Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.LSeq

Description

Synopsis

data LSeq (n :: Nat) a where
- pattern EmptyL :: LSeq n a
- pattern (:<|) :: a -> LSeq n a -> LSeq (1 + n) a
- pattern (:<<) :: a -> LSeq 0 a -> LSeq n a
- pattern (:|>) :: forall n a. LSeq n a -> a -> LSeq (1 + n) a
toSeq :: LSeq n a -> Seq a
empty :: LSeq 0 a
fromList :: Foldable f => f a -> LSeq 0 a
fromNonEmpty :: NonEmpty a -> LSeq 1 a
fromSeq :: Seq a -> LSeq 0 a
(<|) :: a -> LSeq n a -> LSeq (1 + n) a
(|>) :: LSeq n a -> a -> LSeq (1 + n) a
(><) :: LSeq n a -> LSeq m a -> LSeq (n + m) a
eval :: forall proxy n m a. KnownNat n => proxy n -> LSeq m a -> Maybe (LSeq n a)
index :: LSeq n a -> Int -> a
adjust :: (a -> a) -> Int -> LSeq n a -> LSeq n a
partition :: (a -> Bool) -> LSeq n a -> (LSeq 0 a, LSeq 0 a)
mapWithIndex :: (Int -> a -> b) -> LSeq n a -> LSeq n b
take :: Int -> LSeq n a -> LSeq 0 a
drop :: Int -> LSeq n a -> LSeq 0 a
unstableSort :: Ord a => LSeq n a -> LSeq n a
unstableSortBy :: (a -> a -> Ordering) -> LSeq n a -> LSeq n a
head :: LSeq (1 + n) a -> a
tail :: LSeq (1 + n) a -> LSeq n a
last :: LSeq (1 + n) a -> a
init :: LSeq (1 + n) a -> LSeq n a
append :: LSeq n a -> LSeq m a -> LSeq (n + m) a
data ViewL n a where
- (:<) :: a -> LSeq n a -> ViewL (1 + n) a
viewl :: LSeq (1 + n) a -> ViewL (1 + n) a
data ViewR n a where
- (:>) :: LSeq n a -> a -> ViewR (1 + n) a
viewr :: LSeq (1 + n) a -> ViewR (1 + n) a
zipWith :: (a -> b -> c) -> LSeq n a -> LSeq n b -> LSeq n c
promise :: forall m n a. LSeq m a -> LSeq n a
forceLSeq :: KnownNat n => proxy n -> LSeq m a -> LSeq n a

Documentation

data LSeq (n :: Nat) a where Source #

LSeq n a certifies that the sequence has *at least* n items

Bundled Patterns

pattern EmptyL :: LSeq n a	The empty sequence.
pattern (:<\|) :: a -> LSeq n a -> LSeq (1 + n) a infixr 5	A bidirectional pattern synonym viewing the front of a non-empty sequence.
pattern (:<<) :: a -> LSeq 0 a -> LSeq n a infixr 5	A unidirectional pattern synonym viewing the front of a non-empty sequence.
pattern (:\|>) :: forall n a. LSeq n a -> a -> LSeq (1 + n) a infixl 5	A bidirectional pattern synonym viewing the rear of a non-empty sequence.

Instances

Instances details

Functor (LSeq n) Source #
Instance details Defined in Data.LSeq Methods fmap :: (a -> b) -> LSeq n a -> LSeq n b # (<$) :: a -> LSeq n b -> LSeq n a #
Foldable (LSeq n) Source #
Instance details Defined in Data.LSeq Methods fold :: Monoid m => LSeq n m -> m # foldMap :: Monoid m => (a -> m) -> LSeq n a -> m # foldMap' :: Monoid m => (a -> m) -> LSeq n a -> m # foldr :: (a -> b -> b) -> b -> LSeq n a -> b # foldr' :: (a -> b -> b) -> b -> LSeq n a -> b # foldl :: (b -> a -> b) -> b -> LSeq n a -> b # foldl' :: (b -> a -> b) -> b -> LSeq n a -> b # foldr1 :: (a -> a -> a) -> LSeq n a -> a # foldl1 :: (a -> a -> a) -> LSeq n a -> a # toList :: LSeq n a -> [a] # null :: LSeq n a -> Bool # length :: LSeq n a -> Int # elem :: Eq a => a -> LSeq n a -> Bool # maximum :: Ord a => LSeq n a -> a # minimum :: Ord a => LSeq n a -> a # sum :: Num a => LSeq n a -> a # product :: Num a => LSeq n a -> a #
Traversable (LSeq n) Source #
Instance details Defined in Data.LSeq Methods traverse :: Applicative f => (a -> f b) -> LSeq n a -> f (LSeq n b) # sequenceA :: Applicative f => LSeq n (f a) -> f (LSeq n a) # mapM :: Monad m => (a -> m b) -> LSeq n a -> m (LSeq n b) # sequence :: Monad m => LSeq n (m a) -> m (LSeq n a) #
1 <= n => Traversable1 (LSeq n) Source #
Instance details Defined in Data.LSeq Methods traverse1 :: Apply f => (a -> f b) -> LSeq n a -> f (LSeq n b) # sequence1 :: Apply f => LSeq n (f b) -> f (LSeq n b) #
1 <= n => Foldable1 (LSeq n) Source #
Instance details Defined in Data.LSeq Methods fold1 :: Semigroup m => LSeq n m -> m # foldMap1 :: Semigroup m => (a -> m) -> LSeq n a -> m # toNonEmpty :: LSeq n a -> NonEmpty a #
Eq a => Eq (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods (==) :: LSeq n a -> LSeq n a -> Bool # (/=) :: LSeq n a -> LSeq n a -> Bool #
Ord a => Ord (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods compare :: LSeq n a -> LSeq n a -> Ordering # (<) :: LSeq n a -> LSeq n a -> Bool # (<=) :: LSeq n a -> LSeq n a -> Bool # (>) :: LSeq n a -> LSeq n a -> Bool # (>=) :: LSeq n a -> LSeq n a -> Bool # max :: LSeq n a -> LSeq n a -> LSeq n a # min :: LSeq n a -> LSeq n a -> LSeq n a #
Read a => Read (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods readsPrec :: Int -> ReadS (LSeq n a) # readList :: ReadS [LSeq n a] # readPrec :: ReadPrec (LSeq n a) # readListPrec :: ReadPrec [LSeq n a] #
Show a => Show (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods showsPrec :: Int -> LSeq n a -> ShowS # show :: LSeq n a -> String # showList :: [LSeq n a] -> ShowS #
Generic (LSeq n a) Source #
Instance details Defined in Data.LSeq Associated Types type Rep (LSeq n a) :: Type -> Type # Methods from :: LSeq n a -> Rep (LSeq n a) x # to :: Rep (LSeq n a) x -> LSeq n a #
Semigroup (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods (<>) :: LSeq n a -> LSeq n a -> LSeq n a # sconcat :: NonEmpty (LSeq n a) -> LSeq n a # stimes :: Integral b => b -> LSeq n a -> LSeq n a #
Monoid (LSeq 0 a) Source #
Instance details Defined in Data.LSeq Methods mempty :: LSeq 0 a # mappend :: LSeq 0 a -> LSeq 0 a -> LSeq 0 a # mconcat :: [LSeq 0 a] -> LSeq 0 a #
(KnownNat n, Arbitrary a) => Arbitrary (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods arbitrary :: Gen (LSeq n a) # shrink :: LSeq n a -> [LSeq n a] #
ToJSON a => ToJSON (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods toJSON :: LSeq n a -> Value # toEncoding :: LSeq n a -> Encoding # toJSONList :: [LSeq n a] -> Value # toEncodingList :: [LSeq n a] -> Encoding #
FromJSON a => FromJSON (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods parseJSON :: Value -> Parser (LSeq n a) # parseJSONList :: Value -> Parser [LSeq n a] #
NFData a => NFData (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods rnf :: LSeq n a -> () #
Ixed (LSeq n a) Source #
Instance details Defined in Data.LSeq Methods ix :: Index (LSeq n a) -> Traversal' (LSeq n a) (IxValue (LSeq n a)) #
type Rep (LSeq n a) Source #
Instance details Defined in Data.LSeq type Rep (LSeq n a) = D1 ('MetaData "LSeq" "Data.LSeq" "hgeometry-combinatorial-0.12.0.2-BPOszceZMWb3Na6sqXbM08" 'True) (C1 ('MetaCons "LSeq" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Seq a))))
type Index (LSeq n a) Source #
Instance details Defined in Data.LSeq type Index (LSeq n a) = Int
type IxValue (LSeq n a) Source #
Instance details Defined in Data.LSeq type IxValue (LSeq n a) = a

toSeq :: LSeq n a -> Seq a Source #

$ O(1) $ Convert to a sequence by dropping the type-level size.

empty :: LSeq 0 a Source #

$ O(1) $ The empty sequence.

fromList :: Foldable f => f a -> LSeq 0 a Source #

$ O(n) $. Create an l-sequence from a finite list of elements.

fromNonEmpty :: NonEmpty a -> LSeq 1 a Source #

$ O(n) $. Create an l-sequence from a non-empty list.

fromSeq :: Seq a -> LSeq 0 a Source #

$ O(n) $. Create an l-sequence from a sequence of elements.

(<|) :: a -> LSeq n a -> LSeq (1 + n) a infixr 5 Source #

$ O(1) $ Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

(|>) :: LSeq n a -> a -> LSeq (1 + n) a infixl 5 Source #

$ O(1) $ Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

(><) :: LSeq n a -> LSeq m a -> LSeq (n + m) a infix 5 Source #

$ O(log(min(n,m))) $ Concatenate two sequences.

eval :: forall proxy n m a. KnownNat n => proxy n -> LSeq m a -> Maybe (LSeq n a) Source #

$ O(1) $ Prove a sequence has at least n elements.

>>> eval (Proxy :: Proxy 3) (fromList [1,2,3])
Just (LSeq (fromList [1,2,3]))
>>> eval (Proxy :: Proxy 3) (fromList [1,2])
Nothing
>>> eval (Proxy :: Proxy 3) (fromList [1..10])
Just (LSeq (fromList [1,2,3,4,5,6,7,8,9,10]))

index :: LSeq n a -> Int -> a Source #

$ O(log(min(i,n-i))) $ Get the element with index i, counting from the left and starting at 0.

adjust :: (a -> a) -> Int -> LSeq n a -> LSeq n a Source #

$ O(log(min(i,n−i))) $ Update the element at the specified position. If the position is out of range, the original sequence is returned. adjust can lead to poor performance and even memory leaks, because it does not force the new value before installing it in the sequence. adjust' should usually be preferred.

partition :: (a -> Bool) -> LSeq n a -> (LSeq 0 a, LSeq 0 a) Source #

$ O(n) $ The partition function takes a predicate p and a sequence xs and returns sequences of those elements which do and do not satisfy the predicate.

mapWithIndex :: (Int -> a -> b) -> LSeq n a -> LSeq n b Source #

A generalization of fmap, mapWithIndex takes a mapping function that also depends on the element's index, and applies it to every element in the sequence.

take :: Int -> LSeq n a -> LSeq 0 a Source #

$ O(\log(\min(i,n-i))) $. The first i elements of a sequence. If i is negative, take i s yields the empty sequence. If the sequence contains fewer than i elements, the whole sequence is returned.

drop :: Int -> LSeq n a -> LSeq 0 a Source #

$ O(\log(\min(i,n-i))) $. Elements of a sequence after the first i. If i is negative, drop i s yields the whole sequence. If the sequence contains fewer than i elements, the empty sequence is returned.

unstableSort :: Ord a => LSeq n a -> LSeq n a Source #

$ O(n \log n) $. unstableSort sorts the specified LSeq by the natural ordering of its elements, but the sort is not stable. This algorithm is frequently faster and uses less memory than sort.

unstableSortBy :: (a -> a -> Ordering) -> LSeq n a -> LSeq n a Source #

$ O(n \log n) $. A generalization of unstableSort, unstableSortBy takes an arbitrary comparator and sorts the specified sequence. The sort is not stable. This algorithm is frequently faster and uses less memory than sortBy.

head :: LSeq (1 + n) a -> a Source #

Gets the first element of the LSeq

>>> head $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3]
1

tail :: LSeq (1 + n) a -> LSeq n a Source #

Get the LSeq without its first element -- >>> head $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3] LSeq (fromList [2,3])

last :: LSeq (1 + n) a -> a Source #

Get the last element of the LSeq

>>> last $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3]
3

init :: LSeq (1 + n) a -> LSeq n a Source #

The sequence without its last element

>>> init $ forceLSeq (Proxy :: Proxy 3) $ fromList [1,2,3]
LSeq (fromList [1,2])

append :: LSeq n a -> LSeq m a -> LSeq (n + m) a Source #

appends two sequences.

data ViewL n a where Source #

View of the left end of a sequence.

Constructors

(:<) :: a -> LSeq n a -> ViewL (1 + n) a infixr 5

Instances

Instances details

Functor (ViewL n) Source #
Instance details Defined in Data.LSeq Methods fmap :: (a -> b) -> ViewL n a -> ViewL n b # (<$) :: a -> ViewL n b -> ViewL n a #
Foldable (ViewL n) Source #
Instance details Defined in Data.LSeq Methods fold :: Monoid m => ViewL n m -> m # foldMap :: Monoid m => (a -> m) -> ViewL n a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL n a -> m # foldr :: (a -> b -> b) -> b -> ViewL n a -> b # foldr' :: (a -> b -> b) -> b -> ViewL n a -> b # foldl :: (b -> a -> b) -> b -> ViewL n a -> b # foldl' :: (b -> a -> b) -> b -> ViewL n a -> b # foldr1 :: (a -> a -> a) -> ViewL n a -> a # foldl1 :: (a -> a -> a) -> ViewL n a -> a # toList :: ViewL n a -> [a] # null :: ViewL n a -> Bool # length :: ViewL n a -> Int # elem :: Eq a => a -> ViewL n a -> Bool # maximum :: Ord a => ViewL n a -> a # minimum :: Ord a => ViewL n a -> a # sum :: Num a => ViewL n a -> a # product :: Num a => ViewL n a -> a #
Traversable (ViewL n) Source #
Instance details Defined in Data.LSeq Methods traverse :: Applicative f => (a -> f b) -> ViewL n a -> f (ViewL n b) # sequenceA :: Applicative f => ViewL n (f a) -> f (ViewL n a) # mapM :: Monad m => (a -> m b) -> ViewL n a -> m (ViewL n b) # sequence :: Monad m => ViewL n (m a) -> m (ViewL n a) #
1 <= n => Traversable1 (ViewL n) Source #
Instance details Defined in Data.LSeq Methods traverse1 :: Apply f => (a -> f b) -> ViewL n a -> f (ViewL n b) # sequence1 :: Apply f => ViewL n (f b) -> f (ViewL n b) #
1 <= n => Foldable1 (ViewL n) Source #
Instance details Defined in Data.LSeq Methods fold1 :: Semigroup m => ViewL n m -> m # foldMap1 :: Semigroup m => (a -> m) -> ViewL n a -> m # toNonEmpty :: ViewL n a -> NonEmpty a #
Eq a => Eq (ViewL n a) Source #
Instance details Defined in Data.LSeq Methods (==) :: ViewL n a -> ViewL n a -> Bool # (/=) :: ViewL n a -> ViewL n a -> Bool #
Ord a => Ord (ViewL n a) Source #
Instance details Defined in Data.LSeq Methods compare :: ViewL n a -> ViewL n a -> Ordering # (<) :: ViewL n a -> ViewL n a -> Bool # (<=) :: ViewL n a -> ViewL n a -> Bool # (>) :: ViewL n a -> ViewL n a -> Bool # (>=) :: ViewL n a -> ViewL n a -> Bool # max :: ViewL n a -> ViewL n a -> ViewL n a # min :: ViewL n a -> ViewL n a -> ViewL n a #
Show a => Show (ViewL n a) Source #
Instance details Defined in Data.LSeq Methods showsPrec :: Int -> ViewL n a -> ShowS # show :: ViewL n a -> String # showList :: [ViewL n a] -> ShowS #
Semigroup (ViewL n a) Source #
Instance details Defined in Data.LSeq Methods (<>) :: ViewL n a -> ViewL n a -> ViewL n a # sconcat :: NonEmpty (ViewL n a) -> ViewL n a # stimes :: Integral b => b -> ViewL n a -> ViewL n a #

viewl :: LSeq (1 + n) a -> ViewL (1 + n) a Source #

( O(1) ). Analyse the left end of a sequence.

data ViewR n a where Source #

View of the right end of a sequence.

Constructors

(:>) :: LSeq n a -> a -> ViewR (1 + n) a infixl 5

Instances

Instances details

Functor (ViewR n) Source #
Instance details Defined in Data.LSeq Methods fmap :: (a -> b) -> ViewR n a -> ViewR n b # (<$) :: a -> ViewR n b -> ViewR n a #
Foldable (ViewR n) Source #
Instance details Defined in Data.LSeq Methods fold :: Monoid m => ViewR n m -> m # foldMap :: Monoid m => (a -> m) -> ViewR n a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR n a -> m # foldr :: (a -> b -> b) -> b -> ViewR n a -> b # foldr' :: (a -> b -> b) -> b -> ViewR n a -> b # foldl :: (b -> a -> b) -> b -> ViewR n a -> b # foldl' :: (b -> a -> b) -> b -> ViewR n a -> b # foldr1 :: (a -> a -> a) -> ViewR n a -> a # foldl1 :: (a -> a -> a) -> ViewR n a -> a # toList :: ViewR n a -> [a] # null :: ViewR n a -> Bool # length :: ViewR n a -> Int # elem :: Eq a => a -> ViewR n a -> Bool # maximum :: Ord a => ViewR n a -> a # minimum :: Ord a => ViewR n a -> a # sum :: Num a => ViewR n a -> a # product :: Num a => ViewR n a -> a #
Traversable (ViewR n) Source #
Instance details Defined in Data.LSeq Methods traverse :: Applicative f => (a -> f b) -> ViewR n a -> f (ViewR n b) # sequenceA :: Applicative f => ViewR n (f a) -> f (ViewR n a) # mapM :: Monad m => (a -> m b) -> ViewR n a -> m (ViewR n b) # sequence :: Monad m => ViewR n (m a) -> m (ViewR n a) #
Eq a => Eq (ViewR n a) Source #
Instance details Defined in Data.LSeq Methods (==) :: ViewR n a -> ViewR n a -> Bool # (/=) :: ViewR n a -> ViewR n a -> Bool #
Ord a => Ord (ViewR n a) Source #
Instance details Defined in Data.LSeq Methods compare :: ViewR n a -> ViewR n a -> Ordering # (<) :: ViewR n a -> ViewR n a -> Bool # (<=) :: ViewR n a -> ViewR n a -> Bool # (>) :: ViewR n a -> ViewR n a -> Bool # (>=) :: ViewR n a -> ViewR n a -> Bool # max :: ViewR n a -> ViewR n a -> ViewR n a # min :: ViewR n a -> ViewR n a -> ViewR n a #
Show a => Show (ViewR n a) Source #
Instance details Defined in Data.LSeq Methods showsPrec :: Int -> ViewR n a -> ShowS # show :: ViewR n a -> String # showList :: [ViewR n a] -> ShowS #
Semigroup (ViewR n a) Source #
Instance details Defined in Data.LSeq Methods (<>) :: ViewR n a -> ViewR n a -> ViewR n a # sconcat :: NonEmpty (ViewR n a) -> ViewR n a # stimes :: Integral b => b -> ViewR n a -> ViewR n a #

viewr :: LSeq (1 + n) a -> ViewR (1 + n) a Source #

$ O(1) $. Analyse the right end of a sequence.

zipWith :: (a -> b -> c) -> LSeq n a -> LSeq n b -> LSeq n c Source #

Zips two equal length LSeqs

promise :: forall m n a. LSeq m a -> LSeq n a Source #

Promises that the length of this LSeq is actually n. This is not checked.

This function should be a noop

forceLSeq :: KnownNat n => proxy n -> LSeq m a -> LSeq n a Source #

Forces the first n elements of the LSeq