Q4C12.TwoFinger.Internal

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.)

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

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

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

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

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

data Digit e a

Constructors

One e

Two e a e

Three e a e a e

Four e a e a e a e

Instances

Bifunctor Digit

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Digit a b -> f (Digit c d)

Bifoldable Digit

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

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

Methods

bifold1 :: Semigroup m => Digit m m -> m

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Digit a b -> m

Functor (Digit e)

Methods

fmap :: (a -> b) -> Digit e a -> Digit e b

(<$) :: a -> Digit e b -> Digit e a

Foldable (Digit e)

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)

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)

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)

Methods

rnf :: Digit e a -> ()

type Rep (Digit e a)

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

Constructors

Node2 e a e

Node3 e a e a e

Instances

Bifunctor Node

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Node a b -> f (Node c d)

Bifoldable Node

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

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

Methods

bifold1 :: Semigroup m => Node m m -> m

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Node a b -> m

Functor (Node e)

Methods

fmap :: (a -> b) -> Node e a -> Node e b

(<$) :: a -> Node e b -> Node e a

Foldable (Node e)

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)

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)

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)

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)

Methods

(==) :: Node e a -> Node e a -> Bool

(/=) :: Node e a -> Node e a -> Bool

Generic (Node e a)

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)

Methods

rnf :: Node e a -> ()

type Rep (Node e a)

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

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

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerOddA a c -> TwoFingerOddA b d -> Bool

Show2 TwoFingerOddA

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

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerOddA a b -> f (TwoFingerOddA c d)

Bifoldable TwoFingerOddA

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

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

Methods

bifold1 :: Semigroup m => TwoFingerOddA m m -> m

bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> TwoFingerOddA a b -> m

Monad (TwoFingerOddA e)

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)

Methods

fmap :: (a -> b) -> TwoFingerOddA e a -> TwoFingerOddA e b

(<$) :: a -> TwoFingerOddA e b -> TwoFingerOddA e a

Applicative (TwoFingerOddA e)

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)

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)

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)

Methods

liftEq :: (a -> b -> Bool) -> TwoFingerOddA e a -> TwoFingerOddA e b -> Bool

Show e => Show1 (TwoFingerOddA e)

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)

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)

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)

Methods

(>>-) :: TwoFingerOddA e a -> (a -> TwoFingerOddA e b) -> TwoFingerOddA e b

join :: TwoFingerOddA e (TwoFingerOddA e a) -> TwoFingerOddA e a

Foldable1 (TwoFingerOddA e)

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)

Methods

(==) :: TwoFingerOddA e a -> TwoFingerOddA e a -> Bool

(/=) :: TwoFingerOddA e a -> TwoFingerOddA e a -> Bool

(Show e, Show a) => Show (TwoFingerOddA e a)

Methods

showsPrec :: Int -> TwoFingerOddA e a -> ShowS

show :: TwoFingerOddA e a -> String

showList :: [TwoFingerOddA e a] -> ShowS

Generic (TwoFingerOddA e a)

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)

\(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)

\(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)

Methods

rnf :: TwoFingerOddA e a -> ()

type Rep (TwoFingerOddA e a)

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)

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)

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

Isomorphic to e, (a, e)*

Constructors

SingleOddE e

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

Instances

Eq2 TwoFingerOddE

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerOddE a c -> TwoFingerOddE b d -> Bool

Show2 TwoFingerOddE

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

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerOddE a b -> f (TwoFingerOddE c d)

Bifoldable TwoFingerOddE

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)

Methods

fmap :: (a -> b) -> TwoFingerOddE e a -> TwoFingerOddE e b

(<$) :: a -> TwoFingerOddE e b -> TwoFingerOddE e a

Foldable (TwoFingerOddE e)

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)

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)

Methods

liftEq :: (a -> b -> Bool) -> TwoFingerOddE e a -> TwoFingerOddE e b -> Bool

Show e => Show1 (TwoFingerOddE e)

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)

Methods

(==) :: TwoFingerOddE e a -> TwoFingerOddE e a -> Bool

(/=) :: TwoFingerOddE e a -> TwoFingerOddE e a -> Bool

(Show e, Show a) => Show (TwoFingerOddE e a)

Methods

showsPrec :: Int -> TwoFingerOddE e a -> ShowS

show :: TwoFingerOddE e a -> String

showList :: [TwoFingerOddE e a] -> ShowS

Generic (TwoFingerOddE e a)

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)

Methods

rnf :: TwoFingerOddE e a -> ()

type Rep (TwoFingerOddE e a)

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

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

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerEvenE a c -> TwoFingerEvenE b d -> Bool

Show2 TwoFingerEvenE

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

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerEvenE a b -> f (TwoFingerEvenE c d)

Bifoldable TwoFingerEvenE

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)

Methods

fmap :: (a -> b) -> TwoFingerEvenE e a -> TwoFingerEvenE e b

(<$) :: a -> TwoFingerEvenE e b -> TwoFingerEvenE e a

Foldable (TwoFingerEvenE e)

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)

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)

Methods

liftEq :: (a -> b -> Bool) -> TwoFingerEvenE e a -> TwoFingerEvenE e b -> Bool

Show e => Show1 (TwoFingerEvenE e)

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)

Methods

zero :: TwoFingerEvenE e a

Alt (TwoFingerEvenE e)

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)

Methods

(==) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> Bool

(/=) :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> Bool

(Show e, Show a) => Show (TwoFingerEvenE e a)

Methods

showsPrec :: Int -> TwoFingerEvenE e a -> ShowS

show :: TwoFingerEvenE e a -> String

showList :: [TwoFingerEvenE e a] -> ShowS

Generic (TwoFingerEvenE e a)

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)

\(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)

\(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)

Methods

rnf :: TwoFingerEvenE e a -> ()

type Rep (TwoFingerEvenE e a)

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

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

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> TwoFingerEvenA a c -> TwoFingerEvenA b d -> Bool

Show2 TwoFingerEvenA

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

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

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> TwoFingerEvenA a b -> f (TwoFingerEvenA c d)

Bifoldable TwoFingerEvenA

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)

Methods

fmap :: (a -> b) -> TwoFingerEvenA e a -> TwoFingerEvenA e b

(<$) :: a -> TwoFingerEvenA e b -> TwoFingerEvenA e a

Foldable (TwoFingerEvenA e)

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)

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)

Methods

liftEq :: (a -> b -> Bool) -> TwoFingerEvenA e a -> TwoFingerEvenA e b -> Bool

Show e => Show1 (TwoFingerEvenA e)

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)

Methods

zero :: TwoFingerEvenA e a

Alt (TwoFingerEvenA e)

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)

Methods

(==) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> Bool

(/=) :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> Bool

(Show e, Show a) => Show (TwoFingerEvenA e a)

Methods

showsPrec :: Int -> TwoFingerEvenA e a -> ShowS

show :: TwoFingerEvenA e a -> String

showList :: [TwoFingerEvenA e a] -> ShowS

Generic (TwoFingerEvenA e a)

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)

\(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)

\(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)

Methods

rnf :: TwoFingerEvenA e a -> ()

type Rep (TwoFingerEvenA e a)

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

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

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

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

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

Node operations.

nodeToDigit :: Node e a -> Digit e a

Tree rotations

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

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

(Un)conses/snocs for TwoFingerOddA.

consOddA :: a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a

snocOddA :: TwoFingerOddA e a -> e -> a -> TwoFingerOddA e a

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

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

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

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

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

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

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

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

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

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

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

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

\(O(1)\) 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

snocOddE :: TwoFingerOddE e a -> a -> e -> TwoFingerOddE e a

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

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

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

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

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

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

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

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

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

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

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

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

\(O(\log n)\) 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

snocEvenE :: TwoFingerEvenE e a -> e -> a -> TwoFingerEvenE e a

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

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

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

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

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

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

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

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

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

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

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

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

\(O(1)\) 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

snocEvenA :: TwoFingerEvenA e a -> a -> e -> TwoFingerEvenA e a

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

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

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

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

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

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

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

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

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

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

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

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

\(O(\log n)\) 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

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

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

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

Construction and deconstruction of TwoFingerOddA.

singletonOddA :: a -> TwoFingerOddA e a

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

Surrounds the argument with mempty.

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

onlyOddA :: TwoFingerOddA e a -> Maybe a

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

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

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

Construction of TwoFingerOddE

singletonOddE :: e -> TwoFingerOddE e a

Concatenation of TwoFingerOddA.

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

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

appendOddA1 :: TwoFingerOddA e a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a

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

appendOddA2 :: TwoFingerOddA e a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a

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

appendOddA3 :: TwoFingerOddA e a -> e -> a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a

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

appendOddA4 :: TwoFingerOddA e a -> e -> a -> e -> a -> e -> a -> e -> TwoFingerOddA e a -> TwoFingerOddA e a

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

Concatenation of TwoFingerEvenE.

appendEvenE :: TwoFingerEvenE e a -> TwoFingerEvenE e a -> TwoFingerEvenE e a

Concatenation of TwoFingerEvenA.

appendEvenA :: TwoFingerEvenA e a -> TwoFingerEvenA e a -> TwoFingerEvenA e a

Monoid actions

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

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

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

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

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

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

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

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

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

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

QuickCheck stuff.

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

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

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

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]

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

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

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

newtype AnyOddA

Constructors

AnyOddA

Fields

• getAnyOddA :: TwoFingerOddA Int [Int]

Instances

Show AnyOddA

Methods

showsPrec :: Int -> AnyOddA -> ShowS

show :: AnyOddA -> String

showList :: [AnyOddA] -> ShowS

Arbitrary AnyOddA

Methods

arbitrary :: Gen AnyOddA

shrink :: AnyOddA -> [AnyOddA]

newtype AnyOddE

Constructors

AnyOddE

Fields

• getAnyOddE :: TwoFingerOddE Int [Int]

Instances

Show AnyOddE

Methods

showsPrec :: Int -> AnyOddE -> ShowS

show :: AnyOddE -> String

showList :: [AnyOddE] -> ShowS

Arbitrary AnyOddE

Methods

arbitrary :: Gen AnyOddE

shrink :: AnyOddE -> [AnyOddE]

newtype AnyEvenA

Constructors

AnyEvenA

Fields

• getAnyEvenA :: TwoFingerEvenA Int [Int]

Instances

Show AnyEvenA

Methods

showsPrec :: Int -> AnyEvenA -> ShowS

show :: AnyEvenA -> String

showList :: [AnyEvenA] -> ShowS

Arbitrary AnyEvenA

Methods

arbitrary :: Gen AnyEvenA

shrink :: AnyEvenA -> [AnyEvenA]

newtype AnyEvenE

Constructors

AnyEvenE

Fields

• getAnyEvenE :: TwoFingerEvenE Int [Int]

Instances

Show AnyEvenE

Methods

showsPrec :: Int -> AnyEvenE -> ShowS

show :: AnyEvenE -> String

showList :: [AnyEvenE] -> ShowS

Arbitrary AnyEvenE

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'))

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')

>>> 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'))

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

>>> 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')

\(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'))

Creating infinite sequences.

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

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

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

repeatOddA :: a -> e -> TwoFingerOddA e a

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

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

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

>>> 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

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

>>> 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

\(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

>>> 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)]