-- |
--   Module      :  Data.Edison.Seq.MyersStack
--   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)
--
--   Meyers Stacks.  All operations are as listed in "Data.Edison.Seq" except
--   the following:
--
-- * lookup, inBounds, drop  @O( min(i, log n) )@
--
-- * rhead*, size  @O( log n )@
--
-- * subseq        @O( min (i, log n) + len )@
--
--   /References:/
--
-- * Eugene Myers. \"An applicative random-access stack\". /Information
--   Processing Letters/, 17(5):241-248, December 1983.

module Data.Edison.Seq.MyersStack (
    -- * 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,foldrWithIndex',foldlWithIndex,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 Data.Edison.Prelude ( runFail_ )
import qualified Data.Edison.Seq as S ( Sequence(..) )
import Data.Edison.Seq.Defaults
import qualified Control.Monad.Fail as Fail
import Control.Monad
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.MyersStack"


data Seq a = E | C !Int a (Seq a) (Seq a)
  -- what about strictness flags on tail and jump-tail?

-- auxiliary function
jump :: Seq t -> Seq t
jump :: forall t. Seq t -> Seq t
jump (C Int
_ t
_ Seq t
_ (C Int
_ t
_ Seq t
_ Seq t
xs')) = Seq t
xs'
jump Seq t
_ = String -> Seq t
forall a. HasCallStack => String -> a
error String
"MyersStack.jump: bug!"

empty :: forall a. Seq a
empty = Seq a
forall a. Seq a
E
singleton :: forall a. a -> Seq a
singleton a
x = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
1 a
x Seq a
forall a. Seq a
E Seq a
forall a. Seq a
E

lcons :: forall a. a -> Seq a -> Seq a
lcons a
x xs :: Seq a
xs@(C Int
i a
_  Seq a
_  (C Int
j a
_ Seq a
_ Seq a
xs'))
    | Int
i Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
j = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C (Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
j) a
x Seq a
xs Seq a
xs'
lcons a
x Seq a
xs = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
1 a
x Seq a
xs Seq a
xs

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
"MyersStack.lview: empty sequence"
lview (C Int
_ a
x Seq a
xs Seq a
_) = (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)

lhead :: forall a. Seq a -> a
lhead Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"MyersStack.lhead: empty sequence"
lhead (C Int
_ a
x Seq a
_ Seq a
_) = a
x

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
"MyersStack.lheadM: empty sequence"
lheadM (C Int
_ a
x Seq a
_ Seq a
_) = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x

ltail :: forall t. Seq t -> Seq t
ltail Seq a
E = String -> Seq a
forall a. HasCallStack => String -> a
error String
"MyersStack.ltail: empty sequence"
ltail (C Int
_ a
_ Seq a
xs Seq a
_) = Seq a
xs

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
"MyersStack.ltailM: empty sequence"
ltailM (C Int
_ a
_ Seq a
xs Seq a
_) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return Seq a
xs

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
"MyersStack.rview: empty sequence"
rview Seq a
xs = (a, Seq a) -> m (a, Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (Seq a -> a
forall a. Seq a -> a
rhead Seq a
xs, Seq a -> Seq a
forall t. Seq t -> Seq t
rtail Seq a
xs)

rhead :: forall a. Seq a -> a
rhead Seq a
E = String -> a
forall a. HasCallStack => String -> a
error String
"MyersStack.rhead: empty sequence"
rhead (C Int
_ a
x Seq a
xs Seq a
xs') = a -> Seq a -> Seq a -> a
forall {t}. t -> Seq t -> Seq t -> t
rh a
x Seq a
xs Seq a
xs'
  where rh :: t -> Seq t -> Seq t -> t
rh t
_ Seq t
_ (C Int
_ t
y Seq t
ys Seq t
ys') = t -> Seq t -> Seq t -> t
rh t
y Seq t
ys Seq t
ys'
        rh t
_ (C Int
_ t
y Seq t
ys Seq t
ys') Seq t
E = t -> Seq t -> Seq t -> t
rh t
y Seq t
ys Seq t
ys'
        rh t
x Seq t
E Seq t
E = t
x

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
"MyersStack.rheadM: empty sequence"
rheadM (C Int
_ a
x Seq a
xs Seq a
xs') = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> Seq a -> Seq a -> a
forall {t}. t -> Seq t -> Seq t -> t
rh a
x Seq a
xs Seq a
xs')
  where rh :: t -> Seq t -> Seq t -> t
rh t
_ Seq t
_ (C Int
_ t
y Seq t
ys Seq t
ys') = t -> Seq t -> Seq t -> t
rh t
y Seq t
ys Seq t
ys'
        rh t
_ (C Int
_ t
y Seq t
ys Seq t
ys') Seq t
E = t -> Seq t -> Seq t -> t
rh t
y Seq t
ys Seq t
ys'
        rh t
x Seq t
E Seq t
E = t
x

rtail :: forall t. Seq t -> Seq t
rtail Seq a
E = String -> Seq a
forall a. HasCallStack => String -> a
error String
"MyersStack.rtail: empty sequence"
rtail (C Int
_ a
x Seq a
xs Seq a
_) = a -> Seq a -> Seq a
forall a. a -> Seq a -> Seq a
rt a
x Seq a
xs
  where rt :: t -> Seq t -> Seq t
rt t
_ Seq t
E = Seq t
forall a. Seq a
E
        rt t
y (C Int
_ t
x Seq t
xs Seq t
_) = t -> Seq t -> Seq t
forall a. a -> Seq a -> Seq a
lcons t
y (t -> Seq t -> Seq t
rt t
x Seq t
xs)

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
"MyersStack.rtailM: empty sequence"
rtailM (C Int
_ a
x Seq a
xs Seq a
_) = Seq a -> m (Seq a)
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return (a -> Seq a -> Seq a
forall a. a -> Seq a -> Seq a
rt a
x Seq a
xs)
  where rt :: t -> Seq t -> Seq t
rt t
_ Seq t
E = Seq t
forall a. Seq a
E
        rt t
y (C Int
_ t
x Seq t
xs Seq t
_) = t -> Seq t -> Seq t
forall a. a -> Seq a -> Seq a
lcons t
y (t -> Seq t -> Seq t
rt t
x Seq t
xs)

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
forall a. Seq a -> Int
go Seq a
xs
  where go :: Seq a -> Int
go Seq a
E = (Int
0::Int)
        go (C Int
j a
_ Seq a
_ Seq a
xs') = Int
j Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Seq a -> Int
forall a. Seq a -> Int
size Seq a
xs'

reverseOnto :: forall a. Seq a -> Seq a -> Seq a
reverseOnto Seq a
E Seq a
ys = Seq a
ys
reverseOnto (C Int
_ a
x Seq a
xs Seq a
_) Seq a
ys = Seq a -> Seq a -> Seq a
forall a. Seq a -> Seq a -> Seq a
reverseOnto Seq a
xs (a -> Seq a -> Seq a
forall a. a -> Seq a -> Seq a
lcons a
x Seq a
ys)

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 (C Int
j a
x Seq a
xs Seq a
_')
    | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
ys Seq b
ys
    | Bool
otherwise = Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
ys (Seq b -> Seq b
forall t. Seq t -> Seq t
jump Seq b
ys)
  where ys :: Seq b
ys = (a -> b) -> Seq a -> Seq b
forall a b. (a -> b) -> Seq a -> Seq b
map a -> b
f Seq a
xs

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
f = (b -> a -> b) -> b -> Seq a -> b
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' ((a -> b -> b) -> b -> a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip a -> b -> b
f)
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 (C Int
_ a
x Seq a
xs Seq a
_) = a -> b -> b
f a
x ((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
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 (C Int
_ a
x Seq a
xs Seq a
_) = a -> b -> b
f a
x (b -> b) -> b -> 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
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 (C Int
_ a
x Seq a
xs Seq a
_) = (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
f b
e a
x) 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 (C Int
_ a
x Seq a
xs Seq a
_) = 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
f b
e a
x) 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
"MyersStack.foldr1: empty sequence"
foldr1 a -> a -> a
f (C Int
_ a
x Seq a
xs Seq a
_) = a -> Seq a -> a
fr a
x Seq a
xs
  where fr :: a -> Seq a -> a
fr a
y Seq a
E = a
y
        fr a
y (C Int
_ a
x Seq a
xs Seq a
_) = a -> a -> a
f a
y (a -> Seq a -> a
fr a
x 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
"MyersStack.foldr1': empty sequence"
foldr1' a -> a -> a
f (C Int
_ a
x Seq a
xs Seq a
_) = a -> Seq a -> a
fr a
x Seq a
xs
  where fr :: a -> Seq a -> a
fr a
y Seq a
E = a
y
        fr a
y (C Int
_ a
x Seq a
xs Seq a
_) = a -> a -> a
f a
y (a -> a) -> a -> a
forall a b. (a -> b) -> a -> b
$! (a -> Seq a -> a
fr a
x 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
"MyersStack.foldl1: empty sequence"
foldl1 a -> a -> a
f (C Int
_ a
x Seq a
xs Seq a
_) = (a -> a -> a) -> a -> Seq a -> a
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl a -> a -> a
f a
x 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
"MyersStack.foldl1': empty sequence"
foldl1' a -> a -> a
f (C Int
_ a
x Seq a
xs Seq a
_ ) = (a -> a -> a) -> a -> Seq a -> a
forall b a. (b -> a -> b) -> b -> Seq a -> b
foldl' a -> a -> a
f a
x Seq a
xs

inBounds :: forall a. Int -> Seq a -> Bool
inBounds Int
i Seq a
xs = Seq a -> Int -> Bool
forall {a}. Seq a -> Int -> Bool
inb Seq a
xs Int
i
  where inb :: Seq a -> Int -> Bool
inb Seq a
E Int
_ = Bool
False
        inb (C Int
j a
_ Seq a
_ Seq a
xs') Int
i
          | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
j     = (Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0)
          | Bool
otherwise = Seq a -> Int -> Bool
inb Seq a
xs' (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
j)

lookup :: forall a. Int -> Seq a -> a
lookup Int
i Seq a
xs = Fail a -> a
forall a. Fail a -> a
runFail_ (Int -> Seq a -> Fail a
forall (m :: * -> *) a. MonadFail m => Int -> Seq a -> m a
lookupM Int
i Seq a
xs)

lookupM :: forall (m :: * -> *) a. MonadFail m => Int -> Seq a -> m a
lookupM Int
i Seq a
xs = Seq a -> Int -> m a
forall {a}. Seq a -> Int -> m a
look Seq a
xs Int
i
  where look :: Seq a -> Int -> m a
look Seq a
E Int
_ = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"MyersStack.lookup: bad subscript"
        look (C Int
j a
x Seq a
xs Seq a
xs') Int
i
          | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
j   = Seq a -> Int -> m a
look Seq a
xs' (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
j)
          | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
0    = Seq a -> Int -> m a
look Seq a
xs  (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)
          | Int
i Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0   = a -> m a
forall a. a -> m a
forall (m :: * -> *) a. Monad m => a -> m a
return a
x
          | Bool
otherwise = m a
forall {a}. m a
nothing
        nothing :: m a
nothing = String -> m a
forall a. String -> m a
forall (m :: * -> *) a. MonadFail m => String -> m a
fail String
"MyersStack.lookup: not found"

lookupWithDefault :: forall a. a -> Int -> Seq a -> a
lookupWithDefault a
d Int
i Seq a
xs = Seq a -> Int -> a
look Seq a
xs Int
i
  where look :: Seq a -> Int -> a
look Seq a
E Int
_ = a
d
        look (C Int
j a
x Seq a
xs Seq a
xs') Int
i
          | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
j   = Seq a -> Int -> a
look Seq a
xs' (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
j)
          | Int
i Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
0    = Seq a -> Int -> a
look Seq a
xs  (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)
          | Int
i Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
0   = a
x
          | Bool
otherwise = a
d

update :: forall a. Int -> a -> Seq a -> Seq a
update Int
i a
y Seq a
xs = Int -> Seq a -> Seq a
forall {p}. (Eq p, Num p) => p -> Seq a -> Seq a
upd Int
i Seq a
xs
  where upd :: p -> Seq a -> Seq a
upd p
_ Seq a
E = Seq a
forall a. Seq a
E
        upd p
0 (C Int
j a
_ Seq a
xs Seq a
xs') = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
y Seq a
xs Seq a
xs'
        upd p
i (C Int
j a
x Seq a
xs Seq a
_)
            | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
ys Seq a
ys
            | Bool
otherwise = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
ys (Seq a -> Seq a
forall t. Seq t -> Seq t
jump Seq a
ys)
          where ys :: Seq a
ys = p -> Seq a -> Seq a
upd (p
i p -> p -> p
forall a. Num a => a -> a -> a
- p
1) Seq a
xs

adjust :: forall a. (a -> a) -> Int -> Seq a -> Seq a
adjust a -> a
f Int
i Seq a
xs = Int -> Seq a -> Seq a
adj Int
i Seq a
xs
  where adj :: Int -> Seq a -> Seq a
adj Int
_ Seq a
E = Seq a
forall a. Seq a
E
        adj Int
0 (C Int
j a
x Seq a
xs Seq a
xs') = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> a
f a
x) Seq a
xs Seq a
xs'
        adj Int
i (C Int
j a
x Seq a
xs Seq a
_)
            | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
ys Seq a
ys
            | Bool
otherwise = Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
ys (Seq a -> Seq a
forall t. Seq t -> Seq t
jump Seq a
ys)
          where ys :: Seq a
ys = Int -> Seq a -> Seq a
adj (Int
i Int -> Int -> Int
forall a. Num a => a -> a -> a
- (Int
1::Int)) Seq a
xs

drop :: forall a. Int -> Seq a -> Seq a
drop Int
n Seq a
xs = Int -> Seq a -> Seq a
forall a. Int -> Seq a -> Seq a
drp Int
n Seq a
xs
  where drp :: Int -> Seq a -> Seq a
drp Int
n Seq a
xs | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
0 = Seq a
xs
        drp Int
_ Seq a
E = Seq a
forall a. Seq a
E
        drp Int
n (C Int
j a
_ Seq a
xs Seq a
xs')
          | Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
j     = Int -> Seq a -> Seq a
drp (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) Seq a
xs
          | Bool
otherwise = Int -> Seq a -> Seq a
drp (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
j) Seq a
xs'

unzip :: forall a b. Seq (a, b) -> (Seq a, Seq b)
unzip Seq (a, b)
E = (Seq a
forall a. Seq a
E, Seq b
forall a. Seq a
E)
unzip (C Int
j (a
x,b
y) Seq (a, b)
ps Seq (a, b)
_')
    | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = (Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
xs Seq a
xs, Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j b
y Seq b
ys Seq b
ys)
    | Bool
otherwise = (Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
xs (Seq a -> Seq a
forall t. Seq t -> Seq t
jump Seq a
xs), Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j b
y Seq b
ys (Seq b -> Seq b
forall t. Seq t -> Seq t
jump Seq b
ys))
  where (Seq a
xs,Seq b
ys) = Seq (a, b) -> (Seq a, Seq b)
forall a b. Seq (a, b) -> (Seq a, Seq b)
unzip Seq (a, b)
ps

unzip3 :: forall a b c. Seq (a, b, c) -> (Seq a, Seq b, Seq c)
unzip3 Seq (a, b, c)
E = (Seq a
forall a. Seq a
E, Seq b
forall a. Seq a
E, Seq c
forall a. Seq a
E)
unzip3 (C Int
j (a
x,b
y,c
z) Seq (a, b, c)
ts Seq (a, b, c)
_')
    | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = (Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
xs Seq a
xs, Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j b
y Seq b
ys Seq b
ys, Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j c
z Seq c
zs Seq c
zs)
    | Bool
otherwise = (Int -> a -> Seq a -> Seq a -> Seq a
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j a
x Seq a
xs (Seq a -> Seq a
forall t. Seq t -> Seq t
jump Seq a
xs), Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j b
y Seq b
ys (Seq b -> Seq b
forall t. Seq t -> Seq t
jump Seq b
ys), Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j c
z Seq c
zs (Seq c -> Seq c
forall t. Seq t -> Seq t
jump Seq c
zs))
  where (Seq a
xs,Seq b
ys,Seq c
zs) = 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 Seq (a, b, c)
ts

unzipWith :: forall a b c. (a -> b) -> (a -> c) -> Seq a -> (Seq b, Seq c)
unzipWith a -> b
_ a -> c
_ Seq a
E = (Seq b
forall a. Seq a
E, Seq c
forall a. Seq a
E)
unzipWith a -> b
f a -> c
g (C Int
j a
x Seq a
xs Seq a
_)
    | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = (Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
as Seq b
as, Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> c
g a
x) Seq c
bs Seq c
bs)
    | Bool
otherwise = (Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
as (Seq b -> Seq b
forall t. Seq t -> Seq t
jump Seq b
as), Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> c
g a
x) Seq c
bs (Seq c -> Seq c
forall t. Seq t -> Seq t
jump Seq c
bs))
  where (Seq b
as,Seq c
bs) = (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 a -> b
f a -> c
g Seq a
xs

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
E = (Seq b
forall a. Seq a
E, Seq c
forall a. Seq a
E, Seq d
forall a. Seq a
E)
unzipWith3 a -> b
f a -> c
g a -> d
h (C Int
j a
x Seq a
xs Seq a
_)
    | Int
j Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
1    = (Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
as Seq b
as, Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> c
g a
x) Seq c
bs Seq c
bs, Int -> d -> Seq d -> Seq d -> Seq d
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> d
h a
x) Seq d
cs Seq d
cs)
    | Bool
otherwise = (Int -> b -> Seq b -> Seq b -> Seq b
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> b
f a
x) Seq b
as (Seq b -> Seq b
forall t. Seq t -> Seq t
jump Seq b
as), Int -> c -> Seq c -> Seq c -> Seq c
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> c
g a
x) Seq c
bs (Seq c -> Seq c
forall t. Seq t -> Seq t
jump Seq c
bs),
                   Int -> d -> Seq d -> Seq d -> Seq d
forall a. Int -> a -> Seq a -> Seq a -> Seq a
C Int
j (a -> d
h a
x) Seq d
cs (Seq d -> Seq d
forall t. Seq t -> Seq t
jump Seq d
cs))
  where (Seq b
as,Seq c
bs,Seq d
cs) = (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 a -> b
f a -> c
g a -> d
h Seq a
xs

strict :: forall t. Seq t -> Seq t
strict s :: Seq a
s@Seq a
E = Seq a
s
strict s :: Seq a
s@(C Int
_ a
_ Seq a
xs Seq a
_) = Seq a -> Seq a
forall t. Seq t -> Seq t
strict Seq a
xs 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@(C Int
_ a
x Seq a
xs Seq a
_) = a -> b
f a
x b -> 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
xs Seq a -> Seq a -> Seq a
forall a b. a -> b -> b
`seq` Seq a
s

-- the remaining functions all use defaults

rcons :: forall a. a -> Seq a -> Seq a
rcons = a -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => a -> s a -> s a
rconsUsingFoldr
append :: forall a. Seq a -> Seq a -> Seq a
append = Seq a -> Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => s a -> s a -> s a
appendUsingFoldr
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
reverse :: forall t. Seq t -> Seq t
reverse = Seq a -> Seq a
forall (s :: * -> *) a. Sequence s => s a -> s a
reverseUsingReverseOnto
fromList :: forall a. [a] -> Seq a
fromList = [a] -> Seq a
forall (s :: * -> *) a. Sequence s => [a] -> s a
fromListUsingCons
toList :: forall a. Seq a -> [a]
toList = Seq a -> [a]
forall (s :: * -> *) a. Sequence s => s a -> [a]
toListUsingFoldr
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
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
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
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
filterUsingFoldr
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
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

-- for zips, could optimize by calculating which one is shorter and
-- retaining its shape

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

-- FIXME what are the structural invariants?
structuralInvariant :: forall a. Seq a -> Bool
structuralInvariant = Bool -> Seq a -> Bool
forall a b. a -> b -> a
const Bool
True

-- 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 t. Seq t -> Seq t
ltail = Seq a -> Seq a
forall t. Seq t -> Seq t
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 t. Seq t -> Seq t
rtail = Seq a -> Seq a
forall t. Seq t -> Seq t
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 t. Seq t -> Seq t
reverse = Seq a -> Seq a
forall t. Seq t -> Seq t
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 t. Seq t -> Seq t
strict = Seq a -> Seq a
forall t. Seq t -> Seq t
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 -> Int
forall a. Seq a -> Int
size Seq a
xs Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Seq a -> Int
forall a. Seq a -> Int
size Seq a
ys) Bool -> Bool -> Bool
&& (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 = do [a]
xs <- 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 ([a] -> Seq a
forall a. [a] -> Seq a
fromList [a]
xs)

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

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.<>)

-------------

{-
questions:
  - any benefit to
      E | C1 x xs | CJ Int# x xs xs'

  - any benefit to length instead of delta?

  - any benefit to delta not counting x (i.e., base 0 instead of base 1)?

I don't believe any will do any better, except possibly the first
-}