Maps¶
Maps (sometimes referred to as dictionaries in other languages) allow you to
store associations between unique keys and values. There are three
implementations provided by the containers package:
Data.Map.Strict, Data.Map.Lazy, and
Data.IntMap. You almost never want the lazy version so use
Data.Map.Strict, or if your keys are Int use Data.IntMap.
data Map k v = ...
data IntMap v = ...
Important
Map relies on the key type k having instances of the Eq and
Ord typeclass for its internal representation. These are already defined
for builtin types, and if you are using your own data type you can use the
deriving
mechanism.
All of these implementations are immutable which means that any update functions do not modify the map that you passed in, they creates a new map. In order to keep the changes you need to assign it to a new variable. For example:
let m1 = Map.fromList [("a", 1), ("b", 2)]
let m2 = Map.delete "a" m1
print m1
> fromList [("a",1),("b",2)]
print m2
> fromList [("b",2)]
Short Example¶
The following GHCi session shows some of the basic map functionality:
import qualified Data.Map.Strict as Map
let nums = Map.fromList [(1,"one"), (2,"two"), (3,"three")]
-- Get the English word for the number 3 and 4.
Map.lookup 3 nums
> Just "three"
Map.lookup 4 nums
> Nothing
-- Add (4, "four") to our original map.
let moreNums = Map.insert 4 "four" nums
Map.member 4 moreNums
> True
-- Remove the entry for 1 from our original map.
let fewerNums = Map.delete 1 nums
Map.toAscList fewerNums
> [(2,"two"),(3,"three")]
-- Create a new map and combine it with our original map.
-- fromList is right-biased: if a key is repeated the rightmost value is taken.
let newNums = Map.fromList [(3,"new three"), (4,"new four"), (4,"newer four")]
-- union is left-biased: if a key occurs more than once the value from the
-- left map is taken.
Map.union newNums nums
> fromList [(1,"one"),(2,"two"),(3,"new three"),(4,"newer four")]
Tip
- You can use the `OverloadedLists
- <https://downloads.haskell.org/ghc/latest/docs/users_guide/exts/overloaded_lists.html>`_
extension so you don’t need to write fromList [1, 2, 3] everywhere;
instead you can just write [1, 2, 3] and if the function is
expecting a map it will be converted automatically! The code here
will continue to use fromList for clarity though.
Importing Map and IntMap¶
When using Map or IntMap in a Haskell source file you should always use
a qualified import because these modules export names that clash with the
standard Prelude (you can import the type constructor on its own though!). You
should also import Prelude and hide lookup because if you accidentally
leave off the Map. qualifier you’ll get confusing type errors. You can
always import any specific identifiers you want unqualified. Most of the time,
that will include the type constructor (Map).
import Prelude hiding (lookup)
import Data.Map.Strict (Map)
import qualified Data.Map.Strict as Map
import Data.IntMap (IntMap)
import qualified Data.IntMap.Strict as IntMap
Common API Functions¶
Tip
All of these functions that work for Map will also work for IntMap,
which has the key type k specialized to Int. Anywhere that you
see Map Int v you can replace it with IntMap v. This will speed up
most operations tremendously (see Performance) with the exception of
size which is O(1) for Map and O(n) for IntMap.
Note
A Map is printed as an association list preceeded by fromList. For
example, it might look like fromList [(Key1,True),(Key2,False)].
Construction and Conversion¶
Create an empty map¶
Map.empty :: Map k v
Map.empty = ...
empty creates a map without any entries.
Map.empty
> fromList []
Create a map with one entry (singleton)¶
Map.singleton :: k -> v -> Map k v
Map.singleton key value = ...
singleton creates a map with a single
(key,value) entry in it.
Map.singleton 1 "one"
> fromList [(1,"one")]
Map.singleton "containers" ["base"]
> fromList [("containers",["base"])]
Create a map from a list¶
Map.fromList :: Ord k => [(k, v)] -> Map k v
Map.fromList xs = ...
fromList creates a map containing the entries
of the list xs where the keys comes from the first entries of the pairs and
the values from the second. If the same key appears more than once then the last
value is taken.
Map.fromList []
> fromList []
Map.fromList [(1,"uno"), (1,"one"), (2,"two"), (3,"three")]
> fromList [(1,"one"),(2,"two"),(3,"three")]
There’s another incredibly useful function for constructing a map from a list:
Map.fromListWith :: Ord k => (a -> a -> a) -> [(k, a)] -> Map.Map k a
Map.fromListWith f xs = ...
fromListWith allows you to build a map from a
list xs with repeated keys, where f is used to “combine” (or “choose”)
values with the same key.
-- Build a map from a list, but only keep the largest value for each key.
Map.fromListWith max [("a", 2), ("a", 1), ("b", 2)]
> fromList [("a",2),("b",2)]
-- Build a histogram from a list of elements.
Map.fromListWith (+) (map (\x -> (x, 1)) ["a", "a", "b", "c", "c", "c"])
> fromList [("a",2),("b",1),("c",3)]
-- Build a map from a list, combining the string values for the same key.
Map.fromListWith (++) [(1, "a"), (1, "b"), (2, "x"), (2, "y")]
> fromList [(1,"ba"),(2,"yx")]
Create a list from a map¶
Map.toAscList, Map.toList, Map.assocs :: Map k v -> [(k, v)]
Map.toAscList m = ...
Note
These all do the same thing; use toAscList because its name indicates
the ordering.
Note
Map.toList is not the same as Foldable.toList; the latter is
equivalent to elems, although is rarely useful for maps. In general, use
toAscList.
toAscList,
toList, and
assocs returns a list containing the (key,
value) pairs in the map m in ascending key order.
Map.toDescList :: Map k v -> [(k, v)]
Map.toDescList m = ...
toDescList returns a list containing the (key,
value) pairs in the map m in descending key order.
Map.toAscList (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> [(1,"one"),(2,"two"),(3,"three")]
Map.toDescList (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> [(3,"three"),(2,"two"),(1,"one")]
Querying¶
Lookup an entry in the map (lookup)¶
Map.lookup :: Ord k => k -> Map k v -> Maybe v
Map.lookup key m = ...
Map.!? :: Ord k => Map k v -> k -> Maybe v
Map.!? m key = ...
lookup the value corresponding to the given
key, returns Nothing if the key is not present; the !? operator
(since 0.5.10) is a flipped version of lookup and can often be imported
unqualified.
If you want to provide a default value if the key doesn’t exist you can do:
import Data.Maybe (fromMaybe)
-- fromMaybe :: a -> Maybe a -> a
fromMaybe defaultValue (lookup k m)
For example:
import Data.Map.Strict ((!?))
import Data.Maybe (fromMaybe)
Map.lookup 1 Map.empty
> Nothing
Map.lookup 1 (Map.fromList [(1,"one"),(2,"two"),(3,"three")])
> Just "one"
> (Map.fromList [(1,"one"),(2,"two"),(3,"three")]) !? 1
> Just "one"
fromMaybe "?" (Map.empty !? 1)
> "?"
fromMaybe "?" (Map.fromList [(1,"one"), (2,"two"), (3,"three")] !? 1)
> "one"
Warning
DO NOT Use Map.!. It is partial and throws a runtime error if the key
doesn’t exist.
Check if a map is empty¶
Map.null :: Map k v -> Bool
Map.null m = ...
null returns True if the map m is
empty and False otherwise.
Map.null Map.empty
> True
Map.null (Map.fromList [(1,"one")])
> False
The number of entries in a map¶
Map.size :: Map k v -> Int
Map.size m = ...
size returns the number of entries in the map
m.
Map.size Map.empty
> 0
Map.size (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> 3
Find the minimum/maximum¶
Since version 0.5.9
Map.lookupMin, Map.lookupMax :: Map k v -> Maybe (k, v)
Map.lookupMin m = ...
Map.lookupMax m = ...
lookupMin and
lookupMax respectively return the
minimum or maximum element of the map m, or Nothing if the map is empty.
Map.lookupMin Map.empty
> Nothing
Map.lookupMin (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> Just (1,"one")
Map.lookupMax (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> Just (3,"three")
Warning
DO NOT use Map.findMin or Map.findMax. They are partial and throw
a runtime error if the map is empty.
Modification¶
Adding a new entry to a map¶
Map.insert :: Ord k => k -> v -> Map k v -> Map k v
Map.insert key value m = ...
insert adds the value into the map m
with the given key, replacing the existing value if the key already exists.
Map.insert 1 "one" Map.empty
> Map.fromList [(1,"one")]
Map.insert 4 "four" (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"one"),(2,"two"),(3,"three"),(4,"four")]
Map.insert 1 "uno" (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"uno"),(2,"two"),(3,"three")]
Removing an entry from a map¶
Map.delete :: Ord k => k -> Map k v -> Map k v
Map.delete key m = ...
delete removes the entry with the specified
key from the map m. If the key doesn’t exist it leaves the map
unchanged.
Map.delete 1 Map.empty
> Map.empty
Map.delete 1 (Map.fromList [(1,"one"),(2,"two"),(3,"three")])
> fromList [(2,"two"),(3,"three")]
Filtering map entries¶
Map.filterWithKey :: (k -> v -> Bool) -> Map k v -> Map k v
Map.filterWithKey predicate m = ...
filterWithKey produces a map consisting of all
entries of m for which the predicate returns True.
let f key value = key == 2 || value == "one"
Map.filterWithKey f (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"one"),(2,"two"]
Modifying a map entry¶
Map.adjust :: Ord k => (v -> v) -> k -> Map k v -> Map k v
Map.adjust f key m = ...
adjust applies the value transformation
function f to the entry with given key. If no entry for that key exists
then the map is left unchanged.
Map.alter :: Ord k => (Maybe v -> Maybe v) -> k -> Map k v -> Map k v
Map.alter f key m = ...
Apply the value transformation function f to the entry with given key,
if no entry for that key exists then the function is passed Nothing. If the
function returns Nothing then the entry is deleted, if the function returns
Just v2 then the value for the key is updated to v2. In other words,
alter can be used to insert, update, or delete a value.
import Data.Maybe (isJust)
let addValueIfMissing mv = if isJust mv then mv else (Just 1)
Map.alter addValueIfMissing "key" (Map.fromList [("key", 0)])
> fromList [("key",0)]
let addValueIfMissing mv = if isJust mv then mv else (Just 1)
Map.alter addValueIfMissing "new_key" (Map.fromList [("key", 0)])
> fromList [("key",0),("new_key",1)]
The function doubleIfPositive below will need to be placed in a Haskell
source file.
doubleIfPositive :: Maybe Int -> Maybe Int
doubleIfPositive mv = case mv of
-- Do nothing if the key doesn't exist.
Nothing -> Nothing
-- If the key does exist, double the value if it is positive.
Just v -> if v > 0 then (Just v*2) else (Just v)
-- In GHCi
Map.alter doubleIfPositive "a" (Map.fromList [("a", 1), ("b", -1)])
> Map.fromList [("a",2), ("b",-1)]
Map.alter doubleIfPositive "b" (Map.fromList [("a", 1), ("b", -1)])
> Map.fromList [("a", 1), ("b",-1)]
Modifying all map entries (mapping and traversing)¶
Map.map :: (a -> b) -> Map k a -> Map k v
Map.map f m = ...
Map.mapWithKey :: (k -> a -> b) -> Map.Map k a -> Map.Map k b
Map.mapWithKey g m = ...
map creates a new map by applying the
transformation function f to each entries value. This is how Functor is defined for maps.
mapWithKey does the same as map but gives
you access to the key in the transformation function g.
Map.map (*10) (Map.fromList [("haskell", 45), ("idris", 15)])
> fromList [("haskell",450),("idris",150)]
-- Use the Functor instance for Map.
(*10) <$> Map.fromList [("haskell", 45), ("idris", 15)]
> fromList [("haskell",450),("idris",150)]
let g key value = if key == "haskell" then (value * 1000) else value
Map.mapWithKey g (Map.fromList [("haskell", 45), ("idris", 15)])
> fromList [("haskell",45000),("idris",15)]
You can also apply a function which performs actions (such as printing) to each entry in the map.
Map.traverseWithKey :: Applicative t => (k -> a -> t b) -> Map.Map k a -> t (Map.Map k b)
Map.traverseWithKey f m = ...
traverseWithKey maps each element of the map
m to an action that produces a result of type b. The actions are
performed and the values of the map are replaced with the results from the
function. You can think of this as a map with affects.
-- | Ask the user how they want to schedule a bunch of tasks
-- that the boss has assigned certain priorities.
makeSchedule :: Map Task Priority -> IO (Map Task DateTime)
makeSchedule = traverseWithKey $ \task priority ->
do
putStrLn $ "The boss thinks " ++ show task ++
" has priority " ++ show priority ++
". When do you want to do it?"
readLn
Set-like Operations¶
Union¶
Map.unionWith :: Ord k => (v -> v -> v) -> Map k v -> Map k v -> Map k v
Map.unionWith f l r = ...
union returns a map containing all entries that
are keyed in either of the two maps. If the same key appears in both maps, the
value is determined by calling f passing in the left and right value (set
union).
Map.unionWith (++) Map.empty (Map.fromList [(1,"x"),(2,"y")])
> fromList [(1,"x"),(2,"y")]
let f lv rv = lv
Map.unionWith f (Map.fromList [(1, "a")]) (Map.fromList [(1,"x"),(2,"y")])
> fromList [(1,"a"),(2,"y")]
Map.unionWith (++) (Map.fromList [(1, "a")]) (Map.fromList [(1,"x"),(2,"y")])
> fromList [(1,"ax"),(2,"y")]
Intersection¶
Map.intersectionWith :: Ord k => (v -> v -> v) -> Map k v -> Map k v -> Map k v
Map.intersectionWith f l r = ...
intersection returns a map containing all
entries that have a key in both maps l and r. The value in the returned
map is determined by calling f on the values from the left and right map
(set intersection).
Map.intersectionWith (++) Map.empty (Map.fromList [(1,"x"), (2,"y")])
> fromList []
Map.intersectionWith (++) (Map.fromList [(1, "a")]) (Map.fromList [(1,"x"),(2,"y")])
> fromList [(1,"ax")]
Difference¶
Map.difference :: Ord k => Map k v -> Map k v -> Map k v
Map.difference l r = ...
difference returns a map containing all entries
that have a key in the l map but not the r map (set difference/relative
complement).
Map.difference (Map.fromList [(1,"one"), (2,"two"), (3,"three")]) Map.empty
> fromList [(1,"uno"),(2,"two"),(3,"three")]
Map.difference (Map.fromList[(1,"one"), (2,"two")]) (Map.fromList [(1,"uno")])
> fromList [(2,"two")]
Serialization¶
The best way to serialize and deserialize maps is to use one of the many libraries which already support serializing maps. binary, cereal, and store are some common libraries that people use.
Tip
If you are writing custom serialization code use fromDistinctAscList (see #405 for more info).
Performance¶
The API docs are annotated with the Big-O complexities of each of the map operations. For benchmarks see the haskell-perf/dictionaries page.
