{-# LANGUAGE CPP                    #-}
{-# LANGUAGE DeriveAnyClass         #-}
{-# LANGUAGE DeriveGeneric          #-}
{-# LANGUAGE FlexibleInstances      #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE UndecidableInstances   #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.FingerTree
-- Copyright   :  (c) Ross Paterson, Ralf Hinze 2006
-- License     :  BSD-style
-- Maintainer  :  R.Paterson@city.ac.uk
-- Stability   :  experimental
-- Portability :  non-portable (MPTCs and functional dependencies)
--
-- A general sequence representation with arbitrary annotations, for
-- use as a base for implementations of various collection types, as
-- described in section 4 of
--
--  * Ralf Hinze and Ross Paterson,
--    \"Finger trees: a simple general-purpose data structure\",
--    /Journal of Functional Programming/ 16:2 (2006) pp 197-217.
--    <http://staff.city.ac.uk/~ross/papers/FingerTree.html>
--
-- For a directly usable sequence type, see @Data.Sequence@, which is
-- a specialization of this structure.
--
-- An amortized running time is given for each operation, with /n/
-- referring to the length of the sequence.  These bounds hold even in
-- a persistent (shared) setting.
--
-- /Note/: Many of these operations have the same names as similar
-- operations on lists in the "Prelude".  The ambiguity may be resolved
-- using either qualification or the @hiding@ clause.
--
-----------------------------------------------------------------------------

module HaskellWorks.Data.FingerTree.Strict (
    FingerTree(..), Digit(..), Node(..), deep, node2, node3,
    Measured(..),
    -- * Construction
    empty, singleton,
    (<|), (|>), (><),
    fromList,
    -- * Deconstruction
    null,
    ViewL(..), ViewR(..), viewl, viewr,
    split, takeUntil, dropUntil,
    -- * Transformation
    reverse,
    fmap', fmapWithPos, unsafeFmap,
    traverse', traverseWithPos, unsafeTraverse,
    maybeHead, maybeLast
    -- * Example
    -- $example
    ) where

import Prelude hiding (null, reverse)

import Control.Applicative (Applicative (pure, (<*>)), (<$>))
import Control.DeepSeq     (NFData)
import Data.Foldable       (Foldable (foldMap), foldr', toList)
import GHC.Generics        (Generic)

import qualified Data.Semigroup as S

infixr 5 ><
infixr 5 <|, :<
infixl 5 |>, :>

{- HLINT ignore "Reduce duplication"  -}
{- HLINT ignore "Use record patterns" -}

-- | View of the left end of a sequence.
data ViewL s a
    = EmptyL        -- ^ empty sequence
    | !a :< !(s a)  -- ^ leftmost element and the rest of the sequence
    deriving (ViewL s a -> ViewL s a -> Bool
(ViewL s a -> ViewL s a -> Bool)
-> (ViewL s a -> ViewL s a -> Bool) -> Eq (ViewL s a)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewL s a -> ViewL s a -> Bool
/= :: ViewL s a -> ViewL s a -> Bool
$c/= :: forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewL s a -> ViewL s a -> Bool
== :: ViewL s a -> ViewL s a -> Bool
$c== :: forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewL s a -> ViewL s a -> Bool
Eq, Eq (ViewL s a)
Eq (ViewL s a)
-> (ViewL s a -> ViewL s a -> Ordering)
-> (ViewL s a -> ViewL s a -> Bool)
-> (ViewL s a -> ViewL s a -> Bool)
-> (ViewL s a -> ViewL s a -> Bool)
-> (ViewL s a -> ViewL s a -> Bool)
-> (ViewL s a -> ViewL s a -> ViewL s a)
-> (ViewL s a -> ViewL s a -> ViewL s a)
-> Ord (ViewL s a)
ViewL s a -> ViewL s a -> Bool
ViewL s a -> ViewL s a -> Ordering
ViewL s a -> ViewL s a -> ViewL s a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall (s :: * -> *) a. (Ord a, Ord (s a)) => Eq (ViewL s a)
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Bool
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Ordering
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> ViewL s a
min :: ViewL s a -> ViewL s a -> ViewL s a
$cmin :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> ViewL s a
max :: ViewL s a -> ViewL s a -> ViewL s a
$cmax :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> ViewL s a
>= :: ViewL s a -> ViewL s a -> Bool
$c>= :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Bool
> :: ViewL s a -> ViewL s a -> Bool
$c> :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Bool
<= :: ViewL s a -> ViewL s a -> Bool
$c<= :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Bool
< :: ViewL s a -> ViewL s a -> Bool
$c< :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Bool
compare :: ViewL s a -> ViewL s a -> Ordering
$ccompare :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewL s a -> ViewL s a -> Ordering
$cp1Ord :: forall (s :: * -> *) a. (Ord a, Ord (s a)) => Eq (ViewL s a)
Ord, Int -> ViewL s a -> ShowS
[ViewL s a] -> ShowS
ViewL s a -> String
(Int -> ViewL s a -> ShowS)
-> (ViewL s a -> String)
-> ([ViewL s a] -> ShowS)
-> Show (ViewL s a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall (s :: * -> *) a.
(Show a, Show (s a)) =>
Int -> ViewL s a -> ShowS
forall (s :: * -> *) a.
(Show a, Show (s a)) =>
[ViewL s a] -> ShowS
forall (s :: * -> *) a. (Show a, Show (s a)) => ViewL s a -> String
showList :: [ViewL s a] -> ShowS
$cshowList :: forall (s :: * -> *) a.
(Show a, Show (s a)) =>
[ViewL s a] -> ShowS
show :: ViewL s a -> String
$cshow :: forall (s :: * -> *) a. (Show a, Show (s a)) => ViewL s a -> String
showsPrec :: Int -> ViewL s a -> ShowS
$cshowsPrec :: forall (s :: * -> *) a.
(Show a, Show (s a)) =>
Int -> ViewL s a -> ShowS
Show, ReadPrec [ViewL s a]
ReadPrec (ViewL s a)
Int -> ReadS (ViewL s a)
ReadS [ViewL s a]
(Int -> ReadS (ViewL s a))
-> ReadS [ViewL s a]
-> ReadPrec (ViewL s a)
-> ReadPrec [ViewL s a]
-> Read (ViewL s a)
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec [ViewL s a]
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec (ViewL s a)
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
Int -> ReadS (ViewL s a)
forall (s :: * -> *) a. (Read a, Read (s a)) => ReadS [ViewL s a]
readListPrec :: ReadPrec [ViewL s a]
$creadListPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec [ViewL s a]
readPrec :: ReadPrec (ViewL s a)
$creadPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec (ViewL s a)
readList :: ReadS [ViewL s a]
$creadList :: forall (s :: * -> *) a. (Read a, Read (s a)) => ReadS [ViewL s a]
readsPrec :: Int -> ReadS (ViewL s a)
$creadsPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
Int -> ReadS (ViewL s a)
Read, (forall x. ViewL s a -> Rep (ViewL s a) x)
-> (forall x. Rep (ViewL s a) x -> ViewL s a)
-> Generic (ViewL s a)
forall x. Rep (ViewL s a) x -> ViewL s a
forall x. ViewL s a -> Rep (ViewL s a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall (s :: * -> *) a x. Rep (ViewL s a) x -> ViewL s a
forall (s :: * -> *) a x. ViewL s a -> Rep (ViewL s a) x
$cto :: forall (s :: * -> *) a x. Rep (ViewL s a) x -> ViewL s a
$cfrom :: forall (s :: * -> *) a x. ViewL s a -> Rep (ViewL s a) x
Generic, ViewL s a -> ()
(ViewL s a -> ()) -> NFData (ViewL s a)
forall a. (a -> ()) -> NFData a
forall (s :: * -> *) a. (NFData a, NFData (s a)) => ViewL s a -> ()
rnf :: ViewL s a -> ()
$crnf :: forall (s :: * -> *) a. (NFData a, NFData (s a)) => ViewL s a -> ()
NFData)

-- | View of the right end of a sequence.
data ViewR s a
    = EmptyR        -- ^ empty sequence
    | !(s a) :> !a      -- ^ the sequence minus the rightmost element,
                    -- and the rightmost element
    deriving (ViewR s a -> ViewR s a -> Bool
(ViewR s a -> ViewR s a -> Bool)
-> (ViewR s a -> ViewR s a -> Bool) -> Eq (ViewR s a)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewR s a -> ViewR s a -> Bool
/= :: ViewR s a -> ViewR s a -> Bool
$c/= :: forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewR s a -> ViewR s a -> Bool
== :: ViewR s a -> ViewR s a -> Bool
$c== :: forall (s :: * -> *) a.
(Eq a, Eq (s a)) =>
ViewR s a -> ViewR s a -> Bool
Eq, Eq (ViewR s a)
Eq (ViewR s a)
-> (ViewR s a -> ViewR s a -> Ordering)
-> (ViewR s a -> ViewR s a -> Bool)
-> (ViewR s a -> ViewR s a -> Bool)
-> (ViewR s a -> ViewR s a -> Bool)
-> (ViewR s a -> ViewR s a -> Bool)
-> (ViewR s a -> ViewR s a -> ViewR s a)
-> (ViewR s a -> ViewR s a -> ViewR s a)
-> Ord (ViewR s a)
ViewR s a -> ViewR s a -> Bool
ViewR s a -> ViewR s a -> Ordering
ViewR s a -> ViewR s a -> ViewR s a
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall (s :: * -> *) a. (Ord a, Ord (s a)) => Eq (ViewR s a)
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Bool
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Ordering
forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> ViewR s a
min :: ViewR s a -> ViewR s a -> ViewR s a
$cmin :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> ViewR s a
max :: ViewR s a -> ViewR s a -> ViewR s a
$cmax :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> ViewR s a
>= :: ViewR s a -> ViewR s a -> Bool
$c>= :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Bool
> :: ViewR s a -> ViewR s a -> Bool
$c> :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Bool
<= :: ViewR s a -> ViewR s a -> Bool
$c<= :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Bool
< :: ViewR s a -> ViewR s a -> Bool
$c< :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Bool
compare :: ViewR s a -> ViewR s a -> Ordering
$ccompare :: forall (s :: * -> *) a.
(Ord a, Ord (s a)) =>
ViewR s a -> ViewR s a -> Ordering
$cp1Ord :: forall (s :: * -> *) a. (Ord a, Ord (s a)) => Eq (ViewR s a)
Ord, Int -> ViewR s a -> ShowS
[ViewR s a] -> ShowS
ViewR s a -> String
(Int -> ViewR s a -> ShowS)
-> (ViewR s a -> String)
-> ([ViewR s a] -> ShowS)
-> Show (ViewR s a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall (s :: * -> *) a.
(Show a, Show (s a)) =>
Int -> ViewR s a -> ShowS
forall (s :: * -> *) a.
(Show a, Show (s a)) =>
[ViewR s a] -> ShowS
forall (s :: * -> *) a. (Show a, Show (s a)) => ViewR s a -> String
showList :: [ViewR s a] -> ShowS
$cshowList :: forall (s :: * -> *) a.
(Show a, Show (s a)) =>
[ViewR s a] -> ShowS
show :: ViewR s a -> String
$cshow :: forall (s :: * -> *) a. (Show a, Show (s a)) => ViewR s a -> String
showsPrec :: Int -> ViewR s a -> ShowS
$cshowsPrec :: forall (s :: * -> *) a.
(Show a, Show (s a)) =>
Int -> ViewR s a -> ShowS
Show, ReadPrec [ViewR s a]
ReadPrec (ViewR s a)
Int -> ReadS (ViewR s a)
ReadS [ViewR s a]
(Int -> ReadS (ViewR s a))
-> ReadS [ViewR s a]
-> ReadPrec (ViewR s a)
-> ReadPrec [ViewR s a]
-> Read (ViewR s a)
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec [ViewR s a]
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec (ViewR s a)
forall (s :: * -> *) a.
(Read a, Read (s a)) =>
Int -> ReadS (ViewR s a)
forall (s :: * -> *) a. (Read a, Read (s a)) => ReadS [ViewR s a]
readListPrec :: ReadPrec [ViewR s a]
$creadListPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec [ViewR s a]
readPrec :: ReadPrec (ViewR s a)
$creadPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
ReadPrec (ViewR s a)
readList :: ReadS [ViewR s a]
$creadList :: forall (s :: * -> *) a. (Read a, Read (s a)) => ReadS [ViewR s a]
readsPrec :: Int -> ReadS (ViewR s a)
$creadsPrec :: forall (s :: * -> *) a.
(Read a, Read (s a)) =>
Int -> ReadS (ViewR s a)
Read, (forall x. ViewR s a -> Rep (ViewR s a) x)
-> (forall x. Rep (ViewR s a) x -> ViewR s a)
-> Generic (ViewR s a)
forall x. Rep (ViewR s a) x -> ViewR s a
forall x. ViewR s a -> Rep (ViewR s a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall (s :: * -> *) a x. Rep (ViewR s a) x -> ViewR s a
forall (s :: * -> *) a x. ViewR s a -> Rep (ViewR s a) x
$cto :: forall (s :: * -> *) a x. Rep (ViewR s a) x -> ViewR s a
$cfrom :: forall (s :: * -> *) a x. ViewR s a -> Rep (ViewR s a) x
Generic, ViewR s a -> ()
(ViewR s a -> ()) -> NFData (ViewR s a)
forall a. (a -> ()) -> NFData a
forall (s :: * -> *) a. (NFData a, NFData (s a)) => ViewR s a -> ()
rnf :: ViewR s a -> ()
$crnf :: forall (s :: * -> *) a. (NFData a, NFData (s a)) => ViewR s a -> ()
NFData)

instance Functor s => Functor (ViewL s) where
    fmap :: (a -> b) -> ViewL s a -> ViewL s b
fmap a -> b
_ ViewL s a
EmptyL    = ViewL s b
forall (s :: * -> *) a. ViewL s a
EmptyL
    fmap a -> b
f (a
x :< s a
xs) = a -> b
f a
x b -> s b -> ViewL s b
forall (s :: * -> *) a. a -> s a -> ViewL s a
:< (a -> b) -> s a -> s b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f s a
xs

instance Functor s => Functor (ViewR s) where
    fmap :: (a -> b) -> ViewR s a -> ViewR s b
fmap a -> b
_ ViewR s a
EmptyR    = ViewR s b
forall (s :: * -> *) a. ViewR s a
EmptyR
    fmap a -> b
f (s a
xs :> a
x) = (a -> b) -> s a -> s b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f s a
xs s b -> b -> ViewR s b
forall (s :: * -> *) a. s a -> a -> ViewR s a
:> a -> b
f a
x

instance Measured v a => S.Semigroup (FingerTree v a) where
  <> :: FingerTree v a -> FingerTree v a -> FingerTree v a
(<>) = FingerTree v a -> FingerTree v a -> FingerTree v a
forall v a.
Measured v a =>
FingerTree v a -> FingerTree v a -> FingerTree v a
(><)
  {-# INLINE (<>) #-}

-- | 'empty' and '><'.
instance Measured v a => Monoid (FingerTree v a) where
  mempty :: FingerTree v a
mempty = FingerTree v a
forall v a. FingerTree v a
empty
  {-# INLINE mempty #-}

-- Explicit Digit type (Exercise 1)

data Digit a
    = One !a
    | Two !a !a
    | Three !a !a !a
    | Four !a !a !a !a
    deriving (Digit a -> Digit a -> Bool
(Digit a -> Digit a -> Bool)
-> (Digit a -> Digit a -> Bool) -> Eq (Digit a)
forall a. Eq a => Digit a -> Digit a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Digit a -> Digit a -> Bool
$c/= :: forall a. Eq a => Digit a -> Digit a -> Bool
== :: Digit a -> Digit a -> Bool
$c== :: forall a. Eq a => Digit a -> Digit a -> Bool
Eq, Int -> Digit a -> ShowS
[Digit a] -> ShowS
Digit a -> String
(Int -> Digit a -> ShowS)
-> (Digit a -> String) -> ([Digit a] -> ShowS) -> Show (Digit a)
forall a. Show a => Int -> Digit a -> ShowS
forall a. Show a => [Digit a] -> ShowS
forall a. Show a => Digit a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Digit a] -> ShowS
$cshowList :: forall a. Show a => [Digit a] -> ShowS
show :: Digit a -> String
$cshow :: forall a. Show a => Digit a -> String
showsPrec :: Int -> Digit a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> Digit a -> ShowS
Show, (forall x. Digit a -> Rep (Digit a) x)
-> (forall x. Rep (Digit a) x -> Digit a) -> Generic (Digit a)
forall x. Rep (Digit a) x -> Digit a
forall x. Digit a -> Rep (Digit a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (Digit a) x -> Digit a
forall a x. Digit a -> Rep (Digit a) x
$cto :: forall a x. Rep (Digit a) x -> Digit a
$cfrom :: forall a x. Digit a -> Rep (Digit a) x
Generic, Digit a -> ()
(Digit a -> ()) -> NFData (Digit a)
forall a. NFData a => Digit a -> ()
forall a. (a -> ()) -> NFData a
rnf :: Digit a -> ()
$crnf :: forall a. NFData a => Digit a -> ()
NFData)

instance Foldable Digit where
    foldMap :: (a -> m) -> Digit a -> m
foldMap a -> m
f (One a
a)        = a -> m
f a
a
    foldMap a -> m
f (Two a
a a
b)      = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b
    foldMap a -> m
f (Three a
a a
b a
c)  = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c
    foldMap a -> m
f (Four a
a a
b a
c a
d) = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
d

-------------------
-- 4.1 Measurements
-------------------

-- | Things that can be measured.
class (Monoid v) => Measured v a | a -> v where
    measure :: a -> v

instance Measured v a => Measured v (Digit a) where
    measure :: Digit a -> v
measure = (a -> v) -> Digit a -> v
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> v
forall v a. Measured v a => a -> v
measure

---------------------------
-- 4.2 Caching measurements
---------------------------

data Node v a = Node2 !v !a !a | Node3 !v !a !a !a
    deriving (Int -> Node v a -> ShowS
[Node v a] -> ShowS
Node v a -> String
(Int -> Node v a -> ShowS)
-> (Node v a -> String) -> ([Node v a] -> ShowS) -> Show (Node v a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall v a. (Show v, Show a) => Int -> Node v a -> ShowS
forall v a. (Show v, Show a) => [Node v a] -> ShowS
forall v a. (Show v, Show a) => Node v a -> String
showList :: [Node v a] -> ShowS
$cshowList :: forall v a. (Show v, Show a) => [Node v a] -> ShowS
show :: Node v a -> String
$cshow :: forall v a. (Show v, Show a) => Node v a -> String
showsPrec :: Int -> Node v a -> ShowS
$cshowsPrec :: forall v a. (Show v, Show a) => Int -> Node v a -> ShowS
Show, (forall x. Node v a -> Rep (Node v a) x)
-> (forall x. Rep (Node v a) x -> Node v a) -> Generic (Node v a)
forall x. Rep (Node v a) x -> Node v a
forall x. Node v a -> Rep (Node v a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall v a x. Rep (Node v a) x -> Node v a
forall v a x. Node v a -> Rep (Node v a) x
$cto :: forall v a x. Rep (Node v a) x -> Node v a
$cfrom :: forall v a x. Node v a -> Rep (Node v a) x
Generic, Node v a -> ()
(Node v a -> ()) -> NFData (Node v a)
forall a. (a -> ()) -> NFData a
forall v a. (NFData v, NFData a) => Node v a -> ()
rnf :: Node v a -> ()
$crnf :: forall v a. (NFData v, NFData a) => Node v a -> ()
NFData)

instance Foldable (Node v) where
    foldMap :: (a -> m) -> Node v a -> m
foldMap a -> m
f (Node2 v
_ a
a a
b)   = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b
    foldMap a -> m
f (Node3 v
_ a
a a
b a
c) = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
b m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` a -> m
f a
c

node2        ::  Measured v a => a -> a -> Node v a
node2 :: a -> a -> Node v a
node2 a
a a
b    =   v -> a -> a -> Node v a
forall v a. v -> a -> a -> Node v a
Node2 (a -> v
forall v a. Measured v a => a -> v
measure a
a v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b) a
a a
b

node3        ::  Measured v a => a -> a -> a -> Node v a
node3 :: a -> a -> a -> Node v a
node3 a
a a
b a
c  =   v -> a -> a -> a -> Node v a
forall v a. v -> a -> a -> a -> Node v a
Node3 (a -> v
forall v a. Measured v a => a -> v
measure a
a v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
c) a
a a
b a
c

instance (Monoid v) => Measured v (Node v a) where
    measure :: Node v a -> v
measure (Node2 v
v a
_ a
_)   =  v
v
    measure (Node3 v
v a
_ a
_ a
_) =  v
v

nodeToDigit :: Node v a -> Digit a
nodeToDigit :: Node v a -> Digit a
nodeToDigit (Node2 v
_ a
a a
b)   = a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b
nodeToDigit (Node3 v
_ a
a a
b a
c) = a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
a a
b a
c

-- | A representation of a sequence of values of type @a@, allowing
-- access to the ends in constant time, and append and split in time
-- logarithmic in the size of the smaller piece.
--
-- The collection is also parameterized by a measure type @v@, which
-- is used to specify a position in the sequence for the 'split' operation.
-- The types of the operations enforce the constraint @'Measured' v a@,
-- which also implies that the type @v@ is determined by @a@.
--
-- A variety of abstract data types can be implemented by using different
-- element types and measurements.
data FingerTree v a
    = Empty
    | Single !a
    | Deep !v !(Digit a) !(FingerTree v (Node v a)) !(Digit a)
    deriving (Int -> FingerTree v a -> ShowS
[FingerTree v a] -> ShowS
FingerTree v a -> String
(Int -> FingerTree v a -> ShowS)
-> (FingerTree v a -> String)
-> ([FingerTree v a] -> ShowS)
-> Show (FingerTree v a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall v a. (Show a, Show v) => Int -> FingerTree v a -> ShowS
forall v a. (Show a, Show v) => [FingerTree v a] -> ShowS
forall v a. (Show a, Show v) => FingerTree v a -> String
showList :: [FingerTree v a] -> ShowS
$cshowList :: forall v a. (Show a, Show v) => [FingerTree v a] -> ShowS
show :: FingerTree v a -> String
$cshow :: forall v a. (Show a, Show v) => FingerTree v a -> String
showsPrec :: Int -> FingerTree v a -> ShowS
$cshowsPrec :: forall v a. (Show a, Show v) => Int -> FingerTree v a -> ShowS
Show, (forall x. FingerTree v a -> Rep (FingerTree v a) x)
-> (forall x. Rep (FingerTree v a) x -> FingerTree v a)
-> Generic (FingerTree v a)
forall x. Rep (FingerTree v a) x -> FingerTree v a
forall x. FingerTree v a -> Rep (FingerTree v a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall v a x. Rep (FingerTree v a) x -> FingerTree v a
forall v a x. FingerTree v a -> Rep (FingerTree v a) x
$cto :: forall v a x. Rep (FingerTree v a) x -> FingerTree v a
$cfrom :: forall v a x. FingerTree v a -> Rep (FingerTree v a) x
Generic, FingerTree v a -> ()
(FingerTree v a -> ()) -> NFData (FingerTree v a)
forall a. (a -> ()) -> NFData a
forall v a. (NFData a, NFData v) => FingerTree v a -> ()
rnf :: FingerTree v a -> ()
$crnf :: forall v a. (NFData a, NFData v) => FingerTree v a -> ()
NFData)

deep ::  Measured v a =>
     Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep :: Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr FingerTree v (Node v a)
m Digit a
sf = v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep ((Digit a -> v
forall v a. Measured v a => a -> v
measure Digit a
pr v -> FingerTree v (Node v a) -> v
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v (Node v a)
m) v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` Digit a -> v
forall v a. Measured v a => a -> v
measure Digit a
sf) Digit a
pr FingerTree v (Node v a)
m Digit a
sf

-- | /O(1)/. The cached measure of a tree.
instance Measured v a => Measured v (FingerTree v a) where
    measure :: FingerTree v a -> v
measure FingerTree v a
Empty          =  v
forall a. Monoid a => a
mempty
    measure (Single a
x)     =  a -> v
forall v a. Measured v a => a -> v
measure a
x
    measure (Deep v
v Digit a
_ FingerTree v (Node v a)
_ Digit a
_) =  v
v

instance Foldable (FingerTree v) where
    foldMap :: (a -> m) -> FingerTree v a -> m
foldMap a -> m
_ FingerTree v a
Empty = m
forall a. Monoid a => a
mempty
    foldMap a -> m
f (Single a
x) = a -> m
f a
x
    foldMap a -> m
f (Deep v
_ Digit a
pr FingerTree v (Node v a)
m Digit a
sf) =
        (a -> m) -> Digit a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f Digit a
pr m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (Node v a -> m) -> FingerTree v (Node v a) -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap ((a -> m) -> Node v a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f) FingerTree v (Node v a)
m m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (a -> m) -> Digit a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f Digit a
sf

instance Eq a => Eq (FingerTree v a) where
    FingerTree v a
xs == :: FingerTree v a -> FingerTree v a -> Bool
== FingerTree v a
ys = FingerTree v a -> [a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList FingerTree v a
xs [a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
== FingerTree v a -> [a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList FingerTree v a
ys

instance Ord a => Ord (FingerTree v a) where
    compare :: FingerTree v a -> FingerTree v a -> Ordering
compare FingerTree v a
xs FingerTree v a
ys = [a] -> [a] -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (FingerTree v a -> [a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList FingerTree v a
xs) (FingerTree v a -> [a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList FingerTree v a
ys)

-- #if !TESTING
-- instance Show a => Show (FingerTree v a) where
--     showsPrec p xs = showParen (p > 10) $
--         showString "fromList " . shows (toList xs)
-- #endif

-- | Like 'fmap', but with a more constrained type.
fmap' :: (Measured v1 a1, Measured v2 a2) =>
    (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
fmap' :: (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
fmap' = (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
mapTree

mapTree :: (Measured v2 a2) =>
    (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
mapTree :: (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
mapTree a1 -> a2
_ FingerTree v1 a1
Empty = FingerTree v2 a2
forall v a. FingerTree v a
Empty
mapTree a1 -> a2
f (Single a1
x) = a2 -> FingerTree v2 a2
forall v a. a -> FingerTree v a
Single (a1 -> a2
f a1
x)
mapTree a1 -> a2
f (Deep v1
_ Digit a1
pr FingerTree v1 (Node v1 a1)
m Digit a1
sf) =
    Digit a2
-> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep ((a1 -> a2) -> Digit a1 -> Digit a2
forall a b. (a -> b) -> Digit a -> Digit b
mapDigit a1 -> a2
f Digit a1
pr) ((Node v1 a1 -> Node v2 a2)
-> FingerTree v1 (Node v1 a1) -> FingerTree v2 (Node v2 a2)
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
mapTree ((a1 -> a2) -> Node v1 a1 -> Node v2 a2
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> Node v1 a1 -> Node v2 a2
mapNode a1 -> a2
f) FingerTree v1 (Node v1 a1)
m) ((a1 -> a2) -> Digit a1 -> Digit a2
forall a b. (a -> b) -> Digit a -> Digit b
mapDigit a1 -> a2
f Digit a1
sf)

mapNode :: (Measured v2 a2) =>
    (a1 -> a2) -> Node v1 a1 -> Node v2 a2
mapNode :: (a1 -> a2) -> Node v1 a1 -> Node v2 a2
mapNode a1 -> a2
f (Node2 v1
_ a1
a a1
b)   = a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> Node v a
node2 (a1 -> a2
f a1
a) (a1 -> a2
f a1
b)
mapNode a1 -> a2
f (Node3 v1
_ a1
a a1
b a1
c) = a2 -> a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> a -> Node v a
node3 (a1 -> a2
f a1
a) (a1 -> a2
f a1
b) (a1 -> a2
f a1
c)

mapDigit :: (a -> b) -> Digit a -> Digit b
mapDigit :: (a -> b) -> Digit a -> Digit b
mapDigit a -> b
f (One a
a)        = b -> Digit b
forall a. a -> Digit a
One (a -> b
f a
a)
mapDigit a -> b
f (Two a
a a
b)      = b -> b -> Digit b
forall a. a -> a -> Digit a
Two (a -> b
f a
a) (a -> b
f a
b)
mapDigit a -> b
f (Three a
a a
b a
c)  = b -> b -> b -> Digit b
forall a. a -> a -> a -> Digit a
Three (a -> b
f a
a) (a -> b
f a
b) (a -> b
f a
c)
mapDigit a -> b
f (Four a
a a
b a
c a
d) = b -> b -> b -> b -> Digit b
forall a. a -> a -> a -> a -> Digit a
Four (a -> b
f a
a) (a -> b
f a
b) (a -> b
f a
c) (a -> b
f a
d)

-- | Map all elements of the tree with a function that also takes the
-- measure of the prefix of the tree to the left of the element.
fmapWithPos :: (Measured v1 a1, Measured v2 a2) =>
    (v1 -> a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
fmapWithPos :: (v1 -> a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
fmapWithPos v1 -> a1 -> a2
f = (v1 -> a1 -> a2) -> v1 -> FingerTree v1 a1 -> FingerTree v2 a2
forall v1 a1 v2 a2.
(Measured v1 a1, Measured v2 a2) =>
(v1 -> a1 -> a2) -> v1 -> FingerTree v1 a1 -> FingerTree v2 a2
mapWPTree v1 -> a1 -> a2
f v1
forall a. Monoid a => a
mempty

mapWPTree :: (Measured v1 a1, Measured v2 a2) =>
    (v1 -> a1 -> a2) -> v1 -> FingerTree v1 a1 -> FingerTree v2 a2
mapWPTree :: (v1 -> a1 -> a2) -> v1 -> FingerTree v1 a1 -> FingerTree v2 a2
mapWPTree v1 -> a1 -> a2
_ v1
_ FingerTree v1 a1
Empty = FingerTree v2 a2
forall v a. FingerTree v a
Empty
mapWPTree v1 -> a1 -> a2
f v1
v (Single a1
x) = a2 -> FingerTree v2 a2
forall v a. a -> FingerTree v a
Single (v1 -> a1 -> a2
f v1
v a1
x)
mapWPTree v1 -> a1 -> a2
f v1
v (Deep v1
_ Digit a1
pr FingerTree v1 (Node v1 a1)
m Digit a1
sf) =
    Digit a2
-> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep ((v1 -> a1 -> a2) -> v1 -> Digit a1 -> Digit a2
forall v a b.
Measured v a =>
(v -> a -> b) -> v -> Digit a -> Digit b
mapWPDigit v1 -> a1 -> a2
f v1
v Digit a1
pr)
         ((v1 -> Node v1 a1 -> Node v2 a2)
-> v1 -> FingerTree v1 (Node v1 a1) -> FingerTree v2 (Node v2 a2)
forall v1 a1 v2 a2.
(Measured v1 a1, Measured v2 a2) =>
(v1 -> a1 -> a2) -> v1 -> FingerTree v1 a1 -> FingerTree v2 a2
mapWPTree ((v1 -> a1 -> a2) -> v1 -> Node v1 a1 -> Node v2 a2
forall v1 a1 v2 a2.
(Measured v1 a1, Measured v2 a2) =>
(v1 -> a1 -> a2) -> v1 -> Node v1 a1 -> Node v2 a2
mapWPNode v1 -> a1 -> a2
f) v1
vpr FingerTree v1 (Node v1 a1)
m)
         ((v1 -> a1 -> a2) -> v1 -> Digit a1 -> Digit a2
forall v a b.
Measured v a =>
(v -> a -> b) -> v -> Digit a -> Digit b
mapWPDigit v1 -> a1 -> a2
f v1
vm Digit a1
sf)
  where
    vpr :: v1
vpr     =  v1
v    v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend`  Digit a1 -> v1
forall v a. Measured v a => a -> v
measure Digit a1
pr
    vm :: v1
vm      =  v1
vpr  v1 -> FingerTree v1 (Node v1 a1) -> v1
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v1 (Node v1 a1)
m

mapWPNode :: (Measured v1 a1, Measured v2 a2) =>
    (v1 -> a1 -> a2) -> v1 -> Node v1 a1 -> Node v2 a2
mapWPNode :: (v1 -> a1 -> a2) -> v1 -> Node v1 a1 -> Node v2 a2
mapWPNode v1 -> a1 -> a2
f v1
v (Node2 v1
_ a1
a a1
b) = a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> Node v a
node2 (v1 -> a1 -> a2
f v1
v a1
a) (v1 -> a1 -> a2
f v1
va a1
b)
  where
    va :: v1
va      = v1
v v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
a
mapWPNode v1 -> a1 -> a2
f v1
v (Node3 v1
_ a1
a a1
b a1
c) = a2 -> a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> a -> Node v a
node3 (v1 -> a1 -> a2
f v1
v a1
a) (v1 -> a1 -> a2
f v1
va a1
b) (v1 -> a1 -> a2
f v1
vab a1
c)
  where
    va :: v1
va      = v1
v v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
a
    vab :: v1
vab     = v1
va v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
b

mapWPDigit :: Measured v a => (v -> a -> b) -> v -> Digit a -> Digit b
mapWPDigit :: (v -> a -> b) -> v -> Digit a -> Digit b
mapWPDigit v -> a -> b
f v
v (One a
a) = b -> Digit b
forall a. a -> Digit a
One (v -> a -> b
f v
v a
a)
mapWPDigit v -> a -> b
f v
v (Two a
a a
b) = b -> b -> Digit b
forall a. a -> a -> Digit a
Two (v -> a -> b
f v
v a
a) (v -> a -> b
f v
va a
b)
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
mapWPDigit v -> a -> b
f v
v (Three a
a a
b a
c) = b -> b -> b -> Digit b
forall a. a -> a -> a -> Digit a
Three (v -> a -> b
f v
v a
a) (v -> a -> b
f v
va a
b) (v -> a -> b
f v
vab a
c)
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
mapWPDigit v -> a -> b
f v
v (Four a
a a
b a
c a
d) = b -> b -> b -> b -> Digit b
forall a. a -> a -> a -> a -> Digit a
Four (v -> a -> b
f v
v a
a) (v -> a -> b
f v
va a
b) (v -> a -> b
f v
vab a
c) (v -> a -> b
f v
vabc a
d)
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
    vabc :: v
vabc    = v
vab v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
c

-- | Like 'fmap', but safe only if the function preserves the measure.
unsafeFmap :: (a -> b) -> FingerTree v a -> FingerTree v b
unsafeFmap :: (a -> b) -> FingerTree v a -> FingerTree v b
unsafeFmap a -> b
_ FingerTree v a
Empty = FingerTree v b
forall v a. FingerTree v a
Empty
unsafeFmap a -> b
f (Single a
x) = b -> FingerTree v b
forall v a. a -> FingerTree v a
Single (a -> b
f a
x)
unsafeFmap a -> b
f (Deep v
v Digit a
pr FingerTree v (Node v a)
m Digit a
sf) =
    v
-> Digit b -> FingerTree v (Node v b) -> Digit b -> FingerTree v b
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep v
v ((a -> b) -> Digit a -> Digit b
forall a b. (a -> b) -> Digit a -> Digit b
mapDigit a -> b
f Digit a
pr) ((Node v a -> Node v b)
-> FingerTree v (Node v a) -> FingerTree v (Node v b)
forall a b v. (a -> b) -> FingerTree v a -> FingerTree v b
unsafeFmap ((a -> b) -> Node v a -> Node v b
forall a b v. (a -> b) -> Node v a -> Node v b
unsafeFmapNode a -> b
f) FingerTree v (Node v a)
m) ((a -> b) -> Digit a -> Digit b
forall a b. (a -> b) -> Digit a -> Digit b
mapDigit a -> b
f Digit a
sf)

unsafeFmapNode :: (a -> b) -> Node v a -> Node v b
unsafeFmapNode :: (a -> b) -> Node v a -> Node v b
unsafeFmapNode a -> b
f (Node2 v
v a
a a
b)   = v -> b -> b -> Node v b
forall v a. v -> a -> a -> Node v a
Node2 v
v (a -> b
f a
a) (a -> b
f a
b)
unsafeFmapNode a -> b
f (Node3 v
v a
a a
b a
c) = v -> b -> b -> b -> Node v b
forall v a. v -> a -> a -> a -> Node v a
Node3 v
v (a -> b
f a
a) (a -> b
f a
b) (a -> b
f a
c)

-- | Like 'traverse', but with a more constrained type.
traverse' :: (Measured v1 a1, Measured v2 a2, Applicative f) =>
    (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverse' :: (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverse' = (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
forall v2 a2 (f :: * -> *) a1 v1.
(Measured v2 a2, Applicative f) =>
(a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseTree

traverseTree :: (Measured v2 a2, Applicative f) =>
    (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseTree :: (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseTree a1 -> f a2
_ FingerTree v1 a1
Empty = FingerTree v2 a2 -> f (FingerTree v2 a2)
forall (f :: * -> *) a. Applicative f => a -> f a
pure FingerTree v2 a2
forall v a. FingerTree v a
Empty
traverseTree a1 -> f a2
f (Single a1
x) = a2 -> FingerTree v2 a2
forall v a. a -> FingerTree v a
Single (a2 -> FingerTree v2 a2) -> f a2 -> f (FingerTree v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a1 -> f a2
f a1
x
traverseTree a1 -> f a2
f (Deep v1
_ Digit a1
pr FingerTree v1 (Node v1 a1)
m Digit a1
sf) =
    Digit a2
-> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (Digit a2
 -> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
-> f (Digit a2)
-> f (FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a1 -> f a2) -> Digit a1 -> f (Digit a2)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Digit a -> f (Digit b)
traverseDigit a1 -> f a2
f Digit a1
pr f (FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
-> f (FingerTree v2 (Node v2 a2))
-> f (Digit a2 -> FingerTree v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (Node v1 a1 -> f (Node v2 a2))
-> FingerTree v1 (Node v1 a1) -> f (FingerTree v2 (Node v2 a2))
forall v2 a2 (f :: * -> *) a1 v1.
(Measured v2 a2, Applicative f) =>
(a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseTree ((a1 -> f a2) -> Node v1 a1 -> f (Node v2 a2)
forall v2 a2 (f :: * -> *) a1 v1.
(Measured v2 a2, Applicative f) =>
(a1 -> f a2) -> Node v1 a1 -> f (Node v2 a2)
traverseNode a1 -> f a2
f) FingerTree v1 (Node v1 a1)
m f (Digit a2 -> FingerTree v2 a2)
-> f (Digit a2) -> f (FingerTree v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (a1 -> f a2) -> Digit a1 -> f (Digit a2)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Digit a -> f (Digit b)
traverseDigit a1 -> f a2
f Digit a1
sf

traverseNode :: (Measured v2 a2, Applicative f) =>
    (a1 -> f a2) -> Node v1 a1 -> f (Node v2 a2)
traverseNode :: (a1 -> f a2) -> Node v1 a1 -> f (Node v2 a2)
traverseNode a1 -> f a2
f (Node2 v1
_ a1
a a1
b)   = a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> Node v a
node2 (a2 -> a2 -> Node v2 a2) -> f a2 -> f (a2 -> Node v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a1 -> f a2
f a1
a f (a2 -> Node v2 a2) -> f a2 -> f (Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a1 -> f a2
f a1
b
traverseNode a1 -> f a2
f (Node3 v1
_ a1
a a1
b a1
c) = a2 -> a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> a -> Node v a
node3 (a2 -> a2 -> a2 -> Node v2 a2)
-> f a2 -> f (a2 -> a2 -> Node v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a1 -> f a2
f a1
a f (a2 -> a2 -> Node v2 a2) -> f a2 -> f (a2 -> Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a1 -> f a2
f a1
b f (a2 -> Node v2 a2) -> f a2 -> f (Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a1 -> f a2
f a1
c

traverseDigit :: (Applicative f) => (a -> f b) -> Digit a -> f (Digit b)
traverseDigit :: (a -> f b) -> Digit a -> f (Digit b)
traverseDigit a -> f b
f (One a
a)        = b -> Digit b
forall a. a -> Digit a
One (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a
traverseDigit a -> f b
f (Two a
a a
b)      = b -> b -> Digit b
forall a. a -> a -> Digit a
Two (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b
traverseDigit a -> f b
f (Three a
a a
b a
c)  = b -> b -> b -> Digit b
forall a. a -> a -> a -> Digit a
Three (b -> b -> b -> Digit b) -> f b -> f (b -> b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
c
traverseDigit a -> f b
f (Four a
a a
b a
c a
d) = b -> b -> b -> b -> Digit b
forall a. a -> a -> a -> a -> Digit a
Four (b -> b -> b -> b -> Digit b) -> f b -> f (b -> b -> b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> b -> b -> Digit b) -> f b -> f (b -> b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b f (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
c f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
d

-- | Traverse the tree with a function that also takes the
-- measure of the prefix of the tree to the left of the element.
traverseWithPos :: (Measured v1 a1, Measured v2 a2, Applicative f) =>
    (v1 -> a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWithPos :: (v1 -> a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWithPos v1 -> a1 -> f a2
f = (v1 -> a1 -> f a2)
-> v1 -> FingerTree v1 a1 -> f (FingerTree v2 a2)
forall v1 a1 v2 a2 (f :: * -> *).
(Measured v1 a1, Measured v2 a2, Applicative f) =>
(v1 -> a1 -> f a2)
-> v1 -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWPTree v1 -> a1 -> f a2
f v1
forall a. Monoid a => a
mempty

traverseWPTree :: (Measured v1 a1, Measured v2 a2, Applicative f) =>
    (v1 -> a1 -> f a2) -> v1 -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWPTree :: (v1 -> a1 -> f a2)
-> v1 -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWPTree v1 -> a1 -> f a2
_ v1
_ FingerTree v1 a1
Empty = FingerTree v2 a2 -> f (FingerTree v2 a2)
forall (f :: * -> *) a. Applicative f => a -> f a
pure FingerTree v2 a2
forall v a. FingerTree v a
Empty
traverseWPTree v1 -> a1 -> f a2
f v1
v (Single a1
x) = a2 -> FingerTree v2 a2
forall v a. a -> FingerTree v a
Single (a2 -> FingerTree v2 a2) -> f a2 -> f (FingerTree v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v1 -> a1 -> f a2
f v1
v a1
x
traverseWPTree v1 -> a1 -> f a2
f v1
v (Deep v1
_ Digit a1
pr FingerTree v1 (Node v1 a1)
m Digit a1
sf) =
    Digit a2
-> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (Digit a2
 -> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
-> f (Digit a2)
-> f (FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (v1 -> a1 -> f a2) -> v1 -> Digit a1 -> f (Digit a2)
forall v a (f :: * -> *) b.
(Measured v a, Applicative f) =>
(v -> a -> f b) -> v -> Digit a -> f (Digit b)
traverseWPDigit v1 -> a1 -> f a2
f v1
v Digit a1
pr f (FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2)
-> f (FingerTree v2 (Node v2 a2))
-> f (Digit a2 -> FingerTree v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (v1 -> Node v1 a1 -> f (Node v2 a2))
-> v1
-> FingerTree v1 (Node v1 a1)
-> f (FingerTree v2 (Node v2 a2))
forall v1 a1 v2 a2 (f :: * -> *).
(Measured v1 a1, Measured v2 a2, Applicative f) =>
(v1 -> a1 -> f a2)
-> v1 -> FingerTree v1 a1 -> f (FingerTree v2 a2)
traverseWPTree ((v1 -> a1 -> f a2) -> v1 -> Node v1 a1 -> f (Node v2 a2)
forall v1 a1 v2 a2 (f :: * -> *).
(Measured v1 a1, Measured v2 a2, Applicative f) =>
(v1 -> a1 -> f a2) -> v1 -> Node v1 a1 -> f (Node v2 a2)
traverseWPNode v1 -> a1 -> f a2
f) v1
vpr FingerTree v1 (Node v1 a1)
m f (Digit a2 -> FingerTree v2 a2)
-> f (Digit a2) -> f (FingerTree v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (v1 -> a1 -> f a2) -> v1 -> Digit a1 -> f (Digit a2)
forall v a (f :: * -> *) b.
(Measured v a, Applicative f) =>
(v -> a -> f b) -> v -> Digit a -> f (Digit b)
traverseWPDigit v1 -> a1 -> f a2
f v1
vm Digit a1
sf
  where
    vpr :: v1
vpr     =  v1
v    v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend`  Digit a1 -> v1
forall v a. Measured v a => a -> v
measure Digit a1
pr
    vm :: v1
vm      =  v1
vpr  v1 -> FingerTree v1 (Node v1 a1) -> v1
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v1 (Node v1 a1)
m

traverseWPNode :: (Measured v1 a1, Measured v2 a2, Applicative f) =>
    (v1 -> a1 -> f a2) -> v1 -> Node v1 a1 -> f (Node v2 a2)
traverseWPNode :: (v1 -> a1 -> f a2) -> v1 -> Node v1 a1 -> f (Node v2 a2)
traverseWPNode v1 -> a1 -> f a2
f v1
v (Node2 v1
_ a1
a a1
b) = a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> Node v a
node2 (a2 -> a2 -> Node v2 a2) -> f a2 -> f (a2 -> Node v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v1 -> a1 -> f a2
f v1
v a1
a f (a2 -> Node v2 a2) -> f a2 -> f (Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v1 -> a1 -> f a2
f v1
va a1
b
  where
    va :: v1
va      = v1
v v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
a
traverseWPNode v1 -> a1 -> f a2
f v1
v (Node3 v1
_ a1
a a1
b a1
c) = a2 -> a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> a -> Node v a
node3 (a2 -> a2 -> a2 -> Node v2 a2)
-> f a2 -> f (a2 -> a2 -> Node v2 a2)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v1 -> a1 -> f a2
f v1
v a1
a f (a2 -> a2 -> Node v2 a2) -> f a2 -> f (a2 -> Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v1 -> a1 -> f a2
f v1
va a1
b f (a2 -> Node v2 a2) -> f a2 -> f (Node v2 a2)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v1 -> a1 -> f a2
f v1
vab a1
c
  where
    va :: v1
va      = v1
v v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
a
    vab :: v1
vab     = v1
va v1 -> v1 -> v1
forall a. Monoid a => a -> a -> a
`mappend` a1 -> v1
forall v a. Measured v a => a -> v
measure a1
b

traverseWPDigit :: (Measured v a, Applicative f) =>
    (v -> a -> f b) -> v -> Digit a -> f (Digit b)
traverseWPDigit :: (v -> a -> f b) -> v -> Digit a -> f (Digit b)
traverseWPDigit v -> a -> f b
f v
v (One a
a) = b -> Digit b
forall a. a -> Digit a
One (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v -> a -> f b
f v
v a
a
traverseWPDigit v -> a -> f b
f v
v (Two a
a a
b) = b -> b -> Digit b
forall a. a -> a -> Digit a
Two (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v -> a -> f b
f v
v a
a f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
va a
b
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
traverseWPDigit v -> a -> f b
f v
v (Three a
a a
b a
c) = b -> b -> b -> Digit b
forall a. a -> a -> a -> Digit a
Three (b -> b -> b -> Digit b) -> f b -> f (b -> b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v -> a -> f b
f v
v a
a f (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
va a
b f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
vab a
c
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
traverseWPDigit v -> a -> f b
f v
v (Four a
a a
b a
c a
d) = b -> b -> b -> b -> Digit b
forall a. a -> a -> a -> a -> Digit a
Four (b -> b -> b -> b -> Digit b) -> f b -> f (b -> b -> b -> Digit b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> v -> a -> f b
f v
v a
a f (b -> b -> b -> Digit b) -> f b -> f (b -> b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
va a
b f (b -> b -> Digit b) -> f b -> f (b -> Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
vab a
c f (b -> Digit b) -> f b -> f (Digit b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> v -> a -> f b
f v
vabc a
d
  where
    va :: v
va      = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
    vabc :: v
vabc    = v
vab v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
c

-- | Like 'traverse', but safe only if the function preserves the measure.
unsafeTraverse :: (Applicative f) =>
    (a -> f b) -> FingerTree v a -> f (FingerTree v b)
unsafeTraverse :: (a -> f b) -> FingerTree v a -> f (FingerTree v b)
unsafeTraverse a -> f b
_ FingerTree v a
Empty = FingerTree v b -> f (FingerTree v b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure FingerTree v b
forall v a. FingerTree v a
Empty
unsafeTraverse a -> f b
f (Single a
x) = b -> FingerTree v b
forall v a. a -> FingerTree v a
Single (b -> FingerTree v b) -> f b -> f (FingerTree v b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
x
unsafeTraverse a -> f b
f (Deep v
v Digit a
pr FingerTree v (Node v a)
m Digit a
sf) =
    v
-> Digit b -> FingerTree v (Node v b) -> Digit b -> FingerTree v b
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep v
v (Digit b -> FingerTree v (Node v b) -> Digit b -> FingerTree v b)
-> f (Digit b)
-> f (FingerTree v (Node v b) -> Digit b -> FingerTree v b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> Digit a -> f (Digit b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Digit a -> f (Digit b)
traverseDigit a -> f b
f Digit a
pr f (FingerTree v (Node v b) -> Digit b -> FingerTree v b)
-> f (FingerTree v (Node v b)) -> f (Digit b -> FingerTree v b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (Node v a -> f (Node v b))
-> FingerTree v (Node v a) -> f (FingerTree v (Node v b))
forall (f :: * -> *) a b v.
Applicative f =>
(a -> f b) -> FingerTree v a -> f (FingerTree v b)
unsafeTraverse ((a -> f b) -> Node v a -> f (Node v b)
forall (f :: * -> *) a b v.
Applicative f =>
(a -> f b) -> Node v a -> f (Node v b)
unsafeTraverseNode a -> f b
f) FingerTree v (Node v a)
m f (Digit b -> FingerTree v b) -> f (Digit b) -> f (FingerTree v b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (a -> f b) -> Digit a -> f (Digit b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Digit a -> f (Digit b)
traverseDigit a -> f b
f Digit a
sf

unsafeTraverseNode :: (Applicative f) =>
    (a -> f b) -> Node v a -> f (Node v b)
unsafeTraverseNode :: (a -> f b) -> Node v a -> f (Node v b)
unsafeTraverseNode a -> f b
f (Node2 v
v a
a a
b)   = v -> b -> b -> Node v b
forall v a. v -> a -> a -> Node v a
Node2 v
v (b -> b -> Node v b) -> f b -> f (b -> Node v b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> Node v b) -> f b -> f (Node v b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b
unsafeTraverseNode a -> f b
f (Node3 v
v a
a a
b a
c) = v -> b -> b -> b -> Node v b
forall v a. v -> a -> a -> a -> Node v a
Node3 v
v (b -> b -> b -> Node v b) -> f b -> f (b -> b -> Node v b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
a f (b -> b -> Node v b) -> f b -> f (b -> Node v b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
b f (b -> Node v b) -> f b -> f (Node v b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f b
f a
c

-----------------------------------------------------
-- 4.3 Construction, deconstruction and concatenation
-----------------------------------------------------

-- | /O(1)/. The empty sequence.
empty :: FingerTree v a
empty :: FingerTree v a
empty = FingerTree v a
forall v a. FingerTree v a
Empty

-- | /O(1)/. A singleton sequence.
singleton :: a -> FingerTree v a
singleton :: a -> FingerTree v a
singleton = a -> FingerTree v a
forall v a. a -> FingerTree v a
Single

-- | /O(n)/. Create a sequence from a finite list of elements.
fromList :: Measured v a => [a] -> FingerTree v a
fromList :: [a] -> FingerTree v a
fromList = (a -> FingerTree v a -> FingerTree v a)
-> FingerTree v a -> [a] -> FingerTree v a
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr' a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
(<|) FingerTree v a
forall v a. FingerTree v a
Empty

-- | /O(1)/. Add an element to the left end of a sequence.
-- Mnemonic: a triangle with the single element at the pointy end.
(<|) :: Measured v a => a -> FingerTree v a -> FingerTree v a
a
a <| :: a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
Empty              =  a -> FingerTree v a
forall v a. a -> FingerTree v a
Single a
a
a
a <| Single a
b           =  Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (a -> Digit a
forall a. a -> Digit a
One a
a) FingerTree v (Node v a)
forall v a. FingerTree v a
Empty (a -> Digit a
forall a. a -> Digit a
One a
b)
a
a <| Deep v
v (Four a
b a
c a
d a
e) FingerTree v (Node v a)
m Digit a
sf = FingerTree v (Node v a)
m FingerTree v (Node v a) -> FingerTree v a -> FingerTree v a
`seq`
    v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (a -> v
forall v a. Measured v a => a -> v
measure a
a v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` v
v) (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
c a
d a
e Node v a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v (Node v a)
m) Digit a
sf
a
a <| Deep v
v Digit a
pr FingerTree v (Node v a)
m Digit a
sf     =
    v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (a -> v
forall v a. Measured v a => a -> v
measure a
a v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` v
v) (a -> Digit a -> Digit a
forall a. a -> Digit a -> Digit a
consDigit a
a Digit a
pr) FingerTree v (Node v a)
m Digit a
sf

consDigit :: a -> Digit a -> Digit a
consDigit :: a -> Digit a -> Digit a
consDigit a
a (One a
b)        = a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b
consDigit a
a (Two a
b a
c)      = a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
a a
b a
c
consDigit a
a (Three a
b a
c a
d)  = a -> a -> a -> a -> Digit a
forall a. a -> a -> a -> a -> Digit a
Four a
a a
b a
c a
d
consDigit a
_ (Four a
_ a
_ a
_ a
_) = String -> Digit a
forall a. String -> a
illegalArgument String
"consDigit"

-- | /O(1)/. Add an element to the right end of a sequence.
-- Mnemonic: a triangle with the single element at the pointy end.
(|>) :: Measured v a => FingerTree v a -> a -> FingerTree v a
FingerTree v a
Empty |> :: FingerTree v a -> a -> FingerTree v a
|> a
a              =  a -> FingerTree v a
forall v a. a -> FingerTree v a
Single a
a
Single a
a |> a
b           =  Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (a -> Digit a
forall a. a -> Digit a
One a
a) FingerTree v (Node v a)
forall v a. FingerTree v a
Empty (a -> Digit a
forall a. a -> Digit a
One a
b)
Deep v
v Digit a
pr FingerTree v (Node v a)
m (Four a
a a
b a
c a
d) |> a
e = FingerTree v (Node v a)
m FingerTree v (Node v a) -> FingerTree v a -> FingerTree v a
`seq`
    v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
e) Digit a
pr (FingerTree v (Node v a)
m FingerTree v (Node v a) -> Node v a -> FingerTree v (Node v a)
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
d a
e)
Deep v
v Digit a
pr FingerTree v (Node v a)
m Digit a
sf |> a
x     =
    v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
x) Digit a
pr FingerTree v (Node v a)
m (Digit a -> a -> Digit a
forall a. Digit a -> a -> Digit a
snocDigit Digit a
sf a
x)

snocDigit :: Digit a -> a -> Digit a
snocDigit :: Digit a -> a -> Digit a
snocDigit (One a
a) a
b        = a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b
snocDigit (Two a
a a
b) a
c      = a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
a a
b a
c
snocDigit (Three a
a a
b a
c) a
d  = a -> a -> a -> a -> Digit a
forall a. a -> a -> a -> a -> Digit a
Four a
a a
b a
c a
d
snocDigit (Four a
_ a
_ a
_ a
_) a
_ = String -> Digit a
forall a. String -> a
illegalArgument String
"snocDigit"

-- | /O(1)/. Is this the empty sequence?
null :: FingerTree v a -> Bool
null :: FingerTree v a -> Bool
null FingerTree v a
Empty = Bool
True
null FingerTree v a
_     = Bool
False

-- | /O(1)/. Analyse the left end of a sequence.
viewl :: Measured v a => FingerTree v a -> ViewL (FingerTree v) a
viewl :: FingerTree v a -> ViewL (FingerTree v) a
viewl FingerTree v a
Empty                 =  ViewL (FingerTree v) a
forall (s :: * -> *) a. ViewL s a
EmptyL
viewl (Single a
x)            =  a
x a -> FingerTree v a -> ViewL (FingerTree v) a
forall (s :: * -> *) a. a -> s a -> ViewL s a
:< FingerTree v a
forall v a. FingerTree v a
Empty
viewl (Deep v
_ (One a
x) FingerTree v (Node v a)
m Digit a
sf) =  a
x a -> FingerTree v a -> ViewL (FingerTree v) a
forall (s :: * -> *) a. a -> s a -> ViewL s a
:< FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
FingerTree v (Node v a) -> Digit a -> FingerTree v a
rotL FingerTree v (Node v a)
m Digit a
sf
viewl (Deep v
_ Digit a
pr FingerTree v (Node v a)
m Digit a
sf)      =  Digit a -> a
forall a. Digit a -> a
lheadDigit Digit a
pr a -> FingerTree v a -> ViewL (FingerTree v) a
forall (s :: * -> *) a. a -> s a -> ViewL s a
:< Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (Digit a -> Digit a
forall a. Digit a -> Digit a
ltailDigit Digit a
pr) FingerTree v (Node v a)
m Digit a
sf

rotL :: Measured v a => FingerTree v (Node v a) -> Digit a -> FingerTree v a
rotL :: FingerTree v (Node v a) -> Digit a -> FingerTree v a
rotL FingerTree v (Node v a)
m Digit a
sf      =   case FingerTree v (Node v a) -> ViewL (FingerTree v) (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> ViewL (FingerTree v) a
viewl FingerTree v (Node v a)
m of
    ViewL (FingerTree v) (Node v a)
EmptyL  ->  Digit a -> FingerTree v a
forall v a. Measured v a => Digit a -> FingerTree v a
digitToTree Digit a
sf
    Node v a
a :< FingerTree v (Node v a)
m' ->  v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (FingerTree v (Node v a) -> v
forall v a. Measured v a => a -> v
measure FingerTree v (Node v a)
m v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` Digit a -> v
forall v a. Measured v a => a -> v
measure Digit a
sf) (Node v a -> Digit a
forall v a. Node v a -> Digit a
nodeToDigit Node v a
a) FingerTree v (Node v a)
m' Digit a
sf

lheadDigit :: Digit a -> a
lheadDigit :: Digit a -> a
lheadDigit (One a
a)        = a
a
lheadDigit (Two a
a a
_)      = a
a
lheadDigit (Three a
a a
_ a
_)  = a
a
lheadDigit (Four a
a a
_ a
_ a
_) = a
a

ltailDigit :: Digit a -> Digit a
ltailDigit :: Digit a -> Digit a
ltailDigit (One a
_)        = String -> Digit a
forall a. String -> a
illegalArgument String
"ltailDigit"
ltailDigit (Two a
_ a
b)      = a -> Digit a
forall a. a -> Digit a
One a
b
ltailDigit (Three a
_ a
b a
c)  = a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
b a
c
ltailDigit (Four a
_ a
b a
c a
d) = a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
b a
c a
d

-- | /O(1)/. Analyse the right end of a sequence.
viewr :: Measured v a => FingerTree v a -> ViewR (FingerTree v) a
viewr :: FingerTree v a -> ViewR (FingerTree v) a
viewr FingerTree v a
Empty                 =  ViewR (FingerTree v) a
forall (s :: * -> *) a. ViewR s a
EmptyR
viewr (Single a
x)            =  FingerTree v a
forall v a. FingerTree v a
Empty FingerTree v a -> a -> ViewR (FingerTree v) a
forall (s :: * -> *) a. s a -> a -> ViewR s a
:> a
x
viewr (Deep v
_ Digit a
pr FingerTree v (Node v a)
m (One a
x)) =  Digit a -> FingerTree v (Node v a) -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> FingerTree v a
rotR Digit a
pr FingerTree v (Node v a)
m FingerTree v a -> a -> ViewR (FingerTree v) a
forall (s :: * -> *) a. s a -> a -> ViewR s a
:> a
x
viewr (Deep v
_ Digit a
pr FingerTree v (Node v a)
m Digit a
sf)      =  Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr FingerTree v (Node v a)
m (Digit a -> Digit a
forall a. Digit a -> Digit a
rtailDigit Digit a
sf) FingerTree v a -> a -> ViewR (FingerTree v) a
forall (s :: * -> *) a. s a -> a -> ViewR s a
:> Digit a -> a
forall a. Digit a -> a
rheadDigit Digit a
sf

rotR :: Measured v a => Digit a -> FingerTree v (Node v a) -> FingerTree v a
rotR :: Digit a -> FingerTree v (Node v a) -> FingerTree v a
rotR Digit a
pr FingerTree v (Node v a)
m = case FingerTree v (Node v a) -> ViewR (FingerTree v) (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> ViewR (FingerTree v) a
viewr FingerTree v (Node v a)
m of
    ViewR (FingerTree v) (Node v a)
EmptyR  ->  Digit a -> FingerTree v a
forall v a. Measured v a => Digit a -> FingerTree v a
digitToTree Digit a
pr
    FingerTree v (Node v a)
m' :> Node v a
a ->  v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
v
-> Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
Deep (Digit a -> v
forall v a. Measured v a => a -> v
measure Digit a
pr v -> FingerTree v (Node v a) -> v
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v (Node v a)
m) Digit a
pr FingerTree v (Node v a)
m' (Node v a -> Digit a
forall v a. Node v a -> Digit a
nodeToDigit Node v a
a)

rheadDigit :: Digit a -> a
rheadDigit :: Digit a -> a
rheadDigit (One a
a)        = a
a
rheadDigit (Two a
_ a
b)      = a
b
rheadDigit (Three a
_ a
_ a
c)  = a
c
rheadDigit (Four a
_ a
_ a
_ a
d) = a
d

rtailDigit :: Digit a -> Digit a
rtailDigit :: Digit a -> Digit a
rtailDigit (One a
_)        = String -> Digit a
forall a. String -> a
illegalArgument String
"rtailDigit"
rtailDigit (Two a
a a
_)      = a -> Digit a
forall a. a -> Digit a
One a
a
rtailDigit (Three a
a a
b a
_)  = a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b
rtailDigit (Four a
a a
b a
c a
_) = a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
a a
b a
c

digitToTree :: Measured v a => Digit a -> FingerTree v a
digitToTree :: Digit a -> FingerTree v a
digitToTree (One a
a)        = a -> FingerTree v a
forall v a. a -> FingerTree v a
Single a
a
digitToTree (Two a
a a
b)      = Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (a -> Digit a
forall a. a -> Digit a
One a
a) FingerTree v (Node v a)
forall v a. FingerTree v a
Empty (a -> Digit a
forall a. a -> Digit a
One a
b)
digitToTree (Three a
a a
b a
c)  = Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b) FingerTree v (Node v a)
forall v a. FingerTree v a
Empty (a -> Digit a
forall a. a -> Digit a
One a
c)
digitToTree (Four a
a a
b a
c a
d) = Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b) FingerTree v (Node v a)
forall v a. FingerTree v a
Empty (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
c a
d)

----------------
-- Concatenation
----------------

-- | /O(log(min(n1,n2)))/. Concatenate two sequences.
(><) :: Measured v a => FingerTree v a -> FingerTree v a -> FingerTree v a
>< :: FingerTree v a -> FingerTree v a -> FingerTree v a
(><) =  FingerTree v a -> FingerTree v a -> FingerTree v a
forall v a.
Measured v a =>
FingerTree v a -> FingerTree v a -> FingerTree v a
appendTree0

appendTree0 :: Measured v a => FingerTree v a -> FingerTree v a -> FingerTree v a
appendTree0 :: FingerTree v a -> FingerTree v a -> FingerTree v a
appendTree0 FingerTree v a
Empty FingerTree v a
xs =
    FingerTree v a
xs
appendTree0 FingerTree v a
xs FingerTree v a
Empty =
    FingerTree v a
xs
appendTree0 (Single a
x) FingerTree v a
xs =
    a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree0 FingerTree v a
xs (Single a
x) =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
x
appendTree0 (Deep v
_ Digit a
pr1 FingerTree v (Node v a)
m1 Digit a
sf1) (Deep v
_ Digit a
pr2 FingerTree v (Node v a)
m2 Digit a
sf2) =
    Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr1 (FingerTree v (Node v a)
-> Digit a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v (Node v a)
-> Digit a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits0 FingerTree v (Node v a)
m1 Digit a
sf1 Digit a
pr2 FingerTree v (Node v a)
m2) Digit a
sf2

addDigits0 :: Measured v a => FingerTree v (Node v a) -> Digit a -> Digit a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
addDigits0 :: FingerTree v (Node v a)
-> Digit a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits0 FingerTree v (Node v a)
m1 (One a
a) (One a
b) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (One a
a) (Two a
b a
c) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (One a
a) (Three a
b a
c a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (One a
a) (Four a
b a
c a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Two a
a a
b) (One a
c) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Two a
a a
b) (Two a
c a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Two a
a a
b) (Three a
c a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Two a
a a
b) (Four a
c a
d a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) (One a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) (Two a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) (Three a
d a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) (Four a
d a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) (One a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) (Two a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) (Three a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits0 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) (Four a
e a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2

appendTree1 :: Measured v a => FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 :: FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 FingerTree v a
Empty a
a FingerTree v a
xs =
    a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree1 FingerTree v a
xs a
a FingerTree v a
Empty =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a
appendTree1 (Single a
x) a
a FingerTree v a
xs =
    a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree1 FingerTree v a
xs a
a (Single a
x) =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
x
appendTree1 (Deep v
_ Digit a
pr1 FingerTree v (Node v a)
m1 Digit a
sf1) a
a (Deep v
_ Digit a
pr2 FingerTree v (Node v a)
m2 Digit a
sf2) =
    Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr1 (FingerTree v (Node v a)
-> Digit a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v (Node v a)
-> Digit a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits1 FingerTree v (Node v a)
m1 Digit a
sf1 a
a Digit a
pr2 FingerTree v (Node v a)
m2) Digit a
sf2

addDigits1 :: Measured v a => FingerTree v (Node v a) -> Digit a -> a -> Digit a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
addDigits1 :: FingerTree v (Node v a)
-> Digit a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits1 FingerTree v (Node v a)
m1 (One a
a) a
b (One a
c) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> FingerTree v a -> FingerTree v a
appendTree1 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (One a
a) a
b (Two a
c a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (One a
a) a
b (Three a
c a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (One a
a) a
b (Four a
c a
d a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c (One a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c (Two a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c (Three a
d a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c (Four a
d a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d (One a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d (Two a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d (Three a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d (Four a
e a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e (One a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e (Two a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e (Three a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits1 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e (Four a
f a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2

appendTree2 :: Measured v a => FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 :: FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v a
Empty a
a a
b FingerTree v a
xs =
    a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree2 FingerTree v a
xs a
a a
b FingerTree v a
Empty =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b
appendTree2 (Single a
x) a
a a
b FingerTree v a
xs =
    a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree2 FingerTree v a
xs a
a a
b (Single a
x) =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
x
appendTree2 (Deep v
_ Digit a
pr1 FingerTree v (Node v a)
m1 Digit a
sf1) a
a a
b (Deep v
_ Digit a
pr2 FingerTree v (Node v a)
m2 Digit a
sf2) =
    Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr1 (FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits2 FingerTree v (Node v a)
m1 Digit a
sf1 a
a a
b Digit a
pr2 FingerTree v (Node v a)
m2) Digit a
sf2

addDigits2 :: Measured v a => FingerTree v (Node v a) -> Digit a -> a -> a -> Digit a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
addDigits2 :: FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits2 FingerTree v (Node v a)
m1 (One a
a) a
b a
c (One a
d) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
a a
b) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
c a
d) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (One a
a) a
b a
c (Two a
d a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (One a
a) a
b a
c (Three a
d a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (One a
a) a
b a
c (Four a
d a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d (One a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d (Two a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d (Three a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d (Four a
e a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e (One a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e (Two a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e (Three a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e (Four a
f a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f (One a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f (Two a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f (Three a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits2 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f (Four a
g a
h a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2

appendTree3 :: Measured v a => FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 :: FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v a
Empty a
a a
b a
c FingerTree v a
xs =
    a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
c a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree3 FingerTree v a
xs a
a a
b a
c FingerTree v a
Empty =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
c
appendTree3 (Single a
x) a
a a
b a
c FingerTree v a
xs =
    a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
c a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree3 FingerTree v a
xs a
a a
b a
c (Single a
x) =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
c FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
x
appendTree3 (Deep v
_ Digit a
pr1 FingerTree v (Node v a)
m1 Digit a
sf1) a
a a
b a
c (Deep v
_ Digit a
pr2 FingerTree v (Node v a)
m2 Digit a
sf2) =
    Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr1 (FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits3 FingerTree v (Node v a)
m1 Digit a
sf1 a
a a
b a
c Digit a
pr2 FingerTree v (Node v a)
m2) Digit a
sf2

addDigits3 :: Measured v a => FingerTree v (Node v a) -> Digit a -> a -> a -> a -> Digit a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
addDigits3 :: FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits3 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d (One a
e) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d (Two a
e a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d (Three a
e a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d (Four a
e a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e (One a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e (Two a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e (Three a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e (Four a
f a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f (One a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f (Two a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f (Three a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f (Four a
g a
h a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g (One a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g (Two a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g (Three a
h a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2
addDigits3 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g (Four a
h a
i a
j a
k) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
j a
k) FingerTree v (Node v a)
m2

appendTree4 :: Measured v a => FingerTree v a -> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 :: FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v a
Empty a
a a
b a
c a
d FingerTree v a
xs =
    a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
c a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
d a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree4 FingerTree v a
xs a
a a
b a
c a
d FingerTree v a
Empty =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
c FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
d
appendTree4 (Single a
x) a
a a
b a
c a
d FingerTree v a
xs =
    a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
a a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
b a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
c a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| a
d a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
xs
appendTree4 FingerTree v a
xs a
a a
b a
c a
d (Single a
x) =
    FingerTree v a
xs FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
a FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
b FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
c FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
d FingerTree v a -> a -> FingerTree v a
forall v a. Measured v a => FingerTree v a -> a -> FingerTree v a
|> a
x
appendTree4 (Deep v
_ Digit a
pr1 FingerTree v (Node v a)
m1 Digit a
sf1) a
a a
b a
c a
d (Deep v
_ Digit a
pr2 FingerTree v (Node v a)
m2 Digit a
sf2) =
    Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr1 (FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits4 FingerTree v (Node v a)
m1 Digit a
sf1 a
a a
b a
c a
d Digit a
pr2 FingerTree v (Node v a)
m2) Digit a
sf2

addDigits4 :: Measured v a => FingerTree v (Node v a) -> Digit a -> a -> a -> a -> a -> Digit a -> FingerTree v (Node v a) -> FingerTree v (Node v a)
addDigits4 :: FingerTree v (Node v a)
-> Digit a
-> a
-> a
-> a
-> a
-> Digit a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
addDigits4 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d a
e (One a
f) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree2 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d a
e (Two a
f a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d a
e (Three a
f a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (One a
a) a
b a
c a
d a
e (Four a
f a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e a
f (One a
g) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
d a
e) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
f a
g) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e a
f (Two a
g a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e a
f (Three a
g a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Two a
a a
b) a
c a
d a
e a
f (Four a
g a
h a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f a
g (One a
h) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f a
g (Two a
h a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f a
g (Three a
h a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Three a
a a
b a
c) a
d a
e a
f a
g (Four a
h a
i a
j a
k) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
j a
k) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g a
h (One a
i) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree3 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g a
h (Two a
i a
j) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
g a
h) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
i a
j) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g a
h (Three a
i a
j a
k) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) (a -> a -> Node v a
forall v a. Measured v a => a -> a -> Node v a
node2 a
j a
k) FingerTree v (Node v a)
m2
addDigits4 FingerTree v (Node v a)
m1 (Four a
a a
b a
c a
d) a
e a
f a
g a
h (Four a
i a
j a
k a
l) FingerTree v (Node v a)
m2 =
    FingerTree v (Node v a)
-> Node v a
-> Node v a
-> Node v a
-> Node v a
-> FingerTree v (Node v a)
-> FingerTree v (Node v a)
forall v a.
Measured v a =>
FingerTree v a
-> a -> a -> a -> a -> FingerTree v a -> FingerTree v a
appendTree4 FingerTree v (Node v a)
m1 (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
a a
b a
c) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
d a
e a
f) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
g a
h a
i) (a -> a -> a -> Node v a
forall v a. Measured v a => a -> a -> a -> Node v a
node3 a
j a
k a
l) FingerTree v (Node v a)
m2

----------------
-- 4.4 Splitting
----------------

-- | /O(log(min(i,n-i)))/. Split a sequence at a point where the predicate
-- on the accumulated measure changes from 'False' to 'True'.
--
-- For predictable results, one should ensure that there is only one such
-- point, i.e. that the predicate is /monotonic/.
split ::  Measured v a =>
      (v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
split :: (v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
split v -> Bool
_ FingerTree v a
Empty  =  (FingerTree v a
forall v a. FingerTree v a
Empty, FingerTree v a
forall v a. FingerTree v a
Empty)
split v -> Bool
p FingerTree v a
xs
  | v -> Bool
p (FingerTree v a -> v
forall v a. Measured v a => a -> v
measure FingerTree v a
xs) =  (FingerTree v a
l, a
x a -> FingerTree v a -> FingerTree v a
forall v a. Measured v a => a -> FingerTree v a -> FingerTree v a
<| FingerTree v a
r)
  | Bool
otherwise   =  (FingerTree v a
xs, FingerTree v a
forall v a. FingerTree v a
Empty)
  where
    Split FingerTree v a
l a
x FingerTree v a
r = (v -> Bool) -> v -> FingerTree v a -> Split (FingerTree v a) a
forall v a.
Measured v a =>
(v -> Bool) -> v -> FingerTree v a -> Split (FingerTree v a) a
splitTree v -> Bool
p v
forall a. Monoid a => a
mempty FingerTree v a
xs

-- | /O(log(min(i,n-i)))/.
-- Given a monotonic predicate @p@, @'takeUntil' p t@ is the largest
-- prefix of @t@ whose measure does not satisfy @p@.
--
-- *  @'takeUntil' p t = 'fst' ('split' p t)@
takeUntil :: Measured v a => (v -> Bool) -> FingerTree v a -> FingerTree v a
takeUntil :: (v -> Bool) -> FingerTree v a -> FingerTree v a
takeUntil v -> Bool
p  =  (FingerTree v a, FingerTree v a) -> FingerTree v a
forall a b. (a, b) -> a
fst ((FingerTree v a, FingerTree v a) -> FingerTree v a)
-> (FingerTree v a -> (FingerTree v a, FingerTree v a))
-> FingerTree v a
-> FingerTree v a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
forall v a.
Measured v a =>
(v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
split v -> Bool
p

-- | /O(log(min(i,n-i)))/.
-- Given a monotonic predicate @p@, @'dropUntil' p t@ is the rest of @t@
-- after removing the largest prefix whose measure does not satisfy @p@.
--
-- * @'dropUntil' p t = 'snd' ('split' p t)@
dropUntil :: Measured v a => (v -> Bool) -> FingerTree v a -> FingerTree v a
dropUntil :: (v -> Bool) -> FingerTree v a -> FingerTree v a
dropUntil v -> Bool
p  =  (FingerTree v a, FingerTree v a) -> FingerTree v a
forall a b. (a, b) -> b
snd ((FingerTree v a, FingerTree v a) -> FingerTree v a)
-> (FingerTree v a -> (FingerTree v a, FingerTree v a))
-> FingerTree v a
-> FingerTree v a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
forall v a.
Measured v a =>
(v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)
split v -> Bool
p

data Split t a = Split !t !a !t deriving (Split t a -> Split t a -> Bool
(Split t a -> Split t a -> Bool)
-> (Split t a -> Split t a -> Bool) -> Eq (Split t a)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall t a. (Eq t, Eq a) => Split t a -> Split t a -> Bool
/= :: Split t a -> Split t a -> Bool
$c/= :: forall t a. (Eq t, Eq a) => Split t a -> Split t a -> Bool
== :: Split t a -> Split t a -> Bool
$c== :: forall t a. (Eq t, Eq a) => Split t a -> Split t a -> Bool
Eq, Int -> Split t a -> ShowS
[Split t a] -> ShowS
Split t a -> String
(Int -> Split t a -> ShowS)
-> (Split t a -> String)
-> ([Split t a] -> ShowS)
-> Show (Split t a)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall t a. (Show t, Show a) => Int -> Split t a -> ShowS
forall t a. (Show t, Show a) => [Split t a] -> ShowS
forall t a. (Show t, Show a) => Split t a -> String
showList :: [Split t a] -> ShowS
$cshowList :: forall t a. (Show t, Show a) => [Split t a] -> ShowS
show :: Split t a -> String
$cshow :: forall t a. (Show t, Show a) => Split t a -> String
showsPrec :: Int -> Split t a -> ShowS
$cshowsPrec :: forall t a. (Show t, Show a) => Int -> Split t a -> ShowS
Show, (forall x. Split t a -> Rep (Split t a) x)
-> (forall x. Rep (Split t a) x -> Split t a)
-> Generic (Split t a)
forall x. Rep (Split t a) x -> Split t a
forall x. Split t a -> Rep (Split t a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall t a x. Rep (Split t a) x -> Split t a
forall t a x. Split t a -> Rep (Split t a) x
$cto :: forall t a x. Rep (Split t a) x -> Split t a
$cfrom :: forall t a x. Split t a -> Rep (Split t a) x
Generic, Split t a -> ()
(Split t a -> ()) -> NFData (Split t a)
forall a. (a -> ()) -> NFData a
forall t a. (NFData t, NFData a) => Split t a -> ()
rnf :: Split t a -> ()
$crnf :: forall t a. (NFData t, NFData a) => Split t a -> ()
NFData)

splitTree :: Measured v a =>
    (v -> Bool) -> v -> FingerTree v a -> Split (FingerTree v a) a
splitTree :: (v -> Bool) -> v -> FingerTree v a -> Split (FingerTree v a) a
splitTree v -> Bool
_ v
_ FingerTree v a
Empty = String -> Split (FingerTree v a) a
forall a. String -> a
illegalArgument String
"splitTree"
splitTree v -> Bool
_ v
_ (Single a
x) = FingerTree v a -> a -> FingerTree v a -> Split (FingerTree v a) a
forall t a. t -> a -> t -> Split t a
Split FingerTree v a
forall v a. FingerTree v a
Empty a
x FingerTree v a
forall v a. FingerTree v a
Empty
splitTree v -> Bool
p v
i (Deep v
_ Digit a
pr FingerTree v (Node v a)
m Digit a
sf)
  | v -> Bool
p v
vpr       =  let  Split Maybe (Digit a)
l a
x Maybe (Digit a)
r     =  (v -> Bool) -> v -> Digit a -> Split (Maybe (Digit a)) a
forall v a.
Measured v a =>
(v -> Bool) -> v -> Digit a -> Split (Maybe (Digit a)) a
splitDigit v -> Bool
p v
i Digit a
pr
                   in   FingerTree v a -> a -> FingerTree v a -> Split (FingerTree v a) a
forall t a. t -> a -> t -> Split t a
Split (FingerTree v a
-> (Digit a -> FingerTree v a) -> Maybe (Digit a) -> FingerTree v a
forall b a. b -> (a -> b) -> Maybe a -> b
maybe FingerTree v a
forall v a. FingerTree v a
Empty Digit a -> FingerTree v a
forall v a. Measured v a => Digit a -> FingerTree v a
digitToTree Maybe (Digit a)
l) a
x (Maybe (Digit a)
-> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Maybe (Digit a)
-> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deepL Maybe (Digit a)
r FingerTree v (Node v a)
m Digit a
sf)
  | v -> Bool
p v
vm        =  let  Split FingerTree v (Node v a)
ml Node v a
xs FingerTree v (Node v a)
mr  =  (v -> Bool)
-> v
-> FingerTree v (Node v a)
-> Split (FingerTree v (Node v a)) (Node v a)
forall v a.
Measured v a =>
(v -> Bool) -> v -> FingerTree v a -> Split (FingerTree v a) a
splitTree v -> Bool
p v
vpr FingerTree v (Node v a)
m
                        Split Maybe (Digit a)
l a
x Maybe (Digit a)
r     =  (v -> Bool) -> v -> Node v a -> Split (Maybe (Digit a)) a
forall v a.
Measured v a =>
(v -> Bool) -> v -> Node v a -> Split (Maybe (Digit a)) a
splitNode v -> Bool
p (v
vpr v -> FingerTree v (Node v a) -> v
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v (Node v a)
ml) Node v a
xs
                   in   FingerTree v a -> a -> FingerTree v a -> Split (FingerTree v a) a
forall t a. t -> a -> t -> Split t a
Split (Digit a
-> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
forall v a.
Measured v a =>
Digit a
-> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
deepR Digit a
pr  FingerTree v (Node v a)
ml Maybe (Digit a)
l) a
x (Maybe (Digit a)
-> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Maybe (Digit a)
-> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deepL Maybe (Digit a)
r FingerTree v (Node v a)
mr Digit a
sf)
  | Bool
otherwise   =  let  Split Maybe (Digit a)
l a
x Maybe (Digit a)
r     =  (v -> Bool) -> v -> Digit a -> Split (Maybe (Digit a)) a
forall v a.
Measured v a =>
(v -> Bool) -> v -> Digit a -> Split (Maybe (Digit a)) a
splitDigit v -> Bool
p v
vm Digit a
sf
                   in   FingerTree v a -> a -> FingerTree v a -> Split (FingerTree v a) a
forall t a. t -> a -> t -> Split t a
Split (Digit a
-> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
forall v a.
Measured v a =>
Digit a
-> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
deepR Digit a
pr  FingerTree v (Node v a)
m  Maybe (Digit a)
l) a
x (FingerTree v a
-> (Digit a -> FingerTree v a) -> Maybe (Digit a) -> FingerTree v a
forall b a. b -> (a -> b) -> Maybe a -> b
maybe FingerTree v a
forall v a. FingerTree v a
Empty Digit a -> FingerTree v a
forall v a. Measured v a => Digit a -> FingerTree v a
digitToTree Maybe (Digit a)
r)
  where
    vpr :: v
vpr     =  v
i    v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend`  Digit a -> v
forall v a. Measured v a => a -> v
measure Digit a
pr
    vm :: v
vm      =  v
vpr  v -> FingerTree v (Node v a) -> v
forall v a. Measured v a => v -> FingerTree v a -> v
`mappendVal` FingerTree v (Node v a)
m

-- Avoid relying on right identity (cf Exercise 7)
mappendVal :: Measured v a => v -> FingerTree v a -> v
mappendVal :: v -> FingerTree v a -> v
mappendVal v
v FingerTree v a
Empty = v
v
mappendVal v
v FingerTree v a
t     = v
v v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` FingerTree v a -> v
forall v a. Measured v a => a -> v
measure FingerTree v a
t

deepL :: Measured v a =>
    Maybe (Digit a) -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deepL :: Maybe (Digit a)
-> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deepL Maybe (Digit a)
Nothing FingerTree v (Node v a)
m Digit a
sf   =   FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
FingerTree v (Node v a) -> Digit a -> FingerTree v a
rotL FingerTree v (Node v a)
m Digit a
sf
deepL (Just Digit a
pr) FingerTree v (Node v a)
m Digit a
sf =   Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr FingerTree v (Node v a)
m Digit a
sf

deepR :: Measured v a =>
    Digit a -> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
deepR :: Digit a
-> FingerTree v (Node v a) -> Maybe (Digit a) -> FingerTree v a
deepR Digit a
pr FingerTree v (Node v a)
m Maybe (Digit a)
Nothing   =   Digit a -> FingerTree v (Node v a) -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> FingerTree v a
rotR Digit a
pr FingerTree v (Node v a)
m
deepR Digit a
pr FingerTree v (Node v a)
m (Just Digit a
sf) =   Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep Digit a
pr FingerTree v (Node v a)
m Digit a
sf

splitNode :: Measured v a => (v -> Bool) -> v -> Node v a ->
    Split (Maybe (Digit a)) a
splitNode :: (v -> Bool) -> v -> Node v a -> Split (Maybe (Digit a)) a
splitNode v -> Bool
p v
i (Node2 v
_ a
a a
b)
  | v -> Bool
p v
va        = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
b))
  | Bool
otherwise   = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
a)) a
b Maybe (Digit a)
forall a. Maybe a
Nothing
  where
    va :: v
va      = v
i v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
splitNode v -> Bool
p v
i (Node3 v
_ a
a a
b a
c)
  | v -> Bool
p v
va        = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
b a
c))
  | v -> Bool
p v
vab       = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
a)) a
b (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
c))
  | Bool
otherwise   = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b)) a
c Maybe (Digit a)
forall a. Maybe a
Nothing
  where
    va :: v
va      = v
i v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b

splitDigit :: Measured v a => (v -> Bool) -> v -> Digit a ->
    Split (Maybe (Digit a)) a
splitDigit :: (v -> Bool) -> v -> Digit a -> Split (Maybe (Digit a)) a
splitDigit v -> Bool
_ v
i (One a
a) = v
i v -> Split (Maybe (Digit a)) a -> Split (Maybe (Digit a)) a
`seq` Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a Maybe (Digit a)
forall a. Maybe a
Nothing
splitDigit v -> Bool
p v
i (Two a
a a
b)
  | v -> Bool
p v
va        = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
b))
  | Bool
otherwise   = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
a)) a
b Maybe (Digit a)
forall a. Maybe a
Nothing
  where
    va :: v
va      = v
i v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
splitDigit v -> Bool
p v
i (Three a
a a
b a
c)
  | v -> Bool
p v
va        = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
b a
c))
  | v -> Bool
p v
vab       = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
a)) a
b (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
c))
  | Bool
otherwise   = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b)) a
c Maybe (Digit a)
forall a. Maybe a
Nothing
  where
    va :: v
va      = v
i v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
splitDigit v -> Bool
p v
i (Four a
a a
b a
c a
d)
  | v -> Bool
p v
va        = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split Maybe (Digit a)
forall a. Maybe a
Nothing a
a (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
b a
c a
d))
  | v -> Bool
p v
vab       = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
a)) a
b (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
c a
d))
  | v -> Bool
p v
vabc      = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> Digit a
forall a. a -> a -> Digit a
Two a
a a
b)) a
c (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> Digit a
forall a. a -> Digit a
One a
d))
  | Bool
otherwise   = Maybe (Digit a)
-> a -> Maybe (Digit a) -> Split (Maybe (Digit a)) a
forall t a. t -> a -> t -> Split t a
Split (Digit a -> Maybe (Digit a)
forall a. a -> Maybe a
Just (a -> a -> a -> Digit a
forall a. a -> a -> a -> Digit a
Three a
a a
b a
c)) a
d Maybe (Digit a)
forall a. Maybe a
Nothing
  where
    va :: v
va      = v
i v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
a
    vab :: v
vab     = v
va v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
b
    vabc :: v
vabc    = v
vab v -> v -> v
forall a. Monoid a => a -> a -> a
`mappend` a -> v
forall v a. Measured v a => a -> v
measure a
c

------------------
-- Transformations
------------------

-- | /O(n)/. The reverse of a sequence.
reverse :: Measured v a => FingerTree v a -> FingerTree v a
reverse :: FingerTree v a -> FingerTree v a
reverse = (a -> a) -> FingerTree v a -> FingerTree v a
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
reverseTree a -> a
forall a. a -> a
id

reverseTree :: (Measured v2 a2) => (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
reverseTree :: (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
reverseTree a1 -> a2
_ FingerTree v1 a1
Empty = FingerTree v2 a2
forall v a. FingerTree v a
Empty
reverseTree a1 -> a2
f (Single a1
x) = a2 -> FingerTree v2 a2
forall v a. a -> FingerTree v a
Single (a1 -> a2
f a1
x)
reverseTree a1 -> a2
f (Deep v1
_ Digit a1
pr FingerTree v1 (Node v1 a1)
m Digit a1
sf) =
    Digit a2
-> FingerTree v2 (Node v2 a2) -> Digit a2 -> FingerTree v2 a2
forall v a.
Measured v a =>
Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a
deep ((a1 -> a2) -> Digit a1 -> Digit a2
forall a b. (a -> b) -> Digit a -> Digit b
reverseDigit a1 -> a2
f Digit a1
sf) ((Node v1 a1 -> Node v2 a2)
-> FingerTree v1 (Node v1 a1) -> FingerTree v2 (Node v2 a2)
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2
reverseTree ((a1 -> a2) -> Node v1 a1 -> Node v2 a2
forall v2 a2 a1 v1.
Measured v2 a2 =>
(a1 -> a2) -> Node v1 a1 -> Node v2 a2
reverseNode a1 -> a2
f) FingerTree v1 (Node v1 a1)
m) ((a1 -> a2) -> Digit a1 -> Digit a2
forall a b. (a -> b) -> Digit a -> Digit b
reverseDigit a1 -> a2
f Digit a1
pr)

reverseNode :: (Measured v2 a2) => (a1 -> a2) -> Node v1 a1 -> Node v2 a2
reverseNode :: (a1 -> a2) -> Node v1 a1 -> Node v2 a2
reverseNode a1 -> a2
f (Node2 v1
_ a1
a a1
b)   = a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> Node v a
node2 (a1 -> a2
f a1
b) (a1 -> a2
f a1
a)
reverseNode a1 -> a2
f (Node3 v1
_ a1
a a1
b a1
c) = a2 -> a2 -> a2 -> Node v2 a2
forall v a. Measured v a => a -> a -> a -> Node v a
node3 (a1 -> a2
f a1
c) (a1 -> a2
f a1
b) (a1 -> a2
f a1
a)

reverseDigit :: (a -> b) -> Digit a -> Digit b
reverseDigit :: (a -> b) -> Digit a -> Digit b
reverseDigit a -> b
f (One a
a)        = b -> Digit b
forall a. a -> Digit a
One (a -> b
f a
a)
reverseDigit a -> b
f (Two a
a a
b)      = b -> b -> Digit b
forall a. a -> a -> Digit a
Two (a -> b
f a
b) (a -> b
f a
a)
reverseDigit a -> b
f (Three a
a a
b a
c)  = b -> b -> b -> Digit b
forall a. a -> a -> a -> Digit a
Three (a -> b
f a
c) (a -> b
f a
b) (a -> b
f a
a)
reverseDigit a -> b
f (Four a
a a
b a
c a
d) = b -> b -> b -> b -> Digit b
forall a. a -> a -> a -> a -> Digit a
Four (a -> b
f a
d) (a -> b
f a
c) (a -> b
f a
b) (a -> b
f a
a)

illegalArgument :: String -> a
illegalArgument :: String -> a
illegalArgument String
name = String -> a
forall a. HasCallStack => String -> a
error (String -> a) -> String -> a
forall a b. (a -> b) -> a -> b
$ String
"Logic error: " String -> ShowS
forall a. Semigroup a => a -> a -> a
<> String
name String -> ShowS
forall a. Semigroup a => a -> a -> a
<> String
" called with illegal argument"

maybeHead :: Measured v a => FingerTree v a -> Maybe a
maybeHead :: FingerTree v a -> Maybe a
maybeHead FingerTree v a
zs = case FingerTree v a -> ViewL (FingerTree v) a
forall v a.
Measured v a =>
FingerTree v a -> ViewL (FingerTree v) a
viewl FingerTree v a
zs of
  ViewL (FingerTree v) a
EmptyL -> Maybe a
forall a. Maybe a
Nothing
  a
n :< FingerTree v a
_ -> a -> Maybe a
forall a. a -> Maybe a
Just a
n

maybeLast :: Measured v a => FingerTree v a -> Maybe a
maybeLast :: FingerTree v a -> Maybe a
maybeLast FingerTree v a
zs = case FingerTree v a -> ViewR (FingerTree v) a
forall v a.
Measured v a =>
FingerTree v a -> ViewR (FingerTree v) a
viewr FingerTree v a
zs of
  ViewR (FingerTree v) a
EmptyR -> Maybe a
forall a. Maybe a
Nothing
  FingerTree v a
_ :> a
n -> a -> Maybe a
forall a. a -> Maybe a
Just a
n

{- $example

Particular abstract data types may be implemented by defining
element types with suitable 'Measured' instances.

(from section 4.5 of the paper)
Simple sequences can be implemented using a 'Sum' monoid as a measure:

> newtype Elem a = Elem { getElem :: a }
>
> instance Measured (Sum Int) (Elem a) where
>     measure (Elem _) = Sum 1
>
> newtype Seq a = Seq (FingerTree (Sum Int) (Elem a))

Then the measure of a subsequence is simply its length.
This representation supports log-time extraction of subsequences:

> take :: Int -> Seq a -> Seq a
> take k (Seq xs) = Seq (takeUntil (> Sum k) xs)
>
> drop :: Int -> Seq a -> Seq a
> drop k (Seq xs) = Seq (dropUntil (> Sum k) xs)

The module @Data.Sequence@ is an optimized instantiation of this type.

For further examples, see "Data.IntervalMap.FingerTree" and
"Data.PriorityQueue.FingerTree".

-}