply f => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b)
itraverse_ :: forall n f a b. Applicative f => (Wrd n -> a -> f b) -> Tree n a -> f ()
zipWith :: (a -> b -> c) -> Tree n a -> Tree n b -> Tree n c
izipWith :: (Wrd n -> a -> b -> c) -> Tree n a -> Tree n b -> Tree n c
repeat :: SNatI n => a -> Tree n a
universe :: SNatI n => Tree n (Wrd n)
liftArbitrary :: forall n a. SNatI n => Gen a -> Gen (Tree n a)
liftShrink :: forall n a. (a -> [a]) -> Tree n a -> [Tree n a]

Documentation

data Tree (n :: Nat) a where Source #

Perfectly balanced binary tree of depth n, with 2 ^ n elements.

Constructors

Leaf :: a -> Tree 'Z a
Node :: Tree n a -> Tree n a -> Tree ('S n) a

Instances

Instances details

SNatI n => Arbitrary1 (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods liftArbitrary :: Gen a -> Gen (Tree n a) # liftShrink :: (a -> [a]) -> Tree n a -> [Tree n a] #
SNatI n => Representable (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Associated Types type Rep (Tree n) # Methods tabulate :: (Rep (Tree n) -> a) -> Tree n a # index :: Tree n a -> Rep (Tree n) -> a #
Foldable (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods fold :: Monoid m => Tree n m -> m # foldMap :: Monoid m => (a -> m) -> Tree n a -> m # foldMap' :: Monoid m => (a -> m) -> Tree n a -> m # foldr :: (a -> b -> b) -> b -> Tree n a -> b # foldr' :: (a -> b -> b) -> b -> Tree n a -> b # foldl :: (b -> a -> b) -> b -> Tree n a -> b # foldl' :: (b -> a -> b) -> b -> Tree n a -> b # foldr1 :: (a -> a -> a) -> Tree n a -> a # foldl1 :: (a -> a -> a) -> Tree n a -> a # toList :: Tree n a -> [a] # null :: Tree n a -> Bool # length :: Tree n a -> Int # elem :: Eq a => a -> Tree n a -> Bool # maximum :: Ord a => Tree n a -> a # minimum :: Ord a => Tree n a -> a # sum :: Num a => Tree n a -> a # product :: Num a => Tree n a -> a #
Foldable1 (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods fold1 :: Semigroup m => Tree n m -> m # foldMap1 :: Semigroup m => (a -> m) -> Tree n a -> m # foldMap1' :: Semigroup m => (a -> m) -> Tree n a -> m # toNonEmpty :: Tree n a -> NonEmpty a # maximum :: Ord a => Tree n a -> a # minimum :: Ord a => Tree n a -> a # head :: Tree n a -> a # last :: Tree n a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Tree n a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Tree n a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Tree n a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Tree n a -> b #
Traversable (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree n a -> f (Tree n b) # sequenceA :: Applicative f => Tree n (f a) -> f (Tree n a) # mapM :: Monad m => (a -> m b) -> Tree n a -> m (Tree n b) # sequence :: Monad m => Tree n (m a) -> m (Tree n a) #
SNatI n => Applicative (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods pure :: a -> Tree n a # (<>) :: Tree n (a -> b) -> Tree n a -> Tree n b # liftA2 :: (a -> b -> c) -> Tree n a -> Tree n b -> Tree n c # (>) :: Tree n a -> Tree n b -> Tree n b # (<*) :: Tree n a -> Tree n b -> Tree n a #
Functor (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods fmap :: (a -> b) -> Tree n a -> Tree n b # (<$) :: a -> Tree n b -> Tree n a #
SNatI n => Distributive (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods distribute :: Functor f => f (Tree n a) -> Tree n (f a) # collect :: Functor f => (a -> Tree n b) -> f a -> Tree n (f b) # distributeM :: Monad m => m (Tree n a) -> Tree n (m a) # collectM :: Monad m => (a -> Tree n b) -> m a -> Tree n (m b) #
Apply (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods (<.>) :: Tree n (a -> b) -> Tree n a -> Tree n b # (.>) :: Tree n a -> Tree n b -> Tree n b # (<.) :: Tree n a -> Tree n b -> Tree n a # liftF2 :: (a -> b -> c) -> Tree n a -> Tree n b -> Tree n c #
Traversable1 (Tree n) Source #
Instance details Defined in Data.RAVec.Tree Methods traverse1 :: Apply f => (a -> f b) -> Tree n a -> f (Tree n b) # sequence1 :: Apply f => Tree n (f b) -> f (Tree n b) #
FoldableWithIndex (Wrd n) (Tree n) Source #	Since: 0.2
Instance details Defined in Data.RAVec.Tree Methods ifoldMap :: Monoid m => (Wrd n -> a -> m) -> Tree n a -> m # ifoldMap' :: Monoid m => (Wrd n -> a -> m) -> Tree n a -> m # ifoldr :: (Wrd n -> a -> b -> b) -> b -> Tree n a -> b # ifoldl :: (Wrd n -> b -> a -> b) -> b -> Tree n a -> b # ifoldr' :: (Wrd n -> a -> b -> b) -> b -> Tree n a -> b # ifoldl' :: (Wrd n -> b -> a -> b) -> b -> Tree n a -> b #
FunctorWithIndex (Wrd n) (Tree n) Source #	Since: 0.2
Instance details Defined in Data.RAVec.Tree Methods imap :: (Wrd n -> a -> b) -> Tree n a -> Tree n b #
TraversableWithIndex (Wrd n) (Tree n) Source #	Since: 0.2
Instance details Defined in Data.RAVec.Tree Methods itraverse :: Applicative f => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b) #
(SNatI n, Arbitrary a) => Arbitrary (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods arbitrary :: Gen (Tree n a) # shrink :: Tree n a -> [Tree n a] #
CoArbitrary a => CoArbitrary (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods coarbitrary :: Tree n a -> Gen b -> Gen b #
(SNatI n, Function a) => Function (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods function :: (Tree n a -> b) -> Tree n a :-> b #
Semigroup a => Semigroup (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods (<>) :: Tree n a -> Tree n a -> Tree n a # sconcat :: NonEmpty (Tree n a) -> Tree n a # stimes :: Integral b => b -> Tree n a -> Tree n a #
Show a => Show (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods showsPrec :: Int -> Tree n a -> ShowS # show :: Tree n a -> String # showList :: [Tree n a] -> ShowS #
NFData a => NFData (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods rnf :: Tree n a -> () #
Eq a => Eq (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods (==) :: Tree n a -> Tree n a -> Bool # (/=) :: Tree n a -> Tree n a -> Bool #
Ord a => Ord (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods compare :: Tree n a -> Tree n a -> Ordering # (<) :: Tree n a -> Tree n a -> Bool # (<=) :: Tree n a -> Tree n a -> Bool # (>) :: Tree n a -> Tree n a -> Bool # (>=) :: Tree n a -> Tree n a -> Bool # max :: Tree n a -> Tree n a -> Tree n a # min :: Tree n a -> Tree n a -> Tree n a #
Hashable a => Hashable (Tree n a) Source #
Instance details Defined in Data.RAVec.Tree Methods hashWithSalt :: Int -> Tree n a -> Int # hash :: Tree n a -> Int #
type Rep (Tree n) Source #
Instance details Defined in Data.RAVec.Tree type Rep (Tree n) = Wrd n

Construction

singleton :: a -> Tree 'Z a Source #

Tree of zero depth, with single element.

>>> singleton True
Leaf True

Conversions

toList :: Tree n a -> [a] Source #

Convert Tree to list.

>>> toList $ Node (Node (Leaf 'a') (Leaf 'b')) (Node (Leaf 'c') (Leaf 'd'))
"abcd"

reverse :: Tree n a -> Tree n a Source #

Reverse Tree.

>>> let t = Node (Node (Leaf 'a') (Leaf 'b')) (Node (Leaf 'c') (Leaf 'd'))
>>> reverse t
Node (Node (Leaf 'd') (Leaf 'c')) (Node (Leaf 'b') (Leaf 'a'))

Since: 0.1.1

Indexing

(!) :: Tree n a -> Wrd n -> a Source #

Indexing.

tabulate :: forall n a. SNatI n => (Wrd n -> a) -> Tree n a Source #

leftmost :: Tree n a -> a Source #

rightmost :: Tree n a -> a Source #

Folds

foldMap :: Monoid m => (a -> m) -> Tree n a -> m Source #

foldMap1 :: Semigroup s => (a -> s) -> Tree n a -> s Source #

ifoldMap :: Monoid m => (Wrd n -> a -> m) -> Tree n a -> m Source #

ifoldMap1 :: Semigroup s => (Wrd n -> a -> s) -> Tree n a -> s Source #

foldr :: (a -> b -> b) -> b -> Tree n a -> b Source #

>>> foldr (:) [] $ Node (Leaf True) (Leaf False)
[True,False]

ifoldr :: (Wrd n -> a -> b -> b) -> b -> Tree n a -> b Source #

foldr1Map :: (a -> b -> b) -> (a -> b) -> Tree n a -> b Source #

ifoldr1Map :: (Wrd n -> a -> b -> b) -> (Wrd n -> a -> b) -> Tree n a -> b Source #

foldl :: (b -> a -> b) -> b -> Tree n a -> b Source #

>>> foldl (flip (:)) [] $ Node (Leaf True) (Leaf False)
[False,True]

ifoldl :: (Wrd n -> b -> a -> b) -> b -> Tree n a -> b Source #

Special folds

length :: Tree n a -> Int Source #

>>> length (universe :: Tree N.Nat3 (Wrd N.Nat3))
8

null :: Tree n a -> Bool Source #

Since: 0.1.1

sum :: Num a => Tree n a -> a Source #

Non-strict sum.

Since: 0.1.1

product :: Num a => Tree n a -> a Source #

Non-strict product.

Since: 0.1.1

Mapping

map :: (a -> b) -> Tree n a -> Tree n b Source #

>>> map not $ Node (Leaf True) (Leaf False)
Node (Leaf False) (Leaf True)

imap :: (Wrd n -> a -> b) -> Tree n a -> Tree n b Source #

>>> imap (,) $ Node (Leaf True) (Leaf False)
Node (Leaf (0b0,True)) (Leaf (0b1,False))

traverse :: Applicative f => (a -> f b) -> Tree n a -> f (Tree n b) Source #

itraverse :: Applicative f => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b) Source #

traverse1 :: Apply f => (a -> f b) -> Tree n a -> f (Tree n b) Source #

itraverse1 :: Apply f => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b) Source #

itraverse_ :: forall n f a b. Applicative f => (Wrd n -> a -> f b) -> Tree n a -> f () Source #

Since: 0.1.1

Zipping

zipWith :: (a -> b -> c) -> Tree n a -> Tree n b -> Tree n c Source #

Zip two Vecs with a function.

izipWith :: (Wrd n -> a -> b -> c) -> Tree n a -> Tree n b -> Tree n c Source #

Zip two Trees. with a function that also takes the elements' indices.

repeat :: SNatI n => a -> Tree n a Source #

Repeat a value.

>>> repeat 'x' :: Tree N.Nat2 Char
Node (Node (Leaf 'x') (Leaf 'x')) (Node (Leaf 'x') (Leaf 'x'))

Universe

universe :: SNatI n => Tree n (Wrd n) Source #

Get all Vec n Bool indices in Tree n.

>>> universe :: Tree N.Nat2 (Wrd N.Nat2)
Node (Node (Leaf 0b00) (Leaf 0b01)) (Node (Leaf 0b10) (Leaf 0b11))

QuickCheck

liftArbitrary :: forall n a. SNatI n => Gen a -> Gen (Tree n a) Source #

liftShrink :: forall n a. (a -> [a]) -> Tree n a -> [Tree n a] Source #