-- |
--   Module      :  Data.Edison.Seq.JoinList
--   Copyright   :  Copyright (c) 1998-1999, 2008 Chris Okasaki
--   License     :  MIT; see COPYRIGHT file for terms and conditions
--
--   Maintainer  :  robdockins AT fastmail DOT fm
--   Stability   :  stable
--   Portability :  GHC, Hugs (MPTC and FD)
--
--   Join lists. All running times are as listed in "Data.Edison.Seq" except
--   for the following:
--
--   * rcons, append         @O( 1 )@
--
--   * ltail*, lview         @O( 1 )@    when used single-threaded, @O( n )@ otherwise
--
--   * lhead*                @O( n )@
--
--   * inBounds, lookup      @O( n )@
--
--   * copy                  @O( log i )@
--
--   * concat                @O( n1 )@
--
--   * concatMap, (>>=)      @O( n * t )@, where @n@ is the length of the input sequence and
--                                         @t@ is the running time of @f@

module Data.Edison.Seq.JoinList (
    -- * Sequence Type
    Seq, -- instance of Sequence, Functor, Monad, MonadPlus

    -- * Sequence Operations
    empty,singleton,lcons,rcons,append,lview,lhead,ltail,rview,rhead,rtail,
    lheadM,ltailM,rheadM,rtailM,
    null,size,concat,reverse,reverseOnto,fromList,toList,map,concatMap,
    fold,fold',fold1,fold1',foldr,foldr',foldl,foldl',foldr1,foldr1',foldl1,foldl1',
    reducer,reducer',reducel,reducel',reduce1,reduce1',
    copy,inBounds,lookup,lookupM,lookupWithDefault,update,adjust,
    mapWithIndex,foldrWithIndex,foldlWithIndex,
    take,drop,splitAt,subseq,filter,partition,takeWhile,dropWhile,splitWhile,
    zip,zip3,zipWith,zipWith3,unzip,unzip3,unzipWith,unzipWith3,
    strict, strictWith,

    -- * Unit testing
    structuralInvariant,

    -- * Documentation
    moduleName
) where

import Prelude hiding (concat,reverse,map,concatMap,foldr,foldl,foldr1,foldl1,foldl',
                       filter,takeWhile,dropWhile,lookup,take,drop,splitAt,
                       zip,zip3,zipWith,zipWith3,unzip,unzip3,null)

import qualified Data.Edison.Seq as S ( Sequence(..) )
import qualified Control.Applicative as App

import Data.Edison.Seq.Defaults
import Control.Monad
import qualified Control.Monad.Fail as Fail
import Data.Monoid
import Data.Semigroup as SG
import Test.QuickCheck

-- signatures for exported functions
moduleName     :: String
empty          :: Seq a
singleton      :: a -> Seq a
lcons          :: a -> Seq a -> Seq a
rcons          :: a -> Seq a -> Seq a
append         :: Seq a -> Seq a -> Seq a
lview          :: (Fail.MonadFail m) => Seq a -> m (a, Seq a)
lhead          :: Seq a -> a
lheadM         :: (Fail.MonadFail m) => Seq a -> m a
ltail          :: Seq a -> Seq a
ltailM         :: (Fail.MonadFail m) => Seq a -> m (Seq a)
rview          :: (Fail.MonadFail m) => Seq a -> m (a, Seq a)
rhead          :: Seq a -> a
rheadM         :: (Fail.MonadFail m) => Seq a -> m a
rtail          :: Seq a -> Seq a
rtailM         :: (Fail.MonadFail m) => Seq a -> m (Seq a)
null           :: Seq a -> Bool
size           :: Seq a -> Int
concat         :: Seq (Seq a) -> Seq a
reverse        :: Seq a -> Seq a
reverseOnto    :: Seq a -> Seq a -> Seq a
fromList       :: [a] -> Seq a
toList         :: Seq a -> [a]
map            :: (a -> b) -> Seq a -> Seq b
concatMap      :: (a -> Seq b) -> Seq a -> Seq b
fold           :: (a -> b -> b) -> b -> Seq a -> b
fold'          :: (a -> b -> b) -> b -> Seq a -> b
fold1          :: (a -> a -> a) -> Seq a -> a
fold1'         :: (a -> a -> a) -> Seq a -> a
foldr          :: (a -> b -> b) -> b -> Seq a -> b
foldl          :: (b -> a -> b) -> b -> Seq a -> b
foldr1         :: (a -> a -> a) -> Seq a -> a
foldl1         :: (a -> a -> a) -> Seq a -> a
reducer        :: (a -> a -> a) -> a -> Seq a -> a
reducel        :: (a -> a -> a) -> a -> Seq a -> a
reduce1        :: (a -> a -> a) -> Seq a -> a
foldr'         :: (a -> b -> b) -> b -> Seq a -> b
foldl'         :: (b -> a -> b) -> b -> Seq a -> b
foldr1'        :: (a -> a -> a) -> Seq a -> a
foldl1'        :: (a -> a -> a) -> Seq a -> a
reducer'       :: (a -> a -> a) -> a -> Seq a -> a
reducel'       :: (a -> a -> a) -> a -> Seq a -> a
reduce1'       :: (a -> a -> a) -> Seq a -> a
copy           :: Int -> a -> Seq a
inBounds       :: Int -> Seq a -> Bool
lookup         :: Int -> Seq a -> a
lookupM        :: (Fail.MonadFail m) => Int -> Seq a -> m a
lookupWithDefault :: a -> Int -> Seq a -> a
update         :: Int -> a -> Seq a -> Seq a
adjust         :: (a -> a) -> Int -> Seq a -> Seq a
mapWithIndex   :: (Int -> a -> b) -> Seq a -> Seq b
foldrWithIndex :: (Int -> a -> b -> b) -> b -> Seq a -> b
foldlWithIndex :: (b -> Int -> a -> b) -> b -> Seq a -> b
foldrWithIndex' :: (Int -> a -> b -> b) -> b -> Seq a -> b
foldlWithIndex' :: (b -> Int -> a -> b) -> b -> Seq a -> b
take           :: Int -> Seq a -> Seq a
drop           :: Int -> Seq a -> Seq a
splitAt        :: Int -> Seq a -> (Seq a, Seq a)
subseq         :: Int -> Int -> Seq a -> Seq a
filter         :: (a -> Bool) -> Seq a -> Seq a
partition      :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
takeWhile      :: (a -> Bool) -> Seq a -> Seq a
dropWhile      :: (a -> Bool) -> Seq a -> Seq a
splitWhile     :: (a -> Bool) -> Seq a -> (Seq a, Seq a)
zip            :: Seq a -> Seq b -> Seq (a,b)
zip3           :: Seq a -> Seq b -> Seq c -> Seq (a,b,c)
zipWith        :: (a -> b -> c) -> Seq a -> Seq b -> Seq c
zipWith3       :: (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
unzip          :: Seq (a,b) -> (Seq a, Seq b)
unzip3         :: Seq (a,b,c) -> (Seq a, Seq b, Seq c)
unzipWith      :: (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
unzipWith3     :: (a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
strict         :: Seq a -> Seq a
strictWith     :: (a -> b) -> Seq a -> Seq a
structuralInvariant :: Seq a -> Bool

moduleName :: String
moduleName = String
"Data.Edison.Seq.JoinList"

data Seq a = E | L a | A (Seq a) (Seq a)
  -- invariant: E never a child of A

half :: Int -> Int
half :: Int -> Int
half Int
n = Int
n Int -> Int -> Int
forall a. Integral a => a -> a -> a
`div` Int
2

empty :: forall a. Seq a
empty = Seq a
forall a. Seq a
E
singleton :: forall a. a -> Seq a
singleton = a -> Seq a
forall a. a -> Seq a
L

lcons :: forall a. a -> Seq a -> Seq a
lcons a
x Seq a
E = a -> Seq a
forall a. a -> Seq a
L a
x
lcons a
x Seq a
xs = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (a -> Seq a
forall a. a -> Seq a
L a
x) Seq a
xs

rcons :: forall a. a -> Seq a -> Seq a
rcons a
x Seq a
E = a -> Seq a
forall a. a -> Seq a
L a
x
rcons a
x Seq a
xs = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs (a -> Seq a
forall a. a -> Seq a
L a
x)

append :: forall a. Seq a -> Seq a -> Seq a
append Seq a
E Seq a
ys = Seq a
ys
append Seq a
xs Seq a
E = Seq a
xs
append Seq a
xs Seq a
ys = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys


-- path reversal on lview/ltail

lview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
lview Seq a
E = String -> m (a, Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinList.lview: empty sequence"
lview (L a
x) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, Seq a
forall a. Seq a
E)
lview (A Seq a
xs Seq a
ys) = Seq a -> Seq a -> m (a, Seq a)
forall {m :: * -> *} {a}. Monad m => Seq a -> Seq a -> m (a, Seq a)
lvw Seq a
xs Seq a
ys
  where lvw :: Seq a -> Seq a -> m (a, Seq a)
lvw Seq a
E Seq a
_ = String -> m (a, Seq a)
forall a. HasCallStack => String -> a
error String
"JoinList.lvw: bug"
        lvw (L a
x) Seq a
zs = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, Seq a
zs)
        lvw (A Seq a
xs Seq a
ys) Seq a
zs = Seq a -> Seq a -> m (a, Seq a)
lvw Seq a
xs (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
ys Seq a
zs)

lhead :: forall a. Seq a -> a
lhead Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinList.lhead: empty sequence"
lhead (L a
x) = a
x
lhead (A Seq a
xs Seq a
_) = Seq a -> a
forall a. Seq a -> a
lhead Seq a
xs

lheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
lheadM Seq a
E = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinList.lheadM: empty sequence"
lheadM (L a
x) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x
lheadM (A Seq a
xs Seq a
_) = Seq a -> m a
forall (m :: * -> *) a. MonadFail m => Seq a -> m a
lheadM Seq a
xs

ltail :: forall a. Seq a -> Seq a
ltail Seq a
E = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.ltail: empty sequence"
ltail (L a
_) = Seq a
forall a. Seq a
E
ltail (A Seq a
xs Seq a
ys) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
ltl Seq a
xs Seq a
ys
  where ltl :: Seq a -> Seq a -> Seq a
ltl Seq a
E Seq a
_ = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.ltl: bug"
        ltl (L a
_) Seq a
zs = Seq a
zs
        ltl (A Seq a
xs Seq a
ys) Seq a
zs = Seq a -> Seq a -> Seq a
ltl Seq a
xs (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
ys Seq a
zs)

ltailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
ltailM Seq a
E = String -> m (Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinList.ltailM: empty sequence"
ltailM (L a
_) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Seq a
forall a. Seq a
E
ltailM (A Seq a
xs Seq a
ys) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
ltl Seq a
xs Seq a
ys)
  where ltl :: Seq a -> Seq a -> Seq a
ltl Seq a
E Seq a
_ = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.ltl: bug"
        ltl (L a
_) Seq a
zs = Seq a
zs
        ltl (A Seq a
xs Seq a
ys) Seq a
zs = Seq a -> Seq a -> Seq a
ltl Seq a
xs (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
ys Seq a
zs)


-- Don't want to do plain path reversal on rview/rtail because of expectation
-- that left accesses are more common, so we would prefer to keep the left
-- spine short.

rview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
rview Seq a
E = String -> m (a, Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinLis.rview: empty sequence"
rview (L a
x) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, Seq a
forall a. Seq a
E)
rview (A Seq a
xs Seq a
ys) = Seq a -> Seq a -> m (a, Seq a)
forall {m :: * -> *} {a}. Monad m => Seq a -> Seq a -> m (a, Seq a)
rvw Seq a
xs Seq a
ys
  where rvw :: Seq a -> Seq a -> m (a, Seq a)
rvw Seq a
xs (A Seq a
ys (A Seq a
zs Seq a
s)) = Seq a -> Seq a -> m (a, Seq a)
rvw (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
ys Seq a
zs)) Seq a
s
        rvw Seq a
xs (A Seq a
ys (L a
x)) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys)
        rvw Seq a
xs (L a
x) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, Seq a
xs)
        rvw Seq a
_ Seq a
_ = String -> m (a, Seq a)
forall a. HasCallStack => String -> a
error String
"JoinList.rvw: bug"

rhead :: forall a. Seq a -> a
rhead Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinList.rhead: empty sequence"
rhead (L a
x) = a
x
rhead (A Seq a
_ Seq a
ys) = Seq a -> a
forall a. Seq a -> a
rhead Seq a
ys

rheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
rheadM Seq a
E = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinList.rheadM: empty sequence"
rheadM (L a
x) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x
rheadM (A Seq a
_ Seq a
ys) = Seq a -> m a
forall (m :: * -> *) a. MonadFail m => Seq a -> m a
rheadM Seq a
ys

rtail :: forall a. Seq a -> Seq a
rtail Seq a
E = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.rtail: empty sequence"
rtail (L a
_) = Seq a
forall a. Seq a
E
rtail (A Seq a
xs Seq a
ys) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
rtl Seq a
xs Seq a
ys
  where rtl :: Seq a -> Seq a -> Seq a
rtl Seq a
xs (A Seq a
ys (A Seq a
zs Seq a
s)) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys) (Seq a -> Seq a -> Seq a
rtl Seq a
zs Seq a
s)
        rtl Seq a
xs (A Seq a
ys (L a
_)) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys
        rtl Seq a
xs (L a
_) = Seq a
xs
        rtl Seq a
_ Seq a
_ = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.rtl: bug"

rtailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
rtailM Seq a
E = String -> m (Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"JoinList.rtailM: empty sequence"
rtailM (L a
_) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Seq a
forall a. Seq a
E
rtailM (A Seq a
xs Seq a
ys) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
rtl Seq a
xs Seq a
ys)
  where rtl :: Seq a -> Seq a -> Seq a
rtl Seq a
xs (A Seq a
ys (A Seq a
zs Seq a
s)) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys) (Seq a -> Seq a -> Seq a
rtl Seq a
zs Seq a
s)
        rtl Seq a
xs (A Seq a
ys (L a
_)) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
ys
        rtl Seq a
xs (L a
_) = Seq a
xs
        rtl Seq a
_ Seq a
_ = String -> Seq a
forall a. HasCallStack => String -> a
error String
"JoinList.rtl: bug"

null :: forall a. Seq a -> Bool
null Seq a
E = Bool
True
null Seq a
_ = Bool
False

size :: forall a. Seq a -> Int
size Seq a
xs = Seq a -> Int -> Int
forall {a}. Seq a -> Int -> Int
sz Seq a
xs (Int
0::Int)
  where sz :: Seq a -> Int -> Int
sz Seq a
E Int
n = Int
n
        sz (L a
_) Int
n = Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
+ (Int
1::Int)
        sz (A Seq a
xs Seq a
ys) Int
n = Seq a -> Int -> Int
sz Seq a
xs (Seq a -> Int -> Int
sz Seq a
ys Int
n)

reverse :: forall a. Seq a -> Seq a
reverse (A Seq a
xs Seq a
ys) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (Seq a -> Seq a
forall a. Seq a -> Seq a
reverse Seq a
ys) (Seq a -> Seq a
forall a. Seq a -> Seq a
reverse Seq a
xs)
reverse Seq a
xs = Seq a
xs -- L x or E

toList :: forall a. Seq a -> [a]
toList Seq a
xs = Seq a -> [a] -> [a]
forall {a}. Seq a -> [a] -> [a]
tol Seq a
xs []
  where tol :: Seq a -> [a] -> [a]
tol Seq a
E [a]
rest = [a]
rest
        tol (L a
x) [a]
rest = a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
rest
        tol (A Seq a
xs Seq a
ys) [a]
rest = Seq a -> [a] -> [a]
tol Seq a
xs (Seq a -> [a] -> [a]
tol Seq a
ys [a]
rest)

map :: forall a b. (a -> b) -> Seq a -> Seq b
map a -> b
_ Seq a
E = Seq b
forall a. Seq a
E
map a -> b
f (L a
x) = b -> Seq b
forall a. a -> Seq a
L (a -> b
f a
x)
map a -> b
f (A Seq a
xs Seq a
ys) = Seq b -> Seq b -> Seq b
forall a. Seq a -> Seq a -> Seq a
A ((a -> b) -> Seq a -> Seq b
forall a b. (a -> b) -> Seq a -> Seq b
map a -> b
f Seq a
xs) ((a -> b) -> Seq a -> Seq b
forall a b. (a -> b) -> Seq a -> Seq b
map a -> b
f Seq a
ys)

fold :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold   = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr
fold' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold'  = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr'
fold1 :: forall a. (a -> a -> a) -> Seq a -> a
fold1  = (a -> a -> a) -> Seq a -> a
forall (s :: * -> *) a. Sequence s => (a -> a -> a) -> s a -> a
fold1UsingFold
fold1' :: forall a. (a -> a -> a) -> Seq a -> a
fold1' = (a -> a -> a) -> Seq a -> a
forall (s :: * -> *) a. Sequence s => (a -> a -> a) -> s a -> a
fold1'UsingFold'

foldr :: forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr a -> b -> b
_ b
e Seq a
E = b
e
foldr a -> b -> b
f b
e (L a
x) = a -> b -> b
f a
x b
e
foldr a -> b -> b
f b
e (A Seq a
xs Seq a
ys) = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr a -> b -> b
f ((a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr a -> b -> b
f b
e Seq a
ys) Seq a
xs
foldr' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' a -> b -> b
_ b
e Seq a
E = b
e
foldr' a -> b -> b
f b
e (L a
x) = a -> b -> b
f a
x (b -> b) -> b -> b
forall a b. (a -> b) -> a -> b
$! b
e
foldr' a -> b -> b
f b
e (A Seq a
xs Seq a
ys) = ((a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' a -> b -> b
f (b -> Seq a -> b) -> b -> Seq a -> b
forall a b. (a -> b) -> a -> b
$! ((a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' a -> b -> b
f b
e Seq a
ys)) Seq a
xs

foldl :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl b -> a -> b
_ b
e Seq a
E = b
e
foldl b -> a -> b
f b
e (L a
x) = b -> a -> b
f b
e a
x
foldl b -> a -> b
f b
e (A Seq a
xs Seq a
ys) = (b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl b -> a -> b
f ((b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl b -> a -> b
f b
e Seq a
xs) Seq a
ys

foldl' :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' b -> a -> b
_ b
e Seq a
E = b
e
foldl' b -> a -> b
f b
e (L a
x) = b
e b -> b -> b
forall a b. a -> b -> b
`seq` b -> a -> b
f b
e a
x
foldl' b -> a -> b
f b
e (A Seq a
xs Seq a
ys) = b
e b -> b -> b
forall a b. a -> b -> b
`seq` (b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' b -> a -> b
f ((b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' b -> a -> b
f b
e Seq a
xs) Seq a
ys

foldr1 :: forall a. (a -> a -> a) -> Seq a -> a
foldr1 a -> a -> a
_ Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinList.foldr1: empty sequence"
foldr1 a -> a -> a
_ (L a
x) = a
x
foldr1 a -> a -> a
f (A Seq a
xs Seq a
ys) = (a -> a -> a) -> a -> Seq a -> a
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr a -> a -> a
f ((a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldr1 a -> a -> a
f Seq a
ys) Seq a
xs

foldr1' :: forall a. (a -> a -> a) -> Seq a -> a
foldr1' a -> a -> a
_ Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinLis.foldr1': empty sequence"
foldr1' a -> a -> a
_ (L a
x) = a
x
foldr1' a -> a -> a
f (A Seq a
xs Seq a
ys) = (a -> a -> a) -> a -> Seq a -> a
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' a -> a -> a
f ((a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldr1' a -> a -> a
f Seq a
ys) Seq a
xs

foldl1 :: forall a. (a -> a -> a) -> Seq a -> a
foldl1 a -> a -> a
_ Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinList.foldl1: empty sequence"
foldl1 a -> a -> a
_ (L a
x) = a
x
foldl1 a -> a -> a
f (A Seq a
xs Seq a
ys) = (a -> a -> a) -> a -> Seq a -> a
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl a -> a -> a
f ((a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldl1 a -> a -> a
f Seq a
xs) Seq a
ys

foldl1' :: forall a. (a -> a -> a) -> Seq a -> a
foldl1' a -> a -> a
_ Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"JoinList.foldl1': empty sequence"
foldl1' a -> a -> a
_ (L a
x) = a
x
foldl1' a -> a -> a
f (A Seq a
xs Seq a
ys) = (a -> a -> a) -> a -> Seq a -> a
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' a -> a -> a
f ((a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldl1' a -> a -> a
f Seq a
xs) Seq a
ys

copy :: forall a. Int -> a -> Seq a
copy Int
n a
x
    | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
0 = Seq a
forall a. Seq a
E
    | Bool
otherwise = Int -> a -> Seq a
forall a. Int -> a -> Seq a
cpy Int
n a
x
  where cpy :: Int -> a -> Seq a
cpy Int
n a
x  -- n > 0
          | Int -> Bool
forall a. Integral a => a -> Bool
even Int
n = let xs :: Seq a
xs = Int -> a -> Seq a
cpy (Int -> Int
half Int
n) a
x
                     in Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
xs
          | Int
n Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1 = a -> Seq a
forall a. a -> Seq a
L a
x
          | Bool
otherwise = let xs :: Seq a
xs = Int -> a -> Seq a
cpy (Int -> Int
half Int
n) a
x
                        in Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (a -> Seq a
forall a. a -> Seq a
L a
x) (Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A Seq a
xs Seq a
xs)


strict :: forall a. Seq a -> Seq a
strict s :: Seq a
s@Seq a
E = Seq a
s
strict s :: Seq a
s@(L a
_) = Seq a
s
strict s :: Seq a
s@(A Seq a
l Seq a
r) = Seq a -> Seq a
forall a. Seq a -> Seq a
strict Seq a
l Seq a -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a -> Seq a
forall a. Seq a -> Seq a
strict Seq a
r Seq a -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a
s

strictWith :: forall a b. (a -> b) -> Seq a -> Seq a
strictWith a -> b
_ s :: Seq a
s@Seq a
E = Seq a
s
strictWith a -> b
f s :: Seq a
s@(L a
x) = a -> b
f a
x b -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a
s
strictWith a -> b
f s :: Seq a
s@(A Seq a
l Seq a
_) = (a -> b) -> Seq a -> Seq a
forall a b. (a -> b) -> Seq a -> Seq a
strictWith a -> b
f Seq a
l Seq a -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` (a -> b) -> Seq a -> Seq a
forall a b. (a -> b) -> Seq a -> Seq a
strictWith a -> b
f Seq a
l Seq a -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a
s

-- invariants:
--   * 'E' is never a child of 'A'

structuralInvariant :: forall a. Seq a -> Bool
structuralInvariant Seq a
E = Bool
True
structuralInvariant Seq a
s = Seq a -> Bool
forall a. Seq a -> Bool
check Seq a
s
  where check :: Seq a -> Bool
check Seq a
E = Bool
False
        check (L a
_) = Bool
True
        check (A Seq a
s1 Seq a
s2) = Seq a -> Bool
check Seq a
s1 Bool -> Bool -> Bool
&& Seq a -> Bool
check Seq a
s2


concat :: forall a. Seq (Seq a) -> Seq a
concat = Seq (Seq a) -> Seq a
forall (s :: * -> *) a. Sequence s => s (s a) -> s a
concatUsingFoldr
reverseOnto :: forall a. Seq a -> Seq a -> Seq a
reverseOnto = Seq a -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => s a -> s a -> s a
reverseOntoUsingReverse
fromList :: forall a. [a] -> Seq a
fromList = [a] -> Seq a
forall (s :: * -> *) a. Sequence s => [a] -> s a
fromListUsingCons
concatMap :: forall a b. (a -> Seq b) -> Seq a -> Seq b
concatMap = (a -> Seq b) -> Seq a -> Seq b
forall (s :: * -> *) a b. Sequence s => (a -> s b) -> s a -> s b
concatMapUsingFoldr

reducer :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducer  = (a -> a -> a) -> a -> Seq a -> a
forall (s :: * -> *) a.
Sequence s =>
(a -> a -> a) -> a -> s a -> a
reducerUsingReduce1
reducer' :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducer' = (a -> a -> a) -> a -> Seq a -> a
forall (s :: * -> *) a.
Sequence s =>
(a -> a -> a) -> a -> s a -> a
reducer'UsingReduce1'
reducel :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducel  = (a -> a -> a) -> a -> Seq a -> a
forall (s :: * -> *) a.
Sequence s =>
(a -> a -> a) -> a -> s a -> a
reducelUsingReduce1
reducel' :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducel' = (a -> a -> a) -> a -> Seq a -> a
forall (s :: * -> *) a.
Sequence s =>
(a -> a -> a) -> a -> s a -> a
reducel'UsingReduce1'
reduce1 :: forall a. (a -> a -> a) -> Seq a -> a
reduce1  = (a -> a -> a) -> Seq a -> a
forall (s :: * -> *) a. Sequence s => (a -> a -> a) -> s a -> a
reduce1UsingLists
reduce1' :: forall a. (a -> a -> a) -> Seq a -> a
reduce1' = (a -> a -> a) -> Seq a -> a
forall (s :: * -> *) a. Sequence s => (a -> a -> a) -> s a -> a
reduce1'UsingLists

inBounds :: forall a. Int -> Seq a -> Bool
inBounds = Int -> Seq a -> Bool
forall (s :: * -> *) a. Sequence s => Int -> s a -> Bool
inBoundsUsingDrop
lookup :: forall a. Int -> Seq a -> a
lookup = Int -> Seq a -> a
forall (s :: * -> *) a. Sequence s => Int -> s a -> a
lookupUsingDrop
lookupM :: forall (m :: * -> *) a. MonadFail m => Int -> Seq a -> m a
lookupM = Int -> Seq a -> m a
forall (m :: * -> *) (s :: * -> *) a.
(MonadFail m, Sequence s) =>
Int -> s a -> m a
lookupMUsingDrop
lookupWithDefault :: forall a. a -> Int -> Seq a -> a
lookupWithDefault = a -> Int -> Seq a -> a
forall (s :: * -> *) a. Sequence s => a -> Int -> s a -> a
lookupWithDefaultUsingDrop

update :: forall a. Int -> a -> Seq a -> Seq a
update = Int -> a -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> a -> s a -> s a
updateUsingSplitAt
adjust :: forall a. (a -> a) -> Int -> Seq a -> Seq a
adjust = (a -> a) -> Int -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => (a -> a) -> Int -> s a -> s a
adjustUsingSplitAt

mapWithIndex :: forall a b. (Int -> a -> b) -> Seq a -> Seq b
mapWithIndex = (Int -> a -> b) -> Seq a -> Seq b
forall (s :: * -> *) a b.
Sequence s =>
(Int -> a -> b) -> s a -> s b
mapWithIndexUsingLists
foldrWithIndex :: forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex  = (Int -> a -> b -> b) -> b -> Seq a -> b
forall (s :: * -> *) a b.
Sequence s =>
(Int -> a -> b -> b) -> b -> s a -> b
foldrWithIndexUsingLists
foldrWithIndex' :: forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex' = (Int -> a -> b -> b) -> b -> Seq a -> b
forall (s :: * -> *) a b.
Sequence s =>
(Int -> a -> b -> b) -> b -> s a -> b
foldrWithIndex'UsingLists
foldlWithIndex :: forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex  = (b -> Int -> a -> b) -> b -> Seq a -> b
forall (s :: * -> *) b a.
Sequence s =>
(b -> Int -> a -> b) -> b -> s a -> b
foldlWithIndexUsingLists
foldlWithIndex' :: forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex' = (b -> Int -> a -> b) -> b -> Seq a -> b
forall (s :: * -> *) b a.
Sequence s =>
(b -> Int -> a -> b) -> b -> s a -> b
foldlWithIndex'UsingLists

take :: forall a. Int -> Seq a -> Seq a
take = Int -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> s a -> s a
takeUsingLview
drop :: forall a. Int -> Seq a -> Seq a
drop = Int -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> s a -> s a
dropUsingLtail
splitAt :: forall a. Int -> Seq a -> (Seq a, Seq a)
splitAt = Int -> Seq a -> (Seq a, Seq a)
forall (s :: * -> *) a. Sequence s => Int -> s a -> (s a, s a)
splitAtUsingLview
subseq :: forall a. Int -> Int -> Seq a -> Seq a
subseq = Int -> Int -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> Int -> s a -> s a
subseqDefault

filter :: forall a. (a -> Bool) -> Seq a -> Seq a
filter = (a -> Bool) -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => (a -> Bool) -> s a -> s a
filterUsingLview
partition :: forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
partition = (a -> Bool) -> Seq a -> (Seq a, Seq a)
forall (s :: * -> *) a.
Sequence s =>
(a -> Bool) -> s a -> (s a, s a)
partitionUsingFoldr
takeWhile :: forall a. (a -> Bool) -> Seq a -> Seq a
takeWhile = (a -> Bool) -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => (a -> Bool) -> s a -> s a
takeWhileUsingLview
dropWhile :: forall a. (a -> Bool) -> Seq a -> Seq a
dropWhile = (a -> Bool) -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => (a -> Bool) -> s a -> s a
dropWhileUsingLview
splitWhile :: forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
splitWhile = (a -> Bool) -> Seq a -> (Seq a, Seq a)
forall (s :: * -> *) a.
Sequence s =>
(a -> Bool) -> s a -> (s a, s a)
splitWhileUsingLview

zip :: forall a b. Seq a -> Seq b -> Seq (a, b)
zip = Seq a -> Seq b -> Seq (a, b)
forall (s :: * -> *) a b. Sequence s => s a -> s b -> s (a, b)
zipUsingLview
zip3 :: forall a b c. Seq a -> Seq b -> Seq c -> Seq (a, b, c)
zip3 = Seq a -> Seq b -> Seq c -> Seq (a, b, c)
forall (s :: * -> *) a b c.
Sequence s =>
s a -> s b -> s c -> s (a, b, c)
zip3UsingLview
zipWith :: forall a b c. (a -> b -> c) -> Seq a -> Seq b -> Seq c
zipWith = (a -> b -> c) -> Seq a -> Seq b -> Seq c
forall (s :: * -> *) a b c.
Sequence s =>
(a -> b -> c) -> s a -> s b -> s c
zipWithUsingLview
zipWith3 :: forall a b c d.
(a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
zipWith3 = (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
forall (s :: * -> *) a b c d.
Sequence s =>
(a -> b -> c -> d) -> s a -> s b -> s c -> s d
zipWith3UsingLview

unzip :: forall a b. Seq (a, b) -> (Seq a, Seq b)
unzip = Seq (a, b) -> (Seq a, Seq b)
forall (s :: * -> *) a b. Sequence s => s (a, b) -> (s a, s b)
unzipUsingFoldr
unzip3 :: forall a b c. Seq (a, b, c) -> (Seq a, Seq b, Seq c)
unzip3 = Seq (a, b, c) -> (Seq a, Seq b, Seq c)
forall (s :: * -> *) a b c.
Sequence s =>
s (a, b, c) -> (s a, s b, s c)
unzip3UsingFoldr
unzipWith :: forall a b c. (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
unzipWith = (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
forall (s :: * -> *) a b c.
Sequence s =>
(a -> b) -> (a -> c) -> s a -> (s b, s c)
unzipWithUsingFoldr
unzipWith3 :: forall a b c d.
(a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
unzipWith3 = (a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
forall (s :: * -> *) a b c d.
Sequence s =>
(a -> b) -> (a -> c) -> (a -> d) -> s a -> (s b, s c, s d)
unzipWith3UsingFoldr

-- instances

instance S.Sequence Seq where
  {lcons :: forall a. a -> Seq a -> Seq a
lcons = a -> Seq a -> Seq a
forall a. a -> Seq a -> Seq a
lcons; rcons :: forall a. a -> Seq a -> Seq a
rcons = a -> Seq a -> Seq a
forall a. a -> Seq a -> Seq a
rcons;
   lview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
lview = Seq a -> m (a, Seq a)
forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
lview; lhead :: forall a. Seq a -> a
lhead = Seq a -> a
forall a. Seq a -> a
lhead; ltail :: forall a. Seq a -> Seq a
ltail = Seq a -> Seq a
forall a. Seq a -> Seq a
ltail;
   lheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
lheadM = Seq a -> m a
forall (m :: * -> *) a. MonadFail m => Seq a -> m a
lheadM; ltailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
ltailM = Seq a -> m (Seq a)
forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
ltailM; rheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
rheadM = Seq a -> m a
forall (m :: * -> *) a. MonadFail m => Seq a -> m a
rheadM; rtailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
rtailM = Seq a -> m (Seq a)
forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
rtailM;
   rview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
rview = Seq a -> m (a, Seq a)
forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
rview; rhead :: forall a. Seq a -> a
rhead = Seq a -> a
forall a. Seq a -> a
rhead; rtail :: forall a. Seq a -> Seq a
rtail = Seq a -> Seq a
forall a. Seq a -> Seq a
rtail; null :: forall a. Seq a -> Bool
null = Seq a -> Bool
forall a. Seq a -> Bool
null;
   size :: forall a. Seq a -> Int
size = Seq a -> Int
forall a. Seq a -> Int
size; concat :: forall a. Seq (Seq a) -> Seq a
concat = Seq (Seq a) -> Seq a
forall a. Seq (Seq a) -> Seq a
concat; reverse :: forall a. Seq a -> Seq a
reverse = Seq a -> Seq a
forall a. Seq a -> Seq a
reverse;
   reverseOnto :: forall a. Seq a -> Seq a -> Seq a
reverseOnto = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
reverseOnto; fromList :: forall a. [a] -> Seq a
fromList = [a] -> Seq a
forall a. [a] -> Seq a
fromList; toList :: forall a. Seq a -> [a]
toList = Seq a -> [a]
forall a. Seq a -> [a]
toList;
   fold :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
fold; fold' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold' = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
fold'; fold1 :: forall a. (a -> a -> a) -> Seq a -> a
fold1 = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
fold1; fold1' :: forall a. (a -> a -> a) -> Seq a -> a
fold1' = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
fold1';
   foldr :: forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr; foldr' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' = (a -> b -> b) -> b -> Seq a -> b
forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr'; foldl :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl = (b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl; foldl' :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' = (b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl';
   foldr1 :: forall a. (a -> a -> a) -> Seq a -> a
foldr1 = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldr1; foldr1' :: forall a. (a -> a -> a) -> Seq a -> a
foldr1' = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldr1'; foldl1 :: forall a. (a -> a -> a) -> Seq a -> a
foldl1 = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldl1; foldl1' :: forall a. (a -> a -> a) -> Seq a -> a
foldl1' = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
foldl1';
   reducer :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducer = (a -> a -> a) -> a -> Seq a -> a
forall a. (a -> a -> a) -> a -> Seq a -> a
reducer; reducer' :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducer' = (a -> a -> a) -> a -> Seq a -> a
forall a. (a -> a -> a) -> a -> Seq a -> a
reducer'; reducel :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducel = (a -> a -> a) -> a -> Seq a -> a
forall a. (a -> a -> a) -> a -> Seq a -> a
reducel;
   reducel' :: forall a. (a -> a -> a) -> a -> Seq a -> a
reducel' = (a -> a -> a) -> a -> Seq a -> a
forall a. (a -> a -> a) -> a -> Seq a -> a
reducel'; reduce1 :: forall a. (a -> a -> a) -> Seq a -> a
reduce1 = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
reduce1;  reduce1' :: forall a. (a -> a -> a) -> Seq a -> a
reduce1' = (a -> a -> a) -> Seq a -> a
forall a. (a -> a -> a) -> Seq a -> a
reduce1';
   copy :: forall a. Int -> a -> Seq a
copy = Int -> a -> Seq a
forall a. Int -> a -> Seq a
copy; inBounds :: forall a. Int -> Seq a -> Bool
inBounds = Int -> Seq a -> Bool
forall a. Int -> Seq a -> Bool
inBounds; lookup :: forall a. Int -> Seq a -> a
lookup = Int -> Seq a -> a
forall a. Int -> Seq a -> a
lookup;
   lookupM :: forall (m :: * -> *) a. MonadFail m => Int -> Seq a -> m a
lookupM = Int -> Seq a -> m a
forall (m :: * -> *) a. MonadFail m => Int -> Seq a -> m a
lookupM; lookupWithDefault :: forall a. a -> Int -> Seq a -> a
lookupWithDefault = a -> Int -> Seq a -> a
forall a. a -> Int -> Seq a -> a
lookupWithDefault;
   update :: forall a. Int -> a -> Seq a -> Seq a
update = Int -> a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a
update; adjust :: forall a. (a -> a) -> Int -> Seq a -> Seq a
adjust = (a -> a) -> Int -> Seq a -> Seq a
forall a. (a -> a) -> Int -> Seq a -> Seq a
adjust; mapWithIndex :: forall a b. (Int -> a -> b) -> Seq a -> Seq b
mapWithIndex = (Int -> a -> b) -> Seq a -> Seq b
forall a b. (Int -> a -> b) -> Seq a -> Seq b
mapWithIndex;
   foldrWithIndex :: forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex = (Int -> a -> b -> b) -> b -> Seq a -> b
forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex; foldlWithIndex :: forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex = (b -> Int -> a -> b) -> b -> Seq a -> b
forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex;
   foldrWithIndex' :: forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex' = (Int -> a -> b -> b) -> b -> Seq a -> b
forall a b. (Int -> a -> b -> b) -> b -> Seq a -> b
foldrWithIndex'; foldlWithIndex' :: forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex' = (b -> Int -> a -> b) -> b -> Seq a -> b
forall b a. (b -> Int -> a -> b) -> b -> Seq a -> b
foldlWithIndex';
   take :: forall a. Int -> Seq a -> Seq a
take = Int -> Seq a -> Seq a
forall a. Int -> Seq a -> Seq a
take; drop :: forall a. Int -> Seq a -> Seq a
drop = Int -> Seq a -> Seq a
forall a. Int -> Seq a -> Seq a
drop; splitAt :: forall a. Int -> Seq a -> (Seq a, Seq a)
splitAt = Int -> Seq a -> (Seq a, Seq a)
forall a. Int -> Seq a -> (Seq a, Seq a)
splitAt; subseq :: forall a. Int -> Int -> Seq a -> Seq a
subseq = Int -> Int -> Seq a -> Seq a
forall a. Int -> Int -> Seq a -> Seq a
subseq;
   filter :: forall a. (a -> Bool) -> Seq a -> Seq a
filter = (a -> Bool) -> Seq a -> Seq a
forall a. (a -> Bool) -> Seq a -> Seq a
filter; partition :: forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
partition = (a -> Bool) -> Seq a -> (Seq a, Seq a)
forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
partition; takeWhile :: forall a. (a -> Bool) -> Seq a -> Seq a
takeWhile = (a -> Bool) -> Seq a -> Seq a
forall a. (a -> Bool) -> Seq a -> Seq a
takeWhile;
   dropWhile :: forall a. (a -> Bool) -> Seq a -> Seq a
dropWhile = (a -> Bool) -> Seq a -> Seq a
forall a. (a -> Bool) -> Seq a -> Seq a
dropWhile; splitWhile :: forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
splitWhile = (a -> Bool) -> Seq a -> (Seq a, Seq a)
forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
splitWhile; zip :: forall a b. Seq a -> Seq b -> Seq (a, b)
zip = Seq a -> Seq b -> Seq (a, b)
forall a b. Seq a -> Seq b -> Seq (a, b)
zip;
   zip3 :: forall a b c. Seq a -> Seq b -> Seq c -> Seq (a, b, c)
zip3 = Seq a -> Seq b -> Seq c -> Seq (a, b, c)
forall a b c. Seq a -> Seq b -> Seq c -> Seq (a, b, c)
zip3; zipWith :: forall a b c. (a -> b -> c) -> Seq a -> Seq b -> Seq c
zipWith = (a -> b -> c) -> Seq a -> Seq b -> Seq c
forall a b c. (a -> b -> c) -> Seq a -> Seq b -> Seq c
zipWith; zipWith3 :: forall a b c d.
(a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
zipWith3 = (a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
forall a b c d.
(a -> b -> c -> d) -> Seq a -> Seq b -> Seq c -> Seq d
zipWith3; unzip :: forall a b. Seq (a, b) -> (Seq a, Seq b)
unzip = Seq (a, b) -> (Seq a, Seq b)
forall a b. Seq (a, b) -> (Seq a, Seq b)
unzip;
   unzip3 :: forall a b c. Seq (a, b, c) -> (Seq a, Seq b, Seq c)
unzip3 = Seq (a, b, c) -> (Seq a, Seq b, Seq c)
forall a b c. Seq (a, b, c) -> (Seq a, Seq b, Seq c)
unzip3; unzipWith :: forall a b c. (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
unzipWith = (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
forall a b c. (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
unzipWith; unzipWith3 :: forall a b c d.
(a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
unzipWith3 = (a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
forall a b c d.
(a -> b) -> (a -> c) -> (a -> d) -> Seq a -> (Seq b, Seq c, Seq d)
unzipWith3;
   strict :: forall a. Seq a -> Seq a
strict = Seq a -> Seq a
forall a. Seq a -> Seq a
strict; strictWith :: forall a b. (a -> b) -> Seq a -> Seq a
strictWith = (a -> b) -> Seq a -> Seq a
forall a b. (a -> b) -> Seq a -> Seq a
strictWith;
   structuralInvariant :: forall a. Seq a -> Bool
structuralInvariant = Seq a -> Bool
forall a. Seq a -> Bool
structuralInvariant; instanceName :: forall a. Seq a -> String
instanceName Seq a
_ = String
moduleName}

instance Functor Seq where
  fmap :: forall a b. (a -> b) -> Seq a -> Seq b
fmap = (a -> b) -> Seq a -> Seq b
forall a b. (a -> b) -> Seq a -> Seq b
map

instance App.Alternative Seq where
  empty :: forall a. Seq a
empty = Seq a
forall a. Seq a
empty
  <|> :: forall a. Seq a -> Seq a -> Seq a
(<|>) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
append

instance App.Applicative Seq where
  pure :: forall a. a -> Seq a
pure = a -> Seq a
forall a. a -> Seq a
forall (m :: * -> *) a. Monad m => a -> m a
return
  Seq (a -> b)
x <*> :: forall a b. Seq (a -> b) -> Seq a -> Seq b
<*> Seq a
y = do
     a -> b
x' <- Seq (a -> b)
x
     a
y' <- Seq a
y
     b -> Seq b
forall a. a -> Seq a
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> b
x' a
y')

instance Monad Seq where
  return :: forall a. a -> Seq a
return = a -> Seq a
forall a. a -> Seq a
singleton
  Seq a
xs >>= :: forall a b. Seq a -> (a -> Seq b) -> Seq b
>>= a -> Seq b
k = (a -> Seq b) -> Seq a -> Seq b
forall a b. (a -> Seq b) -> Seq a -> Seq b
concatMap a -> Seq b
k Seq a
xs

instance MonadPlus Seq where
  mplus :: forall a. Seq a -> Seq a -> Seq a
mplus = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
append
  mzero :: forall a. Seq a
mzero = Seq a
forall a. Seq a
empty

instance Eq a => Eq (Seq a) where
  Seq a
xs == :: Seq a -> Seq a -> Bool
== Seq a
ys = Seq a -> [a]
forall a. Seq a -> [a]
toList Seq a
xs [a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
== Seq a -> [a]
forall a. Seq a -> [a]
toList Seq a
ys

instance Ord a => Ord (Seq a) where
  compare :: Seq a -> Seq a -> Ordering
compare = Seq a -> Seq a -> Ordering
forall a (s :: * -> *).
(Ord a, Sequence s) =>
s a -> s a -> Ordering
defaultCompare

instance Show a => Show (Seq a) where
  showsPrec :: Int -> Seq a -> ShowS
showsPrec = Int -> Seq a -> ShowS
forall a (s :: * -> *). (Show a, Sequence s) => Int -> s a -> ShowS
showsPrecUsingToList

instance Read a => Read (Seq a) where
  readsPrec :: Int -> ReadS (Seq a)
readsPrec = Int -> ReadS (Seq a)
forall a (s :: * -> *). (Read a, Sequence s) => Int -> ReadS (s a)
readsPrecUsingFromList

instance Arbitrary a => Arbitrary (Seq a) where
  arbitrary :: Gen (Seq a)
arbitrary = (Int -> Gen (Seq a)) -> Gen (Seq a)
forall a. (Int -> Gen a) -> Gen a
sized Int -> Gen (Seq a)
forall {t} {a}. (Arbitrary a, Integral t) => t -> Gen (Seq a)
arbTree
    where arbTree :: t -> Gen (Seq a)
arbTree t
0 = Seq a -> Gen (Seq a)
forall a. a -> Gen a
forall (m :: * -> *) a. Monad m => a -> m a
return Seq a
forall a. Seq a
E
          arbTree t
1 = (a -> Seq a) -> Gen a -> Gen (Seq a)
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM a -> Seq a
forall a. a -> Seq a
L Gen a
forall a. Arbitrary a => Gen a
arbitrary
          arbTree t
n =
            [(Int, Gen (Seq a))] -> Gen (Seq a)
forall a. HasCallStack => [(Int, Gen a)] -> Gen a
frequency [(Int
1, (a -> Seq a) -> Gen a -> Gen (Seq a)
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM a -> Seq a
forall a. a -> Seq a
L Gen a
forall a. Arbitrary a => Gen a
arbitrary),
                       (Int
4, (Seq a -> Seq a -> Seq a)
-> Gen (Seq a) -> Gen (Seq a) -> Gen (Seq a)
forall (m :: * -> *) a1 a2 r.
Monad m =>
(a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM2 Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
A (t -> Gen (Seq a)
arbTree (t
n t -> t -> t
forall a. Integral a => a -> a -> a
`div` t
2))
                                    (t -> Gen (Seq a)
arbTree (t
n t -> t -> t
forall a. Integral a => a -> a -> a
`div` t
2)))]

instance CoArbitrary a => CoArbitrary (Seq a) where
  coarbitrary :: forall b. Seq a -> Gen b -> Gen b
coarbitrary Seq a
E = Integer -> Gen b -> Gen b
forall n a. Integral n => n -> Gen a -> Gen a
variant Integer
0
  coarbitrary (L a
x) = Integer -> Gen b -> Gen b
forall n a. Integral n => n -> Gen a -> Gen a
variant Integer
1 (Gen b -> Gen b) -> (Gen b -> Gen b) -> Gen b -> Gen b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Gen b -> Gen b
forall b. a -> Gen b -> Gen b
forall a b. CoArbitrary a => a -> Gen b -> Gen b
coarbitrary a
x
  coarbitrary (A Seq a
xs Seq a
ys) = Integer -> Gen b -> Gen b
forall n a. Integral n => n -> Gen a -> Gen a
variant Integer
2 (Gen b -> Gen b) -> (Gen b -> Gen b) -> Gen b -> Gen b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Seq a -> Gen b -> Gen b
forall a b. CoArbitrary a => a -> Gen b -> Gen b
forall b. Seq a -> Gen b -> Gen b
coarbitrary Seq a
xs (Gen b -> Gen b) -> (Gen b -> Gen b) -> Gen b -> Gen b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Seq a -> Gen b -> Gen b
forall a b. CoArbitrary a => a -> Gen b -> Gen b
forall b. Seq a -> Gen b -> Gen b
coarbitrary Seq a
ys

instance Semigroup (Seq a) where
  <> :: Seq a -> Seq a -> Seq a
(<>) = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
append
instance Monoid (Seq a) where
  mempty :: Seq a
mempty  = Seq a
forall a. Seq a
empty
  mappend :: Seq a -> Seq a -> Seq a
mappend = Seq a -> Seq a -> Seq a
forall a. Semigroup a => a -> a -> a
(SG.<>)