Data.RAVec.Tree.DF

Depth indexed perfect tree as data family.

Documentation

data family Tree (n :: Nat) a

Instances

SNatI n => Functor (Tree n)

Defined in Data.RAVec.Tree.DF

Methods

fmap :: (a -> b) -> Tree n a -> Tree n b

(<$) :: a -> Tree n b -> Tree n a

SNatI n => Applicative (Tree n)

Defined in Data.RAVec.Tree.DF

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

SNatI n => Foldable (Tree n)

Defined in Data.RAVec.Tree.DF

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

SNatI n => Traversable (Tree n)

Defined in Data.RAVec.Tree.DF

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 => Arbitrary1 (Tree n)

Defined in Data.RAVec.Tree.DF

Methods

liftArbitrary :: Gen a -> Gen (Tree n a)

liftShrink :: (a -> [a]) -> Tree n a -> [Tree n a]

SNatI n => Distributive (Tree n)

Defined in Data.RAVec.Tree.DF

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)

SNatI n => Representable (Tree n)

Defined in Data.RAVec.Tree.DF

Associated Types

type Rep (Tree n)

Methods

tabulate :: (Rep (Tree n) -> a) -> Tree n a

index :: Tree n a -> Rep (Tree n) -> a

SNatI n => Traversable1 (Tree n)

Defined in Data.RAVec.Tree.DF

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)

SNatI n => Apply (Tree n)

Defined in Data.RAVec.Tree.DF

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

SNatI n => Foldable1 (Tree n)

Defined in Data.RAVec.Tree.DF

Methods

fold1 :: Semigroup m => Tree n m -> m

foldMap1 :: Semigroup m => (a -> m) -> Tree n a -> m

toNonEmpty :: Tree n a -> NonEmpty a

SNatI n => FunctorWithIndex (Wrd n) (Tree n)

Since: 0.2

Defined in Data.RAVec.Tree.DF

Methods

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

SNatI n => FoldableWithIndex (Wrd n) (Tree n)

Since: 0.2

Defined in Data.RAVec.Tree.DF

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

SNatI n => TraversableWithIndex (Wrd n) (Tree n)

Since: 0.2

Defined in Data.RAVec.Tree.DF

Methods

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

(Eq a, SNatI n) => Eq (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

(==) :: Tree n a -> Tree n a -> Bool

(/=) :: Tree n a -> Tree n a -> Bool

(Ord a, SNatI n) => Ord (Tree n a)

Defined in Data.RAVec.Tree.DF

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

(Show a, SNatI n) => Show (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

showsPrec :: Int -> Tree n a -> ShowS

show :: Tree n a -> String

showList :: [Tree n a] -> ShowS

(Semigroup a, SNatI n) => Semigroup (Tree n a)

Defined in Data.RAVec.Tree.DF

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

(Monoid a, SNatI n) => Monoid (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

mempty :: Tree n a

mappend :: Tree n a -> Tree n a -> Tree n a

mconcat :: [Tree n a] -> Tree n a

(SNatI n, Function a) => Function (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

function :: (Tree n a -> b) -> Tree n a :-> b

(SNatI n, Arbitrary a) => Arbitrary (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

arbitrary :: Gen (Tree n a)

shrink :: Tree n a -> [Tree n a]

(SNatI n, CoArbitrary a) => CoArbitrary (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

coarbitrary :: Tree n a -> Gen b -> Gen b

(NFData a, SNatI n) => NFData (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

rnf :: Tree n a -> ()

(Hashable a, SNatI n) => Hashable (Tree n a)

Defined in Data.RAVec.Tree.DF

Methods

hashWithSalt :: Int -> Tree n a -> Int

hash :: Tree n a -> Int

newtype Tree 'Z a

Defined in Data.RAVec.Tree.DF

newtype Tree 'Z a = Leaf a

type Rep (Tree n)

Defined in Data.RAVec.Tree.DF

type Rep (Tree n) = Wrd n

data Tree ('S n) a

Defined in Data.RAVec.Tree.DF

data Tree ('S n) a = Node (Tree n a) (Tree n a)

Construction

singleton :: a -> Tree 'Z a

Tree with exactly one element.

>>> singleton True
Leaf True

Conversions

toList :: forall n a. SNatI n => Tree n a -> [a]

Convert Tree to list.

>>> toList $ Node (Node (Leaf 'f') (Leaf 'o')) (Node (Leaf 'o') (Leaf 'd'))
"food"

reverse :: forall n a. SNatI n => Tree n a -> Tree n a

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'))

Indexing

(!) :: SNatI n => Tree n a -> Wrd n -> a

Indexing.

>>> let t = Node (Node (Leaf 'a') (Leaf 'b')) (Node (Leaf 'c') (Leaf 'd'))
>>> t ! W1 (W0 WE)
'c'

tabulate :: SNatI n => (Wrd n -> a) -> Tree n a

Tabulating, inverse of !.

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

leftmost :: SNatI n => Tree n a -> a

rightmost :: SNatI n => Tree n a -> a

Folds

foldMap :: forall a n m. (Monoid m, SNatI n) => (a -> m) -> Tree n a -> m

See Foldable.

foldMap1 :: forall s a n. (Semigroup s, SNatI n) => (a -> s) -> Tree n a -> s

See Foldable1.

ifoldMap :: forall a n m. (Monoid m, SNatI n) => (Wrd n -> a -> m) -> Tree n a -> m

See FoldableWithIndex.

ifoldMap1 :: forall a n s. (Semigroup s, SNatI n) => (Wrd ('S n) -> a -> s) -> Tree ('S n) a -> s

There is no type-class for this :(

foldr :: forall a b n. SNatI n => (a -> b -> b) -> b -> Tree n a -> b

Right fold.

ifoldr :: forall a b n. SNatI n => (Wrd n -> a -> b -> b) -> b -> Tree n a -> b

Right fold with an index.

foldr1Map :: forall a b n. SNatI n => (a -> b -> b) -> (a -> b) -> Tree n a -> b

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

foldl :: forall a b n. SNatI n => (b -> a -> b) -> b -> Tree n a -> b

Left fold.

ifoldl :: forall a b n. SNatI n => (Wrd n -> b -> a -> b) -> b -> Tree n a -> b

Left fold with an index.

Special folds

length :: forall n a. SNatI n => Tree n a -> Int

Yield the length of a Tree. O(n)

null :: Tree n a -> Bool

Test whether a Tree is empty. It never is. O(1)

sum :: (Num a, SNatI n) => Tree n a -> a

Non-strict sum.

product :: (Num a, SNatI n) => Tree n a -> a

Non-strict product.

Mapping

map :: forall a b n. SNatI n => (a -> b) -> Tree n a -> Tree n b

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

imap :: SNatI n => (Wrd n -> a -> b) -> Tree n a -> Tree n b

>>> let t = Node (Node (Leaf 'a') (Leaf 'b')) (Node (Leaf 'c') (Leaf 'd'))
>>> imap (,) t
Node (Node (Leaf (0b00,'a')) (Leaf (0b01,'b'))) (Node (Leaf (0b10,'c')) (Leaf (0b11,'d')))

traverse :: forall n f a b. (Applicative f, SNatI n) => (a -> f b) -> Tree n a -> f (Tree n b)

Apply an action to every element of a Tree, yielding a Tree of results.

itraverse :: forall n f a b. (Applicative f, SNatI n) => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b)

Apply an action to every element of a Tree and its index, yielding a Tree of results.

traverse1 :: forall n f a b. (Apply f, SNatI n) => (a -> f b) -> Tree n a -> f (Tree n b)

Apply an action to non-empty Tree, yielding a Tree of results.

itraverse1 :: forall n f a b. (Apply f, SNatI n) => (Wrd n -> a -> f b) -> Tree n a -> f (Tree n b)

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

Apply an action to every element of a Tree and its index, ignoring the results.

Zipping

zipWith :: forall a b c n. SNatI n => (a -> b -> c) -> Tree n a -> Tree n b -> Tree n c

Zip two Trees with a function.

izipWith :: SNatI n => (Wrd n -> a -> b -> c) -> Tree n a -> Tree n b -> Tree n c

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

repeat :: SNatI n => x -> Tree n x

Repeat 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)

Get all Wrd n in a 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)

liftShrink :: forall n a. SNatI n => (a -> [a]) -> Tree n a -> [Tree n a]

Ensure spine

ensureSpine :: SNatI n => Tree n a -> Tree n a

Ensure spine.

If we have an undefined Tree,

>>> let v = error "err" :: Tree N.Nat2 Char

And insert data into it later:

>>> let setHead :: a -> Tree N.Nat2 a -> Tree N.Nat2 a; setHead x (Node (Node _ u) v) = Node (Node (Leaf x) u) v

Then without a spine, it will fail:

>>> leftmost $ setHead 'x' v
*** Exception: err
...

But with the spine, it won't:

>>> leftmost $ setHead 'x' $ ensureSpine v
'x'