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)
- last2' :: a -> a -> [a] -> (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
- (!!) :: HasCallStack => [a] -> Int -> 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]

- suffixesSatisfying :: (a -> Bool) -> [a] -> [Bool]
- findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int)
- chop :: Int -> [a] -> [[a]]
- chopWhen :: forall a. (a -> Bool) -> [a] -> [[a]]
- hasElem :: Ord a => [a] -> a -> Bool
- sorted :: Ord a => [a] -> Bool
- allConsecutive :: (a -> a -> Bool) -> [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]
- nubFavouriteOn :: forall a b c. (Ord b, Eq c, Hashable c) => (a -> b) -> (a -> c) -> [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)`

last2' :: a -> a -> [a] -> (a, a) Source #

`last2' x y zs`

computes the last two elements of `x:y:zs`

.
O(n).

initWithDefault :: [a] -> [a] -> [a] Source #

`init`

, safe.
O(n).

# Lookup and indexing

(!!) :: HasCallStack => [a] -> Int -> a Source #

A variant of `!!`

that might provide more informative
error messages if the index is out of bounds.

Precondition: The index should not be out of bounds.

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.

`>>>`

(1 :| [3,5,2],[4,7,8])`breakAfter1 even 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.

`>>>`

([1,3,5,2],[4,7,8])`breakAfter even [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. |

suffixesSatisfying :: (a -> Bool) -> [a] -> [Bool] Source #

Returns a list with one boolean for each non-empty suffix of the
list, starting with the longest suffix (the entire list). Each
boolean is `True`

exactly when every element in the corresponding
suffix satisfies the predicate.

An example:
```
```

`suffixesSatisfying`

`isLower`

AbCde =
[False, False, False, True, True]

For total predicates `p`

and finite and total lists `xs`

the
following holds:
```
```

`suffixesSatisfying`

p xs = `map`

(`all`

p) (`init`

(`tails`

xs))

## Finding overlap

findOverlap :: forall a. Eq a => [a] -> [a] -> (Int, Int) Source #

Find the longest suffix of the first string `xs`

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.

Worst-case time complexity is quadratic: `O(min(n,m)²)`

where `n = length xs`

and `m = length ys`

.

There might be asymptotically better implementations following Knuth-Morris-Pratt (KMP), but for rather short lists this is good enough.

# Chunks

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.

allConsecutive :: (a -> a -> Bool) -> [a] -> Bool Source #

Check whether all consecutive elements of a list satisfy the given relation. O(n).

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.

:: forall a b c. (Ord b, Eq c, Hashable c) | |

=> (a -> b) | The values returned by this function are used to determine which element from a group of equal elements that is returned: the smallest one is chosen (and if two elements are equally small, then the first one is chosen). |

-> (a -> c) | Two elements are treated as equal if this function returns the same value for both elements. |

-> [a] | |

-> [a] |

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 #