h&4/2*      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\ Safe-Inferred)*051dependent-monoidal-mapO(1). The empty map. )empty == fromList [] size empty == 0dependent-monoidal-mapO(1). A map with a single element. singleton 1 'a' == fromList [(1, 'a')] size (singleton 1 'a') == 1dependent-monoidal-mapO(1). Is the map empty? dependent-monoidal-mapO(1)$. The number of elements in the map. dependent-monoidal-mapO(log n)'. Lookup the value at a key in the map.4The function will return the corresponding value as (] value), or ^ if the key isn't in the map. dependent-monoidal-mapO(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 map dependent-monoidal-mapO(log n). Retrieves the minimal (key :=> value) entry of the map, and the map stripped of that element, or ^ if passed an empty map. dependent-monoidal-mapO(log n). Retrieves the maximal (key :=> value) entry of the map, and the map stripped of that element, or ^ if passed an empty map.dependent-monoidal-mapO(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 mapdependent-monoidal-mapO(log n)+. Is the key a member of the map? See also .dependent-monoidal-mapO(log n)/. Is the key not a member of the map? See also .dependent-monoidal-mapO(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.dependent-monoidal-mapO(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.dependent-monoidal-mapO(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  `.dependent-monoidal-mapO(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.dependent-monoidal-mapSame as , but the combining function is applied strictly. This is often the most desirable behavior.dependent-monoidal-mapO(log n). 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 .dependent-monoidal-mapSame as 1, but the combining function is applied strictly.dependent-monoidal-mapO(log n). 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$) and the second element equal to ( f k x map).dependent-monoidal-mapO(log n). A strict version of .dependent-monoidal-mapO(log n). Delete a key and its value from the map. When the key is not a member of the map, the original map is returned.dependent-monoidal-mapO(log n). Update a value at a specific key with the result of the provided function. When the key is not a member of the map, the original map is returned.dependent-monoidal-mapO(log n). Adjust a value at a specific key. When the key is not a member of the map, the original map is returned.dependent-monoidal-mapO(log n). A strict version of .dependent-monoidal-mapO(log n). The expression ( f k map) updates the value x at k (if it is in the map). If (f x) is ^%, the element is deleted. If it is (] y ), the key k is bound to the new value y.dependent-monoidal-mapO(log n). The expression ( f k map) updates the value x at k (if it is in the map). If (f k x) is ^%, the element is deleted. If it is (] y ), the key k is bound to the new value y. dependent-monoidal-mapO(log n). Lookup and update. See also . The function returns changed value, if it is updated. Returns the original key value if the map entry is deleted.!dependent-monoidal-mapO(log n). The expression (! f k map) alters the value x at k, or absence thereof. !7 can be used to insert, delete, or update a value in a Map. In short :   k (! f k m) = f (  k m)."dependent-monoidal-mapO(log n) . Return the index' of a key. The index is a number from 0 up to, but not including, the   of the map. Calls _ when the key is not a  of the map.#dependent-monoidal-mapO(log n) . Lookup the index' of a key. The index is a number from 0 up to, but not including, the   of the map.$dependent-monoidal-mapO(log n). Retrieve an element by index. Calls _ when an invalid index is used.%dependent-monoidal-mapO(log n). Update the element at index.. Does nothing when an invalid index is used.&dependent-monoidal-mapO(log n). Delete the element at index. Defined as (& i map = % (k x -> ^) i map).'dependent-monoidal-mapO(log n)$. The minimal key of the map. Calls _ is the map is empty.)dependent-monoidal-mapO(log n)$. The maximal key of the map. Calls _ is the map is empty.+dependent-monoidal-mapO(log n). Delete the minimal key. Returns an empty map if the map is empty.,dependent-monoidal-mapO(log n). Delete the maximal key. Returns an empty map if the map is empty.-dependent-monoidal-mapO(log n)&. Update the value at the minimal key..dependent-monoidal-mapO(log n)&. Update the value at the maximal key./dependent-monoidal-map=The union of a list of maps, with a combining operation: (/ f == a (0 f) ).0dependent-monoidal-mapO(n+m)#. Union with a combining function.1dependent-monoidal-mapO(m * log (n/m + 1)), m <= n. Difference of two maps. Return elements of the first map not existing in the second map.2dependent-monoidal-mapO(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 ^, the element is discarded (proper set difference). If it returns (] y+), the element is updated with a new value y.3dependent-monoidal-mapO(m * log (n/m + 1), m <= n). Intersection with a combining function.4dependent-monoidal-mapO(n+m) . This function is defined as (4 = 5 b)).5dependent-monoidal-mapO(n+m). The expression (5 f t1 t2 ) returns c if all keys in t1 are in tree t2 , and when f returns c3 when applied to their respective keys and values.6dependent-monoidal-mapO(n+m). Is this a proper submap? (ie. a submap but not equal). Defined as (6 = 7 b).7dependent-monoidal-mapO(n+m). Is this a proper submap? (ie. a submap but not equal). The expression (7 f m1 m2 ) returns c when m1 and m2 are not equal, all keys in m1 are in m2 , and when f returns c3 when applied to their respective keys and values.8dependent-monoidal-mapO(n)4. Filter all keys/values that satisfy the predicate.9dependent-monoidal-mapO(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 L.:dependent-monoidal-mapO(n)". Map keys/values and collect the ] results.;dependent-monoidal-mapO(n)#. Map keys/values and separate the d and e results.<dependent-monoidal-mapO(n),. Map a function over all values in the map.=dependent-monoidal-mapO(n),. Map a function over all values in the map.>dependent-monoidal-mapO(n). > f m == fromList  $ f ((k, v) -> (,) k  $ f k v) (H m)* That is, behaves exactly like a regular f except that the traversing function also has access to the key associated with a value.?dependent-monoidal-mapO(n). The function ? threads an accumulating argument throught the map in ascending order of keys.@dependent-monoidal-mapO(n). The function @ threads an accumulating argument through the map in descending order of keys.Adependent-monoidal-map O(n*log n). A c f s! is the map obtained by applying 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 the associated values will be combined using c.Bdependent-monoidal-mapO(n). B 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 f maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys.Cdependent-monoidal-mapO(n). Post-order fold. The function will be applied from the lowest value to the highest.Ddependent-monoidal-mapO(n). Pre-order fold. The function will be applied from the highest value to the lowest.Edependent-monoidal-mapO(n)0. Return all keys of the map in ascending order. ?@ABCDEFGHIJKLMNOP  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOP      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_]^`]ab]cd]efghijkl]mn]mo]pq5dependent-monoidal-map-0.1.1.3-AHrTHcucDdkDjpQG9Y6oxEData.Dependent.Map.MonoidalFakeDSum unFakeDSum MonoidalDMapunMonoidalDMapempty singletonnullsizelookup deleteFindMinminViewWithKeymaxViewWithKey deleteFindMaxmember notMemberfindfindWithDefaultinsert insertWith insertWith' insertWithKeyinsertWithKey'insertLookupWithKeyinsertLookupWithKey'deleteadjust adjustWithKeyadjustWithKey'update updateWithKeyupdateLookupWithKeyalter findIndex lookupIndexelemAtupdateAtdeleteAtfindMin lookupMinfindMax lookupMax deleteMin deleteMaxupdateMinWithKeyupdateMaxWithKey unionsWithKey unionWithKey differencedifferenceWithKeyintersectionWithKey isSubmapOf isSubmapOfByisProperSubmapOfisProperSubmapOfBy filterWithKeypartitionWithKeymapMaybeWithKeymapEitherWithKeymap mapWithKeytraverseWithKeymapAccumLWithKeymapAccumRWithKey mapKeysWithmapKeysMonotonic foldrWithKey foldlWithKeykeysassocsfromListWithKeytoList toAscList toDescListfromAscListWithKeysplit splitLookupshowTree showTreeWithvalid$fMonoidMonoidalDMap$fSemigroupMonoidalDMap$fReadMonoidalDMap$fShowMonoidalDMap$fOrdMonoidalDMap$fEqMonoidalDMap$fReadFakeDSum$fShowFakeDSum $fOrdFakeDSum $fEqFakeDSum$fFromJSONMonoidalDMap$fToJSONMonoidalDMapbase GHC.MaybeJustNothingGHC.ErrerrorGHC.Baseconst Data.Foldablefoldl,dependent-sum-0.7.1.0-LAJFJBI2D5p4UTyzpM8wXMData.Dependent.SumeqTaggedghc-prim GHC.TypesTrue Data.EitherLeftRightData.Traversabletraverse