d      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcNoneBdChecks if two pointers are equal. Yes means yes; no means maybe. The values should be forced to at least WHNF before comparison to get moderately reliable results.eChecks if two pointers are equal, without requiring them to have the same type. The values should be forced to at least WHNF before comparison to get moderately reliable results.dededed4e4Safe %&+0DQRT fA strict pair. Dependent maps: k is a GADT-like thing with a facility for rediscovering its type parameter, elements of which function as identifiers tagged with the type of the thing they identify. Real GADTs are one useful instantiation of k , as are Tags from Data.Unique.Tag in the  'prim-uniq' package.Semantically,   k f is equivalent to a set of  k f* where no two elements have the same tag.More informally,   is to dependent products as  is to (->)i. Thus it could also be thought of as a partial (in the sense of "partial function") dependent product. O(1). The empty map. )empty == fromList [] size empty == 0 O(1). A map with a single element. Isingleton 1 'a' == fromList [(1, 'a')] size (singleton 1 'a') == 1O(1). Is the map empty?O(1)$. The number of elements in the map.O(log n)'. Lookup the value at a key in the map.4The function will return the corresponding value as (g value), or h if the key isn't in the map.O(log n)&. Delete and find the minimal element. deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")]) deleteFindMin Error: can not return the minimal element of an empty mapi Convert a strict pair to a pair.j$Convert a strict triple to a triple.O(log n)d. Retrieves the minimal (key :=> value) entry of the map, and the map stripped of that element, or h if passed an empty map.O(log n)d. Retrieves the maximal (key :=> value) entry of the map, and the map stripped of that element, or h if passed an empty map.O(log n)&. Delete and find the maximal element. deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")]) deleteFindMax empty Error: can not return the maximal element of an empty map&klfm no pqrstuijvwxyz{|}~&klfm on pqrstuijvwxyz{|}~"klfm no pqrstuijvwxyz{|}~f1m1 Trustworthy %&+DOQRTMO(log n)". Find the value at a key. Calls # when the element can not be found. gfromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map fromList [(5,'a'), (3,'b')] ! 5 == 'a'Same as :.O(log n)+. Is the key a member of the map? See also .O(log n)/. Is the key not a member of the map? See also .O(log n)". Find the value at a key. Calls 4 when the element can not be found. Consider using " when elements may not be present.O(log n). The expression ( def k map) returns the value at key k or returns default value def! when the key is not in the map.O(log n). Insert a new key and value in the map. If the key is already present in the map, the associated value is replaced with the supplied value.  is equivalent to  .O(log n)k. Insert a new key and value in the map if the key is not already present. If the key is already present, insertR does nothing.O(log n)>. Insert with a function, combining new value and old value.  f key value mp will insert the entry  key :=> value into mp_ if key does not exist in the map. If the key does exist, the function will insert the entry key :=> f new_value old_value.Same as ], but the combining function is applied strictly. This is often the most desirable behavior.O(log n)C. Insert with a function, combining key, new value and old value.  f key value mp will insert the entry  key :=> value into mp_ if key does not exist in the map. If the key does exist, the function will insert the entry !key :=> f key new_value old_value;. Note that the key passed to f is the same key passed to .Same as 1, but the combining function is applied strictly.O(log n)G. Combines insert operation with old value retrieval. The expression ( f k x map2) is a pair where the first element is equal to ( k map$) and the second element equal to ( f k x map). O(log n). A strict version of .!O(log n)r. Delete a key and its value from the map. When the key is not a member of the map, the original map is returned."O(log n). Update a value at a specific key with the result of the provided function. When the key is not a member of the map, the original map is returned.#O(log n)k. Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.$O(log n). A strict version of #.%O(log n). The expression (% f k map) updates the value x at k (if it is in the map). If (f x) is h%, the element is deleted. If it is (g y ), the key k is bound to the new value y.&O(log n). The expression (& f k map) updates the value x at k (if it is in the map). If (f k x) is h%, the element is deleted. If it is (g y ), the key k is bound to the new value y.'O(log n). Lookup and update. See also &v. The function returns changed value, if it is updated. Returns the original key value if the map entry is deleted. (O(log n). The expression (( f k map) alters the value x at k, or absence thereof. (7 can be used to insert, delete, or update a value in a Map. In short :  k (( f k m) = f ( k m).)O(log n) . Return the index' of a key. The index is a number from 0 up to, but not including, the  of the map. Calls  when the key is not a  of the map.*O(log n) . Lookup the index' of a key. The index is a number from 0 up to, but not including, the  of the map.+O(log n). Retrieve an element by index. Calls  when an invalid index is used.,O(log n). Update the element at index.. Does nothing when an invalid index is used.-O(log n). Delete the element at index. Defined as (- i map = , (k x -> h) i map)..O(log n)$. The minimal key of the map. Calls  is the map is empty.0O(log n)$. The maximal key of the map. Calls  is the map is empty.2O(log n)C. Delete the minimal key. Returns an empty map if the map is empty.3O(log n)C. Delete the maximal key. Returns an empty map if the map is empty.4O(log n)&. Update the value at the minimal key.5O(log n)&. Update the value at the maximal key.6!The union of a list of maps: (6 ==  8  ).7=The union of a list of maps, with a combining operation: (7 f ==  (9 f)  ).8O(m*log(n/m + 1)), m <= n. The expression (8 t1 t2!) takes the left-biased union of t1 and t2. It prefers t1- when duplicate keys are encountered, i.e. (8 ==  unionWith ).9O(n+m)#. Union with a combining function.:O(m * log (n/m + 1)), m <= n\. Difference of two maps. Return elements of the first map not existing in the second map.;O(n+m). Difference with a combining function. When two equal keys are encountered, the combining function is applied to the key and both values. If it returns hD, the element is discarded (proper set difference). If it returns (g y+), the element is updated with a new value y. <O(m * log (n/m + 1), m <= n`. Intersection of two maps. Return data in the first map for the keys existing in both maps. (< m1 m2 == intersectionWith  m1 m2).=O(m * log (n/m + 1), m <= n). Intersection with a combining function.>O(n+m) . This function is defined as (> = ? )).?O(n+m). The expression (? f t1 t2 ) returns  if all keys in t1 are in tree t2 , and when f returns 3 when applied to their respective keys and values.@O(n+m)G. Is this a proper submap? (ie. a submap but not equal). Defined as (@ = A ).AO(n+m)J. Is this a proper submap? (ie. a submap but not equal). The expression (A f m1 m2 ) returns  when m1 and m2 are not equal, all keys in m1 are in m2 , and when f returns 4 when applied to their respective keys and values. BO(n)4. Filter all keys/values that satisfy the predicate.CO(n). Partition the map according to a predicate. The first map contains all elements that satisfy the predicate, the second all elements that fail the predicate. See also Z.DO(n)". Map keys/values and collect the g results.EO(n)#. Map keys/values and separate the  and  results.FO(n),. Map a function over all values in the map.GO(n),. Map a function over all values in the map.HO(n). H f m == R  $  ((k, v) -> (,) k  $ f k v) (T m)* That is, behaves exactly like a regular Y except that the traversing function also has access to the key associated with a value.IO(n). The function IO threads an accumulating argument throught the map in ascending order of keys.JO(n). The function JO threads an accumulating argument through the map in descending order of keys.K O(n*log n). K c f s! is the map obtained by applying f to each key of s.)The size of the result may be smaller if fr maps two or more distinct keys to the same new key. In this case the associated values will be combined using c.LO(n). L f s == mapKeys f s, but works only when f2 is strictly monotonic. That is, for any values x and y, if x < y then f x < f y.  The precondition is not checked. Semi-formally, we have: and [x < y ==> f x < f y | x <- ls, y <- ls] ==> mapKeysMonotonic f s == mapKeys f s where ls = keys sThis means that fd maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys.MO(n)2. Fold the keys and values in the map, such that M f z ==  ( f) z . U.This is identical to Nb, and you should use that one instead of this one. This name is kept for backward compatibility.NO(n)W. Post-order fold. The function will be applied from the lowest value to the highest.OO(n)V. Pre-order fold. The function will be applied from the highest value to the lowest.PO(n)0. Return all keys of the map in ascending order. <keys (fromList [(5,"a"), (3,"b")]) == [3,5] keys empty == []QO(n)?. Return all key/value pairs in the map in ascending key order.R O(n*log n)7. Build a map from a list of key/value pairs. See also Wf. If the list contains more than one value for the same key, the last value for the key is retained.S O(n*log n)Q. Build a map from a list of key/value pairs with a combining function. See also X.TO(n)'. Convert to a list of key/value pairs.UO(n). Convert to an ascending list.VO(n). Convert to a descending list.WO(n)6. Build a map from an ascending list in linear time. :The precondition (input list is ascending) is not checked.XO(n)`. Build a map from an ascending list in linear time with a combining function for equal keys. :The precondition (input list is ascending) is not checked.YO(n)K. Build a map from an ascending list of distinct elements in linear time.  The precondition is not checked.ZO(log n). The expression (Z k map ) is a pair  (map1,map2) where the keys in map1 are smaller than k and the keys in map2 larger than k. Any key equal to k is found in neither map1 nor map2.[O(log n). The expression ([ k map) splits a map just like Z but also returns  k map.O(log n). The expression ( k map) splits a map just like Z but also returns  k map.O(log n).\O(n)a. Show the tree that implements the map. The tree is shown in a compressed, hanging format. See ].]O(n). The expression (] showelem hang wide mapH) shows the tree that implements the map. Elements are shown using the showElem function. If hang is , a hanging6 tree is shown otherwise a rotated tree is shown. If wide is !, an extra wide version is shown.^O(n).. 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