Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
Utility functions for lists.
Synopsis
- snoc :: [a] -> a -> [a]
- caseList :: [a] -> b -> (a -> [a] -> b) -> b
- caseListM :: Monad m => m [a] -> m b -> (a -> [a] -> m b) -> m b
- listCase :: b -> (a -> [a] -> b) -> [a] -> b
- headWithDefault :: a -> [a] -> a
- tailMaybe :: [a] -> Maybe [a]
- tailWithDefault :: [a] -> [a] -> [a]
- lastMaybe :: [a] -> Maybe a
- lastWithDefault :: a -> [a] -> a
- last1 :: a -> [a] -> a
- last2 :: [a] -> Maybe (a, a)
- uncons :: [a] -> Maybe (a, [a])
- mcons :: Maybe a -> [a] -> [a]
- initLast :: [a] -> Maybe ([a], a)
- initLast1 :: a -> [a] -> ([a], a)
- init1 :: a -> [a] -> [a]
- initMaybe :: [a] -> Maybe [a]
- initWithDefault :: [a] -> [a] -> [a]
- (!!!) :: [a] -> Int -> Maybe a
- indexWithDefault :: a -> [a] -> Int -> a
- findWithIndex :: (a -> Bool) -> [a] -> Maybe (a, Int)
- genericElemIndex :: (Eq a, Integral i) => a -> [a] -> Maybe i
- downFrom :: Integral a => a -> [a]
- updateHead :: (a -> a) -> [a] -> [a]
- updateLast :: (a -> a) -> [a] -> [a]
- updateAt :: Int -> (a -> a) -> [a] -> [a]
- type Prefix a = [a]
- type Suffix a = [a]
- splitExactlyAt :: Integral n => n -> [a] -> Maybe (Prefix a, Suffix a)
- dropEnd :: forall a. Int -> [a] -> Prefix a
- spanEnd :: forall a. (a -> Bool) -> [a] -> (Prefix a, Suffix a)
- breakAfter1 :: (a -> Bool) -> a -> [a] -> (List1 a, [a])
- breakAfter :: (a -> Bool) -> [a] -> ([a], [a])
- takeWhileJust :: (a -> Maybe b) -> [a] -> Prefix b
- spanJust :: (a -> Maybe b) -> [a] -> (Prefix b, Suffix a)
- partitionMaybe :: (a -> Maybe b) -> [a] -> ([a], [b])
- filterAndRest :: (a -> Bool) -> [a] -> ([a], Suffix a)
- mapMaybeAndRest :: (a -> Maybe b) -> [a] -> ([b], Suffix a)
- isSublistOf :: Eq a => [a] -> [a] -> Bool
- holes :: [a] -> [(a, [a])]
- commonPrefix :: Eq a => [a] -> [a] -> Prefix a
- dropCommon :: [a] -> [b] -> (Suffix a, Suffix b)
- stripPrefixBy :: (a -> a -> Bool) -> Prefix a -> [a] -> Maybe (Suffix a)
- commonSuffix :: Eq a => [a] -> [a] -> Suffix a
- stripSuffix :: Eq a => Suffix a -> [a] -> Maybe (Prefix a)
- type ReversedSuffix a = [a]
- stripReversedSuffix :: forall a. Eq a => ReversedSuffix a -> [a] -> Maybe (Prefix a)
- data StrSufSt a
- = SSSMismatch
- | SSSStrip (ReversedSuffix a)
- | SSSResult [a]
- findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
- groupOn :: Ord b => (a -> b) -> [a] -> [[a]]
- groupBy' :: (a -> a -> Bool) -> [a] -> [[a]]
- wordsBy :: (a -> Bool) -> [a] -> [[a]]
- chop :: Int -> [a] -> [[a]]
- chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
- hasElem :: Ord a => [a] -> a -> Bool
- sorted :: Ord a => [a] -> Bool
- distinct :: Eq a => [a] -> Bool
- fastDistinct :: Ord a => [a] -> Bool
- duplicates :: Ord a => [a] -> [a]
- allDuplicates :: Ord a => [a] -> [a]
- nubAndDuplicatesOn :: Ord b => (a -> b) -> [a] -> ([a], [a])
- nubOn :: Ord b => (a -> b) -> [a] -> [a]
- uniqOn :: Ord b => (a -> b) -> [a] -> [a]
- allEqual :: Eq a => [a] -> Bool
- nubM :: Monad m => (a -> a -> m Bool) -> [a] -> m [a]
- zipWith' :: (a -> b -> c) -> [a] -> [b] -> Maybe [c]
- zipWithKeepRest :: (a -> b -> b) -> [a] -> [b] -> [b]
- unzipWith :: (a -> (b, c)) -> [a] -> ([b], [c])
- editDistanceSpec :: Eq a => [a] -> [a] -> Int
- editDistance :: forall a. Eq a => [a] -> [a] -> Int
- mergeStrictlyOrderedBy :: (a -> a -> Bool) -> [a] -> [a] -> Maybe [a]
Variants of list case, cons, head, tail, init, last
snoc :: [a] -> a -> [a] Source #
Append a single element at the end. Time: O(length); use only on small lists.
caseList :: [a] -> b -> (a -> [a] -> b) -> b Source #
Case distinction for lists, with list first. O(1).
Cf. ifNull
.
caseListM :: Monad m => m [a] -> m b -> (a -> [a] -> m b) -> m b Source #
Case distinction for lists, with list first. O(1).
Cf. ifNull
.
listCase :: b -> (a -> [a] -> b) -> [a] -> b Source #
Case distinction for lists, with list last. O(1).
headWithDefault :: a -> [a] -> a Source #
Head function (safe). Returns a default value on empty lists. O(1).
headWithDefault 42 [] = 42 headWithDefault 42 [1,2,3] = 1
tailWithDefault :: [a] -> [a] -> [a] Source #
Tail function (safe). Returns a default list on empty lists. O(1).
lastWithDefault :: a -> [a] -> a Source #
Last element (safe). Returns a default list on empty lists. O(n).
last1 :: a -> [a] -> a Source #
Last element of non-empty list (safe).
O(n).
last1 a as = last (a : as)
initWithDefault :: [a] -> [a] -> [a] Source #
init
, safe.
O(n).
Lookup and indexing
indexWithDefault :: a -> [a] -> Int -> a Source #
Lookup function with default value for index out of range. O(min n index).
The name is chosen akin to genericIndex
.
findWithIndex :: (a -> Bool) -> [a] -> Maybe (a, Int) Source #
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!?
genericElemIndex :: (Eq a, Integral i) => a -> [a] -> Maybe i Source #
A generalised variant of elemIndex
.
O(n).
Update
updateHead :: (a -> a) -> [a] -> [a] Source #
Update the first element of a list, if it exists. O(1).
updateLast :: (a -> a) -> [a] -> [a] Source #
Update the last element of a list, if it exists. O(n).
updateAt :: Int -> (a -> a) -> [a] -> [a] Source #
Update nth element of a list, if it exists.
O(min index n)
.
Precondition: the index is >= 0.
Sublist extraction and partitioning
splitExactlyAt :: Integral n => n -> [a] -> Maybe (Prefix a, Suffix a) Source #
splitExactlyAt n xs = Just (ys, zs)
iff xs = ys ++ zs
and genericLength ys = n
.
dropEnd :: forall a. Int -> [a] -> Prefix a Source #
Drop from the end of a list. O(length).
dropEnd n = reverse . drop n . reverse
Forces the whole list even for n==0
.
spanEnd :: forall a. (a -> Bool) -> [a] -> (Prefix a, Suffix a) Source #
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)
.
breakAfter1 :: (a -> Bool) -> a -> [a] -> (List1 a, [a]) Source #
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])
breakAfter :: (a -> Bool) -> [a] -> ([a], [a]) Source #
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])
takeWhileJust :: (a -> Maybe b) -> [a] -> Prefix b Source #
A generalized version of takeWhile
.
(Cf. mapMaybe
vs. filter
).
@O(length . takeWhileJust f).
takeWhileJust f = fst . spanJust f
.
spanJust :: (a -> Maybe b) -> [a] -> (Prefix b, Suffix a) Source #
A generalized version of span
.
O(length . fst . spanJust f)
.
partitionMaybe :: (a -> Maybe b) -> [a] -> ([a], [b]) Source #
filterAndRest :: (a -> Bool) -> [a] -> ([a], Suffix a) Source #
Like filter
, but additionally return the last partition
of the list where the predicate is False
everywhere.
O(n).
mapMaybeAndRest :: (a -> Maybe b) -> [a] -> ([b], Suffix a) Source #
Like mapMaybe
, but additionally return the last partition
of the list where the function always returns Nothing
.
O(n).
isSublistOf :: Eq a => [a] -> [a] -> Bool Source #
Sublist relation.
Prefix and suffix
Prefix
commonPrefix :: Eq a => [a] -> [a] -> Prefix a Source #
Compute the common prefix of two lists. O(min n m).
dropCommon :: [a] -> [b] -> (Suffix a, Suffix b) Source #
Drops from both lists simultaneously until one list is empty. O(min n m).
stripPrefixBy :: (a -> a -> Bool) -> Prefix a -> [a] -> Maybe (Suffix a) Source #
Check if a list has a given prefix. If so, return the list minus the prefix. O(length prefix).
Suffix
commonSuffix :: Eq a => [a] -> [a] -> Suffix a Source #
Compute the common suffix of two lists. O(n + m).
stripSuffix :: Eq a => Suffix a -> [a] -> Maybe (Prefix a) Source #
stripSuffix suf xs = Just pre
iff xs = pre ++ suf
.
O(n).
type ReversedSuffix a = [a] Source #
stripReversedSuffix :: forall a. Eq a => ReversedSuffix a -> [a] -> Maybe (Prefix a) Source #
stripReversedSuffix rsuf xs = Just pre
iff xs = pre ++ reverse suf
.
O(n).
Internal state for stripping suffix.
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
findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int) Source #
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.
Groups and chunks
wordsBy :: (a -> Bool) -> [a] -> [[a]] Source #
Split a list into sublists. Generalisation of the prelude function
words
.
O(n).
words xs == wordsBy isSpace xs
chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]] Source #
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
List as sets
hasElem :: Ord a => [a] -> a -> Bool Source #
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)
sorted :: Ord a => [a] -> Bool Source #
Check whether a list is sorted. O(n).
Assumes that the Ord
instance implements a partial order.
distinct :: Eq a => [a] -> Bool Source #
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
.
fastDistinct :: Ord a => [a] -> Bool Source #
duplicates :: Ord a => [a] -> [a] Source #
Returns an (arbitrary) representative for each list element that occurs more than once. O(n log n).
allDuplicates :: Ord a => [a] -> [a] Source #
Remove the first representative for each list element. Thus, returns all duplicate copies. O(n log n).
allDuplicates xs == sort $ xs \ nub xs
.
nubAndDuplicatesOn :: Ord b => (a -> b) -> [a] -> ([a], [a]) Source #
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
nubOn :: Ord b => (a -> b) -> [a] -> [a] Source #
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.
uniqOn :: Ord b => (a -> b) -> [a] -> [a] Source #
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.
allEqual :: Eq a => [a] -> Bool Source #
Checks if all the elements in the list are equal. Assumes that
the Eq
instance stands for an equivalence relation.
O(n).
Zipping
zipWith' :: (a -> b -> c) -> [a] -> [b] -> Maybe [c] Source #
Requires both lists to have the same length. O(n).
Otherwise, Nothing
is returned.
zipWithKeepRest :: (a -> b -> b) -> [a] -> [b] -> [b] Source #
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
Unzipping
Edit distance
editDistanceSpec :: Eq a => [a] -> [a] -> Int Source #
Implemented using tree recursion, don't run me at home! O(3^(min n m)).
editDistance :: forall a. Eq a => [a] -> [a] -> Int Source #
Implemented using dynamic programming and Data.Array
.
O(n*m).
mergeStrictlyOrderedBy :: (a -> a -> Bool) -> [a] -> [a] -> Maybe [a] Source #