Stability	unstable
Safe Haskell	Safe
Language	Haskell2010

Q4C12.TwoFinger.Internal

Contents

Types, EqN?/ShowN?/(Bi)Functor/Foldable1?/Traversable1?
Digit operations.
Node operations.
Tree rotations
(Un)conses/snocs for TwoFingerOddA.
(Un)conses/snocs for TwoFingerOddE.
(Un)conses/snocs for TwoFingerEvenE.
(Un)conses/snocs for TwoFingerEvenA.
Monad and Applicative instances, and related operations
Construction and deconstruction of TwoFingerOddA.
Construction of TwoFingerOddE
Concatenation of TwoFingerOddA.
Concatenation of TwoFingerEvenE.
Concatenation of TwoFingerEvenA.
Monoid actions
QuickCheck stuff.
Aligning/zipping.
Creating infinite sequences.

Description

This is an internal module and not subject to the PVP. It may receive arbitrary changes at any time and between any two releases. Import from Q4C12.TwoFinger instead, unless you really need the gory details, and, in that case, you must depend on the exact version of this package. (If you do need them, please file a bug so that, hopefully, your use-case can be accomplished through the public interface.)

Synopsis

Documentation

>>> import Data.List (unfoldr)
>>> import Data.Tuple (swap)
>>> import Control.Lens (over, view)
>>> let hush = either (const Nothing) Just

(<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b infixl 4 Source #

(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b infixl 4 Source #

traverseDefault :: (Applicative f, Traversable1 t) => (a -> f a') -> t a -> f (t a') Source #

bitraverseDefault :: (Applicative f, Bitraversable1 t) => (a -> f a') -> (b -> f b') -> t a b -> f (t a' b') Source #

Types, EqN?/ShowN?/(Bi)Functor/Foldable1?/Traversable1?

data Digit e a Source #

Constructors

One e
Two e a e
Three e a e a e
Four e a e a e a e

Instances

Bifunctor Digit Source #
Methods bimap :: (a -> b) -> (c -> d) -> Digit a c -> Digit b d # first :: (a -> b) -> Digit a c -> Digit b c # second :: (b -> c) -> Digit a b -> Digit a c #
Bitraversable Digit Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Digit a b -> f (Digit c d) #
Bifoldable Digit Source #
Methods bifold :: Monoid m => Digit m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Digit a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Digit a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Digit a b -> c #
Bitraversable1 Digit Source #
Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Digit a c -> f (Digit b d) # bisequence1 :: Apply f => Digit (f a) (f b) -> f (Digit a b) #
Bifoldable1 Digit Source #
Methods bifold1 :: Semigroup m => Digit m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Digit a b -> m #
Functor (Digit e) Source #
Methods fmap :: (a -> b) -> Digit e a -> Digit e b # (<$) :: a -> Digit e b -> Digit e a #
Foldable (Digit e) Source #
Methods fold :: Monoid m => Digit e m -> m # foldMap :: Monoid m => (a -> m) -> Digit e a -> m # foldr :: (a -> b -> b) -> b -> Digit e a -> b # foldr' :: (a -> b -> b) -> b -> Digit e a -> b # foldl :: (b -> a -> b) -> b -> Digit e a -> b # foldl' :: (b -> a -> b) -> b -> Digit e a -> b # foldr1 :: (a -> a -> a) -> Digit e a -> a # foldl1 :: (a -> a -> a) -> Digit e a -> a # toList :: Digit e a -> [a] # null :: Digit e a -> Bool # length :: Digit e a -> Int # elem :: Eq a => a -> Digit e a -> Bool # maximum :: Ord a => Digit e a -> a # minimum :: Ord a => Digit e a -> a # sum :: Num a => Digit e a -> a # product :: Num a => Digit e a -> a #
Traversable (Digit e) Source #
Methods traverse :: Applicative f => (a -> f b) -> Digit e a -> f (Digit e b) # sequenceA :: Applicative f => Digit e (f a) -> f (Digit e a) # mapM :: Monad m => (a -> m b) -> Digit e a -> m (Digit e b) # sequence :: Monad m => Digit e (m a) -> m (Digit e a) #
Generic (Digit e a) Source #
Associated Types type Rep (Digit e a) :: * -> * # Methods from :: Digit e a -> Rep (Digit e a) x # to :: Rep (Digit e a) x -> Digit e a #
(NFData e, NFData a) => NFData (Digit e a) Source #
Methods rnf :: Digit e a -> () #
type Rep (Digit e a) Source #
type Rep (Digit e a) = D1 (MetaData "Digit" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) ((:+:) (C1 (MetaCons "One" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))) (C1 (MetaCons "Two" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))))) ((:+:) (C1 (MetaCons "Three" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))))) (C1 (MetaCons "Four" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))))))))

data Node e a Source #

Constructors

Node2 e a e
Node3 e a e a e

Instances

Bifunctor Node Source #
Methods bimap :: (a -> b) -> (c -> d) -> Node a c -> Node b d # first :: (a -> b) -> Node a c -> Node b c # second :: (b -> c) -> Node a b -> Node a c #
Bitraversable Node Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Node a b -> f (Node c d) #
Bifoldable Node Source #
Methods bifold :: Monoid m => Node m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Node a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Node a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Node a b -> c #
Bitraversable1 Node Source #
Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Node a c -> f (Node b d) # bisequence1 :: Apply f => Node (f a) (f b) -> f (Node a b) #
Bifoldable1 Node Source #
Methods bifold1 :: Semigroup m => Node m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Node a b -> m #
Functor (Node e) Source #
Methods fmap :: (a -> b) -> Node e a -> Node e b # (<$) :: a -> Node e b -> Node e a #
Foldable (Node e) Source #
Methods fold :: Monoid m => Node e m -> m # foldMap :: Monoid m => (a -> m) -> Node e a -> m # foldr :: (a -> b -> b) -> b -> Node e a -> b # foldr' :: (a -> b -> b) -> b -> Node e a -> b # foldl :: (b -> a -> b) -> b -> Node e a -> b # foldl' :: (b -> a -> b) -> b -> Node e a -> b # foldr1 :: (a -> a -> a) -> Node e a -> a # foldl1 :: (a -> a -> a) -> Node e a -> a # toList :: Node e a -> [a] # null :: Node e a -> Bool # length :: Node e a -> Int # elem :: Eq a => a -> Node e a -> Bool # maximum :: Ord a => Node e a -> a # minimum :: Ord a => Node e a -> a # sum :: Num a => Node e a -> a # product :: Num a => Node e a -> a #
Traversable (Node e) Source #
Methods traverse :: Applicative f => (a -> f b) -> Node e a -> f (Node e b) # sequenceA :: Applicative f => Node e (f a) -> f (Node e a) # mapM :: Monad m => (a -> m b) -> Node e a -> m (Node e b) # sequence :: Monad m => Node e (m a) -> m (Node e a) #
Traversable1 (Node e) Source #
Methods traverse1 :: Apply f => (a -> f b) -> Node e a -> f (Node e b) # sequence1 :: Apply f => Node e (f b) -> f (Node e b) #
Foldable1 (Node e) Source #
Methods fold1 :: Semigroup m => Node e m -> m # foldMap1 :: Semigroup m => (a -> m) -> Node e a -> m # toNonEmpty :: Node e a -> NonEmpty a #
(Eq a, Eq e) => Eq (Node e a) Source #
Methods (==) :: Node e a -> Node e a -> Bool # (/=) :: Node e a -> Node e a -> Bool #
Generic (Node e a) Source #
Associated Types type Rep (Node e a) :: * -> * # Methods from :: Node e a -> Rep (Node e a) x # to :: Rep (Node e a) x -> Node e a #
(NFData e, NFData a) => NFData (Node e a) Source #
Methods rnf :: Node e a -> () #
type Rep (Node e a) Source #
type Rep (Node e a) = D1 (MetaData "Node" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) (C1 (MetaCons "Node2" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))))) (C1 (MetaCons "Node3" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))))))

data TwoFingerOddA e a Source #

Isomorphic to a, (e, a)*

Constructors

EmptyOddA a
SingleOddA a e a
DeepOddA a !(Digit e a) (TwoFingerOddA (Node e a) a) !(Digit e a) a

Instances

Eq2 TwoFingerOddA Source #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerOddA a c -> TwoFingerOddA b d -> Bool #
Show2 TwoFingerOddA Source #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> TwoFingerOddA a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [TwoFingerOddA a b] -> ShowS #
Bifunctor TwoFingerOddA Source #
Methods bimap :: (a -> b) -> (c -> d) -> TwoFingerOddA a c -> TwoFingerOddA b d # first :: (a -> b) -> TwoFingerOddA a c -> TwoFingerOddA b c # second :: (b -> c) -> TwoFingerOddA a b -> TwoFingerOddA a c #
Bitraversable TwoFingerOddA Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerOddA a b -> f (TwoFingerOddA c d) #
Bifoldable TwoFingerOddA Source #
Methods bifold :: Monoid m => TwoFingerOddA m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> TwoFingerOddA a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> TwoFingerOddA a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> TwoFingerOddA a b -> c #
Bitraversable1 TwoFingerOddA Source #
Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> TwoFingerOddA a c -> f (TwoFingerOddA b d) # bisequence1 :: Apply f => TwoFingerOddA (f a) (f b) -> f (TwoFingerOddA a b) #
Bifoldable1 TwoFingerOddA Source #
Methods bifold1 :: Semigroup m => TwoFingerOddA m m -> m # bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> TwoFingerOddA a b -> m #
Monad (TwoFingerOddA e) Source #
Methods (>>=) :: TwoFingerOddA e a -> (a -> TwoFingerOddA e b) -> TwoFingerOddA e b # (>>) :: TwoFingerOddA e a -> TwoFingerOddA e b -> TwoFingerOddA e b # return :: a -> TwoFingerOddA e a # fail :: String -> TwoFingerOddA e a #
Functor (TwoFingerOddA e) Source #
Methods fmap :: (a -> b) -> TwoFingerOddA e a -> TwoFingerOddA e b # (<$) :: a -> TwoFingerOddA e b -> TwoFingerOddA e a #
Applicative (TwoFingerOddA e) Source #	A 'producty' instance: `>>>` *`(,) <$> (consOddA 1 "one" $ consOddA 2 "two" $ singletonOddA 3) <> (consOddA 'a' "foo" $ singletonOddA 'b')`**consOddA (1,'a') "foo" (consOddA (1,'b') "one" (consOddA (2,'a') "foo" (consOddA (2,'b') "two" (consOddA (3,'a') "foo" (singletonOddA (3,'b'))))))
Methods pure :: a -> TwoFingerOddA e a # (<>) :: TwoFingerOddA e (a -> b) -> TwoFingerOddA e a -> TwoFingerOddA e b # (>) :: TwoFingerOddA e a -> TwoFingerOddA e b -> TwoFingerOddA e b # (<*) :: TwoFingerOddA e a -> TwoFingerOddA e b -> TwoFingerOddA e a #
Foldable (TwoFingerOddA e) Source #
Methods fold :: Monoid m => TwoFingerOddA e m -> m # foldMap :: Monoid m => (a -> m) -> TwoFingerOddA e a -> m # foldr :: (a -> b -> b) -> b -> TwoFingerOddA e a -> b # foldr' :: (a -> b -> b) -> b -> TwoFingerOddA e a -> b # foldl :: (b -> a -> b) -> b -> TwoFingerOddA e a -> b # foldl' :: (b -> a -> b) -> b -> TwoFingerOddA e a -> b # foldr1 :: (a -> a -> a) -> TwoFingerOddA e a -> a # foldl1 :: (a -> a -> a) -> TwoFingerOddA e a -> a # toList :: TwoFingerOddA e a -> [a] # null :: TwoFingerOddA e a -> Bool # length :: TwoFingerOddA e a -> Int # elem :: Eq a => a -> TwoFingerOddA e a -> Bool # maximum :: Ord a => TwoFingerOddA e a -> a # minimum :: Ord a => TwoFingerOddA e a -> a # sum :: Num a => TwoFingerOddA e a -> a # product :: Num a => TwoFingerOddA e a -> a #
Traversable (TwoFingerOddA e) Source #
Methods traverse :: Applicative f => (a -> f b) -> TwoFingerOddA e a -> f (TwoFingerOddA e b) # sequenceA :: Applicative f => TwoFingerOddA e (f a) -> f (TwoFingerOddA e a) # mapM :: Monad m => (a -> m b) -> TwoFingerOddA e a -> m (TwoFingerOddA e b) # sequence :: Monad m => TwoFingerOddA e (m a) -> m (TwoFingerOddA e a) #
Eq e => Eq1 (TwoFingerOddA e) Source #
Methods liftEq :: (a -> b -> Bool) -> TwoFingerOddA e a -> TwoFingerOddA e b -> Bool #
Show e => Show1 (TwoFingerOddA e) Source #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> TwoFingerOddA e a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [TwoFingerOddA e a] -> ShowS #
Traversable1 (TwoFingerOddA e) Source #
Methods traverse1 :: Apply f => (a -> f b) -> TwoFingerOddA e a -> f (TwoFingerOddA e b) # sequence1 :: Apply f => TwoFingerOddA e (f b) -> f (TwoFingerOddA e b) #
Apply (TwoFingerOddA e) Source #
Methods (<.>) :: TwoFingerOddA e (a -> b) -> TwoFingerOddA e a -> TwoFingerOddA e b # (.>) :: TwoFingerOddA e a -> TwoFingerOddA e b -> TwoFingerOddA e b # (<.) :: TwoFingerOddA e a -> TwoFingerOddA e b -> TwoFingerOddA e a #
Bind (TwoFingerOddA e) Source #
Methods (>>-) :: TwoFingerOddA e a -> (a -> TwoFingerOddA e b) -> TwoFingerOddA e b # join :: TwoFingerOddA e (TwoFingerOddA e a) -> TwoFingerOddA e a #
Foldable1 (TwoFingerOddA e) Source #
Methods fold1 :: Semigroup m => TwoFingerOddA e m -> m # foldMap1 :: Semigroup m => (a -> m) -> TwoFingerOddA e a -> m # toNonEmpty :: TwoFingerOddA e a -> NonEmpty a #
(Eq e, Eq a) => Eq (TwoFingerOddA e a) Source #
Methods (==) :: TwoFingerOddA e a -> TwoFingerOddA e a -> Bool # (/=) :: TwoFingerOddA e a -> TwoFingerOddA e a -> Bool #
(Show e, Show a) => Show (TwoFingerOddA e a) Source #
Methods showsPrec :: Int -> TwoFingerOddA e a -> ShowS # show :: TwoFingerOddA e a -> String # showList :: [TwoFingerOddA e a] -> ShowS #
Generic (TwoFingerOddA e a) Source #
Associated Types type Rep (TwoFingerOddA e a) :: * -> * # Methods from :: TwoFingerOddA e a -> Rep (TwoFingerOddA e a) x # to :: Rep (TwoFingerOddA e a) x -> TwoFingerOddA e a #
Semigroup a => Semigroup (TwoFingerOddA e a) Source #	\(AnyOddA a) (AnyOddA b) (AnyOddA c) -> (a <> b) <> c == a <> (b <> c)
Methods (<>) :: TwoFingerOddA e a -> TwoFingerOddA e a -> TwoFingerOddA e a # sconcat :: NonEmpty (TwoFingerOddA e a) -> TwoFingerOddA e a # stimes :: Integral b => b -> TwoFingerOddA e a -> TwoFingerOddA e a #
(Monoid a, Semigroup a) => Monoid (TwoFingerOddA e a) Source #	\(AnyOddA a) -> a == mempty <> a \(AnyOddA a) -> a == a <> mempty
Methods mempty :: TwoFingerOddA e a # mappend :: TwoFingerOddA e a -> TwoFingerOddA e a -> TwoFingerOddA e a # mconcat :: [TwoFingerOddA e a] -> TwoFingerOddA e a #
(NFData e, NFData a) => NFData (TwoFingerOddA e a) Source #
Methods rnf :: TwoFingerOddA e a -> () #
type Rep (TwoFingerOddA e a) Source #
type Rep (TwoFingerOddA e a) = D1 (MetaData "TwoFingerOddA" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) (C1 (MetaCons "EmptyOddA" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) ((:+:) (C1 (MetaCons "SingleOddA" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))) (C1 (MetaCons "DeepOddA" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a)))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (TwoFingerOddA (Node e a) a))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))))))

firstOddA :: Functor f => (a -> f a) -> TwoFingerOddA e a -> f (TwoFingerOddA e a) Source #

Access the first a of a TwoFingerOddA e a. $O(1)$. This type is Lens' (TwoFingerOddA e a) a in disguise.

>>> view firstOddA (consOddA 3 True $ singletonOddA 15)
3

lastOddA :: Functor f => (a -> f a) -> TwoFingerOddA e a -> f (TwoFingerOddA e a) Source #

Access the last a of a TwoFingerOddA e a. $O(1)$. This type is Lens' (TwoFingerOddA e a) a in disguise.

>>> over lastOddA (+ 5) (consOddA 3 True $ singletonOddA 15)
consOddA 3 True (singletonOddA 20)

data TwoFingerOddE e a Source #

Isomorphic to e, (a, e)*

Constructors

SingleOddE e
DeepOddE !(Digit e a) (TwoFingerOddA (Node e a) a) !(Digit e a)

Instances

Eq2 TwoFingerOddE Source #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerOddE a c -> TwoFingerOddE b d -> Bool #
Show2 TwoFingerOddE Source #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> TwoFingerOddE a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [TwoFingerOddE a b] -> ShowS #
Bifunctor TwoFingerOddE Source #
Methods bimap :: (a -> b) -> (c -> d) -> TwoFingerOddE a c -> TwoFingerOddE b d # first :: (a -> b) -> TwoFingerOddE a c -> TwoFingerOddE b c # second :: (b -> c) -> TwoFingerOddE a b -> TwoFingerOddE a c #
Bitraversable TwoFingerOddE Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerOddE a b -> f (TwoFingerOddE c d) #
Bifoldable TwoFingerOddE Source #
Methods bifold :: Monoid m => TwoFingerOddE m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> TwoFingerOddE a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> TwoFingerOddE a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> TwoFingerOddE a b -> c #
Functor (TwoFingerOddE e) Source #
Methods fmap :: (a -> b) -> TwoFingerOddE e a -> TwoFingerOddE e b # (<$) :: a -> TwoFingerOddE e b -> TwoFingerOddE e a #
Foldable (TwoFingerOddE e) Source #
Methods fold :: Monoid m => TwoFingerOddE e m -> m # foldMap :: Monoid m => (a -> m) -> TwoFingerOddE e a -> m # foldr :: (a -> b -> b) -> b -> TwoFingerOddE e a -> b # foldr' :: (a -> b -> b) -> b -> TwoFingerOddE e a -> b # foldl :: (b -> a -> b) -> b -> TwoFingerOddE e a -> b # foldl' :: (b -> a -> b) -> b -> TwoFingerOddE e a -> b # foldr1 :: (a -> a -> a) -> TwoFingerOddE e a -> a # foldl1 :: (a -> a -> a) -> TwoFingerOddE e a -> a # toList :: TwoFingerOddE e a -> [a] # null :: TwoFingerOddE e a -> Bool # length :: TwoFingerOddE e a -> Int # elem :: Eq a => a -> TwoFingerOddE e a -> Bool # maximum :: Ord a => TwoFingerOddE e a -> a # minimum :: Ord a => TwoFingerOddE e a -> a # sum :: Num a => TwoFingerOddE e a -> a # product :: Num a => TwoFingerOddE e a -> a #
Traversable (TwoFingerOddE e) Source #
Methods traverse :: Applicative f => (a -> f b) -> TwoFingerOddE e a -> f (TwoFingerOddE e b) # sequenceA :: Applicative f => TwoFingerOddE e (f a) -> f (TwoFingerOddE e a) # mapM :: Monad m => (a -> m b) -> TwoFingerOddE e a -> m (TwoFingerOddE e b) # sequence :: Monad m => TwoFingerOddE e (m a) -> m (TwoFingerOddE e a) #
Eq e => Eq1 (TwoFingerOddE e) Source #
Methods liftEq :: (a -> b -> Bool) -> TwoFingerOddE e a -> TwoFingerOddE e b -> Bool #
Show e => Show1 (TwoFingerOddE e) Source #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> TwoFingerOddE e a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [TwoFingerOddE e a] -> ShowS #
(Eq e, Eq a) => Eq (TwoFingerOddE e a) Source #
Methods (==) :: TwoFingerOddE e a -> TwoFingerOddE e a -> Bool # (/=) :: TwoFingerOddE e a -> TwoFingerOddE e a -> Bool #
(Show e, Show a) => Show (TwoFingerOddE e a) Source #
Methods showsPrec :: Int -> TwoFingerOddE e a -> ShowS # show :: TwoFingerOddE e a -> String # showList :: [TwoFingerOddE e a] -> ShowS #
Generic (TwoFingerOddE e a) Source #
Associated Types type Rep (TwoFingerOddE e a) :: * -> * # Methods from :: TwoFingerOddE e a -> Rep (TwoFingerOddE e a) x # to :: Rep (TwoFingerOddE e a) x -> TwoFingerOddE e a #
(NFData e, NFData a) => NFData (TwoFingerOddE e a) Source #
Methods rnf :: TwoFingerOddE e a -> () #
type Rep (TwoFingerOddE e a) Source #
type Rep (TwoFingerOddE e a) = D1 (MetaData "TwoFingerOddE" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) (C1 (MetaCons "SingleOddE" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e))) (C1 (MetaCons "DeepOddE" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (TwoFingerOddA (Node e a) a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a)))))))

data TwoFingerEvenE e a Source #

Isomorphic to (e, a)*

Constructors

EmptyEvenE
SingleEvenE e a
DeepEvenE !(Digit e a) (TwoFingerOddA (Node e a) a) !(Digit e a) a

Instances

Eq2 TwoFingerEvenE Source #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerEvenE a c -> TwoFingerEvenE b d -> Bool #
Show2 TwoFingerEvenE Source #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> TwoFingerEvenE a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [TwoFingerEvenE a b] -> ShowS #
Bifunctor TwoFingerEvenE Source #
Methods bimap :: (a -> b) -> (c -> d) -> TwoFingerEvenE a c -> TwoFingerEvenE b d # first :: (a -> b) -> TwoFingerEvenE a c -> TwoFingerEvenE b c # second :: (b -> c) -> TwoFingerEvenE a b -> TwoFingerEvenE a c #
Bitraversable TwoFingerEvenE Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerEvenE a b -> f (TwoFingerEvenE c d) #
Bifoldable TwoFingerEvenE Source #
Methods bifold :: Monoid m => TwoFingerEvenE m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> TwoFingerEvenE a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> TwoFingerEvenE a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> TwoFingerEvenE a b -> c #
Functor (TwoFingerEvenE e) Source #
Methods fmap :: (a -> b) -> TwoFingerEvenE e a -> TwoFingerEvenE e b # (<$) :: a -> TwoFingerEvenE e b -> TwoFingerEvenE e a #
Foldable (TwoFingerEvenE e) Source #
Methods fold :: Monoid m => TwoFingerEvenE e m -> m # foldMap :: Monoid m => (a -> m) -> TwoFingerEvenE e a -> m # foldr :: (a -> b -> b) -> b -> TwoFingerEvenE e a -> b # foldr' :: (a -> b -> b) -> b -> TwoFingerEvenE e a -> b # foldl :: (b -> a -> b) -> b -> TwoFingerEvenE e a -> b # foldl' :: (b -> a -> b) -> b -> TwoFingerEvenE e a -> b # foldr1 :: (a -> a -> a) -> TwoFingerEvenE e a -> a # foldl1 :: (a -> a -> a) -> TwoFingerEvenE e a -> a # toList :: TwoFingerEvenE e a -> [a] # null :: TwoFingerEvenE e a -> Bool # length :: TwoFingerEvenE e a -> Int # elem :: Eq a => a -> TwoFingerEvenE e a -> Bool # maximum :: Ord a => TwoFingerEvenE e a -> a # minimum :: Ord a => TwoFingerEvenE e a -> a # sum :: Num a => TwoFingerEvenE e a -> a # product :: Num a => TwoFingerEvenE e a -> a #
Traversable (TwoFingerEvenE e) Source #
Methods traverse :: Applicative f => (a -> f b) -> TwoFingerEvenE e a -> f (TwoFingerEvenE e b) # sequenceA :: Applicative f => TwoFingerEvenE e (f a) -> f (TwoFingerEvenE e a) # mapM :: Monad m => (a -> m b) -> TwoFingerEvenE e a -> m (TwoFingerEvenE e b) # sequence :: Monad m => TwoFingerEvenE e (m a) -> m (TwoFingerEvenE e a) #
Eq e => Eq1 (TwoFingerEvenE e) Source #
Methods liftEq :: (a -> b -> Bool) -> TwoFingerEvenE e a -> TwoFingerEvenE e b -> Bool #
Show e => Show1 (TwoFingerEvenE e) Source #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> TwoFingerEvenE e a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [TwoFingerEvenE e a] -> ShowS #
Plus (TwoFingerEvenE e) Source #
Methods zero :: TwoFingerEvenE e a #
Alt (TwoFingerEvenE e) Source #
Methods (<!>) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> TwoFingerEvenE e a # some :: Applicative (TwoFingerEvenE e) => TwoFingerEvenE e a -> TwoFingerEvenE e [a] # many :: Applicative (TwoFingerEvenE e) => TwoFingerEvenE e a -> TwoFingerEvenE e [a] #
(Eq e, Eq a) => Eq (TwoFingerEvenE e a) Source #
Methods (==) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> Bool # (/=) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> Bool #
(Show e, Show a) => Show (TwoFingerEvenE e a) Source #
Methods showsPrec :: Int -> TwoFingerEvenE e a -> ShowS # show :: TwoFingerEvenE e a -> String # showList :: [TwoFingerEvenE e a] -> ShowS #
Generic (TwoFingerEvenE e a) Source #
Associated Types type Rep (TwoFingerEvenE e a) :: * -> * # Methods from :: TwoFingerEvenE e a -> Rep (TwoFingerEvenE e a) x # to :: Rep (TwoFingerEvenE e a) x -> TwoFingerEvenE e a #
Semigroup (TwoFingerEvenE e a) Source #	\(AnyEvenE a) (AnyEvenE b) (AnyEvenE c) -> (a <> b) <> c == a <> (b <> c)
Methods (<>) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> TwoFingerEvenE e a # sconcat :: NonEmpty (TwoFingerEvenE e a) -> TwoFingerEvenE e a # stimes :: Integral b => b -> TwoFingerEvenE e a -> TwoFingerEvenE e a #
Monoid (TwoFingerEvenE e a) Source #	\(AnyEvenE a) -> a == a <> mempty \(AnyEvenE a) -> a == mempty <> a
Methods mempty :: TwoFingerEvenE e a # mappend :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> TwoFingerEvenE e a # mconcat :: [TwoFingerEvenE e a] -> TwoFingerEvenE e a #
(NFData e, NFData a) => NFData (TwoFingerEvenE e a) Source #
Methods rnf :: TwoFingerEvenE e a -> () #
type Rep (TwoFingerEvenE e a) Source #
type Rep (TwoFingerEvenE e a) = D1 (MetaData "TwoFingerEvenE" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) (C1 (MetaCons "EmptyEvenE" PrefixI False) U1) ((:+:) (C1 (MetaCons "SingleEvenE" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))) (C1 (MetaCons "DeepEvenE" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (TwoFingerOddA (Node e a) a)))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))))))

data TwoFingerEvenA e a Source #

Isomorphic to (a, e)*

Constructors

EmptyEvenA
SingleEvenA a e
DeepEvenA a !(Digit e a) (TwoFingerOddA (Node e a) a) !(Digit e a)

Instances

Eq2 TwoFingerEvenA Source #
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerEvenA a c -> TwoFingerEvenA b d -> Bool #
Show2 TwoFingerEvenA Source #
Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> TwoFingerEvenA a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [TwoFingerEvenA a b] -> ShowS #
Bifunctor TwoFingerEvenA Source #
Methods bimap :: (a -> b) -> (c -> d) -> TwoFingerEvenA a c -> TwoFingerEvenA b d # first :: (a -> b) -> TwoFingerEvenA a c -> TwoFingerEvenA b c # second :: (b -> c) -> TwoFingerEvenA a b -> TwoFingerEvenA a c #
Bitraversable TwoFingerEvenA Source #
Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerEvenA a b -> f (TwoFingerEvenA c d) #
Bifoldable TwoFingerEvenA Source #
Methods bifold :: Monoid m => TwoFingerEvenA m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> TwoFingerEvenA a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> TwoFingerEvenA a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> TwoFingerEvenA a b -> c #
Functor (TwoFingerEvenA e) Source #
Methods fmap :: (a -> b) -> TwoFingerEvenA e a -> TwoFingerEvenA e b # (<$) :: a -> TwoFingerEvenA e b -> TwoFingerEvenA e a #
Foldable (TwoFingerEvenA e) Source #
Methods fold :: Monoid m => TwoFingerEvenA e m -> m # foldMap :: Monoid m => (a -> m) -> TwoFingerEvenA e a -> m # foldr :: (a -> b -> b) -> b -> TwoFingerEvenA e a -> b # foldr' :: (a -> b -> b) -> b -> TwoFingerEvenA e a -> b # foldl :: (b -> a -> b) -> b -> TwoFingerEvenA e a -> b # foldl' :: (b -> a -> b) -> b -> TwoFingerEvenA e a -> b # foldr1 :: (a -> a -> a) -> TwoFingerEvenA e a -> a # foldl1 :: (a -> a -> a) -> TwoFingerEvenA e a -> a # toList :: TwoFingerEvenA e a -> [a] # null :: TwoFingerEvenA e a -> Bool # length :: TwoFingerEvenA e a -> Int # elem :: Eq a => a -> TwoFingerEvenA e a -> Bool # maximum :: Ord a => TwoFingerEvenA e a -> a # minimum :: Ord a => TwoFingerEvenA e a -> a # sum :: Num a => TwoFingerEvenA e a -> a # product :: Num a => TwoFingerEvenA e a -> a #
Traversable (TwoFingerEvenA e) Source #
Methods traverse :: Applicative f => (a -> f b) -> TwoFingerEvenA e a -> f (TwoFingerEvenA e b) # sequenceA :: Applicative f => TwoFingerEvenA e (f a) -> f (TwoFingerEvenA e a) # mapM :: Monad m => (a -> m b) -> TwoFingerEvenA e a -> m (TwoFingerEvenA e b) # sequence :: Monad m => TwoFingerEvenA e (m a) -> m (TwoFingerEvenA e a) #
Eq e => Eq1 (TwoFingerEvenA e) Source #
Methods liftEq :: (a -> b -> Bool) -> TwoFingerEvenA e a -> TwoFingerEvenA e b -> Bool #
Show e => Show1 (TwoFingerEvenA e) Source #
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> TwoFingerEvenA e a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [TwoFingerEvenA e a] -> ShowS #
Plus (TwoFingerEvenA e) Source #
Methods zero :: TwoFingerEvenA e a #
Alt (TwoFingerEvenA e) Source #
Methods (<!>) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> TwoFingerEvenA e a # some :: Applicative (TwoFingerEvenA e) => TwoFingerEvenA e a -> TwoFingerEvenA e [a] # many :: Applicative (TwoFingerEvenA e) => TwoFingerEvenA e a -> TwoFingerEvenA e [a] #
(Eq e, Eq a) => Eq (TwoFingerEvenA e a) Source #
Methods (==) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> Bool # (/=) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> Bool #
(Show e, Show a) => Show (TwoFingerEvenA e a) Source #
Methods showsPrec :: Int -> TwoFingerEvenA e a -> ShowS # show :: TwoFingerEvenA e a -> String # showList :: [TwoFingerEvenA e a] -> ShowS #
Generic (TwoFingerEvenA e a) Source #
Associated Types type Rep (TwoFingerEvenA e a) :: * -> * # Methods from :: TwoFingerEvenA e a -> Rep (TwoFingerEvenA e a) x # to :: Rep (TwoFingerEvenA e a) x -> TwoFingerEvenA e a #
Semigroup (TwoFingerEvenA e a) Source #	\(AnyEvenA a) (AnyEvenA b) (AnyEvenA c) -> (a <> b) <> c == a <> (b <> c)
Methods (<>) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> TwoFingerEvenA e a # sconcat :: NonEmpty (TwoFingerEvenA e a) -> TwoFingerEvenA e a # stimes :: Integral b => b -> TwoFingerEvenA e a -> TwoFingerEvenA e a #
Monoid (TwoFingerEvenA e a) Source #	\(AnyEvenA a) -> a == a <> mempty \(AnyEvenA a) -> a == mempty <> a
Methods mempty :: TwoFingerEvenA e a # mappend :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> TwoFingerEvenA e a # mconcat :: [TwoFingerEvenA e a] -> TwoFingerEvenA e a #
(NFData e, NFData a) => NFData (TwoFingerEvenA e a) Source #
Methods rnf :: TwoFingerEvenA e a -> () #
type Rep (TwoFingerEvenA e a) Source #
type Rep (TwoFingerEvenA e a) = D1 (MetaData "TwoFingerEvenA" "Q4C12.TwoFinger.Internal" "q4c12-twofinger-0.0.0.1-8syHtPdDjE8313bgi8LFJc" False) ((:+:) (C1 (MetaCons "EmptyEvenA" PrefixI False) U1) ((:+:) (C1 (MetaCons "SingleEvenA" PrefixI False) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 e)))) (C1 (MetaCons "DeepEvenA" PrefixI False) ((::) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a)))) ((::) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (TwoFingerOddA (Node e a) a))) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit e a))))))))

Digit operations.

digitToTree :: Digit e a -> TwoFingerOddE e a Source #

digitCons :: e -> a -> Digit e a -> Either (Digit e a, a, Node e a) (Digit e a) Source #

digitSnoc :: Digit e a -> a -> e -> Either (Node e a, a, Digit e a) (Digit e a) Source #

digitUncons :: Digit e a -> (e, Maybe (a, Digit e a)) Source #

digitUnsnoc :: Digit e a -> (Maybe (Digit e a, a), e) Source #

Node operations.

nodeToDigit :: Node e a -> Digit e a Source #

Tree rotations

rotl :: TwoFingerOddA (Node e a) a -> Digit e a -> TwoFingerEvenA e a Source #

rotr :: Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerEvenE e a Source #

(Un)conses/snocs for TwoFingerOddA.

consOddA :: a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

snocOddA :: TwoFingerOddA e a -> e -> a -> TwoFingerOddA e a Source #

unconsOddA :: TwoFingerOddA e a -> Either a ((a, e), TwoFingerOddA e a) Source #

unsnocOddA :: TwoFingerOddA e a -> Either a (TwoFingerOddA e a, (e, a)) Source #

halfconsOddA :: e -> TwoFingerOddA e a -> TwoFingerEvenE e a Source #

$O(\log n)$ worst case. Inverse: halfunconsEvenE

\e (AnyOddA as) -> halfunconsEvenE (halfconsOddA e as) == Just (e, as)

halfsnocOddA :: TwoFingerOddA e a -> e -> TwoFingerEvenA e a Source #

$O(\log n)$ worst case. Inverse: halfunsnocEvenA

\(AnyOddA as) e -> halfunsnocEvenA (halfsnocOddA as e) == Just (as, e)

halfunconsOddA :: TwoFingerOddA e a -> (a, TwoFingerEvenE e a) Source #

$O(1)$ worst case. Inverse: halfconsEvenE

\(AnyOddA as) -> as == uncurry halfconsEvenE (halfunconsOddA as)

halfunsnocOddA :: TwoFingerOddA e a -> (TwoFingerEvenA e a, a) Source #

$O(1)$ worst case. Inverse: halfsnocOddA

\(AnyOddA as) -> as == uncurry halfsnocEvenA (halfunsnocOddA as)

(Un)conses/snocs for TwoFingerOddE.

consOddE :: e -> a -> TwoFingerOddE e a -> TwoFingerOddE e a Source #

snocOddE :: TwoFingerOddE e a -> a -> e -> TwoFingerOddE e a Source #

unconsOddE :: TwoFingerOddE e a -> Either e ((e, a), TwoFingerOddE e a) Source #

unsnocOddE :: TwoFingerOddE e a -> Either e (TwoFingerOddE e a, (a, e)) Source #

halfconsOddE :: a -> TwoFingerOddE e a -> TwoFingerEvenA e a Source #

$O(1)$ worst case. Inverse: halfunconsEvenA

\a (AnyOddE as) -> halfunconsEvenA (halfconsOddE a as) == Just (a, as)

halfsnocOddE :: TwoFingerOddE e a -> a -> TwoFingerEvenE e a Source #

$O(1)$ worst case. Inverse: halfunsnocEvenE

\(AnyOddE as) a -> halfunsnocEvenE (halfsnocOddE as a) == Just (as, a)

halfunconsOddE :: TwoFingerOddE e a -> (e, TwoFingerEvenA e a) Source #

$O(\log n)$ worst case. Inverse: halfconsEvenA

\(AnyOddE as) -> as == uncurry halfconsEvenA (halfunconsOddE as)

halfunsnocOddE :: TwoFingerOddE e a -> (TwoFingerEvenE e a, e) Source #

$O(\log n)$ worst case. Inverse: halfsnocEvenE

\(AnyOddE as) -> as == uncurry halfsnocEvenE (halfunsnocOddE as)

(Un)conses/snocs for TwoFingerEvenE.

consEvenE :: e -> a -> TwoFingerEvenE e a -> TwoFingerEvenE e a Source #

snocEvenE :: TwoFingerEvenE e a -> e -> a -> TwoFingerEvenE e a Source #

unconsEvenE :: TwoFingerEvenE e a -> Maybe ((e, a), TwoFingerEvenE e a) Source #

unsnocEvenE :: TwoFingerEvenE e a -> Maybe (TwoFingerEvenE e a, (e, a)) Source #

halfconsEvenE :: a -> TwoFingerEvenE e a -> TwoFingerOddA e a Source #

$O(1)$ worst case. Inverse: halfunconsOddA

\a (AnyEvenE as) -> halfunconsOddA (halfconsEvenE a as) == (a, as)

halfsnocEvenE :: TwoFingerEvenE e a -> e -> TwoFingerOddE e a Source #

$O(\log n)$ worst case. Inverse: halfunsnocOddE.

\(AnyEvenE as) e -> halfunsnocOddE (halfsnocEvenE as e) == (as, e)

halfunconsEvenE :: TwoFingerEvenE e a -> Maybe (e, TwoFingerOddA e a) Source #

$O(\log n)$ worst case. Inverse: halfconsOddA.

\(AnyEvenE as) -> as == maybe mempty (uncurry halfconsOddA) (halfunconsEvenE as)

halfunsnocEvenE :: TwoFingerEvenE e a -> Maybe (TwoFingerOddE e a, a) Source #

$O(1)$ worst case. Inverse: halfsnocOddE.

\(AnyEvenE as) -> as == maybe mempty (uncurry halfsnocOddE) (halfunsnocEvenE as)

(Un)conses/snocs for TwoFingerEvenA.

consEvenA :: a -> e -> TwoFingerEvenA e a -> TwoFingerEvenA e a Source #

snocEvenA :: TwoFingerEvenA e a -> a -> e -> TwoFingerEvenA e a Source #

unconsEvenA :: TwoFingerEvenA e a -> Maybe ((a, e), TwoFingerEvenA e a) Source #

unsnocEvenA :: TwoFingerEvenA e a -> Maybe (TwoFingerEvenA e a, (a, e)) Source #

halfconsEvenA :: e -> TwoFingerEvenA e a -> TwoFingerOddE e a Source #

$O(\log n)$ worst case. Inverse: halfunconsOddE.

\e (AnyEvenA as) -> halfunconsOddE (halfconsEvenA e as) == (e, as)

halfsnocEvenA :: TwoFingerEvenA e a -> a -> TwoFingerOddA e a Source #

$O(1)$ worst case. Inverse: halfunsnocOddA.

\(AnyEvenA as) a -> halfunsnocOddA (halfsnocEvenA as a) == (as, a)

halfunconsEvenA :: TwoFingerEvenA e a -> Maybe (a, TwoFingerOddE e a) Source #

$O(1)$ worst case. Inverse: halfconsOddE.

\(AnyEvenA as) -> as == maybe mempty (uncurry halfconsOddE) (halfunconsEvenA as)

halfunsnocEvenA :: TwoFingerEvenA e a -> Maybe (TwoFingerOddA e a, e) Source #

$O(\log n)$ worst case. Inverse: halfsnocOddA.

\(AnyEvenA as) -> as == maybe mempty (uncurry halfsnocOddA) (halfunsnocEvenA as)

Monad and Applicative instances, and related operations

joinOddA :: TwoFingerOddA (TwoFingerOddE e a) (TwoFingerOddA e a) -> TwoFingerOddA e a Source #

joinOddE :: TwoFingerOddE (TwoFingerOddE e a) (TwoFingerOddA e a) -> TwoFingerOddE e a Source #

joinEvenA :: TwoFingerEvenA (TwoFingerOddE e a) (TwoFingerOddA e a) -> TwoFingerEvenA e a Source #

joinEvenE :: TwoFingerEvenE (TwoFingerOddE e a) (TwoFingerOddA e a) -> TwoFingerEvenE e a Source #

Construction and deconstruction of TwoFingerOddA.

singletonOddA :: a -> TwoFingerOddA e a Source #

unitOddA :: (Monoid a, Semigroup a) => e -> TwoFingerOddA e a Source #

Surrounds the argument with mempty.

>>> unitOddA 3 :: TwoFingerOddA Int String
consOddA "" 3 (singletonOddA "")

onlyOddA :: TwoFingerOddA e a -> Maybe a Source #

>>> onlyOddA (singletonOddA "Hello!")
Just "Hello!"
>>> onlyOddA (consOddA True 3 $ singletonOddA False)
Nothing

interleavingOddA :: e -> NonEmpty a -> TwoFingerOddA e a Source #

>>> interleavingOddA "sep" (3 :| [4, 5])
consOddA 3 "sep" (consOddA 4 "sep" (singletonOddA 5))

Construction of TwoFingerOddE

singletonOddE :: e -> TwoFingerOddE e a Source #

Concatenation of TwoFingerOddA.

appendOddA0 :: Semigroup a => TwoFingerOddA e a -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

addDigits0 :: TwoFingerOddA (Node e a) a -> Digit e a -> a -> Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerOddA (Node e a) a Source #

appendOddA1 :: TwoFingerOddA e a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

addDigits1 :: TwoFingerOddA (Node e a) a -> Digit e a -> a -> e -> a -> Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerOddA (Node e a) a Source #

appendOddA2 :: TwoFingerOddA e a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

addDigits2 :: TwoFingerOddA (Node e a) a -> Digit e a -> a -> e -> a -> e -> a -> Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerOddA (Node e a) a Source #

appendOddA3 :: TwoFingerOddA e a -> e -> a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

addDigits3 :: TwoFingerOddA (Node e a) a -> Digit e a -> a -> e -> a -> e -> a -> e -> a -> Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerOddA (Node e a) a Source #

appendOddA4 :: TwoFingerOddA e a -> e -> a -> e -> a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

addDigits4 :: TwoFingerOddA (Node e a) a -> Digit e a -> a -> e -> a -> e -> a -> e -> a -> e -> a -> Digit e a -> TwoFingerOddA (Node e a) a -> TwoFingerOddA (Node e a) a Source #

Concatenation of TwoFingerEvenE.

appendEvenE :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> TwoFingerEvenE e a Source #

Concatenation of TwoFingerEvenA.

appendEvenA :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> TwoFingerEvenA e a Source #

Monoid actions

appendOddAEvenE :: TwoFingerOddA e a -> TwoFingerEvenE e a -> TwoFingerOddA e a Source #

\(AnyOddA a) -> a == appendOddAEvenE a mempty

appendEvenAOddA :: TwoFingerEvenA e a -> TwoFingerOddA e a -> TwoFingerOddA e a Source #

\(AnyOddA a) -> a == appendEvenAOddA mempty a

appendOddAOddE :: TwoFingerOddA e a -> TwoFingerOddE e a -> TwoFingerEvenA e a Source #

appendOddEOddA :: TwoFingerOddE e a -> TwoFingerOddA e a -> TwoFingerEvenE e a Source #

appendOddEEvenA :: TwoFingerOddE e a -> TwoFingerEvenA e a -> TwoFingerOddE e a Source #

\(AnyOddE a) -> a == appendOddEEvenA a mempty

appendEvenEOddE :: TwoFingerEvenE e a -> TwoFingerOddE e a -> TwoFingerOddE e a Source #

\(AnyOddE a) -> a == appendEvenEOddE mempty a

QuickCheck stuff.

genDigit :: Gen e -> Gen a -> Gen (Digit e a) Source #

genNode :: Gen e -> Gen a -> Gen (Node e a) Source #

genOddA :: Gen e -> Gen a -> Int -> Gen (TwoFingerOddA e a) Source #

The Int parameter is expontential size: for a value $n$, the generated tree will have (slightly more than) $2^n$ to $3^n$ elements.

shrinkOddA :: TwoFingerOddA e a -> [TwoFingerOddA e a] Source #

shrinkOddE :: TwoFingerOddE e a -> [TwoFingerOddE e a] Source #

shrinkEvenA :: TwoFingerEvenA e a -> [TwoFingerEvenA e a] Source #

shrinkEvenE :: TwoFingerEvenE e a -> [TwoFingerEvenE e a] Source #

newtype AnyOddA Source #

Constructors

AnyOddA
Fields getAnyOddA :: TwoFingerOddA Int [Int]

Instances

Show AnyOddA Source #
Methods showsPrec :: Int -> AnyOddA -> ShowS # show :: AnyOddA -> String # showList :: [AnyOddA] -> ShowS #
Arbitrary AnyOddA Source #
Methods arbitrary :: Gen AnyOddA # shrink :: AnyOddA -> [AnyOddA] #

newtype AnyOddE Source #

Constructors

AnyOddE
Fields getAnyOddE :: TwoFingerOddE Int [Int]

Instances

Show AnyOddE Source #
Methods showsPrec :: Int -> AnyOddE -> ShowS # show :: AnyOddE -> String # showList :: [AnyOddE] -> ShowS #
Arbitrary AnyOddE Source #
Methods arbitrary :: Gen AnyOddE # shrink :: AnyOddE -> [AnyOddE] #

newtype AnyEvenA Source #

Constructors

AnyEvenA
Fields getAnyEvenA :: TwoFingerEvenA Int [Int]

Instances

Show AnyEvenA Source #
Methods showsPrec :: Int -> AnyEvenA -> ShowS # show :: AnyEvenA -> String # showList :: [AnyEvenA] -> ShowS #
Arbitrary AnyEvenA Source #
Methods arbitrary :: Gen AnyEvenA # shrink :: AnyEvenA -> [AnyEvenA] #

newtype AnyEvenE Source #

Constructors

AnyEvenE
Fields getAnyEvenE :: TwoFingerEvenE Int [Int]

Instances

Show AnyEvenE Source #
Methods showsPrec :: Int -> AnyEvenE -> ShowS # show :: AnyEvenE -> String # showList :: [AnyEvenE] -> ShowS #
Arbitrary AnyEvenE Source #
Methods arbitrary :: Gen AnyEvenE # shrink :: AnyEvenE -> [AnyEvenE] #

Aligning/zipping.

alignLeftOddAOddA :: TwoFingerOddA e a -> TwoFingerOddA e' a' -> (TwoFingerOddA (e, e') (a, a'), Either (TwoFingerEvenE e a) (TwoFingerEvenE e' a')) Source #

Align two TwoFingerOddA sequences elementwise, and return the excess remainder.

>>> alignLeftOddAOddA (consOddA 'a' 1 $ consOddA 'b' 2 $ singletonOddA 'c') (consOddA "foo" 10 $ singletonOddA "bar")
(consOddA ('a',"foo") (1,10) (singletonOddA ('b',"bar")),Left (consEvenE 2 'c' mempty))

>>> alignLeftOddAOddA (consOddA 'a' 1 $ singletonOddA 'b') (consOddA "foo" 10 $ consOddA "bar" 20 $ singletonOddA "baz")
(consOddA ('a',"foo") (1,10) (singletonOddA ('b',"bar")),Right (consEvenE 20 "baz" mempty))

\(AnyOddA as) (AnyOddA bs) -> let { (aligned, rest) = alignLeftOddAOddA as bs ; as' = appendOddAEvenE (bimap fst fst aligned) (either id (const mempty) rest) ; bs' = appendOddAEvenE (bimap snd snd aligned) (either (const mempty) id rest) } in as == as' && bs == bs'

alignLeftOddAEvenA :: TwoFingerOddA e a -> TwoFingerEvenA e' a' -> Either (TwoFingerEvenA (e, e') (a, a'), TwoFingerOddA e a) (TwoFingerOddA (e, e') (a, a'), TwoFingerOddE e' a') Source #

>>> alignLeftOddAEvenA (consOddA 'a' 1 $ consOddA 'b' 2 $ singletonOddA 'c') (consEvenA "foo" 10 mempty)
Left (consEvenA ('a',"foo") (1,10) mempty,consOddA 'b' 2 (singletonOddA 'c'))

>>> alignLeftOddAEvenA (consOddA 'a' 1 $ singletonOddA 'b') (consEvenA "foo" 10 $ consEvenA "bar" 20 $ consEvenA "baz" 30 mempty)
Right (consOddA ('a',"foo") (1,10) (singletonOddA ('b',"bar")),consOddE 20 "baz" (singletonOddE 30))

\(AnyOddA as) (AnyEvenA bs) -> let { (as', bs') = case alignLeftOddAEvenA as bs of { Left (aligned, rest) -> (appendEvenAOddA (bimap fst fst aligned) rest, bimap snd snd aligned) ; Right (aligned, rest) -> (bimap fst fst aligned, appendOddAOddE (bimap snd snd aligned) rest) } } in as == as' && bs == bs'

alignLeftEvenAEvenA :: TwoFingerEvenA e a -> TwoFingerEvenA e' a' -> (TwoFingerEvenA (e, e') (a, a'), Either (TwoFingerEvenA e a) (TwoFingerEvenA e' a')) Source #

alignLeftOddEOddE :: TwoFingerOddE e a -> TwoFingerOddE e' a' -> (TwoFingerOddE (e, e') (a, a'), Either (TwoFingerEvenA e a) (TwoFingerEvenA e' a')) Source #

>>> alignLeftOddEOddE (consOddE 'a' 1 $ consOddE 'b' 2 $ singletonOddE 'c') (consOddE "foo" 10 $ singletonOddE "bar")
(consOddE ('a',"foo") (1,10) (singletonOddE ('b',"bar")),Left (consEvenA 2 'c' mempty))

>>> alignLeftOddEOddE (consOddE 'a' 1 $ singletonOddE 'b') (consOddE "foo" 10 $ consOddE "bar" 20 $ singletonOddE "baz")
(consOddE ('a',"foo") (1,10) (singletonOddE ('b',"bar")),Right (consEvenA 20 "baz" mempty))

\(AnyOddE as) (AnyOddE bs) -> let { (aligned, rest) = alignLeftOddEOddE as bs ; as' = appendOddEEvenA (bimap fst fst aligned) (either id (const mempty) rest) ; bs' = appendOddEEvenA (bimap snd snd aligned) (either (const mempty) id rest) } in as == as' && bs == bs'

alignLeftOddEEvenE :: TwoFingerOddE e a -> TwoFingerEvenE e' a' -> Either (TwoFingerEvenE (e, e') (a, a'), TwoFingerOddE e a) (TwoFingerOddE (e, e') (a, a'), TwoFingerOddA e' a') Source #

\(AnyOddE as) (AnyEvenE bs) -> let { (as', bs') = case alignLeftOddEEvenE as bs of { Left (aligned, rest) -> (appendEvenEOddE (bimap fst fst aligned) rest, bimap snd snd aligned) ; Right (aligned, rest) -> (bimap fst fst aligned, appendOddEOddA (bimap snd snd aligned) rest) } } in as == as' && bs == bs'

alignLeftEvenEEvenE :: TwoFingerEvenE e a -> TwoFingerEvenE e' a' -> (TwoFingerEvenE (e, e') (a, a'), Either (TwoFingerEvenE e a) (TwoFingerEvenE e' a')) Source #

Creating infinite sequences.

takeNodeLeft :: (Stream a -> es -> (e, Stream a, es)) -> Stream a -> es -> (Node e a, Stream a, es) Source #

takeNodeRight :: (es -> Stream a -> (e, es, Stream a)) -> es -> Stream a -> (Node e a, es, Stream a) Source #

infiniteOddA' :: (Stream a -> Stream e -> (Node e' a, Stream a, Stream e)) -> (Stream e -> Stream a -> (Node e' a, Stream e, Stream a)) -> Stream a -> Stream e -> Stream e -> Stream a -> TwoFingerOddA e' a Source #

repeatOddA :: a -> e -> TwoFingerOddA e a Source #

Infinitely repeat the given a and e.

\(AnyOddA as) -> as == bimap (uncurry ($)) (uncurry ($)) (fst $ alignLeftOddAOddA (repeatOddA id id) as)

\(AnyEvenA as) -> either ((as ==) . bimap (uncurry ($)) (uncurry ($)) . fst) (const False) (alignLeftOddAEvenA (repeatOddA id id) as)

infiniteOddA :: Stream a -> Stream e -> Stream e -> Stream a -> TwoFingerOddA e a Source #

From streams of leftward a, leftward e, rightward e and rightward a, build an infinite TwoFingerOddA.

>>> let infinite = infiniteOddA (Stream.iterate (+ 1) 0) (Stream.iterate (+ 1) 10) (Stream.iterate (+ 1) 20) (Stream.iterate (+ 1) 30)
>>> take 5 $ unfoldr (hush . unconsOddA) infinite
[(0,10),(1,11),(2,12),(3,13),(4,14)]
>>> take 5 $ unfoldr (fmap swap . hush . unsnocOddA) infinite
[(20,30),(21,31),(22,32),(23,33),(24,34)]

repeatOddE :: e -> a -> TwoFingerOddE e a Source #

Infinitely repeat the given a and e.

\(AnyOddE as) -> as == bimap (uncurry ($)) (uncurry ($)) (fst $ alignLeftOddEOddE (repeatOddE id id) as)

\(AnyEvenE as) -> either ((==) as . bimap (uncurry ($)) (uncurry ($)) . fst) (const False) $ alignLeftOddEEvenE (repeatOddE id id) as

infiniteOddE :: Stream e -> Stream a -> Stream a -> Stream e -> TwoFingerOddE e a Source #

>>> let infinite = infiniteOddE (Stream.iterate (+ 1) 0) (Stream.iterate (+ 1) 10) (Stream.iterate (+ 1) 20) (Stream.iterate (+ 1) 30)
>>> take 5 $ unfoldr (hush . unconsOddE) infinite
[(0,10),(1,11),(2,12),(3,13),(4,14)]
>>> take 5 $ unfoldr (fmap swap . hush . unsnocOddE) infinite
[(20,30),(21,31),(22,32),(23,33),(24,34)]

repeatEvenA :: a -> e -> TwoFingerEvenA e a Source #

Infinitely repeat the given a and e.

\(AnyEvenA as) -> as == bimap (uncurry ($)) (uncurry ($)) (fst $ alignLeftEvenAEvenA (repeatEvenA id id) as)

\(AnyOddA as) -> either (const False) ((==) as . bimap (uncurry $ flip ($)) (uncurry $ flip ($)) . fst) $ alignLeftOddAEvenA as (repeatEvenA id id)

infiniteEvenA :: Stream a -> Stream e -> Stream a -> Stream e -> TwoFingerEvenA e a Source #

>>> let infinite = infiniteEvenA (Stream.iterate (+ 1) 0) (Stream.iterate (+ 1) 10) (Stream.iterate (+ 1) 20) (Stream.iterate (+ 1) 30)
>>> take 5 $ unfoldr unconsEvenA infinite
[(0,10),(1,11),(2,12),(3,13),(4,14)]
>>> take 5 $ unfoldr (fmap swap . unsnocEvenA) infinite
[(20,30),(21,31),(22,32),(23,33),(24,34)]

repeatEvenE :: e -> a -> TwoFingerEvenE e a Source #

\(AnyEvenE as) -> as == bimap (uncurry ($)) (uncurry ($)) (fst $ alignLeftEvenEEvenE (repeatEvenE id id) as)

\(AnyOddE as) -> either (const False) ((==) as . bimap (uncurry $ flip ($)) (uncurry $ flip ($)) . fst) $ alignLeftOddEEvenE as (repeatEvenE id id)

infiniteEvenE :: Stream e -> Stream a -> Stream e -> Stream a -> TwoFingerEvenE e a Source #

>>> let infinite = infiniteEvenE (Stream.iterate (+ 1) 0) (Stream.iterate (+ 1) 10) (Stream.iterate (+ 1) 20) (Stream.iterate (+ 1) 30)
>>> take 5 $ unfoldr unconsEvenE infinite
[(0,10),(1,11),(2,12),(3,13),(4,14)]
>>> take 5 $ unfoldr (fmap swap . unsnocEvenE) infinite
[(20,30),(21,31),(22,32),(23,33),(24,34)]