-- |
--   Module      :  Data.Edison.Seq.SimpleQueue
--   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)
--
--   Simple Queues.  All operations have running times as listed in
--   "Data.Edison.Seq" except for the following:
--
--   * rcons, fromList   @O( 1 )@
--
--   * lview, ltail*   @O( 1 )@ if single threaded, @O( n )@ otherwise
--
--   * inBounds, lookup, update, drop, splitAt  @O( n )@
--
--   /References:/
--
--   * Chris Okasaki. /Purely Functional Data Structures/. 1998.
--     Section 5.2.
--
--   * F. Warren Burton. \"An efficient functional implementation of FIFO queues\".
--     /Information Processing Letters/, 14(5):205-206, July 1982.

module Data.Edison.Seq.SimpleQueue (
    -- * 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,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 Control.Applicative as App

import qualified Data.Edison.Seq as S ( Sequence(..) )
import Data.Edison.Seq.Defaults
import qualified Data.Edison.Seq.ListSeq as L
import Data.Monoid
import Data.Semigroup as SG
import Control.Monad
import qualified Control.Monad.Fail as Fail
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.SimpleQueue"


data Seq a = Q [a] [a]
  -- invariant: front empty only if rear also empty

-- not exported
makeQ :: [a] -> [a] -> Seq a
makeQ :: forall a. [a] -> [a] -> Seq a
makeQ [] [a]
ys = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
ys) []
makeQ [a]
xs [a]
ys = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys

empty :: forall a. Seq a
empty = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [] []
singleton :: forall a. a -> Seq a
singleton a
x = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a
x] []
lcons :: forall a. a -> Seq a -> Seq a
lcons a
x (Q [a]
xs [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q (a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
xs) [a]
ys

rcons :: forall a. a -> Seq a -> Seq a
rcons a
y (Q [] [a]
_) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a
y] []
rcons a
y (Q [a]
xs [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs (a
ya -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
ys)

append :: forall a. Seq a -> Seq a -> Seq a
append (Q [a]
xs1 [a]
ys1) (Q [a]
xs2 [a]
ys2) =
    [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a]
xs1 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
L.reverseOnto [a]
ys1 [a]
xs2) [a]
ys2

lview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
lview (Q [] [a]
_) = String -> m (a, Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.lview: empty sequence"
lview (Q [a
x] [a]
ys) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
ys) [])
lview (Q (a
x:[a]
xs) [a]
ys) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys)

lhead :: forall a. Seq a -> a
lhead (Q [] [a]
_) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.lhead: empty sequence"
lhead (Q (a
x:[a]
_) [a]
_) = a
x

lheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
lheadM (Q [] [a]
_) = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.lheadM: empty sequence"
lheadM (Q (a
x:[a]
_) [a]
_) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x

ltail :: forall a. Seq a -> Seq a
ltail (Q [a
_] [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
ys) []
ltail (Q (a
_:[a]
xs) [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys
ltail (Q [] [a]
_) = String -> Seq a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.ltail: empty sequence"

ltailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
ltailM (Q [a
_] [a]
ys) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
ys) [])
ltailM (Q (a
_:[a]
xs) [a]
ys) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys)
ltailM (Q [] [a]
_) = String -> m (Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.ltailM: empty sequence"

rview :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (a, Seq a)
rview (Q [a]
xs (a
y:[a]
ys)) = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
y, [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys)
rview (Q [a]
xs []) =
  case [a] -> Maybe (a, [a])
forall (rm :: * -> *) a. MonadFail rm => [a] -> rm (a, [a])
L.rview [a]
xs of
    Maybe (a, [a])
Nothing      -> String -> m (a, Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.rview: empty sequence"
    Just (a
x,[a]
xs') -> (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a
x, [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs' [])

rhead :: forall a. Seq a -> a
rhead (Q [a]
_ (a
y:[a]
_)) = a
y
rhead (Q [] []) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.rhead: empty sequence"
rhead (Q [a]
xs []) = [a] -> a
forall a. [a] -> a
L.rhead [a]
xs

rheadM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m a
rheadM (Q [a]
_ (a
y:[a]
_)) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
y
rheadM (Q [] []) = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.rheadM: empty sequence"
rheadM (Q [a]
xs []) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([a] -> a
forall a. [a] -> a
L.rhead [a]
xs)

rtail :: forall a. Seq a -> Seq a
rtail (Q [a]
xs (a
_:[a]
ys)) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys
rtail (Q [] []) = String -> Seq a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.rtail: empty sequence"
rtail (Q [a]
xs []) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.rtail [a]
xs) []

rtailM :: forall (m :: * -> *) a. MonadFail m => Seq a -> m (Seq a)
rtailM (Q [a]
xs (a
_:[a]
ys)) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys)
rtailM (Q [] []) = String -> m (Seq a)
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"SimpleQueue.rtailM: empty sequence"
rtailM (Q [a]
xs []) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return ([a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.rtail [a]
xs) [])

null :: forall a. Seq a -> Bool
null (Q [] [a]
_) = Bool
True
null Seq a
_ = Bool
False

size :: forall a. Seq a -> Int
size (Q [a]
xs [a]
ys) = [a] -> Int
forall a. [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs Int -> Int -> Int
forall a. Num a => a -> a -> a
+ [a] -> Int
forall a. [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
ys

reverse :: forall a. Seq a -> Seq a
reverse (Q [a]
xs []) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
xs) []
reverse (Q [a]
xs [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
ys [a]
xs

reverseOnto :: forall a. Seq a -> Seq a -> Seq a
reverseOnto (Q [a]
xs1 [a]
ys1) (Q [a]
xs2 [a]
ys2) =
    [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q ([a]
ys1 [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
L.reverseOnto [a]
xs1 [a]
xs2) [a]
ys2

fromList :: forall a. [a] -> Seq a
fromList [a]
xs = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs []

toList :: forall a. Seq a -> [a]
toList (Q [a]
xs []) = [a]
xs
toList (Q [a]
xs [a]
ys) = [a]
xs [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a] -> [a]
forall a. [a] -> [a]
L.reverse [a]
ys

map :: forall a b. (a -> b) -> Seq a -> Seq b
map a -> b
f (Q [a]
xs [a]
ys) = [b] -> [b] -> Seq b
forall a. [a] -> [a] -> Seq a
Q ((a -> b) -> [a] -> [b]
forall a b. (a -> b) -> [a] -> [b]
L.map a -> b
f [a]
xs) ((a -> b) -> [a] -> [b]
forall a b. (a -> b) -> [a] -> [b]
L.map a -> b
f [a]
ys)

-- local fn on lists
revfoldr :: (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr :: forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr t -> t1 -> t1
_ t1
e [] = t1
e
revfoldr t -> t1 -> t1
f t1
e (t
x:[t]
xs) = (t -> t1 -> t1) -> t1 -> [t] -> t1
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr t -> t1 -> t1
f (t -> t1 -> t1
f t
x t1
e) [t]
xs

revfoldr' :: (t -> a -> a) -> a -> [t] -> a
revfoldr' :: forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr' t -> a -> a
_ a
e [] = a
e
revfoldr' t -> a -> a
f a
e (t
x:[t]
xs) = a
e a -> a -> a
forall a b. a -> b -> b
`seq` (t -> a -> a) -> a -> [t] -> a
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr' t -> a -> a
f (t -> a -> a
f t
x a
e) [t]
xs

-- local fn on lists
revfoldl :: (t -> t1 -> t) -> t -> [t1] -> t
revfoldl :: forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl t -> t1 -> t
_ t
e [] = t
e
revfoldl t -> t1 -> t
f t
e (t1
x:[t1]
xs) = t -> t1 -> t
f ((t -> t1 -> t) -> t -> [t1] -> t
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl t -> t1 -> t
f t
e [t1]
xs) t1
x

revfoldl' :: (a -> t -> a) -> a -> [t] -> a
revfoldl' :: forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl' a -> t -> a
_ a
e [] = a
e
revfoldl' a -> t -> a
f a
e (t
x:[t]
xs) = a
e a -> a -> a
forall a b. a -> b -> b
`seq` a -> t -> a
f ((a -> t -> a) -> a -> [t] -> a
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl' a -> t -> a
f a
e [t]
xs) t
x

fold :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold   a -> b -> b
f b
e (Q [a]
xs [a]
ys) = (a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr a -> b -> b
f ((a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr a -> b -> b
f b
e [a]
ys) [a]
xs
fold' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
fold'  a -> b -> b
f b
e (Q [a]
xs [a]
ys) = (b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl' ((a -> b -> b) -> b -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> b
f) ((b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl' ((a -> b -> b) -> b -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> b
f) b
e [a]
ys) [a]
xs
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
f b
e (Q [a]
xs [a]
ys) = (a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr  a -> b -> b
f ((a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr  a -> b -> b
f b
e [a]
ys) [a]
xs
foldr' :: forall a b. (a -> b -> b) -> b -> Seq a -> b
foldr' a -> b -> b
f b
e (Q [a]
xs [a]
ys) = (a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr' a -> b -> b
f ((a -> b -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr' a -> b -> b
f b
e [a]
ys) [a]
xs

foldl :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl  b -> a -> b
f b
e (Q [a]
xs [a]
ys) = (b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl  b -> a -> b
f ((b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl  b -> a -> b
f b
e [a]
xs) [a]
ys
foldl' :: forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' b -> a -> b
f b
e (Q [a]
xs [a]
ys) = (b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl' b -> a -> b
f ((b -> a -> b) -> b -> [a] -> b
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl' b -> a -> b
f b
e [a]
xs) [a]
ys

foldr1 :: forall a. (a -> a -> a) -> Seq a -> a
foldr1  a -> a -> a
f (Q [a]
xs (a
y:[a]
ys)) = (a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr a -> a -> a
f ((a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr a -> a -> a
f a
y [a]
ys) [a]
xs
foldr1  a -> a -> a
_ (Q [] []) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.foldr1: empty sequence"
foldr1  a -> a -> a
f (Q [a]
xs []) = (a -> a -> a) -> [a] -> a
forall a. (a -> a -> a) -> [a] -> a
L.foldr1 a -> a -> a
f [a]
xs

foldr1' :: forall a. (a -> a -> a) -> Seq a -> a
foldr1' a -> a -> a
f (Q [a]
xs (a
y:[a]
ys)) = (a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
L.foldr' a -> a -> a
f ((a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t1) -> t1 -> [t] -> t1
revfoldr' a -> a -> a
f a
y [a]
ys) [a]
xs
foldr1' a -> a -> a
_ (Q [] []) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueye.foldr1': empty sequence"
foldr1' a -> a -> a
f (Q [a]
xs []) = (a -> a -> a) -> [a] -> a
forall a. (a -> a -> a) -> [a] -> a
L.foldr1' a -> a -> a
f [a]
xs

foldl1 :: forall a. (a -> a -> a) -> Seq a -> a
foldl1  a -> a -> a
f (Q (a
x:[a]
xs) [a]
ys) = (a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl a -> a -> a
f ((a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl a -> a -> a
f a
x [a]
xs) [a]
ys
foldl1  a -> a -> a
_ (Q [] [a]
_) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.foldl1: empty sequence"

foldl1' :: forall a. (a -> a -> a) -> Seq a -> a
foldl1' a -> a -> a
f (Q (a
x:[a]
xs) [a]
ys) = (a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
revfoldl' a -> a -> a
f ((a -> a -> a) -> a -> [a] -> a
forall t t1. (t -> t1 -> t) -> t -> [t1] -> t
L.foldl' a -> a -> a
f a
x [a]
xs) [a]
ys
foldl1' a -> a -> a
_ (Q [] [a]
_) = String -> a
forall a. HasCallStack => String -> a
error String
"SimpleQueue.foldl1': empty sequence"

filter :: forall a. (a -> Bool) -> Seq a -> Seq a
filter a -> Bool
p (Q [a]
xs [a]
ys) = [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
makeQ ((a -> Bool) -> [a] -> [a]
forall a. (a -> Bool) -> [a] -> [a]
L.filter a -> Bool
p [a]
xs) ((a -> Bool) -> [a] -> [a]
forall a. (a -> Bool) -> [a] -> [a]
L.filter a -> Bool
p [a]
ys)

partition :: forall a. (a -> Bool) -> Seq a -> (Seq a, Seq a)
partition a -> Bool
p (Q [a]
xs [a]
ys)
  = ([a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
makeQ [a]
xsT [a]
ysT, [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
makeQ [a]
xsF [a]
ysF)
 where
   ([a]
xsT,[a]
xsF) = (a -> Bool) -> [a] -> ([a], [a])
forall a. (a -> Bool) -> [a] -> ([a], [a])
L.partition a -> Bool
p [a]
xs
   ([a]
ysT,[a]
ysF) = (a -> Bool) -> [a] -> ([a], [a])
forall a. (a -> Bool) -> [a] -> ([a], [a])
L.partition a -> Bool
p [a]
ys

strict :: forall a. Seq a -> Seq a
strict s :: Seq a
s@(Q [a]
xs [a]
ys) = [a] -> [a]
forall a. [a] -> [a]
L.strict [a]
xs [a] -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` [a] -> [a]
forall a. [a] -> [a]
L.strict [a]
ys [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
f s :: Seq a
s@(Q [a]
xs [a]
ys) = (a -> b) -> [a] -> [a]
forall a b. (a -> b) -> [a] -> [a]
L.strictWith a -> b
f [a]
xs [a] -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` (a -> b) -> [a] -> [a]
forall a b. (a -> b) -> [a] -> [a]
L.strictWith a -> b
f [a]
ys [a] -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a
s

-- the remaining functions all use defaults

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
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
copy :: forall a. Int -> a -> Seq a
copy = Int -> a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> a -> s a
copyUsingLists
inBounds :: forall a. Int -> Seq a -> Bool
inBounds = Int -> Seq a -> Bool
forall (s :: * -> *) a. Sequence s => Int -> s a -> Bool
inBoundsUsingLookupM
lookup :: forall a. Int -> Seq a -> a
lookup = Int -> Seq a -> a
forall (s :: * -> *) a. Sequence s => Int -> s a -> a
lookupUsingLookupM
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
lookupWithDefaultUsingLookupM
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
updateUsingAdjust
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
adjustUsingLists
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
takeUsingLists
drop :: forall a. Int -> Seq a -> Seq a
drop = Int -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => Int -> s a -> s a
dropUsingLists
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)
splitAtDefault
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
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)
zipUsingLists
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)
zip3UsingLists
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
zipWithUsingLists
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
zipWith3UsingLists
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)
unzipUsingLists
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)
unzip3UsingLists
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)
unzipWithUsingLists
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)
unzipWith3UsingLists

-- invariant:
--   * front empty only if rear also empty

structuralInvariant :: forall a. Seq a -> Bool
structuralInvariant (Q [a]
x [a]
y) = Bool -> Bool
not ([a] -> Bool
forall a. [a] -> Bool
L.null [a]
x) Bool -> Bool -> Bool
|| [a] -> Bool
forall a. [a] -> Bool
L.null [a]
y

-- 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; 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; 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
q1 == :: Seq a -> Seq a -> Bool
== Seq a
q2 = Seq a -> [a]
forall a. Seq a -> [a]
toList Seq a
q1 [a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
== Seq a -> [a]
forall a. Seq a -> [a]
toList Seq a
q2

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 = do [a]
xs <- Gen [a]
forall a. Arbitrary a => Gen a
arbitrary
                 [a]
ys <- Gen [a]
forall a. Arbitrary a => Gen a
arbitrary
                 Seq a -> Gen (Seq a)
forall a. a -> Gen a
forall (m :: * -> *) a. Monad m => a -> m a
return (if [a] -> Bool
forall a. [a] -> Bool
L.null [a]
xs then [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
ys [] else [a] -> [a] -> Seq a
forall a. [a] -> [a] -> Seq a
Q [a]
xs [a]
ys)

instance CoArbitrary a => CoArbitrary (Seq a) where
  coarbitrary :: forall b. Seq a -> Gen b -> Gen b
coarbitrary (Q [a]
xs [a]
ys) = [a] -> Gen b -> Gen b
forall b. [a] -> Gen b -> Gen b
forall a b. CoArbitrary a => a -> Gen b -> Gen b
coarbitrary [a]
xs (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]
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.<>)