Data.Map.Monoidal.Strict

This module provides a Map variant which uses the value's Monoid instance to accumulate conflicting entries when merging Maps.

While some functions mirroring those of Map are provided here for convenience, more specialized needs will likely want to use either the Newtype or Wrapped instances to manipulate the underlying Map.

Documentation

newtype MonoidalMap k a

A Map with monoidal accumulation

Constructors

MonoidalMap

Fields

• getMonoidalMap :: Map k a

Instances

FoldableWithIndex k (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

ifoldMap :: Monoid m => (k -> a -> m) -> MonoidalMap k a -> m

ifoldMap' :: Monoid m => (k -> a -> m) -> MonoidalMap k a -> m

ifoldr :: (k -> a -> b -> b) -> b -> MonoidalMap k a -> b

ifoldl :: (k -> b -> a -> b) -> b -> MonoidalMap k a -> b

ifoldr' :: (k -> a -> b -> b) -> b -> MonoidalMap k a -> b

ifoldl' :: (k -> b -> a -> b) -> b -> MonoidalMap k a -> b

FunctorWithIndex k (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

imap :: (k -> a -> b) -> MonoidalMap k a -> MonoidalMap k b

TraversableWithIndex k (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

itraverse :: Applicative f => (k -> a -> f b) -> MonoidalMap k a -> f (MonoidalMap k b)

Ord k => TraverseMax k (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

traverseMax :: IndexedTraversal' k (MonoidalMap k v) v

Ord k => TraverseMin k (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

traverseMin :: IndexedTraversal' k (MonoidalMap k v) v

Functor (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

fmap :: (a -> b) -> MonoidalMap k a -> MonoidalMap k b

(<$) :: a -> MonoidalMap k b -> MonoidalMap k a

Foldable (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

fold :: Monoid m => MonoidalMap k m -> m

foldMap :: Monoid m => (a -> m) -> MonoidalMap k a -> m

foldr :: (a -> b -> b) -> b -> MonoidalMap k a -> b

foldr' :: (a -> b -> b) -> b -> MonoidalMap k a -> b

foldl :: (b -> a -> b) -> b -> MonoidalMap k a -> b

foldl' :: (b -> a -> b) -> b -> MonoidalMap k a -> b

foldr1 :: (a -> a -> a) -> MonoidalMap k a -> a

foldl1 :: (a -> a -> a) -> MonoidalMap k a -> a

toList :: MonoidalMap k a -> [a]

null :: MonoidalMap k a -> Bool

length :: MonoidalMap k a -> Int

elem :: Eq a => a -> MonoidalMap k a -> Bool

maximum :: Ord a => MonoidalMap k a -> a

minimum :: Ord a => MonoidalMap k a -> a

sum :: Num a => MonoidalMap k a -> a

product :: Num a => MonoidalMap k a -> a

Traversable (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

traverse :: Applicative f => (a -> f b) -> MonoidalMap k a -> f (MonoidalMap k b)

sequenceA :: Applicative f => MonoidalMap k (f a) -> f (MonoidalMap k a)

mapM :: Monad m => (a -> m b) -> MonoidalMap k a -> m (MonoidalMap k b)

sequence :: Monad m => MonoidalMap k (m a) -> m (MonoidalMap k a)

Ord k => Eq1 (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

liftEq :: (a -> b -> Bool) -> MonoidalMap k a -> MonoidalMap k b -> Bool

Ord k => Ord1 (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

liftCompare :: (a -> b -> Ordering) -> MonoidalMap k a -> MonoidalMap k b -> Ordering

Show k => Show1 (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> MonoidalMap k a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [MonoidalMap k a] -> ShowS

Ord k => Align (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

nil :: MonoidalMap k a

Ord k => Semialign (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

align :: MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k (These a b)

alignWith :: (These a b -> c) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k c

Ord k => Unalign (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

unalign :: MonoidalMap k (These a b) -> (MonoidalMap k a, MonoidalMap k b)

unalignWith :: (c -> These a b) -> MonoidalMap k c -> (MonoidalMap k a, MonoidalMap k b)

Ord k => Zip (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

zip :: MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k (a, b)

zipWith :: (a -> b -> c) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k c

Filterable (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

mapMaybe :: (a -> Maybe b) -> MonoidalMap k a -> MonoidalMap k b

catMaybes :: MonoidalMap k (Maybe a) -> MonoidalMap k a

filter :: (a -> Bool) -> MonoidalMap k a -> MonoidalMap k a

Ord k => Witherable (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

wither :: Applicative f => (a -> f (Maybe b)) -> MonoidalMap k a -> f (MonoidalMap k b)

witherM :: Monad m => (a -> m (Maybe b)) -> MonoidalMap k a -> m (MonoidalMap k b)

filterA :: Applicative f => (a -> f Bool) -> MonoidalMap k a -> f (MonoidalMap k a)

witherMap :: Applicative m => (MonoidalMap k b -> r) -> (a -> m (Maybe b)) -> MonoidalMap k a -> m r

(FromJSONKey k, Ord k) => FromJSON1 (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

liftParseJSON :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser (MonoidalMap k a)

liftParseJSONList :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser [MonoidalMap k a]

ToJSONKey k => ToJSON1 (MonoidalMap k)

Defined in Data.Map.Monoidal.Strict

Methods

liftToJSON :: (a -> Value) -> ([a] -> Value) -> MonoidalMap k a -> Value

liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [MonoidalMap k a] -> Value

liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> MonoidalMap k a -> Encoding

liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [MonoidalMap k a] -> Encoding

(Ord k, Semigroup a) => IsList (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Associated Types

type Item (MonoidalMap k a) :: Type

Methods

fromList :: [Item (MonoidalMap k a)] -> MonoidalMap k a

fromListN :: Int -> [Item (MonoidalMap k a)] -> MonoidalMap k a

toList :: MonoidalMap k a -> [Item (MonoidalMap k a)]

(Eq k, Eq a) => Eq (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

(==) :: MonoidalMap k a -> MonoidalMap k a -> Bool

(/=) :: MonoidalMap k a -> MonoidalMap k a -> Bool

(Data k, Data a, Ord k) => Data (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MonoidalMap k a -> c (MonoidalMap k a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MonoidalMap k a)

toConstr :: MonoidalMap k a -> Constr

dataTypeOf :: MonoidalMap k a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (MonoidalMap k a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MonoidalMap k a))

gmapT :: (forall b. Data b => b -> b) -> MonoidalMap k a -> MonoidalMap k a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MonoidalMap k a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MonoidalMap k a -> r

gmapQ :: (forall d. Data d => d -> u) -> MonoidalMap k a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> MonoidalMap k a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> MonoidalMap k a -> m (MonoidalMap k a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MonoidalMap k a -> m (MonoidalMap k a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MonoidalMap k a -> m (MonoidalMap k a)

(Ord k, Ord a) => Ord (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

compare :: MonoidalMap k a -> MonoidalMap k a -> Ordering

(<) :: MonoidalMap k a -> MonoidalMap k a -> Bool

(<=) :: MonoidalMap k a -> MonoidalMap k a -> Bool

(>) :: MonoidalMap k a -> MonoidalMap k a -> Bool

(>=) :: MonoidalMap k a -> MonoidalMap k a -> Bool

max :: MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

min :: MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

(Ord k, Read k, Read a) => Read (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

readsPrec :: Int -> ReadS (MonoidalMap k a)

readList :: ReadS [MonoidalMap k a]

readPrec :: ReadPrec (MonoidalMap k a)

readListPrec :: ReadPrec [MonoidalMap k a]

(Show k, Show a) => Show (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

showsPrec :: Int -> MonoidalMap k a -> ShowS

show :: MonoidalMap k a -> String

showList :: [MonoidalMap k a] -> ShowS

(Ord k, Semigroup a) => Semigroup (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

(<>) :: MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

sconcat :: NonEmpty (MonoidalMap k a) -> MonoidalMap k a

stimes :: Integral b => b -> MonoidalMap k a -> MonoidalMap k a

(Ord k, Semigroup a) => Monoid (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

mempty :: MonoidalMap k a

mappend :: MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

mconcat :: [MonoidalMap k a] -> MonoidalMap k a

(NFData k, NFData a) => NFData (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

rnf :: MonoidalMap k a -> ()

Ord k => At (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

at :: Index (MonoidalMap k a) -> Lens' (MonoidalMap k a) (Maybe (IxValue (MonoidalMap k a)))

Ord k => Ixed (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

ix :: Index (MonoidalMap k a) -> Traversal' (MonoidalMap k a) (IxValue (MonoidalMap k a))

AsEmpty (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

_Empty :: Prism' (MonoidalMap k a) ()

Wrapped (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Associated Types

type Unwrapped (MonoidalMap k a) :: Type

Methods

_Wrapped' :: Iso' (MonoidalMap k a) (Unwrapped (MonoidalMap k a))

(FromJSONKey k, Ord k, FromJSON a) => FromJSON (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

parseJSON :: Value -> Parser (MonoidalMap k a)

parseJSONList :: Value -> Parser [MonoidalMap k a]

(ToJSON a, ToJSONKey k) => ToJSON (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Methods

toJSON :: MonoidalMap k a -> Value

toEncoding :: MonoidalMap k a -> Encoding

toJSONList :: [MonoidalMap k a] -> Value

toEncodingList :: [MonoidalMap k a] -> Encoding

Newtype (MonoidalMap k a) (Map k a)

Defined in Data.Map.Monoidal.Strict

Methods

pack :: Map k a -> MonoidalMap k a

unpack :: MonoidalMap k a -> Map k a

Ord k => Rewrapped (Map k a) (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

Ord k => Rewrapped (MonoidalMap k a) (Map k a)

Defined in Data.Map.Monoidal.Strict

Each (MonoidalMap k a) (MonoidalMap k b) a b

Defined in Data.Map.Monoidal.Strict

Methods

each :: Traversal (MonoidalMap k a) (MonoidalMap k b) a b

type Item (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

type Item (MonoidalMap k a) = (k, a)

type Index (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

type Index (MonoidalMap k a) = k

type IxValue (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

type IxValue (MonoidalMap k a) = a

type Unwrapped (MonoidalMap k a)

Defined in Data.Map.Monoidal.Strict

type Unwrapped (MonoidalMap k a) = Map k a

Often-needed functions

singleton :: k -> a -> MonoidalMap k a

O(1). A map with a single element.

size :: MonoidalMap k a -> Int

O(1). The number of elements in the map.

member :: Ord k => k -> MonoidalMap k a -> Bool

O(log n). Is the key a member of the map? See also notMember.

notMember :: Ord k => k -> MonoidalMap k a -> Bool

O(log n). Is the key not a member of the map? See also member.

findWithDefault :: Ord k => a -> k -> MonoidalMap k a -> a

O(log n). The expression (findWithDefault def k map) returns the value at key k or returns default value def when the key is not in the map.

assocs :: MonoidalMap k a -> [(k, a)]

O(n). Return all elements of the map and their keys

elems :: MonoidalMap k a -> [a]

O(n). Return all elements of the map in the ascending order of their keys. Subject to list fusion.

keys :: MonoidalMap k a -> [k]

O(n). Return all keys of the map in ascending order. Subject to list fusion.

(!?) :: forall k a. Ord k => MonoidalMap k a -> k -> Maybe a infixl 9

(!) :: forall k a. Ord k => MonoidalMap k a -> k -> a infixl 9

(\\) :: forall k a b. Ord k => MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k a infixl 9

adjust :: forall k a. Ord k => (a -> a) -> k -> MonoidalMap k a -> MonoidalMap k a

adjustWithKey :: forall k a. Ord k => (k -> a -> a) -> k -> MonoidalMap k a -> MonoidalMap k a

alter :: forall k a. Ord k => (Maybe a -> Maybe a) -> k -> MonoidalMap k a -> MonoidalMap k a

delete :: Ord k => k -> MonoidalMap k a -> MonoidalMap k a

O(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.

deleteAt :: forall k a. Int -> MonoidalMap k a -> MonoidalMap k a

take :: forall k a. Int -> MonoidalMap k a -> MonoidalMap k a

drop :: forall k a. Int -> MonoidalMap k a -> MonoidalMap k a

splitAt :: forall k a. Int -> MonoidalMap k a -> (MonoidalMap k a, MonoidalMap k a)

lookupMin :: forall k a. MonoidalMap k a -> Maybe (k, a)

lookupMax :: forall k a. MonoidalMap k a -> Maybe (k, a)

deleteFindMax :: forall k a. MonoidalMap k a -> ((k, a), MonoidalMap k a)

deleteFindMin :: forall k a. MonoidalMap k a -> ((k, a), MonoidalMap k a)

deleteMax :: forall k a. MonoidalMap k a -> MonoidalMap k a

deleteMin :: forall k a. MonoidalMap k a -> MonoidalMap k a

difference :: forall k a b. Ord k => MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k a

differenceWith :: forall k a b. Ord k => (a -> b -> Maybe a) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k a

differenceWithKey :: forall k a b. Ord k => (k -> a -> b -> Maybe a) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k a

elemAt :: forall k a. Int -> MonoidalMap k a -> (k, a)

empty :: forall k a. MonoidalMap k a

filter :: forall k a. (a -> Bool) -> MonoidalMap k a -> MonoidalMap k a

filterWithKey :: forall k a. (k -> a -> Bool) -> MonoidalMap k a -> MonoidalMap k a

restrictKeys :: forall k a. Ord k => MonoidalMap k a -> Set k -> MonoidalMap k a

withoutKeys :: forall k a. Ord k => MonoidalMap k a -> Set k -> MonoidalMap k a

findIndex :: forall k a. Ord k => k -> MonoidalMap k a -> Int

findMax :: forall k a. MonoidalMap k a -> (k, a)

findMin :: forall k a. MonoidalMap k a -> (k, a)

foldMapWithKey :: forall k a m. Monoid m => (k -> a -> m) -> MonoidalMap k a -> m

foldl :: forall k a b. (a -> b -> a) -> a -> MonoidalMap k b -> a

foldl' :: forall k a b. (a -> b -> a) -> a -> MonoidalMap k b -> a

foldlWithKey :: forall k a b. (a -> k -> b -> a) -> a -> MonoidalMap k b -> a

foldlWithKey' :: forall k a b. (a -> k -> b -> a) -> a -> MonoidalMap k b -> a

foldr :: forall k a b. (a -> b -> b) -> b -> MonoidalMap k a -> b

foldr' :: forall k a b. (a -> b -> b) -> b -> MonoidalMap k a -> b

foldrWithKey :: forall k a b. (k -> a -> b -> b) -> b -> MonoidalMap k a -> b

foldrWithKey' :: forall k a b. (k -> a -> b -> b) -> b -> MonoidalMap k a -> b

fromAscList :: forall k a. Eq k => [(k, a)] -> MonoidalMap k a

fromAscListWith :: forall k a. Eq k => (a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromAscListWithKey :: forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromDistinctAscList :: forall k a. [(k, a)] -> MonoidalMap k a

fromDistinctList :: forall k a. Ord k => [(k, a)] -> MonoidalMap k a

fromDescList :: forall k a. Eq k => [(k, a)] -> MonoidalMap k a

fromDescListWith :: forall k a. Eq k => (a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromDescListWithKey :: forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromDistinctDescList :: forall k a. [(k, a)] -> MonoidalMap k a

fromList :: forall k a. Ord k => [(k, a)] -> MonoidalMap k a

fromListWith :: forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromListWithKey :: forall k a. Ord k => (k -> a -> a -> a) -> [(k, a)] -> MonoidalMap k a

fromSet :: forall k a. (k -> a) -> Set k -> MonoidalMap k a

insert :: forall k a. Ord k => k -> a -> MonoidalMap k a -> MonoidalMap k a

insertLookupWithKey :: forall k a. Ord k => (k -> a -> a -> a) -> k -> a -> MonoidalMap k a -> (Maybe a, MonoidalMap k a)

insertWith :: forall k a. Ord k => (a -> a -> a) -> k -> a -> MonoidalMap k a -> MonoidalMap k a

insertWithKey :: forall k a. Ord k => (k -> a -> a -> a) -> k -> a -> MonoidalMap k a -> MonoidalMap k a

intersectionWith :: forall k a b c. Ord k => (a -> b -> c) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k c

intersectionWithKey :: forall k a b c. Ord k => (k -> a -> b -> c) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k c

isProperSubmapOf :: forall k a. (Ord k, Eq a) => MonoidalMap k a -> MonoidalMap k a -> Bool

isProperSubmapOfBy :: forall k a b. Ord k => (a -> b -> Bool) -> MonoidalMap k a -> MonoidalMap k b -> Bool

isSubmapOf :: forall k a. (Ord k, Eq a) => MonoidalMap k a -> MonoidalMap k a -> Bool

isSubmapOfBy :: forall k a b. Ord k => (a -> b -> Bool) -> MonoidalMap k a -> MonoidalMap k b -> Bool

keysSet :: forall k a. MonoidalMap k a -> Set k

lookup :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe a

lookupGE :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe (k, a)

lookupGT :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe (k, a)

lookupIndex :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe Int

lookupLE :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe (k, a)

lookupLT :: forall k a. Ord k => k -> MonoidalMap k a -> Maybe (k, a)

map :: (a -> b) -> MonoidalMap k a -> MonoidalMap k b

mapAccum :: forall k a b c. (a -> b -> (a, c)) -> a -> MonoidalMap k b -> (a, MonoidalMap k c)

mapAccumRWithKey :: forall k a b c. (a -> k -> b -> (a, c)) -> a -> MonoidalMap k b -> (a, MonoidalMap k c)

mapAccumWithKey :: forall k a b c. (a -> k -> b -> (a, c)) -> a -> MonoidalMap k b -> (a, MonoidalMap k c)

mapEither :: forall k a b c. (a -> Either b c) -> MonoidalMap k a -> (MonoidalMap k b, MonoidalMap k c)

mapEitherWithKey :: forall k a b c. (k -> a -> Either b c) -> MonoidalMap k a -> (MonoidalMap k b, MonoidalMap k c)

mapKeys :: forall k1 k2 a. Ord k2 => (k1 -> k2) -> MonoidalMap k1 a -> MonoidalMap k2 a

mapKeysMonotonic :: forall k1 k2 a. (k1 -> k2) -> MonoidalMap k1 a -> MonoidalMap k2 a

O(n). mapKeysMonotonic f s == mapKeys f s, but works only when f is strictly increasing (both monotonic and injective). That is, for any values x and y, if x < y then f x < f y and f is injective (i.e. it never maps two input keys to the same output key). 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 s

This means that f maps distinct original keys to distinct resulting keys. This function has better performance than mapKeys.

mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]
valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True
valid (mapKeysMonotonic (\ _ -> 1)     (fromList [(5,"a"), (3,"b")])) == False

mapKeysWith :: forall k1 k2 a. Ord k2 => (a -> a -> a) -> (k1 -> k2) -> MonoidalMap k1 a -> MonoidalMap k2 a

mapMaybe :: forall k a b. (a -> Maybe b) -> MonoidalMap k a -> MonoidalMap k b

mapMaybeWithKey :: forall k a b. (k -> a -> Maybe b) -> MonoidalMap k a -> MonoidalMap k b

mapWithKey :: forall k a b. (k -> a -> b) -> MonoidalMap k a -> MonoidalMap k b

maxView :: forall k a. MonoidalMap k a -> Maybe (a, MonoidalMap k a)

maxViewWithKey :: forall k a. MonoidalMap k a -> Maybe ((k, a), MonoidalMap k a)

mergeWithKey :: forall k a b c. Ord k => (k -> a -> b -> Maybe c) -> (MonoidalMap k a -> MonoidalMap k c) -> (MonoidalMap k b -> MonoidalMap k c) -> MonoidalMap k a -> MonoidalMap k b -> MonoidalMap k c

minView :: forall k a. MonoidalMap k a -> Maybe (a, MonoidalMap k a)

minViewWithKey :: forall k a. MonoidalMap k a -> Maybe ((k, a), MonoidalMap k a)

null :: forall k a. MonoidalMap k a -> Bool

partition :: forall k a. (a -> Bool) -> MonoidalMap k a -> (MonoidalMap k a, MonoidalMap k a)

partitionWithKey :: forall k a. (k -> a -> Bool) -> MonoidalMap k a -> (MonoidalMap k a, MonoidalMap k a)

takeWhileAntitone :: forall k a. (k -> Bool) -> MonoidalMap k a -> MonoidalMap k a

dropWhileAntitone :: forall k a. (k -> Bool) -> MonoidalMap k a -> MonoidalMap k a

spanAntitone :: forall k a. (k -> Bool) -> MonoidalMap k a -> (MonoidalMap k a, MonoidalMap k a)

split :: forall k a. Ord k => k -> MonoidalMap k a -> (MonoidalMap k a, MonoidalMap k a)

splitLookup :: forall k a. Ord k => k -> MonoidalMap k a -> (MonoidalMap k a, Maybe a, MonoidalMap k a)

splitRoot :: forall k a. MonoidalMap k a -> [MonoidalMap k a]

toAscList :: forall k a. MonoidalMap k a -> [(k, a)]

toDescList :: forall k a. MonoidalMap k a -> [(k, a)]

toList :: forall k a. MonoidalMap k a -> [(k, a)]

traverseWithKey :: Applicative t => (k -> a -> t b) -> MonoidalMap k a -> t (MonoidalMap k b)

traverseMaybeWithKey :: forall f k a b. Applicative f => (k -> a -> f (Maybe b)) -> MonoidalMap k a -> f (MonoidalMap k b)

unionWith :: forall k a. Ord k => (a -> a -> a) -> MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

unionWithKey :: forall k a. Ord k => (k -> a -> a -> a) -> MonoidalMap k a -> MonoidalMap k a -> MonoidalMap k a

unionsWith :: forall k a. Ord k => (a -> a -> a) -> [MonoidalMap k a] -> MonoidalMap k a

update :: forall k a. Ord k => (a -> Maybe a) -> k -> MonoidalMap k a -> MonoidalMap k a

updateAt :: forall k a. (k -> a -> Maybe a) -> Int -> MonoidalMap k a -> MonoidalMap k a

updateLookupWithKey :: forall k a. Ord k => (k -> a -> Maybe a) -> k -> MonoidalMap k a -> (Maybe a, MonoidalMap k a)

updateMax :: forall k a. (a -> Maybe a) -> MonoidalMap k a -> MonoidalMap k a

updateMaxWithKey :: forall k a. (k -> a -> Maybe a) -> MonoidalMap k a -> MonoidalMap k a

updateMin :: forall k a. (a -> Maybe a) -> MonoidalMap k a -> MonoidalMap k a

updateMinWithKey :: forall k a. (k -> a -> Maybe a) -> MonoidalMap k a -> MonoidalMap k a

updateWithKey :: forall k a. Ord k => (k -> a -> Maybe a) -> k -> MonoidalMap k a -> MonoidalMap k a

valid :: forall k a. Ord k => MonoidalMap k a -> Bool