Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell98 |
An implementation of bidirectional maps between values of two
key types. A Bimap
is essentially a bijection between subsets of
its two argument types.
Each element of the left-hand type is associated with an element of the right-hand type, and vice-versa, such that the two mappings are inverses. Deleting an element will cause its twin to be deleted, and inserting a pair of elements will cause any overlapping bindings to be deleted.
Most functions implicitly consider the left-hand type to be the
key, and the right-hand type to be the value.
Functions with an R
suffix reverse this convention, treating the
right-hand type as the key and the left-hand type as the value.
- data Bimap a b
- null :: Bimap a b -> Bool
- size :: Bimap a b -> Int
- member :: (Ord a, Ord b) => a -> Bimap a b -> Bool
- memberR :: (Ord a, Ord b) => b -> Bimap a b -> Bool
- notMember :: (Ord a, Ord b) => a -> Bimap a b -> Bool
- notMemberR :: (Ord a, Ord b) => b -> Bimap a b -> Bool
- pairMember :: (Ord a, Ord b) => (a, b) -> Bimap a b -> Bool
- pairNotMember :: (Ord a, Ord b) => (a, b) -> Bimap a b -> Bool
- lookup :: (Ord a, Ord b, Monad m) => a -> Bimap a b -> m b
- lookupR :: (Ord a, Ord b, Monad m) => b -> Bimap a b -> m a
- (!) :: (Ord a, Ord b) => Bimap a b -> a -> b
- (!>) :: (Ord a, Ord b) => Bimap a b -> b -> a
- empty :: Bimap a b
- singleton :: a -> b -> Bimap a b
- insert :: (Ord a, Ord b) => a -> b -> Bimap a b -> Bimap a b
- tryInsert :: (Ord a, Ord b) => a -> b -> Bimap a b -> Bimap a b
- delete :: (Ord a, Ord b) => a -> Bimap a b -> Bimap a b
- deleteR :: (Ord a, Ord b) => b -> Bimap a b -> Bimap a b
- findMin :: Bimap a b -> (a, b)
- findMinR :: Bimap a b -> (b, a)
- findMax :: Bimap a b -> (a, b)
- findMaxR :: Bimap a b -> (b, a)
- deleteMin :: Ord b => Bimap a b -> Bimap a b
- deleteMinR :: Ord a => Bimap a b -> Bimap a b
- deleteMax :: Ord b => Bimap a b -> Bimap a b
- deleteMaxR :: Ord a => Bimap a b -> Bimap a b
- deleteFindMin :: Ord b => Bimap a b -> ((a, b), Bimap a b)
- deleteFindMinR :: Ord a => Bimap a b -> ((b, a), Bimap a b)
- deleteFindMax :: Ord b => Bimap a b -> ((a, b), Bimap a b)
- deleteFindMaxR :: Ord a => Bimap a b -> ((b, a), Bimap a b)
- filter :: (Ord a, Ord b) => (a -> b -> Bool) -> Bimap a b -> Bimap a b
- partition :: (Ord a, Ord b) => (a -> b -> Bool) -> Bimap a b -> (Bimap a b, Bimap a b)
- fromList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b
- fromAList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b
- fromAscPairList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b
- fromAscPairListUnchecked :: (Ord a, Ord b) => [(a, b)] -> Bimap a b
- toList :: Bimap a b -> [(a, b)]
- toAscList :: Bimap a b -> [(a, b)]
- toAscListR :: Bimap a b -> [(b, a)]
- keys :: Bimap a b -> [a]
- keysR :: Bimap a b -> [b]
- elems :: Bimap a b -> [b]
- assocs :: Bimap a b -> [(a, b)]
- fold :: (a -> b -> c -> c) -> c -> Bimap a b -> c
- map :: Ord c => (a -> c) -> Bimap a b -> Bimap c b
- mapR :: Ord c => (b -> c) -> Bimap a b -> Bimap a c
- mapMonotonic :: (a -> c) -> Bimap a b -> Bimap c b
- mapMonotonicR :: (b -> c) -> Bimap a b -> Bimap a c
- toMap :: Bimap a b -> Map a b
- toMapR :: Bimap a b -> Map b a
- valid :: (Ord a, Ord b) => Bimap a b -> Bool
- twist :: Bimap a b -> Bimap b a
- twisted :: (Bimap a b -> Bimap a b) -> Bimap b a -> Bimap b a
Bimap type
A bidirectional map between values of types a
and b
.
Query
member :: (Ord a, Ord b) => a -> Bimap a b -> Bool Source
O(log n). Is the specified value a member of the bimap? Version: 0.2
memberR :: (Ord a, Ord b) => b -> Bimap a b -> Bool Source
O(log n). A version of member
specialized to the right key.
Version: 0.2
notMember :: (Ord a, Ord b) => a -> Bimap a b -> Bool Source
O(log n). Is the specified value not a member of the bimap? Version: 0.2
notMemberR :: (Ord a, Ord b) => b -> Bimap a b -> Bool Source
O(log n). A version of notMember
specialized to the right key.
Version: 0.2
pairMember :: (Ord a, Ord b) => (a, b) -> Bimap a b -> Bool Source
O(log n). Are the two values associated with each other in the bimap?
This function is uncurried in its first two arguments, so that it can be used infix.
Version: 0.2
pairNotMember :: (Ord a, Ord b) => (a, b) -> Bimap a b -> Bool Source
O(log n).
Are the two values not in the bimap, or not associated
with each other? (Complement of pairMember
.)
Version: 0.2
lookup :: (Ord a, Ord b, Monad m) => a -> Bimap a b -> m b Source
O(log n). Lookup a left key in the bimap, returning the associated right key.
This function will return
the result in the monad, or fail
if
the value isn't in the bimap.
Version: 0.2
lookupR :: (Ord a, Ord b, Monad m) => b -> Bimap a b -> m a Source
O(log n).
A version of lookup
that is specialized to the right key,
and returns the corresponding left key.
Version: 0.2
(!) :: (Ord a, Ord b) => Bimap a b -> a -> b Source
O(log n).
Find the right key corresponding to a given left key.
Calls
when the key is not in the bimap.
Version: 0.2error
(!>) :: (Ord a, Ord b) => Bimap a b -> b -> a Source
O(log n).
A version of (!)
that is specialized to the right key,
and returns the corresponding left key.
Version: 0.2
Construction
Update
insert :: (Ord a, Ord b) => a -> b -> Bimap a b -> Bimap a b Source
O(log n). Insert a pair of values into the bimap, associating them.
If either of the values is already in the bimap, any overlapping bindings are deleted.
Version: 0.2
tryInsert :: (Ord a, Ord b) => a -> b -> Bimap a b -> Bimap a b Source
O(log n). Insert a pair of values into the bimap, but only if neither is already in the bimap. Version: 0.2.2
delete :: (Ord a, Ord b) => a -> Bimap a b -> Bimap a b Source
O(log n). Delete a value and its twin from a bimap.
When the value is not a member of the bimap, the original bimap is returned.
Version: 0.2
deleteR :: (Ord a, Ord b) => b -> Bimap a b -> Bimap a b Source
O(log n) A version of delete
specialized to the right key.
Version: 0.2
Min/Max
findMin :: Bimap a b -> (a, b) Source
O(log n).
Find the element with minimal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
findMinR :: Bimap a b -> (b, a) Source
O(log n).
Find the element with minimal right key. The
right-hand key is the first entry in the pair.
Calls
if the bimap is empty.
Version: 0.2.2error
findMax :: Bimap a b -> (a, b) Source
O(log n).
Find the element with maximal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
findMaxR :: Bimap a b -> (b, a) Source
O(log n).
Find the element with maximal right key. The
right-hand key is the first entry in the pair.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteMin :: Ord b => Bimap a b -> Bimap a b Source
O(log n).
Delete the element with minimal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteMinR :: Ord a => Bimap a b -> Bimap a b Source
O(log n).
Delete the element with minimal right key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteMax :: Ord b => Bimap a b -> Bimap a b Source
O(log n).
Delete the element with maximal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteMaxR :: Ord a => Bimap a b -> Bimap a b Source
O(log n).
Delete the element with maximal right key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteFindMin :: Ord b => Bimap a b -> ((a, b), Bimap a b) Source
O(log n).
Delete and find the element with minimal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteFindMinR :: Ord a => Bimap a b -> ((b, a), Bimap a b) Source
O(log n).
Delete and find the element with minimal right key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteFindMax :: Ord b => Bimap a b -> ((a, b), Bimap a b) Source
O(log n).
Delete and find the element with maximal left key.
Calls
if the bimap is empty.
Version: 0.2.2error
deleteFindMaxR :: Ord a => Bimap a b -> ((b, a), Bimap a b) Source
O(log n).
Delete and find the element with maximal right key.
Calls
if the bimap is empty.
Version: 0.2.2error
Filter
filter :: (Ord a, Ord b) => (a -> b -> Bool) -> Bimap a b -> Bimap a b Source
O(n). Filter all association pairs that satisfy the predicate.
Note that the predicate will be applied twice for each association in the bimap.
Version: 0.2.4
partition :: (Ord a, Ord b) => (a -> b -> Bool) -> Bimap a b -> (Bimap a b, Bimap a b) Source
O(n). Partition the bimap according to a predicate. The first bimap contains all associations that satisfy the predicate; the second contains all associations that fail the predicate.
Note that the predicate will be applied twice for each association in the bimap.
Version: 0.2.4
Conversion/traversal
fromList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b Source
O(n*log n). Build a map from a list of pairs. If there are any overlapping pairs in the list, the later ones will override the earlier ones. Version: 0.2
fromAList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b Source
O(n*log n).
Build a map from a list of pairs. Unlike fromList
, earlier pairs
will take precedence over later ones.
The name fromAList
is a reference to Lisp-style association
lists, where associations can be overridden by prepending new ones.
Note that when duplicates occur in both the keys and in the values,
fromList xs /= fromAList (reverse xs)
. However, if either
contains no duplicates, then the equality holds.
Version: 0.2.2
fromAscPairList :: (Ord a, Ord b) => [(a, b)] -> Bimap a b Source
O(n). Build a bimap from a list of pairs, where both the fst
and snd
halves of the list are in strictly ascending order.
This precondition is checked; an invalid list will cause an error.
Version: 0.2.3
fromAscPairListUnchecked :: (Ord a, Ord b) => [(a, b)] -> Bimap a b Source
O(n). Build a bimap from a list of pairs, where both the fst
and snd
halves of the list are in strictly ascending order.
This precondition is not checked; an invalid list will produce a malformed bimap.
Version: 0.2.3
toAscList :: Bimap a b -> [(a, b)] Source
O(n). Convert to a list of associated pairs, with the left-hand values in ascending order.
Since pair ordering is lexical, the pairs will also be in ascending order.
Version: 0.2
toAscListR :: Bimap a b -> [(b, a)] Source
O(n). Convert to a list of associated pairs, with the right-hand values first in the pair and in ascending order.
Since pair ordering is lexical, the pairs will also be in ascending order.
Version: 0.2
keys :: Bimap a b -> [a] Source
O(n). Return all left-hand keys in the bimap in ascending order. Version: 0.2
keysR :: Bimap a b -> [b] Source
O(n). Return all right-hand keys in the bimap in ascending order. Version: 0.2
assocs :: Bimap a b -> [(a, b)] Source
O(n). Return all associated pairs in the bimap, with the left-hand values in ascending order. Version: 0.2
map :: Ord c => (a -> c) -> Bimap a b -> Bimap c b Source
O(n*log n) Map a function over all the left keys in the map. Version 0.3
mapR :: Ord c => (b -> c) -> Bimap a b -> Bimap a c Source
O(n*log n) Map a function over all the right keys in the map. Version 0.3
mapMonotonic :: (a -> c) -> Bimap a b -> Bimap c b Source
O(n). Map a strictly increasing function over all left keys in the map. The precondition is not checked. Version 0.3
mapMonotonicR :: (b -> c) -> Bimap a b -> Bimap a c Source
O(n). Map a strictly increasing function over all right keys in the map. The precondition is not checked. Version 0.3
toMap :: Bimap a b -> Map a b Source
O(1). Extract only the left-to-right component of a bimap. Version: 0.2.1
toMapR :: Bimap a b -> Map b a Source
O(1). Extract only the right-to-left component of a bimap. Version: 0.2.1
Miscellaneous
valid :: (Ord a, Ord b) => Bimap a b -> Bool Source
O(n*log n).
Test if the internal bimap structure is valid. This should be true
for any bimap created using the public interface, unless
fromAscPairListUnchecked
has been used inappropriately.
Version: 0.2