Data.Vector.NonEmpty

O(1) Length.

>>> length $ unsafeFromList [1..10]10

O(1) First element. Since head is gauranteed, bounds checks are bypassed by deferring to unsafeHead.

>>> head $ unsafeFromList [1..10]1

O(1) Last element. Since a last element is gauranteed, bounds checks are bypassed by deferring to unsafeLast.

>>> last $ unsafeFromList [1..10]10

O(1) Indexing.

>>> (unsafeFromList [1..10]) ! 01

O(1) Safe indexing.

>>> (unsafeFromList [1..10]) !? 0Just 1

>>> (unsafeFromList [1..10]) !? 11Nothing

O(1) Unsafe indexing without bounds checking

O(1) First element of a non-empty vector in a monad.

See indexM for an explanation of why this is useful.

Note that this function defers to unsafeHeadM since head is gauranteed to be safe by construction.

>>> headM @[] (unsafeFromList [1..10])[1]

O(1) Last element of a non-empty vector in a monad. See indexM for an explanation of why this is useful.

Note that this function defers to unsafeHeadM since a last element is gauranteed.

>>> lastM @[] (unsafeFromList [1..10])[10]

O(1) Indexing in a monad.

The monad allows operations to be strict in the non-empty vector when necessary.

See indexM for more details

>>> indexM @[] (unsafeFromList [1..10]) 3[4]

O(1) Indexing in a monad without bounds checks. See indexM for an explanation of why this is useful.

O(1) Yield all but the first element without copying. Since the vector returned may be empty (i.e. input was a singleton), this function returns a normal Vector

>>> tail (unsafeFromList [1..10])[2,3,4,5,6,7,8,9,10]

O(1) Yield a slice of the non-empty vector without copying it. The vector must contain at least i+n elements. Because this is not guaranteed, this function returns a Vector which could be empty

>>> slice 0 3 (unsafeFromList [1..10])[1,2,3]

O(1) Yield all but the last element without copying. Since the vector returned may be empty (i.e. input was a singleton), this function returns a normal Vector

>>> init (unsafeFromList [1..3])[1,2]

O(1) Yield at the first n elements without copying. The non-empty vector may contain less than n elements in which case it is returned as a vector unchanged.

>>> take 2 (unsafeFromList [1..3])[1,2]

O(1) Yield all but the first n elements without copying. The non-empty vector may contain less than n elements in which case an empty vector is returned.

>>> drop 2 (unsafeFromList [1..3])[3]

O(1) Yield a slice of a non-empty vector without copying at the 0th and 1st indices.

>>> uncons (unsafeFromList [1..10])(1,[2,3,4,5,6,7,8,9,10])

O(1) Yield a slice of a non-empty vector without copying at the n-1th and nth indices

>>> unsnoc (unsafeFromList [1..10])([1,2,3,4,5,6,7,8,9],10)

O(1) Yield the first n elements paired with the remainder without copying.

This function returns a pair of vectors, as one may slice a (0, n+1).

>>> splitAt 2 (unsafeFromList [1..3])([1,2],[3])

O(1) Yield a slice of the vector without copying. The vector must contain at least i+n elements but this is not checked.

O(1) Yield the first n elements without copying. The vector must contain at least n elements but this is not checked.

O(1) Yield all but the first n elements without copying. The vector must contain at least n elements but this is not checked.

O(1) Non-empty vector with exactly one element

>>> singleton "a"["a"]

O(n) Non-empty vector of the given length with the same value in each position.

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> replicate 3 "a"Just ["a","a","a"]

>>> replicate 0 "a"Nothing

O(n) Non-empty vector of the given length with the same value in each position.

This variant takes max n 1 for the supplied length parameter.

>>> replicate1 3 "a"["a","a","a"]

>>> replicate1 0 "a"["a"]

>>> replicate1 (-1) "a"["a"]

O(n) Construct a vector of the given length by applying the function to each index.

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> let f 0 = "a"; f _ = "k"; f :: Int -> String

>>> generate 1 fJust ["a"]

>>> generate 0 fNothing

>>> generate 2 fJust ["a","k"]

O(n) Construct a vector of the given length by applying the function to each index.

This variant takes max n 1 for the supplied length parameter.

>>> let f 0 = "a"; f _ = "k"; f :: Int -> String

>>> generate1 2 f["a","k"]

>>> generate1 0 f["a"]

>>> generate1 (-1) f["a"]

O(n) Apply function n times to value. Zeroth element is original value.

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> iterateN 3 (+1) 0Just [0,1,2]

>>> iterateN 0 (+1) 0Nothing

>>> iterateN (-1) (+1) 0Nothing

O(n) Apply function n times to value. Zeroth element is original value.

This variant takes max n 1 for the supplied length parameter.

>>> iterateN1 3 (+1) 0[0,1,2]

>>> iterateN1 0 (+1) 0[0]

>>> iterateN1 (-1) (+1) 0[0]

O(n) Execute the monadic action the given number of times and store the results in a vector.

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> replicateM @Maybe 3 (Just "a")Just (Just ["a","a","a"])

>>> replicateM @Maybe 3 NothingNothing

>>> replicateM @Maybe 0 (Just "a")Just Nothing

>>> replicateM @Maybe (-1) (Just "a")Just Nothing

O(n) Execute the monadic action the given number of times and store the results in a vector.

This variant takes max n 1 for the supplied length parameter.

>>> replicate1M @Maybe 3 (Just "a")Just ["a","a","a"]

>>> replicate1M @Maybe 3 NothingNothing

>>> replicate1M @Maybe 0 (Just "a")Just ["a"]

>>> replicate1M @Maybe (-1) (Just "a")Just ["a"]

O(n) Construct a vector of the given length by applying the monadic action to each index

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> generateM 3 (\i -> if i P.< 1 then ["a"] else ["b"])[Just ["a","b","b"]]

>>> generateM @[] @Int 3 (const [])[]

>>> generateM @[] @Int 0 (const [1])[Nothing]

>>> generateM @Maybe @Int (-1) (const Nothing)Just Nothing

O(n) Construct a vector of the given length by applying the monadic action to each index

This variant takes max n 1 for the supplied length parameter.

>>> generate1M 3 (\i -> if i P.< 1 then Just "a" else Just "b")Just ["a","b","b"]

>>> generate1M 3 (const [])[]

>>> generate1M 0 (const $ Just 1)Just [1]

>>> generate1M (-1) (const Nothing)Nothing

O(n) Apply monadic function n times to value. Zeroth element is original value.

When given a index n <= 0, then Nothing is returned, otherwise Just.

>>> iterateNM @Maybe 3 return "a"Just (Just ["a","a","a"])

>>> iterateNM @Maybe 3 (const Nothing) "a"Nothing

>>> iterateNM @Maybe 0 return "a"Just Nothing

O(n) Apply monadic function n times to value. Zeroth element is original value.

This variant takes max n 1 for the supplied length parameter.

>>> iterateN1M @Maybe 3 return "a"Just ["a","a","a"]

>>> iterateN1M @Maybe 3 (const Nothing) "a"Nothing

>>> iterateN1M @Maybe 0 return "a"Just ["a"]

>>> iterateN1M @Maybe (-1) return "a"Just ["a"]

Execute the monadic action and freeze the resulting non-empty vector.

Execute the monadic action and freeze the resulting non-empty vector, bypassing emptiness checks.

The onus is on the caller to guarantee the created vector is non-empty.

Execute the monadic action and freeze the resulting non-empty vector.

Execute the monadic action and freeze the resulting non-empty vector.

The onus is on the caller to guarantee the created vector is non-empty.

O(n) Construct a non-empty vector by repeatedly applying the generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

If an unfold does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

>>> unfoldr (\b -> case b of "a" -> Just ("a", "b"); _ ->  Nothing) "a"Just ["a"]

>>> unfoldr (const Nothing) "a"Nothing

O(n) Construct a non-empty vector by repeatedly applying the generator function to a seed and a first element.

This variant of unfoldr guarantees the resulting vector is non- empty by supplying an initial element a.

>>> unfoldr1 (\b -> case b of "a" -> Just ("a", "b"); _ ->  Nothing) "first" "a"["first","a"]

>>> unfoldr1 (const Nothing) "first" "a"["first"]

O(n) Construct a vector with at most n elements by repeatedly applying the generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

If an unfold does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

>>> unfoldrN 3 (\b -> Just (b+1, b+1)) 0Just [1,2,3]

>>> unfoldrN 3 (const Nothing) 0Nothing

>>> unfoldrN 0 (\b -> Just (b+1, b+1)) 0Nothing

O(n) Construct a vector with at most n elements by repeatedly applying the generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

This variant of unfoldrN guarantees the resulting vector is non- empty by supplying an initial element a.

>>> unfoldr1N 3 (\b -> Just (b+1, b+1)) 0 0[0,1,2,3]

>>> unfoldr1N 3 (const Nothing) 0 0[0]

>>> unfoldr1N 0 (\b -> Just (b+1, b+1)) 0 0[0]

O(n) Construct a non-empty vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

If an unfold does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

O(n) Construct a non-empty vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

This variant of unfoldrM guarantees the resulting vector is non- empty by supplying an initial element a.

O(n) Construct a non-empty vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

If an unfold does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

O(n) Construct a non-empty vector by repeatedly applying the monadic generator function to a seed. The generator function yields Just the next element and the new seed or Nothing if there are no more elements.

This variant of unfoldrNM guarantees the resulting vector is non- empty by supplying an initial element a.

O(n) Construct a non-empty vector with n elements by repeatedly applying the generator function to the already constructed part of the vector.

If constructN does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

O(n) Construct a vector with n elements from right to left by repeatedly applying the generator function to the already constructed part of the vector.

If constructrN does not create meaningful values, Nothing is returned. Otherwise, Just containing a non-empty vector is returned.

O(n) Yield a non-emptyvector of the given length containing the values x, x+1 etc. This operation is usually more efficient than enumFromTo.

If an enumeration does not use meaningful indices, Nothing is returned, otherwise, Just containing a non-empty vector.

O(n) Yield a non-emptyvector of length max n 1 containing the values x, x+1 etc. This operation is usually more efficient than enumFromTo.

O(n) Yield a non-empty vector of the given length containing the values x, x+y, x+y+y etc. This operations is usually more efficient than enumFromThenTo.

If an enumeration does not use meaningful indices, Nothing is returned, otherwise, Just containing a non-empty vector.

O(n) Yield a non-empty vector of length max n 1 containing the values x, x+y, x+y+y etc. This operations is usually more efficient than enumFromThenTo.

O(n) Enumerate values from x to y.

If an enumeration does not use meaningful indices, Nothing is returned, otherwise, Just containing a non-empty vector.

WARNING: This operation can be very inefficient. If at all possible, use enumFromN instead.

O(n) Enumerate values from x to y with a specific step z.

If an enumeration does not use meaningful indices, Nothing is returned, otherwise, Just containing a non-empty vector.

WARNING: This operation can be very inefficient. If at all possible, use enumFromStepN instead.

O(n) Prepend an element

>>> cons 1 (unsafeFromList [2,3])[1,2,3]

O(n) Prepend an element to a Vector

>>> consV 1 (V.fromList [2,3])[1,2,3]

O(n) Append an element

>>> snoc (unsafeFromList [1,2]) 3[1,2,3]

O(n) Append an element to a Vector

>>> snocV (V.fromList [1,2]) 3[1,2,3]

O(m+n) Concatenate two non-empty vectors

>>> (unsafeFromList [1..3]) ++ (unsafeFromList [4..6])[1,2,3,4,5,6]

O(n) Concatenate all non-empty vectors in the list

If list is empty, Nothing is returned, otherwise Just containing the concatenated non-empty vectors

>>> concat [(unsafeFromList [1..3]), (unsafeFromList [4..6])]Just [1,2,3,4,5,6]

O(n) Concatenate all non-empty vectors in a non-empty list.

>>> concat1 ((unsafeFromList [1..3]) :| [(unsafeFromList [4..6])])[1,2,3,4,5,6]

O(n) Yield the argument but force it not to retain any extra memory, possibly by copying it.

O(n) Convert a non-empty vector to a non-empty list.

>>> toNonEmpty (unsafeFromList [1..3])1 :| [2,3]

O(n) Convert from a non-empty list to a non-empty vector.

>>> fromNonEmpty (1 :| [2,3])[1,2,3]

O(n) Convert from the first n-elements of a non-empty list to a non-empty vector.

Returns Nothing if indices are <= 0, otherwise Just containing the non-empty vector.

>>> fromNonEmptyN 3 (1 :| [2..5])Just [1,2,3]

>>> fromNonEmptyN 0 (1 :| [2..5])Nothing

O(n) Convert from the first n-elements of a non-empty list to a non-empty vector. This is a safe version of fromNonEmptyN which takes max n 1 of the first n-elements of the non-empty list.

>>> fromNonEmptyN1 3 (1 :| [2..5])[1,2,3]

>>> fromNonEmptyN1 0 (1 :| [2..5])[1]

O(n) Convert from a list to a non-empty vector.

Warning: the onus is on the user to ensure that their vector is not empty, otherwise all bets are off!

>>> unsafeFromList [1..3][1,2,3]

O(1) Convert from a non-empty vector to a vector.

>>> let nev :: NonEmptyVector Int = unsafeFromList [1..3] in toVector nev[1,2,3]

O(1) Convert from a vector to a non-empty vector.

If the vector is empty, then Nothing is returned, otherwise Just containing the non-empty vector.

>>> fromVector $ V.fromList [1..3]Just [1,2,3]

>>> fromVector $ V.fromList []Nothing

O(1) Convert from a vector to a non-empty vector without checking bounds.

Warning: the onus is on the user to ensure that their vector is not empty, otherwise all bets are off!

>>> unsafeFromVector $ V.fromList [1..3][1,2,3]

O(n) Convert from a non-empty vector to a list.

>>> let nev :: NonEmptyVector Int = unsafeFromList [1..3] in toList nev[1,2,3]

O(n) Convert from a list to a non-empty vector.

>>> fromList [1..3]Just [1,2,3]

>>> fromList []Nothing

O(n) Convert the first n elements of a list to a non-empty vector.

If the list is empty or <= 0 elements are chosen, Nothing is returned, otherwise Just containing the non-empty vector

>>> fromListN 3 [1..5]Just [1,2,3]

>>> fromListN 3 []Nothing

>>> fromListN 0 [1..5]Nothing

O(m+n) For each pair (i,a) from the list, replace the non-empty vector element at position i by a.

>>> unsafeFromList [1..3] // [(2,4)][1,2,4]

>>> unsafeFromList [1..3] // [][1,2,3]

O(m+n) For each pair (i,a) from the vector of index/value pairs, replace the vector element at position i by a.

>>> unsafeFromList [1..3] `update` V.fromList [(2,4)][1,2,4]

>>> unsafeFromList [1..3] `update` V.empty[1,2,3]

O(m+min(n1,n2)) For each index i from the index vector and the corresponding value a from the value vector, replace the element of the initial vector at position i by a.

>>> update_ (unsafeFromList [1..3]) (V.fromList [2]) (V.fromList [4])[1,2,4]

>>> update_ (unsafeFromList [1..3]) V.empty V.empty[1,2,3]

Same as (//) but without bounds checking.

Same as update but without bounds checking.

Same as update_ but without bounds checking.

O(n) Pair each element in a vector with its index.

>>> indexed $ unsafeFromList ["a","b","c"][(0,"a"),(1,"b"),(2,"c")]

O(n) Map a function over a non-empty vector.

>>> map (+1) $ unsafeFromList [1..3][2,3,4]

O(n) Apply a function to every element of a non-empty vector and its index.

>>> imap (\i a -> if i == 2 then a+1 else a+0) $ unsafeFromList [1..3][1,2,4]

Map a function over a vector and concatenate the results.

>>> concatMap (\a -> unsafeFromList [a,a]) (unsafeFromList [1,2,3])[1,1,2,2,3,3]

O(n) Apply the monadic action to all elements of the non-empty vector, yielding non-empty vector of results.

>>> mapM Just (unsafeFromList [1..3])Just [1,2,3]

>>> mapM (const Nothing) (unsafeFromList [1..3])Nothing

O(n) Apply the monadic action to every element of a non-empty vector and its index, yielding a non-empty vector of results.

>>> imapM (\i a -> if i == 1 then Just a else Just 0) (unsafeFromList [1..3])Just [0,2,0]

>>> imapM (\_ _ -> Nothing) (unsafeFromList [1..3])Nothing

O(n) Apply the monadic action to all elements of a non-empty vector and ignore the results.

>>> mapM_ (const $ Just ()) (unsafeFromList [1..3])Just ()

>>> mapM_ (const Nothing) (unsafeFromList [1..3])Nothing

O(n) Apply the monadic action to every element of a non-emptpy vector and its index, ignoring the results

>>> imapM_ (\i a -> if i == 1 then P.print a else P.putStrLn "0") (unsafeFromList [1..3])020

>>> imapM_ (\_ _ -> Nothing) (unsafeFromList [1..3])Nothing

O(n) Apply the monadic action to all elements of the non-empty vector, yielding a non0empty vector of results.

Equivalent to flip mapM.

O(n) Apply the monadic action to all elements of a non-empty vector and ignore the results.

Equivalent to flip mapM_.

O(min(m,n)) Zip two non-empty vectors with the given function.

>>> zipWith (+) (unsafeFromList [1..3]) (unsafeFromList [1..3])[2,4,6]

Zip three non-empty vectors with the given function.

Zip four non-empty vectors with the given function.

Zip five non-empty vectors with the given function.

Zip six non-empty vectors with the given function.

O(min(m,n)) Zip two non-empty vectors with a function that also takes the elements' indices.

Zip three non-empty vectors and their indices with the given function.

Zip four non-empty vectors and their indices with the given function.

Zip five non-empty vectors and their indices with the given function.

Zip six non-empty vectors and their indices with the given function.

O(min(n,m)) Elementwise pairing of non-empty vector elements. This is a special case of zipWith where the function argument is (,)

Zip together three non-empty vectors.

Zip together four non-empty vectors.

Zip together five non-empty vectors.

Zip together six non-empty vectors.

O(min(m,n)) Zip the two non-empty vectors with the monadic action and yield a non-empty vector of results.

O(min(m,n)) Zip the two non-empty vectors with the monadic action and ignore the results.

O(min(m,n)) Zip the two non-empty vectors with a monadic action that also takes the element index and yield a vector of results.

O(min(m,n)) Zip the two non-empty vectors with a monadic action that also takes the element index and ignore the results.

O(min(m,n)) Unzip a non-empty vector of pairs.

Unzip a non-empty vector of triples.

Unzip a non-empty vector of quadruples.

Unzip a non-empty vector of quintuples.

Unzip a non-empty vector of sextuples.

O(n) Drop repeated adjacent elements.

>>> uniq $ unsafeFromList [1,1,2,2,3,3,1][1,2,3,1]

O(n) Drop elements when predicate returns Nothing

If no elements satisfy the predicate, the resulting vector may be empty.

>>> mapMaybe (\a -> if a == 2 then Nothing else Just a) (unsafeFromList [1..3])[1,3]

O(n) Drop elements when predicate, applied to index and value, returns Nothing

If no elements satisfy the predicate, the resulting vector may be empty.

>>> imapMaybe (\i a -> if a == 2 || i == 2 then Nothing else Just a) (unsafeFromList [1..3])[1]

O(n) Drop elements that do not satisfy the predicate.

If no elements satisfy the predicate, the resulting vector may be empty.

>>> filter (\a -> if a == 2 then False else True) (unsafeFromList [1..3])[1,3]

>>> filter (const False) (unsafeFromList [1..3])[]

O(n) Drop elements that do not satisfy the predicate which is applied to values and their indices.

If no elements satisfy the predicate, the resulting vector may be empty.

>>> ifilter (\i a -> if a == 2 || i == 0 then False else True) (unsafeFromList [1..3])[3]

>>> ifilter (\_ _ -> False) (unsafeFromList [1..3])[]

O(n) Drop elements that do not satisfy the monadic predicate.

If no elements satisfy the predicate, the resulting vector may be empty.

>>> filterM (\a -> if a == 2 then Just False else Just True) (unsafeFromList [1..3])Just [1,3]

>>> filterM (\a -> if a == 2 then Nothing else Just True) (unsafeFromList [1..3])Nothing

>>> filterM (const $ Just False) (unsafeFromList [1..3])Just []

O(n) Drop elements that do not satisfy the monadic predicate that is a function of index and value.

If no elements satisfy the predicate, the resulting vector may be empty.

TODO: this should be a more efficient function in vector.

>>> ifilterM (\i a -> if a == 2 || i == 0 then Just False else Just True) (unsafeFromList [1..3])Just [3]

>>> ifilterM (\i a -> if a == 2 || i == 0 then Nothing else Just True) (unsafeFromList [1..3])Nothing

>>> ifilterM (\_ _ -> Just False) (unsafeFromList [1..3])Just []

O(n) Yield the longest prefix of elements satisfying the predicate without copying.

If no elements satisfy the predicate, the resulting vector may be empty.

>>> takeWhile (/= 3) (unsafeFromList [1..3])[1,2]

O(n) Drop the longest prefix of elements that satisfy the predicate without copying.

If all elements satisfy the predicate, the resulting vector may be empty.

>>> dropWhile (/= 3) (unsafeFromList [1..3])[3]