Copyright  20102012 Johan Tibell 

License  BSDstyle 
Maintainer  johan.tibell@gmail.com 
Stability  provisional 
Portability  portable 
Safe Haskell  Safe 
Language  Haskell2010 
A map from
hashable
keys to values. A map cannot contain
duplicate keys; each key can map to at most one value. A
HashMap
makes no guarantees as to the order of its elements.
The implementation is based on
hash array mapped tries
. A
HashMap
is often faster than other treebased set types,
especially when key comparison is expensive, as in the case of
strings.
Many operations have a averagecase complexity of \(O(\log n)\) . The implementation uses a large base (i.e. 16) so in practice these operations are constant time.
Synopsis
 data HashMap k v
 empty :: HashMap k v
 singleton :: Hashable k => k > v > HashMap k v
 null :: HashMap k v > Bool
 size :: HashMap k v > Int
 member :: ( Eq k, Hashable k) => k > HashMap k a > Bool
 lookup :: ( Eq k, Hashable k) => k > HashMap k v > Maybe v
 (!?) :: ( Eq k, Hashable k) => HashMap k v > k > Maybe v
 findWithDefault :: ( Eq k, Hashable k) => v > k > HashMap k v > v
 lookupDefault :: ( Eq k, Hashable k) => v > k > HashMap k v > v
 (!) :: ( Eq k, Hashable k, HasCallStack ) => HashMap k v > k > v
 insert :: ( Eq k, Hashable k) => k > v > HashMap k v > HashMap k v
 insertWith :: ( Eq k, Hashable k) => (v > v > v) > k > v > HashMap k v > HashMap k v
 delete :: ( Eq k, Hashable k) => k > HashMap k v > HashMap k v
 adjust :: ( Eq k, Hashable k) => (v > v) > k > HashMap k v > HashMap k v
 update :: ( Eq k, Hashable k) => (a > Maybe a) > k > HashMap k a > HashMap k a
 alter :: ( Eq k, Hashable k) => ( Maybe v > Maybe v) > k > HashMap k v > HashMap k v
 alterF :: ( Functor f, Eq k, Hashable k) => ( Maybe v > f ( Maybe v)) > k > HashMap k v > f ( HashMap k v)
 isSubmapOf :: ( Eq k, Hashable k, Eq v) => HashMap k v > HashMap k v > Bool
 isSubmapOfBy :: ( Eq k, Hashable k) => (v1 > v2 > Bool ) > HashMap k v1 > HashMap k v2 > Bool
 union :: ( Eq k, Hashable k) => HashMap k v > HashMap k v > HashMap k v
 unionWith :: ( Eq k, Hashable k) => (v > v > v) > HashMap k v > HashMap k v > HashMap k v
 unionWithKey :: ( Eq k, Hashable k) => (k > v > v > v) > HashMap k v > HashMap k v > HashMap k v
 unions :: ( Eq k, Hashable k) => [ HashMap k v] > HashMap k v
 compose :: ( Eq b, Hashable b) => HashMap b c > HashMap a b > HashMap a c
 map :: (v1 > v2) > HashMap k v1 > HashMap k v2
 mapWithKey :: (k > v1 > v2) > HashMap k v1 > HashMap k v2
 traverseWithKey :: Applicative f => (k > v1 > f v2) > HashMap k v1 > f ( HashMap k v2)
 mapKeys :: ( Eq k2, Hashable k2) => (k1 > k2) > HashMap k1 v > HashMap k2 v
 difference :: ( Eq k, Hashable k) => HashMap k v > HashMap k w > HashMap k v
 differenceWith :: ( Eq k, Hashable k) => (v > w > Maybe v) > HashMap k v > HashMap k w > HashMap k v
 intersection :: ( Eq k, Hashable k) => HashMap k v > HashMap k w > HashMap k v
 intersectionWith :: ( Eq k, Hashable k) => (v1 > v2 > v3) > HashMap k v1 > HashMap k v2 > HashMap k v3
 intersectionWithKey :: ( Eq k, Hashable k) => (k > v1 > v2 > v3) > HashMap k v1 > HashMap k v2 > HashMap k v3
 foldMapWithKey :: Monoid m => (k > v > m) > HashMap k v > m
 foldr :: (v > a > a) > a > HashMap k v > a
 foldl :: (a > v > a) > a > HashMap k v > a
 foldr' :: (v > a > a) > a > HashMap k v > a
 foldl' :: (a > v > a) > a > HashMap k v > a
 foldrWithKey' :: (k > v > a > a) > a > HashMap k v > a
 foldlWithKey' :: (a > k > v > a) > a > HashMap k v > a
 foldrWithKey :: (k > v > a > a) > a > HashMap k v > a
 foldlWithKey :: (a > k > v > a) > a > HashMap k v > a
 filter :: (v > Bool ) > HashMap k v > HashMap k v
 filterWithKey :: forall k v. (k > v > Bool ) > HashMap k v > HashMap k v
 mapMaybe :: (v1 > Maybe v2) > HashMap k v1 > HashMap k v2
 mapMaybeWithKey :: (k > v1 > Maybe v2) > HashMap k v1 > HashMap k v2
 keys :: HashMap k v > [k]
 elems :: HashMap k v > [v]
 toList :: HashMap k v > [(k, v)]
 fromList :: ( Eq k, Hashable k) => [(k, v)] > HashMap k v
 fromListWith :: ( Eq k, Hashable k) => (v > v > v) > [(k, v)] > HashMap k v
 fromListWithKey :: ( Eq k, Hashable k) => (k > v > v > v) > [(k, v)] > HashMap k v
 keysSet :: HashMap k a > HashSet k
Strictness properties
This module satisfies the following strictness properties:
 Key arguments are evaluated to WHNF;
 Keys and values are evaluated to WHNF before they are stored in the map.
A map from keys to values. A map cannot contain duplicate keys; each key can map to at most one value.
Instances
Bifoldable HashMap Source # 
Since: 0.2.11 
Defined in Data.HashMap.Internal 

Eq2 HashMap Source #  
Ord2 HashMap Source #  
Defined in Data.HashMap.Internal 

Show2 HashMap Source #  
Defined in Data.HashMap.Internal 

NFData2 HashMap Source # 
Since: 0.2.14.0 
Defined in Data.HashMap.Internal 

Hashable2 HashMap Source #  
( Lift k, Lift v) => Lift ( HashMap k v :: Type ) Source # 
Since: 0.2.17.0 
Functor ( HashMap k) Source #  
Foldable ( HashMap k) Source #  
Defined in Data.HashMap.Internal fold :: Monoid m => HashMap k m > m Source # foldMap :: Monoid m => (a > m) > HashMap k a > m Source # foldMap' :: Monoid m => (a > m) > HashMap k a > m Source # foldr :: (a > b > b) > b > HashMap k a > b Source # foldr' :: (a > b > b) > b > HashMap k a > b Source # foldl :: (b > a > b) > b > HashMap k a > b Source # foldl' :: (b > a > b) > b > HashMap k a > b Source # foldr1 :: (a > a > a) > HashMap k a > a Source # foldl1 :: (a > a > a) > HashMap k a > a Source # toList :: HashMap k a > [a] Source # null :: HashMap k a > Bool Source # length :: HashMap k a > Int Source # elem :: Eq a => a > HashMap k a > Bool Source # maximum :: Ord a => HashMap k a > a Source # minimum :: Ord a => HashMap k a > a Source # 

Traversable ( HashMap k) Source #  
Defined in Data.HashMap.Internal traverse :: Applicative f => (a > f b) > HashMap k a > f ( HashMap k b) Source # sequenceA :: Applicative f => HashMap k (f a) > f ( HashMap k a) Source # mapM :: Monad m => (a > m b) > HashMap k a > m ( HashMap k b) Source # sequence :: Monad m => HashMap k (m a) > m ( HashMap k a) Source # 

Eq k => Eq1 ( HashMap k) Source #  
Ord k => Ord1 ( HashMap k) Source #  
Defined in Data.HashMap.Internal 

( Eq k, Hashable k, Read k) => Read1 ( HashMap k) Source #  
Defined in Data.HashMap.Internal liftReadsPrec :: ( Int > ReadS a) > ReadS [a] > Int > ReadS ( HashMap k a) Source # liftReadList :: ( Int > ReadS a) > ReadS [a] > ReadS [ HashMap k a] Source # liftReadPrec :: ReadPrec a > ReadPrec [a] > ReadPrec ( HashMap k a) Source # liftReadListPrec :: ReadPrec a > ReadPrec [a] > ReadPrec [ HashMap k a] Source # 

Show k => Show1 ( HashMap k) Source #  
NFData k => NFData1 ( HashMap k) Source # 
Since: 0.2.14.0 
Defined in Data.HashMap.Internal 

Hashable k => Hashable1 ( HashMap k) Source #  
Defined in Data.HashMap.Internal 

( Eq k, Hashable k) => IsList ( HashMap k v) Source #  
( Eq k, Eq v) => Eq ( HashMap k v) Source # 
Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. 
( Data k, Data v, Eq k, Hashable k) => Data ( HashMap k v) Source #  
Defined in Data.HashMap.Internal gfoldl :: ( forall d b. Data d => c (d > b) > d > c b) > ( forall g. g > c g) > HashMap k v > c ( HashMap k v) Source # gunfold :: ( forall b r. Data b => c (b > r) > c r) > ( forall r. r > c r) > Constr > c ( HashMap k v) Source # toConstr :: HashMap k v > Constr Source # dataTypeOf :: HashMap k v > DataType Source # dataCast1 :: Typeable t => ( forall d. Data d => c (t d)) > Maybe (c ( HashMap k v)) Source # dataCast2 :: Typeable t => ( forall d e. ( Data d, Data e) => c (t d e)) > Maybe (c ( HashMap k v)) Source # gmapT :: ( forall b. Data b => b > b) > HashMap k v > HashMap k v Source # gmapQl :: (r > r' > r) > r > ( forall d. Data d => d > r') > HashMap k v > r Source # gmapQr :: forall r r'. (r' > r > r) > r > ( forall d. Data d => d > r') > HashMap k v > r Source # gmapQ :: ( forall d. Data d => d > u) > HashMap k v > [u] Source # gmapQi :: Int > ( forall d. Data d => d > u) > HashMap k v > u Source # gmapM :: Monad m => ( forall d. Data d => d > m d) > HashMap k v > m ( HashMap k v) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d > m d) > HashMap k v > m ( HashMap k v) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d > m d) > HashMap k v > m ( HashMap k v) Source # 

( Ord k, Ord v) => Ord ( HashMap k v) Source # 
The ordering is total and consistent with the

Defined in Data.HashMap.Internal compare :: HashMap k v > HashMap k v > Ordering Source # (<) :: HashMap k v > HashMap k v > Bool Source # (<=) :: HashMap k v > HashMap k v > Bool Source # (>) :: HashMap k v > HashMap k v > Bool Source # (>=) :: HashMap k v > HashMap k v > Bool Source # 

( Eq k, Hashable k, Read k, Read e) => Read ( HashMap k e) Source #  
( Show k, Show v) => Show ( HashMap k v) Source #  
( Eq k, Hashable k) => Semigroup ( HashMap k v) Source # 
If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples

( Eq k, Hashable k) => Monoid ( HashMap k v) Source # 
If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples

( NFData k, NFData v) => NFData ( HashMap k v) Source #  
Defined in Data.HashMap.Internal 

( Hashable k, Hashable v) => Hashable ( HashMap k v) Source #  
type Item ( HashMap k v) Source #  
Defined in Data.HashMap.Internal 
Construction
singleton :: Hashable k => k > v > HashMap k v Source #
\(O(1)\) Construct a map with a single element.
Basic interface
lookup :: ( Eq k, Hashable k) => k > HashMap k v > Maybe v Source #
\(O(\log n)\)
Return the value to which the specified key is mapped,
or
Nothing
if this map contains no mapping for the key.
\(O(\log n)\) Return the value to which the specified key is mapped, or the default value if this map contains no mapping for the key.
Since: 0.2.11
\(O(\log n)\) Return the value to which the specified key is mapped, or the default value if this map contains no mapping for the key.
DEPRECATED: lookupDefault is deprecated as of version 0.2.11, replaced
by
findWithDefault
.
(!) :: ( Eq k, Hashable k, HasCallStack ) => HashMap k v > k > v infixl 9 Source #
\(O(\log n)\)
Return the value to which the specified key is mapped.
Calls
error
if this map contains no mapping for the key.
insert :: ( Eq k, Hashable k) => k > v > HashMap k v > HashMap k v Source #
\(O(\log n)\) Associate the specified value with the specified key in this map. If this map previously contained a mapping for the key, the old value is replaced.
insertWith :: ( Eq k, Hashable k) => (v > v > v) > k > v > HashMap k v > HashMap k v Source #
\(O(\log n)\) Associate the value with the key in this map. If this map previously contained a mapping for the key, the old value is replaced by the result of applying the given function to the new and old value. Example:
insertWith f k v map where f new old = new + old
delete :: ( Eq k, Hashable k) => k > HashMap k v > HashMap k v Source #
\(O(\log n)\) Remove the mapping for the specified key from this map if present.
adjust :: ( Eq k, Hashable k) => (v > v) > k > HashMap k v > HashMap k v Source #
\(O(\log n)\) Adjust the value tied to a given key in this map only if it is present. Otherwise, leave the map alone.
alterF :: ( Functor f, Eq k, Hashable k) => ( Maybe v > f ( Maybe v)) > k > HashMap k v > f ( HashMap k v) Source #
\(O(\log n)\)
The expression (
) alters the value
alterF
f k map
x
at
k
, or absence thereof.
alterF
can be used to insert, delete, or update a value in a map.
Note:
alterF
is a flipped version of the
at
combinator from
Control.Lens.At
.
Since: 0.2.10
isSubmapOf :: ( Eq k, Hashable k, Eq v) => HashMap k v > HashMap k v > Bool Source #
\(O(n \log m)\) Inclusion of maps. A map is included in another map if the keys are subsets and the corresponding values are equal:
isSubmapOf m1 m2 = keys m1 `isSubsetOf` keys m2 && and [ v1 == v2  (k1,v1) < toList m1; let v2 = m2 ! k1 ]
Examples
>>>
fromList [(1,'a')] `isSubmapOf` fromList [(1,'a'),(2,'b')]
True
>>>
fromList [(1,'a'),(2,'b')] `isSubmapOf` fromList [(1,'a')]
False
Since: 0.2.12
isSubmapOfBy :: ( Eq k, Hashable k) => (v1 > v2 > Bool ) > HashMap k v1 > HashMap k v2 > Bool Source #
\(O(n \log m)\) Inclusion of maps with value comparison. A map is included in another map if the keys are subsets and if the comparison function is true for the corresponding values:
isSubmapOfBy cmpV m1 m2 = keys m1 `isSubsetOf` keys m2 && and [ v1 `cmpV` v2  (k1,v1) < toList m1; let v2 = m2 ! k1 ]
Examples
>>>
isSubmapOfBy (<=) (fromList [(1,'a')]) (fromList [(1,'b'),(2,'c')])
True
>>>
isSubmapOfBy (<=) (fromList [(1,'b')]) (fromList [(1,'a'),(2,'c')])
False
Since: 0.2.12
Combine
Union
union :: ( Eq k, Hashable k) => HashMap k v > HashMap k v > HashMap k v Source #
\(O(n+m)\) The union of two maps. If a key occurs in both maps, the mapping from the first will be the mapping in the result.
Examples
>>>
union (fromList [(1,'a'),(2,'b')]) (fromList [(2,'c'),(3,'d')])
fromList [(1,'a'),(2,'b'),(3,'d')]
unionWith :: ( Eq k, Hashable k) => (v > v > v) > HashMap k v > HashMap k v > HashMap k v Source #
\(O(n+m)\) The union of two maps. If a key occurs in both maps, the provided function (first argument) will be used to compute the result.
unionWithKey :: ( Eq k, Hashable k) => (k > v > v > v) > HashMap k v > HashMap k v > HashMap k v Source #
\(O(n+m)\) The union of two maps. If a key occurs in both maps, the provided function (first argument) will be used to compute the result.
unions :: ( Eq k, Hashable k) => [ HashMap k v] > HashMap k v Source #
Construct a set containing all elements from a list of sets.
Compose
compose :: ( Eq b, Hashable b) => HashMap b c > HashMap a b > HashMap a c Source #
Relate the keys of one map to the values of the other, by using the values of the former as keys for lookups in the latter.
Complexity: \( O (n * \log(m)) \) , where \(m\) is the size of the first argument
>>>
compose (fromList [('a', "A"), ('b', "B")]) (fromList [(1,'a'),(2,'b'),(3,'z')])
fromList [(1,"A"),(2,"B")]
(compose
bc ab!?
) = (bc!?
) <=< (ab!?
)
Since: 0.2.13.0
Transformations
map :: (v1 > v2) > HashMap k v1 > HashMap k v2 Source #
\(O(n)\) Transform this map by applying a function to every value.
mapWithKey :: (k > v1 > v2) > HashMap k v1 > HashMap k v2 Source #
\(O(n)\) Transform this map by applying a function to every value.
traverseWithKey :: Applicative f => (k > v1 > f v2) > HashMap k v1 > f ( HashMap k v2) Source #
\(O(n)\)
Perform an
Applicative
action for each keyvalue pair
in a
HashMap
and produce a
HashMap
of all the results. Each
HashMap
will be strict in all its values.
traverseWithKey f = fmap (map
id) . Data.HashMap.Lazy.traverseWithKey
f
Note: the order in which the actions occur is unspecified. In particular, when the map contains hash collisions, the order in which the actions associated with the keys involved will depend in an unspecified way on their insertion order.
mapKeys :: ( Eq k2, Hashable k2) => (k1 > k2) > HashMap k1 v > HashMap k2 v Source #
\(O(n)\)
.
is the map obtained by applying
mapKeys
f s
f
to each key of
s
.
The size of the result may be smaller if
f
maps two or more distinct
keys to the same new key. In this case there is no guarantee which of the
associated values is chosen for the conflicting key.
>>>
mapKeys (+ 1) (fromList [(5,"a"), (3,"b")])
fromList [(4,"b"),(6,"a")]>>>
mapKeys (\ _ > 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")])
fromList [(1,"c")]>>>
mapKeys (\ _ > 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")])
fromList [(3,"c")]
Since: 0.2.14.0
Difference and intersection
difference :: ( Eq k, Hashable k) => HashMap k v > HashMap k w > HashMap k v Source #
\(O(n \log m)\) Difference of two maps. Return elements of the first map not existing in the second.
differenceWith :: ( Eq k, Hashable k) => (v > w > Maybe v) > HashMap k v > HashMap k w > HashMap k v Source #
intersection :: ( Eq k, Hashable k) => HashMap k v > HashMap k w > HashMap k v Source #
\(O(n \log m)\) Intersection of two maps. Return elements of the first map for keys existing in the second.
intersectionWith :: ( Eq k, Hashable k) => (v1 > v2 > v3) > HashMap k v1 > HashMap k v2 > HashMap k v3 Source #
\(O(n+m)\) Intersection of two maps. If a key occurs in both maps the provided function is used to combine the values from the two maps.
intersectionWithKey :: ( Eq k, Hashable k) => (k > v1 > v2 > v3) > HashMap k v1 > HashMap k v2 > HashMap k v3 Source #
\(O(n+m)\) Intersection of two maps. If a key occurs in both maps the provided function is used to combine the values from the two maps.
Folds
foldMapWithKey :: Monoid m => (k > v > m) > HashMap k v > m Source #
\(O(n)\) Reduce the map by applying a function to each element and combining the results with a monoid operation.
foldr :: (v > a > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the rightidentity of the operator).
foldl :: (a > v > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the leftidentity of the operator).
foldr' :: (v > a > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the rightidentity of the operator). Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
foldl' :: (a > v > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the leftidentity of the operator). Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
foldrWithKey' :: (k > v > a > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the rightidentity of the operator). Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
foldlWithKey' :: (a > k > v > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the leftidentity of the operator). Each application of the operator is evaluated before using the result in the next application. This function is strict in the starting value.
foldrWithKey :: (k > v > a > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the rightidentity of the operator).
foldlWithKey :: (a > k > v > a) > a > HashMap k v > a Source #
\(O(n)\) Reduce this map by applying a binary operator to all elements, using the given starting value (typically the leftidentity of the operator).
Filter
filter :: (v > Bool ) > HashMap k v > HashMap k v Source #
\(O(n)\) Filter this map by retaining only elements which values satisfy a predicate.
filterWithKey :: forall k v. (k > v > Bool ) > HashMap k v > HashMap k v Source #
\(O(n)\) Filter this map by retaining only elements satisfying a predicate.
mapMaybe :: (v1 > Maybe v2) > HashMap k v1 > HashMap k v2 Source #
\(O(n)\) Transform this map by applying a function to every value and retaining only some of them.
mapMaybeWithKey :: (k > v1 > Maybe v2) > HashMap k v1 > HashMap k v2 Source #
\(O(n)\) Transform this map by applying a function to every value and retaining only some of them.
Conversions
keys :: HashMap k v > [k] Source #
\(O(n)\) Return a list of this map's keys. The list is produced lazily.
elems :: HashMap k v > [v] Source #
\(O(n)\) Return a list of this map's values. The list is produced lazily.
Lists
toList :: HashMap k v > [(k, v)] Source #
\(O(n)\) Return a list of this map's elements. The list is produced lazily. The order of its elements is unspecified.
fromList :: ( Eq k, Hashable k) => [(k, v)] > HashMap k v Source #
\(O(n \log n)\) Construct a map with the supplied mappings. If the list contains duplicate mappings, the later mappings take precedence.
fromListWith :: ( Eq k, Hashable k) => (v > v > v) > [(k, v)] > HashMap k v Source #
\(O(n \log n)\)
Construct a map from a list of elements. Uses
the provided function
f
to merge duplicate entries with
(f newVal oldVal)
.
Examples
Given a list
xs
, create a map with the number of occurrences of each
element in
xs
:
let xs = ['a', 'b', 'a'] in fromListWith (+) [ (x, 1)  x < xs ] = fromList [('a', 2), ('b', 1)]
Given a list of keyvalue pairs
xs :: [(k, v)]
, group all values by their
keys and return a
HashMap k [v]
.
let xs = ('a', 1), ('b', 2), ('a', 3)] in fromListWith (++) [ (k, [v])  (k, v) < xs ] = fromList [('a', [3, 1]), ('b', [2])]
Note that the lists in the resulting map contain elements in reverse order from their occurences in the original list.
More generally, duplicate entries are accumulated as follows;
this matters when
f
is not commutative or not associative.
fromListWith f [(k, a), (k, b), (k, c), (k, d)] = fromList [(k, f d (f c (f b a)))]
fromListWithKey :: ( Eq k, Hashable k) => (k > v > v > v) > [(k, v)] > HashMap k v Source #
\(O(n \log n)\) Construct a map from a list of elements. Uses the provided function to merge duplicate entries.
Examples
Given a list of keyvalue pairs where the keys are of different flavours, e.g:
data Key = Div  Sub
and the values need to be combined differently when there are duplicates, depending on the key:
combine Div = div combine Sub = ()
then
fromListWithKey
can be used as follows:
fromListWithKey combine [(Div, 2), (Div, 6), (Sub, 2), (Sub, 3)] = fromList [(Div, 3), (Sub, 1)]
More generally, duplicate entries are accumulated as follows;
fromListWith f [(k, a), (k, b), (k, c), (k, d)] = fromList [(k, f k d (f k c (f k b a)))]
Since: 0.2.11