Operators
--------------------------------------------------------------------}
--- | /O(min(n,W))/. Find the value of a key. Calls 'error' when the element can not be found.
+-- | /O(min(n,W))/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
(!) :: IntMap a -> Key -> a
m ! k = find' k m
Nothing -> False
Just x -> True
--- | /O(min(n,W))/. Lookup the value of a key in the map.
+-- | /O(min(n,W))/. Lookup the value at a key in the map.
lookup :: Key -> IntMap a -> Maybe a
lookup k t
= let nk = natFromInt k in seq nk (lookupN nk t)
-- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
--- returns the value of key @k@ or returns @def@ when the key is not an
+-- returns the value at key @k@ or returns @def@ when the key is not an
-- element of the map.
findWithDefault :: a -> Key -> IntMap a -> a
findWithDefault def k m
Nil -> Nil
-- | /O(n)/. The function @'mapAccum'@ threads an accumulating
--- argument through the map in an unspecified order.
+-- argument through the map in ascending order of keys.
mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccum f a m
= mapAccumWithKey (\a k x -> f a x) a m
-- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
--- argument through the map in an unspecified order.
+-- argument through the map in ascending order of keys.
mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumWithKey f a t
= mapAccumL f a t
-- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
--- argument through the map in pre-order.
+-- argument through the map in ascending order of keys.
mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumL f a t
= case t of
-- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
--- argument throught the map in post-order.
+-- argument throught the map in descending order of keys.
mapAccumR :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumR f a t
= case t of
{--------------------------------------------------------------------
Fold
--------------------------------------------------------------------}
--- | /O(n)/. Fold over the elements of a map in an unspecified order.
+-- | /O(n)/. Fold the values in the map, such that
+-- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
+-- For example,
--
--- > sum map = fold (+) 0 map
-- > elems map = fold (:) [] map
+--
fold :: (a -> b -> b) -> b -> IntMap a -> b
fold f z t
= foldWithKey (\k x y -> f x y) z t
--- | /O(n)/. Fold over the elements of a map in an unspecified order.
+-- | /O(n)/. Fold the keys and values in the map, such that
+-- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
+-- For example,
--
-- > keys map = foldWithKey (\k x ks -> k:ks) [] map
+--
foldWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldWithKey f z t
= foldr f z t
{--------------------------------------------------------------------
List variations
--------------------------------------------------------------------}
--- | /O(n)/. Return all elements of the map.
+-- | /O(n)/.
+-- Return all elements of the map in the ascending order of their keys.
elems :: IntMap a -> [a]
elems m
= foldWithKey (\k x xs -> x:xs) [] m
--- | /O(n)/. Return all keys of the map.
+-- | /O(n)/. Return all keys of the map in ascending order.
keys :: IntMap a -> [Key]
keys m
= foldWithKey (\k x ks -> k:ks) [] m
keysSet m = IntSet.fromDistinctAscList (keys m)
--- | /O(n)/. Return all key\/value pairs in the map.
+-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
assocs :: IntMap a -> [(Key,a)]
assocs m
= toList m
--------------------------------------------------------------------}
infixl 9 !,\\ --
--- | /O(log n)/. Find the value of a key. Calls 'error' when the element can not be found.
+-- | /O(log n)/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
(!) :: Ord k => Map k a -> k -> a
m ! k = find k m
Bin sz k x l r -> sz
--- | /O(log n)/. Lookup the value of key in the map.
+-- | /O(log n)/. Lookup the value at a key in the map.
lookup :: Ord k => k -> Map k a -> Maybe a
lookup k t
= case t of
Nothing -> False
Just x -> True
--- | /O(log n)/. Find the value of a key. Calls 'error' when the element can not be found.
+-- | /O(log n)/. Find the value at a key.
+-- Calls 'error' when the element can not be found.
find :: Ord k => k -> Map k a -> a
find k m
= case lookup k m of
Just x -> x
-- | /O(log n)/. The expression @('findWithDefault' def k map)@ returns
--- the value of key @k@ or returns @def@ when the key is not in the map.
+-- the value at key @k@ or returns @def@ when the key is not in the map.
findWithDefault :: Ord k => a -> k -> Map k a -> a
findWithDefault def k m
= case lookup k m of
empty
= Tip
--- | /O(1)/. Create a map with a single element.
+-- | /O(1)/. A map with a single element.
singleton :: k -> a -> Map k a
singleton k x
= Bin 1 k x Tip Tip
deleteMax (Bin _ kx x l r) = balance kx x l (deleteMax r)
deleteMax Tip = Tip
--- | /O(log n)/. Update the minimal key.
+-- | /O(log n)/. Update the value at the minimal key.
updateMin :: (a -> Maybe a) -> Map k a -> Map k a
updateMin f m
= updateMinWithKey (\k x -> f x) m
--- | /O(log n)/. Update the maximal key.
+-- | /O(log n)/. Update the value at the maximal key.
updateMax :: (a -> Maybe a) -> Map k a -> Map k a
updateMax f m
= updateMaxWithKey (\k x -> f x) m
--- | /O(log n)/. Update the minimal key.
+-- | /O(log n)/. Update the value at the minimal key.
updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey f t
= case t of
Bin sx kx x l r -> balance kx x (updateMinWithKey f l) r
Tip -> Tip
--- | /O(log n)/. Update the maximal key.
+-- | /O(log n)/. Update the value at the maximal key.
updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey f t
= case t of
= Bin sx kx (f kx x) (mapWithKey f l) (mapWithKey f r)
-- | /O(n)/. The function 'mapAccum' threads an accumulating
--- argument through the map in an unspecified order.
+-- argument through the map in ascending order of keys.
mapAccum :: (a -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccum f a m
= mapAccumWithKey (\a k x -> f a x) a m
-- | /O(n)/. The function 'mapAccumWithKey' threads an accumulating
--- argument through the map in unspecified order. (= ascending pre-order)
+-- argument through the map in ascending order of keys.
mapAccumWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumWithKey f a t
= mapAccumL f a t
-- | /O(n)/. The function 'mapAccumL' threads an accumulating
--- argument throught the map in (ascending) pre-order.
+-- argument throught the map in ascending order of keys.
mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumL f a t
= case t of
in (a3,Bin sx kx x' l' r')
-- | /O(n)/. The function 'mapAccumR' threads an accumulating
--- argument throught the map in (descending) post-order.
+-- argument throught the map in descending order of keys.
mapAccumR :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumR f a t
= case t of
-- | /O(n*log n)/.
-- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@.
--
--- It's worth noting that the size of the result may be smaller if,
--- for some @(x,y)@, @x \/= y && f x == f y@
+-- The size of the result may be smaller if @f@ maps two or more distinct
+-- keys to the same new key. In this case the value at the smallest of
+-- these keys is retained.
mapKeys :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a
mapKeys = mapKeysWith (\x y->x)
-- | /O(n*log n)/.
-- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
--
--- It's worth noting that the size of the result may be smaller if,
--- for some @(x,y)@, @x \/= y && f x == f y@
--- In such a case, the values will be combined using @c@
+-- The size of the result may be smaller if @f@ maps two or more distinct
+-- keys to the same new key. In this case the associated values will be
+-- combined using @c@.
mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a
mapKeysWith c f = fromListWith c . List.map fFirst . toList
-- | /O(n)/.
--- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@ is monotonic.
+-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
+-- is strictly monotonic.
-- /The precondition is not checked./
-- Semi-formally, we have:
--
{--------------------------------------------------------------------
Folds
--------------------------------------------------------------------}
--- | /O(n)/. Fold the map in an unspecified order. (= descending post-order).
+
+-- | /O(n)/. Fold the values in the map, such that
+-- @'fold' f z == 'Prelude.foldr' f z . 'elems'@.
+-- For example,
+--
+-- > elems map = fold (:) [] map
+--
fold :: (a -> b -> b) -> b -> Map k a -> b
fold f z m
= foldWithKey (\k x z -> f x z) z m
--- | /O(n)/. Fold the map in an unspecified order. (= descending post-order).
+-- | /O(n)/. Fold the keys and values in the map, such that
+-- @'foldWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
+-- For example,
+--
+-- > keys map = foldWithKey (\k x ks -> k:ks) [] map
+--
foldWithKey :: (k -> a -> b -> b) -> b -> Map k a -> b
foldWithKey f z t
= foldr f z t
{--------------------------------------------------------------------
List variations
--------------------------------------------------------------------}
--- | /O(n)/. Return all elements of the map.
+-- | /O(n)/.
+-- Return all elements of the map in the ascending order of their keys.
elems :: Map k a -> [a]
elems m
= [x | (k,x) <- assocs m]
--- | /O(n)/. Return all keys of the map.
+-- | /O(n)/. Return all keys of the map in ascending order.
keys :: Map k a -> [k]
keys m
= [k | (k,x) <- assocs m]
keysSet :: Map k a -> Set.Set k
keysSet m = Set.fromDistinctAscList (keys m)
--- | /O(n)/. Return all key\/value pairs in the map.
+-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
assocs :: Map k a -> [(k,a)]
assocs m
= toList m
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