-- | Utility functions for lists.

module Agda.Utils.List where

import Control.Monad (filterM)

import Data.Array (Array, array, listArray)
import qualified Data.Array as Array
import Data.Bifunctor
import Data.Function
import qualified Data.List as List
import qualified Data.List.NonEmpty as List1
import Data.List.NonEmpty (pattern (:|), (<|))
import Data.Maybe
import qualified Data.Map as Map
import qualified Data.Set as Set

import qualified Agda.Utils.Bag as Bag
import Agda.Utils.Function (applyWhen)
import Agda.Utils.Functor  ((<.>))
import Agda.Utils.Tuple

import {-# SOURCE #-} Agda.Utils.List1 (List1)

import Agda.Utils.Impossible

---------------------------------------------------------------------------
-- * Variants of list case, cons, head, tail, init, last
---------------------------------------------------------------------------

-- | Append a single element at the end.
--   Time: O(length); use only on small lists.
snoc :: [a] -> a -> [a]
snoc :: forall a. [a] -> a -> [a]
snoc [a]
xs a
x = [a]
xs [a] -> [a] -> [a]
forall a. [a] -> [a] -> [a]
++ [a
x]

-- | Case distinction for lists, with list first.
--   O(1).
--
--   Cf. 'Agda.Utils.Null.ifNull'.
caseList :: [a] -> b -> (a -> [a] -> b) -> b
caseList :: forall a b. [a] -> b -> (a -> [a] -> b) -> b
caseList [a]
xs b
n a -> [a] -> b
c = b -> (a -> [a] -> b) -> [a] -> b
forall b a. b -> (a -> [a] -> b) -> [a] -> b
listCase b
n a -> [a] -> b
c [a]
xs

-- | Case distinction for lists, with list first.
--   O(1).
--
--   Cf. 'Agda.Utils.Null.ifNull'.
caseListM :: Monad m => m [a] -> m b -> (a -> [a] -> m b) -> m b
caseListM :: forall (m :: * -> *) a b.
Monad m =>
m [a] -> m b -> (a -> [a] -> m b) -> m b
caseListM m [a]
mxs m b
n a -> [a] -> m b
c = m b -> (a -> [a] -> m b) -> [a] -> m b
forall b a. b -> (a -> [a] -> b) -> [a] -> b
listCase m b
n a -> [a] -> m b
c ([a] -> m b) -> m [a] -> m b
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< m [a]
mxs

-- | Case distinction for lists, with list last.
--   O(1).
--
listCase :: b -> (a -> [a] -> b) -> [a] -> b
listCase :: forall b a. b -> (a -> [a] -> b) -> [a] -> b
listCase b
n a -> [a] -> b
c []     = b
n
listCase b
n a -> [a] -> b
c (a
x:[a]
xs) = a -> [a] -> b
c a
x [a]
xs

-- | Head function (safe). Returns a default value on empty lists.
--   O(1).
--
-- > headWithDefault 42 []      = 42
-- > headWithDefault 42 [1,2,3] = 1
headWithDefault :: a -> [a] -> a
headWithDefault :: forall a. a -> [a] -> a
headWithDefault a
def = a -> Maybe a -> a
forall a. a -> Maybe a -> a
fromMaybe a
def (Maybe a -> a) -> ([a] -> Maybe a) -> [a] -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Maybe a
forall a. [a] -> Maybe a
listToMaybe

-- | Tail function (safe).
--   O(1).
tailMaybe :: [a] -> Maybe [a]
tailMaybe :: forall a. [a] -> Maybe [a]
tailMaybe = ((a, [a]) -> [a]) -> Maybe (a, [a]) -> Maybe [a]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (a, [a]) -> [a]
forall a b. (a, b) -> b
snd (Maybe (a, [a]) -> Maybe [a])
-> ([a] -> Maybe (a, [a])) -> [a] -> Maybe [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Maybe (a, [a])
forall a. [a] -> Maybe (a, [a])
uncons

-- | Tail function (safe).  Returns a default list on empty lists.
--   O(1).
tailWithDefault :: [a] -> [a] -> [a]
tailWithDefault :: forall a. [a] -> [a] -> [a]
tailWithDefault [a]
def = [a] -> Maybe [a] -> [a]
forall a. a -> Maybe a -> a
fromMaybe [a]
def (Maybe [a] -> [a]) -> ([a] -> Maybe [a]) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Maybe [a]
forall a. [a] -> Maybe [a]
tailMaybe

-- | Last element (safe).
--   O(n).
lastMaybe :: [a] -> Maybe a
lastMaybe :: forall a. [a] -> Maybe a
lastMaybe [] = Maybe a
forall a. Maybe a
Nothing
lastMaybe [a]
xs = a -> Maybe a
forall a. a -> Maybe a
Just (a -> Maybe a) -> a -> Maybe a
forall a b. (a -> b) -> a -> b
$ [a] -> a
forall a. [a] -> a
last [a]
xs

-- | Last element (safe).  Returns a default list on empty lists.
--   O(n).
lastWithDefault :: a -> [a] -> a
lastWithDefault :: forall a. a -> [a] -> a
lastWithDefault = a -> [a] -> a
forall a. a -> [a] -> a
last1

-- | Last element of non-empty list (safe).
--   O(n).
--   @last1 a as = last (a : as)@
last1 :: a -> [a] -> a
last1 :: forall a. a -> [a] -> a
last1 a
a = \case
  [] -> a
a
  a
b:[a]
bs -> a -> [a] -> a
forall a. a -> [a] -> a
last1 a
b [a]
bs

-- | Last two elements (safe).
--   O(n).
last2 :: [a] -> Maybe (a, a)
last2 :: forall a. [a] -> Maybe (a, a)
last2 (a
x : a
y : [a]
xs) = (a, a) -> Maybe (a, a)
forall a. a -> Maybe a
Just ((a, a) -> Maybe (a, a)) -> (a, a) -> Maybe (a, a)
forall a b. (a -> b) -> a -> b
$ a -> a -> [a] -> (a, a)
forall {t}. t -> t -> [t] -> (t, t)
loop a
x a
y [a]
xs
  where
  loop :: t -> t -> [t] -> (t, t)
loop t
x t
y []     = (t
x, t
y)
  loop t
x t
y (t
z:[t]
xs) = t -> t -> [t] -> (t, t)
loop t
y t
z [t]
xs
last2 [a]
_ = Maybe (a, a)
forall a. Maybe a
Nothing

-- | Opposite of cons @(:)@, safe.
--   O(1).
uncons :: [a] -> Maybe (a, [a])
uncons :: forall a. [a] -> Maybe (a, [a])
uncons []     = Maybe (a, [a])
forall a. Maybe a
Nothing
uncons (a
x:[a]
xs) = (a, [a]) -> Maybe (a, [a])
forall a. a -> Maybe a
Just (a
x,[a]
xs)

-- | Maybe cons.
--   O(1).
--   @mcons ma as = maybeToList ma ++ as@
mcons :: Maybe a -> [a] -> [a]
mcons :: forall a. Maybe a -> [a] -> [a]
mcons Maybe a
ma [a]
as = [a] -> (a -> [a]) -> Maybe a -> [a]
forall b a. b -> (a -> b) -> Maybe a -> b
maybe [a]
as (a -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
as) Maybe a
ma

-- | 'init' and 'last' in one go, safe.
--   O(n).
initLast :: [a] -> Maybe ([a],a)
initLast :: forall a. [a] -> Maybe ([a], a)
initLast []     = Maybe ([a], a)
forall a. Maybe a
Nothing
initLast (a
a:[a]
as) = ([a], a) -> Maybe ([a], a)
forall a. a -> Maybe a
Just (([a], a) -> Maybe ([a], a)) -> ([a], a) -> Maybe ([a], a)
forall a b. (a -> b) -> a -> b
$ a -> [a] -> ([a], a)
forall a. a -> [a] -> ([a], a)
initLast1 a
a [a]
as

-- | 'init' and 'last' of non-empty list, safe.
--   O(n).
--   @initLast1 a as = (init (a:as), last (a:as)@
initLast1 :: a -> [a] -> ([a], a)
initLast1 :: forall a. a -> [a] -> ([a], a)
initLast1 a
a = \case
  []   -> ([], a
a)
  a
b:[a]
bs -> ([a] -> [a]) -> ([a], a) -> ([a], a)
forall (p :: * -> * -> *) a b c.
Bifunctor p =>
(a -> b) -> p a c -> p b c
first (a
aa -> [a] -> [a]
forall a. a -> [a] -> [a]
:) (([a], a) -> ([a], a)) -> ([a], a) -> ([a], a)
forall a b. (a -> b) -> a -> b
$ a -> [a] -> ([a], a)
forall a. a -> [a] -> ([a], a)
initLast1 a
b [a]
bs

-- | 'init' of non-empty list, safe.
--   O(n).
--   @init1 a as = init (a:as)@
init1 :: a -> [a] -> [a]
init1 :: forall a. a -> [a] -> [a]
init1 a
a = \case
  []   -> []
  a
b:[a]
bs -> a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: a -> [a] -> [a]
forall a. a -> [a] -> [a]
init1 a
b [a]
bs

-- | @init@, safe.
--   O(n).
initMaybe :: [a] -> Maybe [a]
initMaybe :: forall a. [a] -> Maybe [a]
initMaybe = \case
  []   -> Maybe [a]
forall a. Maybe a
Nothing
  a
a:[a]
as -> [a] -> Maybe [a]
forall a. a -> Maybe a
Just ([a] -> Maybe [a]) -> [a] -> Maybe [a]
forall a b. (a -> b) -> a -> b
$ a -> [a] -> [a]
forall a. a -> [a] -> [a]
init1 a
a [a]
as

-- | @init@, safe.
--   O(n).
initWithDefault :: [a] -> [a] -> [a]
initWithDefault :: forall a. [a] -> [a] -> [a]
initWithDefault [a]
as []     = [a]
as
initWithDefault [a]
_  (a
a:[a]
as) = a -> [a] -> [a]
forall a. a -> [a] -> [a]
init1 a
a [a]
as

---------------------------------------------------------------------------
-- * Lookup and indexing
---------------------------------------------------------------------------

-- | Lookup function (partially safe).
--   O(min n index).
(!!!) :: [a] -> Int -> Maybe a
[]       !!! :: forall a. [a] -> Int -> Maybe a
!!! Int
_         = Maybe a
forall a. Maybe a
Nothing
(a
x : [a]
_)  !!! Int
0         = a -> Maybe a
forall a. a -> Maybe a
Just a
x
(a
_ : [a]
xs) !!! Int
n         = [a]
xs [a] -> Int -> Maybe a
forall a. [a] -> Int -> Maybe a
!!! (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)

-- | Lookup function with default value for index out of range.
--   O(min n index).
--
--   The name is chosen akin to 'Data.List.genericIndex'.
indexWithDefault :: a -> [a] -> Int -> a
indexWithDefault :: forall a. a -> [a] -> Int -> a
indexWithDefault a
a []       Int
_ = a
a
indexWithDefault a
a (a
x : [a]
_)  Int
0 = a
x
indexWithDefault a
a (a
_ : [a]
xs) Int
n = a -> [a] -> Int -> a
forall a. a -> [a] -> Int -> a
indexWithDefault a
a [a]
xs (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1)

-- | Find an element satisfying a predicate and return it with its index.
--   O(n) in the worst case, e.g. @findWithIndex f xs = Nothing@.
--
--   TODO: more efficient implementation!?
findWithIndex :: (a -> Bool) -> [a] -> Maybe (a, Int)
findWithIndex :: forall a. (a -> Bool) -> [a] -> Maybe (a, Int)
findWithIndex a -> Bool
p [a]
as = ((a, Int) -> Bool) -> [(a, Int)] -> Maybe (a, Int)
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Maybe a
List.find (a -> Bool
p (a -> Bool) -> ((a, Int) -> a) -> (a, Int) -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a, Int) -> a
forall a b. (a, b) -> a
fst) ([a] -> [Int] -> [(a, Int)]
forall a b. [a] -> [b] -> [(a, b)]
zip [a]
as [Int
0..])

-- | A generalised variant of 'elemIndex'.
-- O(n).
genericElemIndex :: (Eq a, Integral i) => a -> [a] -> Maybe i
genericElemIndex :: forall a i. (Eq a, Integral i) => a -> [a] -> Maybe i
genericElemIndex a
x [a]
xs =
  [i] -> Maybe i
forall a. [a] -> Maybe a
listToMaybe ([i] -> Maybe i) -> [i] -> Maybe i
forall a b. (a -> b) -> a -> b
$
  ((i, Bool) -> i) -> [(i, Bool)] -> [i]
forall a b. (a -> b) -> [a] -> [b]
map (i, Bool) -> i
forall a b. (a, b) -> a
fst ([(i, Bool)] -> [i]) -> [(i, Bool)] -> [i]
forall a b. (a -> b) -> a -> b
$
  ((i, Bool) -> Bool) -> [(i, Bool)] -> [(i, Bool)]
forall a. (a -> Bool) -> [a] -> [a]
filter (i, Bool) -> Bool
forall a b. (a, b) -> b
snd ([(i, Bool)] -> [(i, Bool)]) -> [(i, Bool)] -> [(i, Bool)]
forall a b. (a -> b) -> a -> b
$
  [i] -> [Bool] -> [(i, Bool)]
forall a b. [a] -> [b] -> [(a, b)]
zip [i
0..] ([Bool] -> [(i, Bool)]) -> [Bool] -> [(i, Bool)]
forall a b. (a -> b) -> a -> b
$
  (a -> Bool) -> [a] -> [Bool]
forall a b. (a -> b) -> [a] -> [b]
map (a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
x) [a]
xs

-- | @downFrom n = [n-1,..1,0]@.
--   O(n).
downFrom :: Integral a => a -> [a]
downFrom :: forall a. Integral a => a -> [a]
downFrom a
n | a
n a -> a -> Bool
forall a. Ord a => a -> a -> Bool
<= a
0     = []
           | Bool
otherwise = let n' :: a
n' = a
na -> a -> a
forall a. Num a => a -> a -> a
-a
1 in a
n' a -> [a] -> [a]
forall a. a -> [a] -> [a]
: a -> [a]
forall a. Integral a => a -> [a]
downFrom a
n'

---------------------------------------------------------------------------
-- * Update
---------------------------------------------------------------------------

-- | Update the first element of a list, if it exists.
--   O(1).
updateHead :: (a -> a) -> [a] -> [a]
updateHead :: forall a. (a -> a) -> [a] -> [a]
updateHead a -> a
_ []       = []
updateHead a -> a
f (a
a : [a]
as) = a -> a
f a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: [a]
as

-- | Update the last element of a list, if it exists.
--   O(n).
updateLast :: (a -> a) -> [a] -> [a]
updateLast :: forall a. (a -> a) -> [a] -> [a]
updateLast a -> a
_ [] = []
updateLast a -> a
f (a
a : [a]
as) = a -> [a] -> [a]
loop a
a [a]
as
  -- Using a helper function to minimize the pattern matching.
  where
  loop :: a -> [a] -> [a]
loop a
a []       = [a -> a
f a
a]
  loop a
a (a
b : [a]
bs) = a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: a -> [a] -> [a]
loop a
b [a]
bs

-- | Update nth element of a list, if it exists.
--   @O(min index n)@.
--
--   Precondition: the index is >= 0.
updateAt :: Int -> (a -> a) -> [a] -> [a]
updateAt :: forall a. Int -> (a -> a) -> [a] -> [a]
updateAt Int
_ a -> a
_ [] = []
updateAt Int
0 a -> a
f (a
a : [a]
as) = a -> a
f a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: [a]
as
updateAt Int
n a -> a
f (a
a : [a]
as) = a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: Int -> (a -> a) -> [a] -> [a]
forall a. Int -> (a -> a) -> [a] -> [a]
updateAt (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1) a -> a
f [a]
as

---------------------------------------------------------------------------
-- * Sublist extraction and partitioning
---------------------------------------------------------------------------

type Prefix a = [a]  -- ^ The list before the split point.
type Suffix a = [a]  -- ^ The list after the split point.

-- | @splitExactlyAt n xs = Just (ys, zs)@ iff @xs = ys ++ zs@
--   and @genericLength ys = n@.
splitExactlyAt :: Integral n => n -> [a] -> Maybe (Prefix a, Suffix a)
splitExactlyAt :: forall n a. Integral n => n -> [a] -> Maybe ([a], [a])
splitExactlyAt n
0 [a]
xs       = ([a], [a]) -> Maybe ([a], [a])
forall (m :: * -> *) a. Monad m => a -> m a
return ([], [a]
xs)
splitExactlyAt n
n []       = Maybe ([a], [a])
forall a. Maybe a
Nothing
splitExactlyAt n
n (a
x : [a]
xs) = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
forall a c b. (a -> c) -> (a, b) -> (c, b)
mapFst (a
x a -> [a] -> [a]
forall a. a -> [a] -> [a]
:) (([a], [a]) -> ([a], [a])) -> Maybe ([a], [a]) -> Maybe ([a], [a])
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> n -> [a] -> Maybe ([a], [a])
forall n a. Integral n => n -> [a] -> Maybe ([a], [a])
splitExactlyAt (n
nn -> n -> n
forall a. Num a => a -> a -> a
-n
1) [a]
xs

-- | Drop from the end of a list.
--   O(length).
--
--   @dropEnd n = reverse . drop n . reverse@
--
--   Forces the whole list even for @n==0@.
dropEnd :: forall a. Int -> [a] -> Prefix a
dropEnd :: forall a. Int -> [a] -> [a]
dropEnd Int
n = (Int, Prefix a) -> Prefix a
forall a b. (a, b) -> b
snd ((Int, Prefix a) -> Prefix a)
-> (Prefix a -> (Int, Prefix a)) -> Prefix a -> Prefix a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> (Int, Prefix a) -> (Int, Prefix a))
-> (Int, Prefix a) -> Prefix a -> (Int, Prefix a)
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> (Int, Prefix a) -> (Int, Prefix a)
f (Int
n, [])
  where
  f :: a -> (Int, [a]) -> (Int, [a])
  f :: a -> (Int, Prefix a) -> (Int, Prefix a)
f a
x (Int
n, Prefix a
xs) = (Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1, Bool -> (Prefix a -> Prefix a) -> Prefix a -> Prefix a
forall a. Bool -> (a -> a) -> a -> a
applyWhen (Int
n Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
0) (a
xa -> Prefix a -> Prefix a
forall a. a -> [a] -> [a]
:) Prefix a
xs)

-- | Split off the largest suffix whose elements satisfy a predicate.
--   O(n).
--
--   @spanEnd p xs = (ys, zs)@
--   where @xs = ys ++ zs@
--   and @all p zs@
--   and @maybe True (not . p) (lastMaybe yz)@.
spanEnd :: forall a. (a -> Bool) -> [a] -> (Prefix a, Suffix a)
spanEnd :: forall a. (a -> Bool) -> [a] -> ([a], [a])
spanEnd a -> Bool
p = (Bool, (Prefix a, Prefix a)) -> (Prefix a, Prefix a)
forall a b. (a, b) -> b
snd ((Bool, (Prefix a, Prefix a)) -> (Prefix a, Prefix a))
-> (Prefix a -> (Bool, (Prefix a, Prefix a)))
-> Prefix a
-> (Prefix a, Prefix a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> (Bool, (Prefix a, Prefix a)) -> (Bool, (Prefix a, Prefix a)))
-> (Bool, (Prefix a, Prefix a))
-> Prefix a
-> (Bool, (Prefix a, Prefix a))
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> (Bool, (Prefix a, Prefix a)) -> (Bool, (Prefix a, Prefix a))
f (Bool
True, ([], []))
  where
  f :: a -> (Bool, ([a], [a])) -> (Bool, ([a], [a]))
  f :: a -> (Bool, (Prefix a, Prefix a)) -> (Bool, (Prefix a, Prefix a))
f a
x (Bool
b', (Prefix a
xs, Prefix a
ys)) = (Bool
b, if Bool
b then (Prefix a
xs, a
xa -> Prefix a -> Prefix a
forall a. a -> [a] -> [a]
:Prefix a
ys) else (a
xa -> Prefix a -> Prefix a
forall a. a -> [a] -> [a]
:Prefix a
xs, Prefix a
ys))
    where b :: Bool
b = Bool
b' Bool -> Bool -> Bool
&& a -> Bool
p a
x

-- | Breaks a list just /after/ an element satisfying the predicate is
--   found.
--
--   >>> breakAfter1 even 1 [3,5,2,4,7,8]
--   ([1,3,5,2],[4,7,8])

breakAfter1 :: (a -> Bool) -> a -> [a] -> (List1 a, [a])
breakAfter1 :: forall a. (a -> Bool) -> a -> [a] -> (List1 a, [a])
breakAfter1 a -> Bool
p = a -> [a] -> (NonEmpty a, [a])
loop
  where
  loop :: a -> [a] -> (NonEmpty a, [a])
loop a
x = \case
    xs :: [a]
xs@[]         -> (a
x a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:| [], [a]
xs)
    xs :: [a]
xs@(a
y : [a]
ys)
      | a -> Bool
p a
x       -> (a
x a -> [a] -> NonEmpty a
forall a. a -> [a] -> NonEmpty a
:| [], [a]
xs)
      | Bool
otherwise -> let (NonEmpty a
vs, [a]
ws) = a -> [a] -> (NonEmpty a, [a])
loop a
y [a]
ys in (a
x a -> NonEmpty a -> NonEmpty a
forall a. a -> NonEmpty a -> NonEmpty a
<| NonEmpty a
vs, [a]
ws)

-- | Breaks a list just /after/ an element satisfying the predicate is
--   found.
--
--   >>> breakAfter even [1,3,5,2,4,7,8]
--   ([1,3,5,2],[4,7,8])

breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
breakAfter :: forall a. (a -> Bool) -> [a] -> ([a], [a])
breakAfter a -> Bool
p = \case
  []   -> ([], [])
  a
x:[a]
xs -> (NonEmpty a -> [a]) -> (NonEmpty a, [a]) -> ([a], [a])
forall (p :: * -> * -> *) a b c.
Bifunctor p =>
(a -> b) -> p a c -> p b c
first NonEmpty a -> [a]
forall a. NonEmpty a -> [a]
List1.toList ((NonEmpty a, [a]) -> ([a], [a]))
-> (NonEmpty a, [a]) -> ([a], [a])
forall a b. (a -> b) -> a -> b
$ (a -> Bool) -> a -> [a] -> (NonEmpty a, [a])
forall a. (a -> Bool) -> a -> [a] -> (List1 a, [a])
breakAfter1 a -> Bool
p a
x [a]
xs

-- | A generalized version of @takeWhile@.
--   (Cf. @mapMaybe@ vs. @filter@).
--   @O(length . takeWhileJust f).
--
--   @takeWhileJust f = fst . spanJust f@.
takeWhileJust :: (a -> Maybe b) -> [a] -> Prefix b
takeWhileJust :: forall a b. (a -> Maybe b) -> [a] -> Prefix b
takeWhileJust a -> Maybe b
p = [a] -> [b]
loop
  where
    loop :: [a] -> [b]
loop (a
a : [a]
as) | Just b
b <- a -> Maybe b
p a
a = b
b b -> [b] -> [b]
forall a. a -> [a] -> [a]
: [a] -> [b]
loop [a]
as
    loop [a]
_ = []

-- | A generalized version of @span@.
--   @O(length . fst . spanJust f)@.
spanJust :: (a -> Maybe b) -> [a] -> (Prefix b, Suffix a)
spanJust :: forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
spanJust a -> Maybe b
p = [a] -> ([b], [a])
loop
  where
    loop :: [a] -> ([b], [a])
loop (a
a : [a]
as) | Just b
b <- a -> Maybe b
p a
a = ([b] -> [b]) -> ([b], [a]) -> ([b], [a])
forall a c b. (a -> c) -> (a, b) -> (c, b)
mapFst (b
b b -> [b] -> [b]
forall a. a -> [a] -> [a]
:) (([b], [a]) -> ([b], [a])) -> ([b], [a]) -> ([b], [a])
forall a b. (a -> b) -> a -> b
$ [a] -> ([b], [a])
loop [a]
as
    loop [a]
as                       = ([], [a]
as)

-- | Partition a list into 'Nothing's and 'Just's.
--   O(n).
--
--   @partitionMaybe f = partitionEithers . map (\ a -> maybe (Left a) Right (f a))@
--
--   Note: @'mapMaybe' f = snd . partitionMaybe f@.
partitionMaybe :: (a -> Maybe b) -> [a] -> ([a], [b])
partitionMaybe :: forall a b. (a -> Maybe b) -> [a] -> ([a], [b])
partitionMaybe a -> Maybe b
f = [a] -> ([a], [b])
loop
  where
    loop :: [a] -> ([a], [b])
loop []       = ([], [])
    loop (a
a : [a]
as) = case a -> Maybe b
f a
a of
      Maybe b
Nothing -> ([a] -> [a]) -> ([a], [b]) -> ([a], [b])
forall a c b. (a -> c) -> (a, b) -> (c, b)
mapFst (a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
:) (([a], [b]) -> ([a], [b])) -> ([a], [b]) -> ([a], [b])
forall a b. (a -> b) -> a -> b
$ [a] -> ([a], [b])
loop [a]
as
      Just b
b  -> ([b] -> [b]) -> ([a], [b]) -> ([a], [b])
forall b d a. (b -> d) -> (a, b) -> (a, d)
mapSnd (b
b b -> [b] -> [b]
forall a. a -> [a] -> [a]
:) (([a], [b]) -> ([a], [b])) -> ([a], [b]) -> ([a], [b])
forall a b. (a -> b) -> a -> b
$ [a] -> ([a], [b])
loop [a]
as

-- | Like 'filter', but additionally return the last partition
--   of the list where the predicate is @False@ everywhere.
--   O(n).
filterAndRest :: (a -> Bool) -> [a] -> ([a], Suffix a)
filterAndRest :: forall a. (a -> Bool) -> [a] -> ([a], [a])
filterAndRest a -> Bool
p = (a -> Maybe a) -> [a] -> ([a], [a])
forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
mapMaybeAndRest ((a -> Maybe a) -> [a] -> ([a], [a]))
-> (a -> Maybe a) -> [a] -> ([a], [a])
forall a b. (a -> b) -> a -> b
$ \ a
a -> if a -> Bool
p a
a then a -> Maybe a
forall a. a -> Maybe a
Just a
a else Maybe a
forall a. Maybe a
Nothing

-- | Like 'mapMaybe', but additionally return the last partition
--   of the list where the function always returns @Nothing@.
--   O(n).
mapMaybeAndRest :: (a -> Maybe b) -> [a] -> ([b], Suffix a)
mapMaybeAndRest :: forall a b. (a -> Maybe b) -> [a] -> (Prefix b, [a])
mapMaybeAndRest a -> Maybe b
f = [a] -> [a] -> ([b], [a])
loop [] where
  loop :: [a] -> [a] -> ([b], [a])
loop [a]
acc = \case
    []                   -> ([], [a] -> [a]
forall a. [a] -> [a]
reverse [a]
acc)
    a
x:[a]
xs | Just b
y <- a -> Maybe b
f a
x -> ([b] -> [b]) -> ([b], [a]) -> ([b], [a])
forall (p :: * -> * -> *) a b c.
Bifunctor p =>
(a -> b) -> p a c -> p b c
first (b
yb -> [b] -> [b]
forall a. a -> [a] -> [a]
:) (([b], [a]) -> ([b], [a])) -> ([b], [a]) -> ([b], [a])
forall a b. (a -> b) -> a -> b
$ [a] -> [a] -> ([b], [a])
loop [] [a]
xs
         | Bool
otherwise     -> [a] -> [a] -> ([b], [a])
loop (a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
acc) [a]
xs

-- | Sublist relation.
isSublistOf :: Eq a => [a] -> [a] -> Bool
isSublistOf :: forall a. Eq a => [a] -> [a] -> Bool
isSublistOf = [a] -> [a] -> Bool
forall a. Eq a => [a] -> [a] -> Bool
List.isSubsequenceOf

-- | All ways of removing one element from a list.
--   O(n²).
holes :: [a] -> [(a, [a])]
holes :: forall a. [a] -> [(a, [a])]
holes []     = []
holes (a
x:[a]
xs) = (a
x, [a]
xs) (a, [a]) -> [(a, [a])] -> [(a, [a])]
forall a. a -> [a] -> [a]
: ((a, [a]) -> (a, [a])) -> [(a, [a])] -> [(a, [a])]
forall a b. (a -> b) -> [a] -> [b]
map (([a] -> [a]) -> (a, [a]) -> (a, [a])
forall (p :: * -> * -> *) b c a.
Bifunctor p =>
(b -> c) -> p a b -> p a c
second (a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:)) ([a] -> [(a, [a])]
forall a. [a] -> [(a, [a])]
holes [a]
xs)

---------------------------------------------------------------------------
-- * Prefix and suffix
---------------------------------------------------------------------------

-- ** Prefix

-- | Compute the common prefix of two lists.
--   O(min n m).
commonPrefix :: Eq a => [a] -> [a] -> Prefix a
commonPrefix :: forall a. Eq a => [a] -> [a] -> [a]
commonPrefix [] [a]
_ = []
commonPrefix [a]
_ [] = []
commonPrefix (a
x:[a]
xs) (a
y:[a]
ys)
  | a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
y    = a
x a -> [a] -> [a]
forall a. a -> [a] -> [a]
: [a] -> [a] -> [a]
forall a. Eq a => [a] -> [a] -> [a]
commonPrefix [a]
xs [a]
ys
  | Bool
otherwise = []

-- | Drops from both lists simultaneously until one list is empty.
--   O(min n m).
dropCommon :: [a] -> [b] -> (Suffix a, Suffix b)
dropCommon :: forall a b. [a] -> [b] -> ([a], [b])
dropCommon (a
x : [a]
xs) (b
y : [b]
ys) = [a] -> [b] -> ([a], [b])
forall a b. [a] -> [b] -> ([a], [b])
dropCommon [a]
xs [b]
ys
dropCommon [a]
xs [b]
ys = ([a]
xs, [b]
ys)

-- | Check if a list has a given prefix. If so, return the list
--   minus the prefix.
--   O(length prefix).
stripPrefixBy :: (a -> a -> Bool) -> Prefix a -> [a] -> Maybe (Suffix a)
stripPrefixBy :: forall a.
(a -> a -> Bool) -> Prefix a -> Prefix a -> Maybe (Prefix a)
stripPrefixBy a -> a -> Bool
eq = [a] -> [a] -> Maybe [a]
loop
  where
  loop :: [a] -> [a] -> Maybe [a]
loop []    [a]
rest = [a] -> Maybe [a]
forall a. a -> Maybe a
Just [a]
rest
  loop (a
_:[a]
_) []   = Maybe [a]
forall a. Maybe a
Nothing
  loop (a
p:[a]
pat) (a
r:[a]
rest)
    | a -> a -> Bool
eq a
p a
r    = [a] -> [a] -> Maybe [a]
loop [a]
pat [a]
rest
    | Bool
otherwise = Maybe [a]
forall a. Maybe a
Nothing

-- ** Suffix

-- | Compute the common suffix of two lists.
--   O(n + m).
commonSuffix :: Eq a => [a] -> [a] -> Suffix a
commonSuffix :: forall a. Eq a => [a] -> [a] -> [a]
commonSuffix [a]
xs [a]
ys = [a] -> [a]
forall a. [a] -> [a]
reverse ([a] -> [a]) -> [a] -> [a]
forall a b. (a -> b) -> a -> b
$ ([a] -> [a] -> [a]
forall a. Eq a => [a] -> [a] -> [a]
commonPrefix ([a] -> [a] -> [a]) -> ([a] -> [a]) -> [a] -> [a] -> [a]
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` [a] -> [a]
forall a. [a] -> [a]
reverse) [a]
xs [a]
ys

-- | @stripSuffix suf xs = Just pre@ iff @xs = pre ++ suf@.
-- O(n).
stripSuffix :: Eq a => Suffix a -> [a] -> Maybe (Prefix a)
stripSuffix :: forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
stripSuffix [] = [a] -> Maybe [a]
forall a. a -> Maybe a
Just
stripSuffix [a]
s  = [a] -> [a] -> Maybe [a]
forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
stripReversedSuffix ([a] -> [a]
forall a. [a] -> [a]
reverse [a]
s)

type ReversedSuffix a = [a]

-- | @stripReversedSuffix rsuf xs = Just pre@ iff @xs = pre ++ reverse suf@.
--   O(n).
stripReversedSuffix :: forall a. Eq a => ReversedSuffix a -> [a] -> Maybe (Prefix a)
stripReversedSuffix :: forall a. Eq a => Suffix a -> Suffix a -> Maybe (Suffix a)
stripReversedSuffix ReversedSuffix a
rs = StrSufSt a -> Maybe (ReversedSuffix a)
final (StrSufSt a -> Maybe (ReversedSuffix a))
-> (ReversedSuffix a -> StrSufSt a)
-> ReversedSuffix a
-> Maybe (ReversedSuffix a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> StrSufSt a -> StrSufSt a)
-> StrSufSt a -> ReversedSuffix a -> StrSufSt a
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr a -> StrSufSt a -> StrSufSt a
step (ReversedSuffix a -> StrSufSt a
forall a. ReversedSuffix a -> StrSufSt a
SSSStrip ReversedSuffix a
rs)
  where
  -- Step of the automaton (reading input from right to left).
  step :: a -> StrSufSt a -> StrSufSt a
  step :: a -> StrSufSt a -> StrSufSt a
step a
x = \case
    StrSufSt a
SSSMismatch   -> StrSufSt a
forall a. StrSufSt a
SSSMismatch
    SSSResult ReversedSuffix a
xs  -> ReversedSuffix a -> StrSufSt a
forall a. ReversedSuffix a -> StrSufSt a
SSSResult (a
xa -> ReversedSuffix a -> ReversedSuffix a
forall a. a -> [a] -> [a]
:ReversedSuffix a
xs)
    SSSStrip []   -> ReversedSuffix a -> StrSufSt a
forall a. ReversedSuffix a -> StrSufSt a
SSSResult [a
x]
    SSSStrip (a
y:ReversedSuffix a
ys)
      | a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
y    -> ReversedSuffix a -> StrSufSt a
forall a. ReversedSuffix a -> StrSufSt a
SSSStrip ReversedSuffix a
ys
      | Bool
otherwise -> StrSufSt a
forall a. StrSufSt a
SSSMismatch

  -- Output of the automaton.
  final :: StrSufSt a -> Maybe (Prefix a)
  final :: StrSufSt a -> Maybe (ReversedSuffix a)
final = \case
    SSSResult ReversedSuffix a
xs -> ReversedSuffix a -> Maybe (ReversedSuffix a)
forall a. a -> Maybe a
Just ReversedSuffix a
xs
    SSSStrip []  -> ReversedSuffix a -> Maybe (ReversedSuffix a)
forall a. a -> Maybe a
Just []
    StrSufSt a
_            -> Maybe (ReversedSuffix a)
forall a. Maybe a
Nothing  -- We have not stripped the whole suffix or encountered a mismatch.

-- | Internal state for stripping suffix.
data StrSufSt a
  = SSSMismatch                 -- ^ Error.
  | SSSStrip (ReversedSuffix a) -- ^ "Negative string" to remove from end. List may be empty.
  | SSSResult [a]               -- ^ "Positive string" (result). Non-empty list.

-- ** Finding overlap

-- | Find out whether the first string @xs@
--   has a suffix that is a prefix of the second string @ys@.
--   So, basically, find the overlap where the strings can be glued together.
--   Returns the index where the overlap starts and the length of the overlap.
--   The length of the overlap plus the index is the length of the first string.
--   Note that in the worst case, the empty overlap @(length xs,0)@ is returned.
findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
findOverlap [a]
xs [a]
ys =
  (Int, Int) -> [(Int, Int)] -> (Int, Int)
forall a. a -> [a] -> a
headWithDefault (Int, Int)
forall a. HasCallStack => a
__IMPOSSIBLE__ ([(Int, Int)] -> (Int, Int)) -> [(Int, Int)] -> (Int, Int)
forall a b. (a -> b) -> a -> b
$ ((Int, [a]) -> Maybe (Int, Int)) -> [(Int, [a])] -> [(Int, Int)]
forall a b. (a -> Maybe b) -> [a] -> Prefix b
mapMaybe (Int, [a]) -> Maybe (Int, Int)
maybePrefix ([(Int, [a])] -> [(Int, Int)]) -> [(Int, [a])] -> [(Int, Int)]
forall a b. (a -> b) -> a -> b
$ [Int] -> [[a]] -> [(Int, [a])]
forall a b. [a] -> [b] -> [(a, b)]
zip [Int
0..] ([a] -> [[a]]
forall a. [a] -> [[a]]
List.tails [a]
xs)
  where
  maybePrefix :: (Int, [a]) -> Maybe (Int, Int)
  maybePrefix :: (Int, [a]) -> Maybe (Int, Int)
maybePrefix (Int
k, [a]
xs')
    | [a]
xs' [a] -> [a] -> Bool
forall a. Eq a => [a] -> [a] -> Bool
`List.isPrefixOf` [a]
ys = (Int, Int) -> Maybe (Int, Int)
forall a. a -> Maybe a
Just (Int
k, [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs')
    | Bool
otherwise                = Maybe (Int, Int)
forall a. Maybe a
Nothing

---------------------------------------------------------------------------
-- * Groups and chunks
---------------------------------------------------------------------------

-- | @'groupOn' f = 'groupBy' (('==') \`on\` f) '.' 'List.sortBy' ('compare' \`on\` f)@.
-- O(n log n).
groupOn :: Ord b => (a -> b) -> [a] -> [[a]]
groupOn :: forall b a. Ord b => (a -> b) -> [a] -> [[a]]
groupOn a -> b
f = (a -> a -> Bool) -> [a] -> [[a]]
forall a. (a -> a -> Bool) -> [a] -> [[a]]
List.groupBy (b -> b -> Bool
forall a. Eq a => a -> a -> Bool
(==) (b -> b -> Bool) -> (a -> b) -> a -> a -> Bool
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` a -> b
f) ([a] -> [[a]]) -> ([a] -> [a]) -> [a] -> [[a]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> a -> Ordering) -> [a] -> [a]
forall a. (a -> a -> Ordering) -> [a] -> [a]
List.sortBy (b -> b -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (b -> b -> Ordering) -> (a -> b) -> a -> a -> Ordering
forall b c a. (b -> b -> c) -> (a -> b) -> a -> a -> c
`on` a -> b
f)

-- | A variant of 'List.groupBy' which applies the predicate to consecutive
-- pairs.
-- O(n).
-- DEPRECATED in favor of 'Agda.Utils.List1.groupBy''.
groupBy' :: (a -> a -> Bool) -> [a] -> [[a]]
groupBy' :: forall a. (a -> a -> Bool) -> [a] -> [[a]]
groupBy' a -> a -> Bool
_ []           = []
groupBy' a -> a -> Bool
p xxs :: [a]
xxs@(a
x : [a]
xs) = a -> [(Bool, a)] -> [[a]]
forall {a}. a -> [(Bool, a)] -> [[a]]
grp a
x ([(Bool, a)] -> [[a]]) -> [(Bool, a)] -> [[a]]
forall a b. (a -> b) -> a -> b
$ (a -> a -> (Bool, a)) -> [a] -> [a] -> [(Bool, a)]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith (\a
x a
y -> (a -> a -> Bool
p a
x a
y, a
y)) [a]
xxs [a]
xs
  where
  grp :: a -> [(Bool, a)] -> [[a]]
grp a
x [(Bool, a)]
ys = (a
x a -> [a] -> [a]
forall a. a -> [a] -> [a]
: ((Bool, a) -> a) -> [(Bool, a)] -> [a]
forall a b. (a -> b) -> [a] -> [b]
map (Bool, a) -> a
forall a b. (a, b) -> b
snd [(Bool, a)]
xs) [a] -> [[a]] -> [[a]]
forall a. a -> [a] -> [a]
: [[a]]
tail
    where ([(Bool, a)]
xs, [(Bool, a)]
rest) = ((Bool, a) -> Bool) -> [(Bool, a)] -> ([(Bool, a)], [(Bool, a)])
forall a. (a -> Bool) -> [a] -> ([a], [a])
span (Bool, a) -> Bool
forall a b. (a, b) -> a
fst [(Bool, a)]
ys
          tail :: [[a]]
tail = case [(Bool, a)]
rest of
                   []            -> []
                   ((Bool
_, a
z) : [(Bool, a)]
zs) -> a -> [(Bool, a)] -> [[a]]
grp a
z [(Bool, a)]
zs

-- | Split a list into sublists. Generalisation of the prelude function
--   @words@.
--   O(n).
--
--   > words xs == wordsBy isSpace xs
wordsBy :: (a -> Bool) -> [a] -> [[a]]
wordsBy :: forall a. (a -> Bool) -> [a] -> [[a]]
wordsBy a -> Bool
p [a]
xs = [a] -> [[a]]
yesP [a]
xs
    where
        yesP :: [a] -> [[a]]
yesP [a]
xs = [a] -> [[a]]
noP ((a -> Bool) -> [a] -> [a]
forall a. (a -> Bool) -> [a] -> [a]
dropWhile a -> Bool
p [a]
xs)

        noP :: [a] -> [[a]]
noP []  = []
        noP [a]
xs  = [a]
ys [a] -> [[a]] -> [[a]]
forall a. a -> [a] -> [a]
: [a] -> [[a]]
yesP [a]
zs
            where
                ([a]
ys,[a]
zs) = (a -> Bool) -> [a] -> ([a], [a])
forall a. (a -> Bool) -> [a] -> ([a], [a])
break a -> Bool
p [a]
xs

-- | Chop up a list in chunks of a given length.
-- O(n).
chop :: Int -> [a] -> [[a]]
chop :: forall a. Int -> [a] -> [[a]]
chop Int
_ [] = []
chop Int
n [a]
xs = [a]
ys [a] -> [[a]] -> [[a]]
forall a. a -> [a] -> [a]
: Int -> [a] -> [[a]]
forall a. Int -> [a] -> [[a]]
chop Int
n [a]
zs
    where ([a]
ys,[a]
zs) = Int -> [a] -> ([a], [a])
forall a. Int -> [a] -> ([a], [a])
splitAt Int
n [a]
xs

-- | Chop a list at the positions when the predicate holds. Contrary to
--   'wordsBy', consecutive separator elements will result in an empty segment
--   in the result.
--   O(n).
--
--    > intercalate [x] (chopWhen (== x) xs) == xs
chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
chopWhen a -> Bool
p []     = []
chopWhen a -> Bool
p (a
x:[a]
xs) = List1 a -> [[a]]
loop (a
x a -> [a] -> List1 a
forall a. a -> [a] -> NonEmpty a
:| [a]
xs)
  where
  -- Local function to avoid unnecessary pattern matching.
  loop :: List1 a -> [[a]]
  loop :: List1 a -> [[a]]
loop List1 a
xs = case (a -> Bool) -> List1 a -> ([a], [a])
forall a. (a -> Bool) -> NonEmpty a -> ([a], [a])
List1.break a -> Bool
p List1 a
xs of
    ([a]
w, []        ) -> [[a]
w]
    ([a]
w, a
_ : []    ) -> [[a]
w, []]
    ([a]
w, a
_ : a
y : [a]
ys) -> [a]
w [a] -> [[a]] -> [[a]]
forall a. a -> [a] -> [a]
: List1 a -> [[a]]
loop (a
y a -> [a] -> List1 a
forall a. a -> [a] -> NonEmpty a
:| [a]
ys)

---------------------------------------------------------------------------
-- * List as sets
---------------------------------------------------------------------------

-- | Check membership for the same list often.
--   Use partially applied to create membership predicate
--   @hasElem xs :: a -> Bool@.
--
--   * First time: @O(n log n)@ in the worst case.
--   * Subsequently: @O(log n)@.
--
--   Specification: @hasElem xs == (`elem` xs)@.
hasElem :: Ord a => [a] -> a -> Bool
hasElem :: forall a. Ord a => [a] -> a -> Bool
hasElem [a]
xs = (a -> Set a -> Bool
forall a. Ord a => a -> Set a -> Bool
`Set.member` [a] -> Set a
forall a. Ord a => [a] -> Set a
Set.fromList [a]
xs)

-- | Check whether a list is sorted.
-- O(n).
--
-- Assumes that the 'Ord' instance implements a partial order.

sorted :: Ord a => [a] -> Bool
sorted :: forall a. Ord a => [a] -> Bool
sorted [] = Bool
True
sorted [a]
xs = [Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
and ([Bool] -> Bool) -> [Bool] -> Bool
forall a b. (a -> b) -> a -> b
$ (a -> a -> Bool) -> [a] -> [a] -> [Bool]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith a -> a -> Bool
forall a. Ord a => a -> a -> Bool
(<=) [a]
xs ([a] -> [a]
forall a. [a] -> [a]
tail [a]
xs)

-- | Check whether all elements in a list are distinct from each other.
--   Assumes that the 'Eq' instance stands for an equivalence relation.
--
--   O(n²) in the worst case @distinct xs == True@.
distinct :: Eq a => [a] -> Bool
distinct :: forall a. Eq a => [a] -> Bool
distinct []     = Bool
True
distinct (a
x:[a]
xs) = a
x a -> [a] -> Bool
forall (t :: * -> *) a. (Foldable t, Eq a) => a -> t a -> Bool
`notElem` [a]
xs Bool -> Bool -> Bool
&& [a] -> Bool
forall a. Eq a => [a] -> Bool
distinct [a]
xs

-- | An optimised version of 'distinct'.
--   O(n log n).
--
--   Precondition: The list's length must fit in an 'Int'.

fastDistinct :: Ord a => [a] -> Bool
fastDistinct :: forall a. Ord a => [a] -> Bool
fastDistinct [a]
xs = Set a -> Int
forall a. Set a -> Int
Set.size ([a] -> Set a
forall a. Ord a => [a] -> Set a
Set.fromList [a]
xs) Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs

-- | Returns an (arbitrary) representative for each list element
--   that occurs more than once.
--   O(n log n).
duplicates :: Ord a => [a] -> [a]
duplicates :: forall a. Ord a => [a] -> [a]
duplicates = ([a] -> Maybe a) -> [[a]] -> [a]
forall a b. (a -> Maybe b) -> [a] -> Prefix b
mapMaybe [a] -> Maybe a
forall a. [a] -> Maybe a
dup ([[a]] -> [a]) -> ([a] -> [[a]]) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bag a -> [[a]]
forall a. Bag a -> [[a]]
Bag.groups (Bag a -> [[a]]) -> ([a] -> Bag a) -> [a] -> [[a]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Bag a
forall a. Ord a => [a] -> Bag a
Bag.fromList
  where
    dup :: [a] -> Maybe a
dup (a
a : a
_ : [a]
_) = a -> Maybe a
forall a. a -> Maybe a
Just a
a
    dup [a]
_           = Maybe a
forall a. Maybe a
Nothing

-- | Remove the first representative for each list element.
--   Thus, returns all duplicate copies.
--   O(n log n).
--
--   @allDuplicates xs == sort $ xs \\ nub xs@.
allDuplicates :: Ord a => [a] -> [a]
allDuplicates :: forall a. Ord a => [a] -> [a]
allDuplicates = ([a] -> [a]) -> [[a]] -> [a]
forall (t :: * -> *) a b. Foldable t => (a -> [b]) -> t a -> [b]
concatMap (Int -> [a] -> [a]
forall a. Int -> [a] -> [a]
drop Int
1 ([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> [a]
forall a. [a] -> [a]
reverse) ([[a]] -> [a]) -> ([a] -> [[a]]) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bag a -> [[a]]
forall a. Bag a -> [[a]]
Bag.groups (Bag a -> [[a]]) -> ([a] -> Bag a) -> [a] -> [[a]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Bag a
forall a. Ord a => [a] -> Bag a
Bag.fromList
  -- The reverse is necessary to actually remove the *first* occurrence
  -- of each element.

-- | Partition a list into first and later occurrences of elements
--   (modulo some quotient given by a representation function).
--
--  Time: O(n log n).
--
--  Specification:
--
--  > nubAndDuplicatesOn f xs = (ys, xs List.\\ ys)
--  >   where ys = nubOn f xs

nubAndDuplicatesOn :: Ord b => (a -> b) -> [a] -> ([a], [a])
nubAndDuplicatesOn :: forall b a. Ord b => (a -> b) -> [a] -> ([a], [a])
nubAndDuplicatesOn a -> b
f = Set b -> [a] -> ([a], [a])
loop Set b
forall a. Set a
Set.empty
  where
  loop :: Set b -> [a] -> ([a], [a])
loop Set b
s [] = ([], [])
  loop Set b
s (a
a:[a]
as)
    | b
b b -> Set b -> Bool
forall a. Ord a => a -> Set a -> Bool
`Set.member` Set b
s = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
forall (p :: * -> * -> *) b c a.
Bifunctor p =>
(b -> c) -> p a b -> p a c
second (a
aa -> [a] -> [a]
forall a. a -> [a] -> [a]
:) (([a], [a]) -> ([a], [a])) -> ([a], [a]) -> ([a], [a])
forall a b. (a -> b) -> a -> b
$ Set b -> [a] -> ([a], [a])
loop Set b
s [a]
as
    | Bool
otherwise        = ([a] -> [a]) -> ([a], [a]) -> ([a], [a])
forall (p :: * -> * -> *) a b c.
Bifunctor p =>
(a -> b) -> p a c -> p b c
first  (a
aa -> [a] -> [a]
forall a. a -> [a] -> [a]
:) (([a], [a]) -> ([a], [a])) -> ([a], [a]) -> ([a], [a])
forall a b. (a -> b) -> a -> b
$ Set b -> [a] -> ([a], [a])
loop (b -> Set b -> Set b
forall a. Ord a => a -> Set a -> Set a
Set.insert b
b Set b
s) [a]
as
    where b :: b
b = a -> b
f a
a

-- | Efficient variant of 'nubBy' for lists, using a set to store already seen elements.
-- O(n log n)
--
-- Specification:
--
-- > nubOn f xs == 'nubBy' ((==) `'on'` f) xs.

nubOn :: Ord b => (a -> b) -> [a] -> [a]
nubOn :: forall b a. Ord b => (a -> b) -> [a] -> [a]
nubOn a -> b
f = Set b -> [a] -> [a]
loop Set b
forall a. Set a
Set.empty
  where
  loop :: Set b -> [a] -> [a]
loop Set b
s [] = []
  loop Set b
s (a
a:[a]
as)
    | b
b b -> Set b -> Bool
forall a. Ord a => a -> Set a -> Bool
`Set.member` Set b
s = Set b -> [a] -> [a]
loop Set b
s [a]
as
    | Bool
otherwise        = a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
: Set b -> [a] -> [a]
loop (b -> Set b -> Set b
forall a. Ord a => a -> Set a -> Set a
Set.insert b
b Set b
s) [a]
as
    where b :: b
b = a -> b
f a
a

-- -- | Efficient variant of 'nubBy' for finite lists (using sorting).
-- -- O(n log n)
-- --
-- -- Specification:
-- --
-- -- > nubOn2 f xs == 'nubBy' ((==) `'on'` f) xs.
--
-- nubOn2 :: Ord b => (a -> b) -> [a] -> [a]
-- nubOn2 tag =
--     -- Throw away numbering
--   map snd
--     -- Restore original order
--   . List.sortBy (compare `on` fst)
--     -- Retain first entry of each @tag@ group
--   . map (snd . head)
--   . List.groupBy ((==) `on` fst)
--     -- Sort by tag (stable)
--   . List.sortBy (compare `on` fst)
--     -- Tag with @tag@ and sequential numbering
--   . map (\p@(_, x) -> (tag x, p))
--   . zip [1..]

-- | Efficient variant of 'nubBy' for finite lists.
-- O(n log n).
--
-- > uniqOn f == 'List.sortBy' (compare `'on'` f) . 'nubBy' ((==) `'on'` f)
--
-- If there are several elements with the same @f@-representative,
-- the first of these is kept.
--
uniqOn :: Ord b => (a -> b) -> [a] -> [a]
uniqOn :: forall b a. Ord b => (a -> b) -> [a] -> [a]
uniqOn a -> b
key = Map b a -> [a]
forall k a. Map k a -> [a]
Map.elems (Map b a -> [a]) -> ([a] -> Map b a) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> a -> a) -> [(b, a)] -> Map b a
forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
Map.fromListWith (\ a
_ -> a -> a
forall a. a -> a
id) ([(b, a)] -> Map b a) -> ([a] -> [(b, a)]) -> [a] -> Map b a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> (b, a)) -> [a] -> [(b, a)]
forall a b. (a -> b) -> [a] -> [b]
map (\ a
a -> (a -> b
key a
a, a
a))

-- | Checks if all the elements in the list are equal. Assumes that
--   the 'Eq' instance stands for an equivalence relation.
--   O(n).
allEqual :: Eq a => [a] -> Bool
allEqual :: forall a. Eq a => [a] -> Bool
allEqual []       = Bool
True
allEqual (a
x : [a]
xs) = (a -> Bool) -> [a] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
x) [a]
xs

-- | Non-efficient, monadic 'nub'.
-- O(n²).
nubM :: Monad m => (a -> a -> m Bool) -> [a] -> m [a]
nubM :: forall (m :: * -> *) a.
Monad m =>
(a -> a -> m Bool) -> [a] -> m [a]
nubM a -> a -> m Bool
eq = [a] -> m [a]
loop where
  loop :: [a] -> m [a]
loop []     = [a] -> m [a]
forall (m :: * -> *) a. Monad m => a -> m a
return []
  loop (a
a:[a]
as) = (a
a a -> [a] -> [a]
forall a. a -> [a] -> [a]
:) ([a] -> [a]) -> m [a] -> m [a]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> do [a] -> m [a]
loop ([a] -> m [a]) -> m [a] -> m [a]
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< (a -> m Bool) -> [a] -> m [a]
forall (m :: * -> *) a.
Applicative m =>
(a -> m Bool) -> [a] -> m [a]
filterM (Bool -> Bool
not (Bool -> Bool) -> (a -> m Bool) -> a -> m Bool
forall (m :: * -> *) b c a.
Functor m =>
(b -> c) -> (a -> m b) -> a -> m c
<.> a -> a -> m Bool
eq a
a) [a]
as

---------------------------------------------------------------------------
-- * Zipping
---------------------------------------------------------------------------

-- | Requires both lists to have the same length.
--   O(n).
--
--   Otherwise, @Nothing@ is returned.

zipWith' :: (a -> b -> c) -> [a] -> [b] -> Maybe [c]
zipWith' :: forall a b c. (a -> b -> c) -> [a] -> [b] -> Maybe [c]
zipWith' a -> b -> c
f = [a] -> [b] -> Maybe [c]
loop
  where
  loop :: [a] -> [b] -> Maybe [c]
loop []        []      = [c] -> Maybe [c]
forall a. a -> Maybe a
Just []
  loop (a
x : [a]
xs) (b
y : [b]
ys) = (a -> b -> c
f a
x b
y c -> [c] -> [c]
forall a. a -> [a] -> [a]
:) ([c] -> [c]) -> Maybe [c] -> Maybe [c]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> [a] -> [b] -> Maybe [c]
loop [a]
xs [b]
ys
  loop []       (b
_ : [b]
_)  = Maybe [c]
forall a. Maybe a
Nothing
  loop (a
_ : [a]
_)  []       = Maybe [c]
forall a. Maybe a
Nothing

-- | Like 'zipWith' but keep the rest of the second list as-is
--   (in case the second list is longer).
-- O(n).
--
-- @
--   zipWithKeepRest f as bs == zipWith f as bs ++ drop (length as) bs
-- @
zipWithKeepRest :: (a -> b -> b) -> [a] -> [b] -> [b]
zipWithKeepRest :: forall a b. (a -> b -> b) -> [a] -> [b] -> [b]
zipWithKeepRest a -> b -> b
f = [a] -> [b] -> [b]
loop
  where
  loop :: [a] -> [b] -> [b]
loop []       [b]
bs       = [b]
bs
  loop [a]
as       []       = []
  loop (a
a : [a]
as) (b
b : [b]
bs) = a -> b -> b
f a
a b
b b -> [b] -> [b]
forall a. a -> [a] -> [a]
: [a] -> [b] -> [b]
loop [a]
as [b]
bs

-- -- UNUSED; a better type would be
-- -- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], Either [a] [b])

-- -- | Like zipWith, but returns the leftover elements of the input lists.
-- zipWithTails :: (a -> b -> c) -> [a] -> [b] -> ([c], [a] , [b])
-- zipWithTails f xs       []       = ([], xs, [])
-- zipWithTails f []       ys       = ([], [] , ys)
-- zipWithTails f (x : xs) (y : ys) = (f x y : zs , as , bs)
--   where (zs , as , bs) = zipWithTails f xs ys


---------------------------------------------------------------------------
-- * Unzipping
---------------------------------------------------------------------------

unzipWith :: (a -> (b, c)) -> [a] -> ([b], [c])
unzipWith :: forall a b c. (a -> (b, c)) -> [a] -> ([b], [c])
unzipWith a -> (b, c)
f = [(b, c)] -> ([b], [c])
forall a b. [(a, b)] -> ([a], [b])
unzip ([(b, c)] -> ([b], [c])) -> ([a] -> [(b, c)]) -> [a] -> ([b], [c])
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> (b, c)) -> [a] -> [(b, c)]
forall a b. (a -> b) -> [a] -> [b]
map a -> (b, c)
f

---------------------------------------------------------------------------
-- * Edit distance
---------------------------------------------------------------------------

-- | Implemented using tree recursion, don't run me at home!
--   O(3^(min n m)).
editDistanceSpec :: Eq a => [a] -> [a] -> Int
editDistanceSpec :: forall a. Eq a => [a] -> [a] -> Int
editDistanceSpec [] [a]
ys = [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
ys
editDistanceSpec [a]
xs [] = [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs
editDistanceSpec (a
x : [a]
xs) (a
y : [a]
ys)
  | a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
y    = [a] -> [a] -> Int
forall a. Eq a => [a] -> [a] -> Int
editDistanceSpec [a]
xs [a]
ys
  | Bool
otherwise = Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ [Int] -> Int
forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
minimum [ [a] -> [a] -> Int
forall a. Eq a => [a] -> [a] -> Int
editDistanceSpec (a
x a -> [a] -> [a]
forall a. a -> [a] -> [a]
: [a]
xs) [a]
ys
                            , [a] -> [a] -> Int
forall a. Eq a => [a] -> [a] -> Int
editDistanceSpec [a]
xs (a
y a -> [a] -> [a]
forall a. a -> [a] -> [a]
: [a]
ys)
                            , [a] -> [a] -> Int
forall a. Eq a => [a] -> [a] -> Int
editDistanceSpec [a]
xs [a]
ys ]

-- | Implemented using dynamic programming and @Data.Array@.
--   O(n*m).
editDistance :: forall a. Eq a => [a] -> [a] -> Int
editDistance :: forall a. Eq a => [a] -> [a] -> Int
editDistance [a]
xs [a]
ys = Int -> Int -> Int
editD Int
0 Int
0
  where
  editD :: Int -> Int -> Int
editD Int
i Int
j = Array (Int, Int) Int
tbl Array (Int, Int) Int -> (Int, Int) -> Int
forall i e. Ix i => Array i e -> i -> e
Array.! (Int
i, Int
j)
  -- Tabulate editD' in immutable boxed array (content computed lazily).
  tbl :: Array (Int,Int) Int
  tbl :: Array (Int, Int) Int
tbl = ((Int, Int), (Int, Int))
-> [((Int, Int), Int)] -> Array (Int, Int) Int
forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array ((Int
0,Int
0), (Int
n,Int
m)) [ ((Int
i, Int
j), Int -> Int -> Int
editD' Int
i Int
j) | Int
i <- [Int
0..Int
n], Int
j <- [Int
0..Int
m] ]
  editD' :: Int -> Int -> Int
editD' Int
i Int
j =
    case (Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int
i Int
n, Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
compare Int
j Int
m) of
      -- Interior
      (Ordering
LT, Ordering
LT)
        | Array Int a
xsA Array Int a -> Int -> a
forall i e. Ix i => Array i e -> i -> e
Array.! Int
i a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== Array Int a
ysA Array Int a -> Int -> a
forall i e. Ix i => Array i e -> i -> e
Array.! Int
j
                    -> Int -> Int -> Int
editD Int
i' Int
j'
        | Bool
otherwise -> Int
1 Int -> Int -> Int
forall a. Num a => a -> a -> a
+ [Int] -> Int
forall (t :: * -> *) a. (Foldable t, Ord a) => t a -> a
minimum [ Int -> Int -> Int
editD Int
i' Int
j, Int -> Int -> Int
editD Int
i Int
j', Int -> Int -> Int
editD Int
i' Int
j' ]
      -- Border: one list is empty
      (Ordering
EQ, Ordering
LT)      ->  Int
m Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
j
      (Ordering
LT, Ordering
EQ)      ->  Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
i
      -- Corner (EQ, EQ): both lists are empty
      (Ordering, Ordering)
_             -> Int
0
      -- GT cases are impossible.
    where (Int
i',Int
j') = (Int
iInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1, Int
jInt -> Int -> Int
forall a. Num a => a -> a -> a
+Int
1)
  n :: Int
n   = [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs
  m :: Int
m   = [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
ys
  xsA, ysA :: Array Int a
  xsA :: Array Int a
xsA = (Int, Int) -> [a] -> Array Int a
forall i e. Ix i => (i, i) -> [e] -> Array i e
listArray (Int
0,Int
nInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1) [a]
xs
  ysA :: Array Int a
ysA = (Int, Int) -> [a] -> Array Int a
forall i e. Ix i => (i, i) -> [e] -> Array i e
listArray (Int
0,Int
mInt -> Int -> Int
forall a. Num a => a -> a -> a
-Int
1) [a]
ys


mergeStrictlyOrderedBy :: (a -> a -> Bool) -> [a] -> [a] -> Maybe [a]
mergeStrictlyOrderedBy :: forall a.
(a -> a -> Bool) -> Prefix a -> Prefix a -> Maybe (Prefix a)
mergeStrictlyOrderedBy a -> a -> Bool
(<) = [a] -> [a] -> Maybe [a]
loop where
  loop :: [a] -> [a] -> Maybe [a]
loop [] [a]
ys = [a] -> Maybe [a]
forall a. a -> Maybe a
Just [a]
ys
  loop [a]
xs [] = [a] -> Maybe [a]
forall a. a -> Maybe a
Just [a]
xs
  loop (a
x:[a]
xs) (a
y:[a]
ys)
    | a
x a -> a -> Bool
< a
y = (a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:) ([a] -> [a]) -> Maybe [a] -> Maybe [a]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> [a] -> [a] -> Maybe [a]
loop [a]
xs (a
ya -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
ys)
    | a
y a -> a -> Bool
< a
x = (a
ya -> [a] -> [a]
forall a. a -> [a] -> [a]
:) ([a] -> [a]) -> Maybe [a] -> Maybe [a]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> [a] -> [a] -> Maybe [a]
loop (a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:[a]
xs) [a]
ys
    | Bool
otherwise = Maybe [a]
forall a. Maybe a
Nothing