Hash Maps

Maps (sometimes referred to as dictionaries in other languages) allow you to store associations between unique keys and values. There are two implementations provided by the unordered-containers package: Data.HashMap.Strict and Data.HashMap.Lazy. You almost never want the lazy version so use Data.Map.Strict, and if your keys are Int consider using Data.IntMap from the containers package which is faster for many operations.

data HashMap k v = ...

Important

HashMap relies on the key type k having instances of the Eq and Hashable typeclasses 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 = HashMap.fromList [("a", 1), ("b", 2)]
let m2 = HashMap.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 hash map functionality:

import qualified Data.HashMap.Strict as HashMap

let nums = HashMap.fromList [(1,"one"), (2,"two"), (3,"three")]

-- Get the English word for the number 3 and 4.
HashMap.lookup 3 nums
> Just "three"

HashMap.lookup 4 nums
> Nothing


-- Add (4, "four") to our original map.
let moreNums = HashMap.insert 4 "four" nums

HashMap.member 4 moreNums
> True


-- Remove the entry for 1 from our original map.
let fewerNums = HashMap.delete 1 nums

HashMap.toList 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 = HashMap.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.
HashMap.union newNums nums
> fromList [(1,"one"),(2,"two"),(3,"new three"),(4,"newer four")]

Tip

You can use the OverloadedLists 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 HashMap

When using HashMap 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 HashMap. 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 (HashMap).

import Prelude hiding (lookup)

import Data.HashMap.Strict (HashMap)
import qualified Data.HashMap.Strict as HashMap

Common API Functions

Note

A HashMap 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

HashMap.empty :: HashMap k v
HashMap.empty = ...

empty creates a map without any entries.

HashMap.empty
> fromList []

Create a map with one entry (singleton)

HashMap.singleton :: k -> v -> HashMap k v
HashMap.singleton key value = ...

singleton creates a map with a single (key,value) entry in it.

HashMap.singleton 1 "one"
> fromList [(1,"one")]

HashMap.singleton "containers" ["base"]
> fromList [("containers",["base"])]

Create a map from a list

HashMap.fromList :: [(k, v)] -> HashMap k v
HashMap.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.

HashMap.fromList []
> fromList []

HashMap.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:

HashMap.fromListWith :: (a -> a -> a) -> [(k, a)] -> HashMap k a
HashMap.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.
HashMap.fromListWith max [("a", 2), ("a", 1), ("b", 2)]
> fromList [("a",2),("b",2)]

-- Build a histogram from a list of elements.
HashMap.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.
HashMap.fromListWith (++) [(1, "a"), (1, "b"), (2, "x"), (2, "y")]
> fromList [(1,"ba"),(2,"yx")]

Create a list from a map

HashMap.toList :: HashMap k v -> [(k, v)]
HashMap.toList m = ...

Note

HashMap.toList is not the same as Foldable.toList; the latter is equivalent to elems, although is rarely useful for maps.

toList returns a list containing the (key, value) pairs in the map m, the order is unspecified.

HashMap.toList (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")])
> [(1,"one"),(2,"two"),(3,"three")]

HashMap.toList (HashMap.fromList [(1,"one"), (2,"two"), (-3,"negative three")])
> [(1,"one"),(2,"two"),(-3,"negative three")]

Querying

Lookup an entry in the map (lookup)

HashMap.lookup :: k -> HashMap k v -> Maybe v
HashMap.lookup key m = ...

lookup the value corresponding to the given key, returns Nothing if the key is not present.

If you want to provide a default value if the key doesn’t exist you can use:

HashMap.lookupDefault :: v -> k -> HashMap k v -> v
HashMap.lookupDefault defaultVal key m = ...

For example:

import Data.HashMap.Strict ((!?))

HashMap.lookup 1 HashMap.empty
> Nothing

HashMap.lookup 1 (HashMap.fromList [(1,"one"),(2,"two"),(3,"three")])
> Just "one"

> (HashMap.fromList [(1,"one"),(2,"two"),(3,"three")]) !? 1
> Just "one"

HashMap.lookupDefault "?" k HashMap.empty
> "?"

HashMap.lookupDefault "?" 1 (Map.fromList [(1,"one"), (2,"two"), (3,"three")])
> "one"

Warning

HashMap.!? is a partial function and throws a runtime error if the key doesn’t exist. DO NOT use it if you are expecting a total function or cannot tolerate a runtime failure; prefer to use lookup.

Check if a map is empty

HashMap.null :: HashMap k v -> Bool
HashMap.null m = ...

null returns True if the map m is empty and False otherwise.

HashMap.null HashMap.empty
> True

HashMap.null (HashMap.fromList [(1,"one")])
> False

The number of entries in a map

HashMap.size :: HashMap k v -> Int
HashMap.size m = ...

size returns the number of entries in the map m.

HashMap.size HashMap.empty
> 0

HashMap.size (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")])
> 3

Modification

Adding a new entry to a map

HashMap.insert :: k -> v -> HashMap k v -> HashMap k v
HashMap.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.

HashMap.insert 1 "one" HashMap.empty
> HashMap.fromList [(1,"one")]

HashMap.insert 4 "four" (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"one"),(2,"two"),(3,"three"),(4,"four")]

HashMap.insert 1 "uno" (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"uno"),(2,"two"),(3,"three")]

Removing an entry from a map

HashMap.delete :: k -> HashMap k v -> HashMap k v
HashMap.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.

HashMap.delete 1 HashMap.empty
> HashMap.empty

HashMap.delete 1 (HashMap.fromList [(1,"one"),(2,"two"),(3,"three")])
> fromList [(2,"two"),(3,"three")]

Filtering map entries

HashMap.filterWithKey :: (k -> v -> Bool) -> HashMap k v -> HashMap k v
HashMap.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"
HashMap.filterWithKey f (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")])
> fromList [(1,"one"),(2,"two"]

Modifying a map entry

HashMap.adjust :: (v -> v) -> k -> HashMap k v -> HashMap k v
HashMap.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.

HashMap.alter :: (Maybe v -> Maybe v) -> k -> HashMap k v -> HashMap k v
HashMap.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)
HashMap.alter addValueIfMissing "key" (HashMap.fromList [("key", 0)])
> fromList [("key",0)]

let addValueIfMissing mv = if isJust mv then mv else (Just 1)
HashMap.alter addValueIfMissing "new_key" (HashMap.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
HashMap.alter doubleIfPositive "a" (HashMap.fromList [("a", 1), ("b", -1)])
> HashMap.fromList [("a",2), ("b",-1)]

HashMap.alter doubleIfPositive "b" (HashMap.fromList [("a", 1), ("b", -1)])
> HashMap.fromList [("a", 1), ("b",-1)]

Modifying all map entries (mapping and traversing)

HashMap.map :: (a -> b) -> HashMap k a -> HashMap k v
HashMap.map f m = ...

HashMap.mapWithKey :: (k -> a -> b) -> HashMap k a -> hashMap k b
HashMap.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.

HashMap.map (*10) (HashMap.fromList [("haskell", 45), ("idris", 15)])
> fromList [("haskell",450),("idris",150)]

-- Use the Functor instance for Map.
(*10) <$> HashMap.fromList [("haskell", 45), ("idris", 15)]
> fromList [("haskell",450),("idris",150)]

let g key value = if key == "haskell" then (value * 1000) else value
HashMap.mapWithKey g (HashMap.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.

HashMap.traverseWithKey :: Applicative t => (k -> a -> t b) -> HashMap k a -> t (HashMap k b)
HashMap.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 :: HashMap Task Priority -> IO (HashMap 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

HashMap.unionWith :: (v -> v -> v) -> HashMap k v -> HashMap k v -> HashMap k v
HashMap.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).

HashMap.unionWith (++) HashMap.empty (HashMap.fromList [(1,"x"),(2,"y")])
> fromList [(1,"x"),(2,"y")]

let f lv rv = lv
HashMap.unionWith f (HashMap.fromList [(1, "a")]) (HashMap.fromList [(1,"x"),(2,"y")])
> fromList [(1,"a"),(2,"y")]

HashMap.unionWith (++) (HashMap.fromList [(1, "a")]) (HashMap.fromList [(1,"x"),(2,"y")])
> fromList [(1,"ax"),(2,"y")]

Intersection

HashMap.intersectionWith :: (v -> v -> v) -> HashMap k v -> HashMap k v -> HashMap k v
HashMap.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).

HashMap.intersectionWith (++) HashMap.empty (HashMap.fromList [(1,"x"), (2,"y")])
> fromList []

HashMap.intersectionWith (++) (HashMap.fromList [(1, "a")]) (HashMap.fromList [(1,"x"),(2,"y")])
> fromList [(1,"ax")]

Difference

HashMap.difference :: HashMap k v -> HashMap k v -> HashMap k v
HashMap.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).

HashMap.difference (HashMap.fromList [(1,"one"), (2,"two"), (3,"three")]) HashMap.empty
> fromList [(1,"uno"),(2,"two"),(3,"three")]

HashMap.difference (HashMap.fromList[(1,"one"), (2,"two")]) (HashMap.fromList [(1,"uno")])
> fromList [(2,"two")]

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.

Looking for more?

Didn’t find what you’re looking for? This tutorial only covered the most common map functions, for a full list of functions see the HashMap API documentation.