-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Monoidal map type
--   
--   Monoidal map type with support for semigroup and monoid subclasses.
@package monoidmap
@version 0.0.2.0


-- | Provides the <a>MultiMap</a> class, which models a total relation from
--   unique keys to sets of values.
module Examples.MultiMap.Class

-- | Models a total relation from unique keys to sets of values.
class (Eq (m k v), Ord k, Ord v) => MultiMap m k v

-- | Constructs a multimap from a list of key to value set mappings.
--   
--   Removing empty sets from the input list does not affect the result:
--   
--   <pre>
--   fromList ≡ fromList . filter ((/= Set.empty) . snd)
--   </pre>
fromList :: MultiMap m k v => [(k, Set v)] -> m k v

-- | Converts a multimap to a list of key to value-set mappings.
--   
--   Removing empty sets from the output list does not affect the result:
--   
--   <pre>
--   toList ≡ filter ((/= Set.empty) . snd) . toList
--   </pre>
--   
--   The resulting list can be used to reconstruct the original multimap:
--   
--   <pre>
--   fromList . toList ≡ id
--   </pre>
toList :: MultiMap m k v => m k v -> [(k, Set v)]

-- | Constructs an empty multimap.
--   
--   <pre>
--   empty ≡ fromList []
--   </pre>
empty :: MultiMap m k v => m k v

-- | Returns the set of values associated with a given key.
--   
--   <pre>
--   lookup k (fromList kvs) ≡ foldMap snd (filter ((== k) . fst) kvs)
--   </pre>
lookup :: MultiMap m k v => k -> m k v -> Set v

-- | Indicates whether or not a multimap is empty.
--   
--   <pre>
--   null m ≡ (∀ k. lookup k m == Set.empty)
--   </pre>
null :: MultiMap m k v => m k v -> Bool

-- | Indicates whether or not a multimap is non-empty.
--   
--   <pre>
--   nonNull m ≡ (∃ k. lookup k m /= Set.empty)
--   </pre>
nonNull :: MultiMap m k v => m k v -> Bool

-- | Returns <a>True</a> iff. the given key is associated with a non-empty
--   set.
--   
--   <pre>
--   nonNullKey k m ≡ (lookup k m /= Set.empty)
--   </pre>
nonNullKey :: MultiMap m k v => k -> m k v -> Bool

-- | Returns the set of keys that are associated with non-empty sets.
--   
--   <pre>
--   all (`nonNullKey` m) (nonNullKeys m)
--   </pre>
nonNullKeys :: MultiMap m k v => m k v -> Set k

-- | Indicates how many keys are associated with non-empty sets.
--   
--   <pre>
--   nonNullCount m ≡ Set.size (nonNullKeys m)
--   </pre>
nonNullCount :: MultiMap m k v => m k v -> Int

-- | Indicates whether or not the first map is a sub-map of the second.
--   
--   <pre>
--   m1 `isSubmapOf` m2 ≡ ∀ k. (lookup k m1 `Set.isSubsetOf` lookup k m2)
--   </pre>
isSubmapOf :: MultiMap m k v => m k v -> m k v -> Bool

-- | Updates the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (update k2 vs m) ≡
--       if k1 == k2
--       then vs
--       else lookup k1 m
--   </pre>
update :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Inserts values into the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (insert k2 vs m) ≡
--       if k1 == k2
--       then lookup k1 m `Set.union` vs
--       else lookup k1 m
--   </pre>
insert :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Removes values from the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (remove k2 vs m) ≡
--       if k1 == k2
--       then lookup k1 m `Set.difference` vs
--       else lookup k1 m
--   </pre>
remove :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Computes the union of two multimaps.
--   
--   Instances must satisfy the following properties:
--   
--   <b><i>Idempotence</i></b>
--   
--   <pre>
--   union m m ≡ m
--   </pre>
--   
--   <b><i>Identity</i></b>
--   
--   <pre>
--   union empty m     ≡ m
--   union m     empty ≡ m
--   </pre>
--   
--   <b><i>Commutativity</i></b>
--   
--   <pre>
--   union m1 m2 ≡ union m2 m1
--   </pre>
--   
--   <b><i>Associativity</i></b>
--   
--   <pre>
--   union        m1 (union m2  m3) ≡
--   union (union m1        m2) m3
--   </pre>
--   
--   <b><i>Containment</i></b>
--   
--   <pre>
--   m1 `isSubmapOf` union m1 m2
--   m2 `isSubmapOf` union m1 m2
--   </pre>
--   
--   <b><i>Distributivity</i></b>
--   
--   <pre>
--   lookup k (union m1 m2) ≡ Set.union (lookup k m1)
--                                      (lookup k m2)
--   </pre>
union :: MultiMap m k v => m k v -> m k v -> m k v

-- | Computes the intersection of two multimaps.
--   
--   Instances must satisfy the following properties:
--   
--   <b><i>Idempotence</i></b>
--   
--   <pre>
--   intersection m m ≡ m
--   </pre>
--   
--   <b><i>Identity</i></b>
--   
--   <pre>
--   intersection empty m     ≡ empty
--   intersection m     empty ≡ empty
--   </pre>
--   
--   <b><i>Commutativity</i></b>
--   
--   <pre>
--   intersection m1 m2 ≡ intersection m2 m1
--   </pre>
--   
--   <b><i>Associativity</i></b>
--   
--   <pre>
--   intersection               m1 (intersection m2  m3) ≡
--   intersection (intersection m1               m2) m3
--   </pre>
--   
--   <b><i>Containment</i></b>
--   
--   <pre>
--   intersection m1 m2 `isSubmapOf` m1
--   intersection m1 m2 `isSubmapOf` m2
--   </pre>
--   
--   <b><i>Distributivity</i></b>
--   
--   <pre>
--   lookup k (intersection m1 m2) ≡ Set.intersection (lookup k m1)
--                                                    (lookup k m2)
--   </pre>
intersection :: MultiMap m k v => m k v -> m k v -> m k v


-- | An <b>unlawful</b> implementation of <a>MultiMap</a>, implemented in
--   terms of <a>Map</a> and <a>Set</a>.
--   
--   This implementation has several subtle bugs. 💥
module Examples.MultiMap.Instances.MultiMap1
newtype MultiMap1 k v
MultiMap :: Map k (Set v) -> MultiMap1 k v
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Examples.MultiMap.Instances.MultiMap1.MultiMap1 k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.MultiMap.Instances.MultiMap1.MultiMap1 k v)
instance (GHC.Classes.Ord k, GHC.Classes.Ord v) => Examples.MultiMap.Class.MultiMap Examples.MultiMap.Instances.MultiMap1.MultiMap1 k v


-- | A <b>lawful</b> implementation of <a>MultiMap</a>, implemented in
--   terms of <a>Map</a> and <a>Set</a>.
module Examples.MultiMap.Instances.MultiMap2
newtype MultiMap2 k v
MultiMap :: Map k (Set v) -> MultiMap2 k v
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Examples.MultiMap.Instances.MultiMap2.MultiMap2 k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.MultiMap.Instances.MultiMap2.MultiMap2 k v)
instance (GHC.Classes.Ord k, GHC.Classes.Ord v) => Examples.MultiMap.Class.MultiMap Examples.MultiMap.Instances.MultiMap2.MultiMap2 k v


-- | A <b>lawful</b> implementation of <a>MultiMap</a>, implemented in
--   terms of <a>Map</a> and <a>NESet</a>.
module Examples.MultiMap.Instances.MultiMap3
newtype MultiMap3 k v
MultiMap :: Map k (NESet v) -> MultiMap3 k v
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Examples.MultiMap.Instances.MultiMap3.MultiMap3 k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.MultiMap.Instances.MultiMap3.MultiMap3 k v)
instance (GHC.Classes.Ord k, GHC.Classes.Ord v) => Examples.MultiMap.Class.MultiMap Examples.MultiMap.Instances.MultiMap3.MultiMap3 k v


-- | A <b>lawful</b> implementation of <a>MultiMap</a>, implemented in
--   terms of <a>MonoidMap</a> and <a>Set</a>.
module Examples.MultiMap.Instances.MultiMap4
newtype MultiMap4 k v
MultiMap :: MonoidMap k (Set v) -> MultiMap4 k v
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Examples.MultiMap.Instances.MultiMap4.MultiMap4 k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.MultiMap.Instances.MultiMap4.MultiMap4 k v)
instance (GHC.Classes.Ord k, GHC.Classes.Ord v) => Examples.MultiMap.Class.MultiMap Examples.MultiMap.Instances.MultiMap4.MultiMap4 k v


-- | Provides the <a>MultiMap</a> class, which models a total relation from
--   unique keys to sets of values.
--   
--   <h1>Implementations</h1>
--   
--   The following example implementations are provided:
--   
--   TODO: table
module Examples.MultiMap

-- | Models a total relation from unique keys to sets of values.
class (Eq (m k v), Ord k, Ord v) => MultiMap m k v

-- | Constructs a multimap from a list of key to value set mappings.
--   
--   Removing empty sets from the input list does not affect the result:
--   
--   <pre>
--   fromList ≡ fromList . filter ((/= Set.empty) . snd)
--   </pre>
fromList :: MultiMap m k v => [(k, Set v)] -> m k v

-- | Converts a multimap to a list of key to value-set mappings.
--   
--   Removing empty sets from the output list does not affect the result:
--   
--   <pre>
--   toList ≡ filter ((/= Set.empty) . snd) . toList
--   </pre>
--   
--   The resulting list can be used to reconstruct the original multimap:
--   
--   <pre>
--   fromList . toList ≡ id
--   </pre>
toList :: MultiMap m k v => m k v -> [(k, Set v)]

-- | Constructs an empty multimap.
--   
--   <pre>
--   empty ≡ fromList []
--   </pre>
empty :: MultiMap m k v => m k v

-- | Returns the set of values associated with a given key.
--   
--   <pre>
--   lookup k (fromList kvs) ≡ foldMap snd (filter ((== k) . fst) kvs)
--   </pre>
lookup :: MultiMap m k v => k -> m k v -> Set v

-- | Indicates whether or not a multimap is empty.
--   
--   <pre>
--   null m ≡ (∀ k. lookup k m == Set.empty)
--   </pre>
null :: MultiMap m k v => m k v -> Bool

-- | Indicates whether or not a multimap is non-empty.
--   
--   <pre>
--   nonNull m ≡ (∃ k. lookup k m /= Set.empty)
--   </pre>
nonNull :: MultiMap m k v => m k v -> Bool

-- | Returns <a>True</a> iff. the given key is associated with a non-empty
--   set.
--   
--   <pre>
--   nonNullKey k m ≡ (lookup k m /= Set.empty)
--   </pre>
nonNullKey :: MultiMap m k v => k -> m k v -> Bool

-- | Returns the set of keys that are associated with non-empty sets.
--   
--   <pre>
--   all (`nonNullKey` m) (nonNullKeys m)
--   </pre>
nonNullKeys :: MultiMap m k v => m k v -> Set k

-- | Indicates how many keys are associated with non-empty sets.
--   
--   <pre>
--   nonNullCount m ≡ Set.size (nonNullKeys m)
--   </pre>
nonNullCount :: MultiMap m k v => m k v -> Int

-- | Indicates whether or not the first map is a sub-map of the second.
--   
--   <pre>
--   m1 `isSubmapOf` m2 ≡ ∀ k. (lookup k m1 `Set.isSubsetOf` lookup k m2)
--   </pre>
isSubmapOf :: MultiMap m k v => m k v -> m k v -> Bool

-- | Updates the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (update k2 vs m) ≡
--       if k1 == k2
--       then vs
--       else lookup k1 m
--   </pre>
update :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Inserts values into the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (insert k2 vs m) ≡
--       if k1 == k2
--       then lookup k1 m `Set.union` vs
--       else lookup k1 m
--   </pre>
insert :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Removes values from the set of values associated with a given key.
--   
--   <pre>
--   lookup k1 (remove k2 vs m) ≡
--       if k1 == k2
--       then lookup k1 m `Set.difference` vs
--       else lookup k1 m
--   </pre>
remove :: MultiMap m k v => k -> Set v -> m k v -> m k v

-- | Computes the union of two multimaps.
--   
--   Instances must satisfy the following properties:
--   
--   <b><i>Idempotence</i></b>
--   
--   <pre>
--   union m m ≡ m
--   </pre>
--   
--   <b><i>Identity</i></b>
--   
--   <pre>
--   union empty m     ≡ m
--   union m     empty ≡ m
--   </pre>
--   
--   <b><i>Commutativity</i></b>
--   
--   <pre>
--   union m1 m2 ≡ union m2 m1
--   </pre>
--   
--   <b><i>Associativity</i></b>
--   
--   <pre>
--   union        m1 (union m2  m3) ≡
--   union (union m1        m2) m3
--   </pre>
--   
--   <b><i>Containment</i></b>
--   
--   <pre>
--   m1 `isSubmapOf` union m1 m2
--   m2 `isSubmapOf` union m1 m2
--   </pre>
--   
--   <b><i>Distributivity</i></b>
--   
--   <pre>
--   lookup k (union m1 m2) ≡ Set.union (lookup k m1)
--                                      (lookup k m2)
--   </pre>
union :: MultiMap m k v => m k v -> m k v -> m k v

-- | Computes the intersection of two multimaps.
--   
--   Instances must satisfy the following properties:
--   
--   <b><i>Idempotence</i></b>
--   
--   <pre>
--   intersection m m ≡ m
--   </pre>
--   
--   <b><i>Identity</i></b>
--   
--   <pre>
--   intersection empty m     ≡ empty
--   intersection m     empty ≡ empty
--   </pre>
--   
--   <b><i>Commutativity</i></b>
--   
--   <pre>
--   intersection m1 m2 ≡ intersection m2 m1
--   </pre>
--   
--   <b><i>Associativity</i></b>
--   
--   <pre>
--   intersection               m1 (intersection m2  m3) ≡
--   intersection (intersection m1               m2) m3
--   </pre>
--   
--   <b><i>Containment</i></b>
--   
--   <pre>
--   intersection m1 m2 `isSubmapOf` m1
--   intersection m1 m2 `isSubmapOf` m2
--   </pre>
--   
--   <b><i>Distributivity</i></b>
--   
--   <pre>
--   lookup k (intersection m1 m2) ≡ Set.intersection (lookup k m1)
--                                                    (lookup k m2)
--   </pre>
intersection :: MultiMap m k v => m k v -> m k v -> m k v


-- | A multiset type, implemented in terms of <a>MonoidMap</a>.
--   
--   See: <a>https://en.wikipedia.org/wiki/Multiset</a>
module Examples.MultiSet
fromList :: Ord a => [(a, Natural)] -> MultiSet a
toList :: MultiSet a -> [(a, Natural)]
null :: MultiSet a -> Bool
member :: Ord a => a -> MultiSet a -> Bool
multiplicity :: Ord a => a -> MultiSet a -> Natural
root :: Ord a => MultiSet a -> Set a
cardinality :: MultiSet a -> Natural
dimension :: MultiSet a -> Natural
height :: Ord a => MultiSet a -> Natural
isSubsetOf :: Ord a => MultiSet a -> MultiSet a -> Bool
intersection :: Ord a => MultiSet a -> MultiSet a -> MultiSet a
union :: Ord a => MultiSet a -> MultiSet a -> MultiSet a
disjointUnion :: Ord a => MultiSet a -> MultiSet a -> MultiSet a
add :: Ord a => MultiSet a -> MultiSet a -> MultiSet a
subtract :: Ord a => MultiSet a -> MultiSet a -> MultiSet a
subtractMaybe :: Ord a => MultiSet a -> MultiSet a -> Maybe (MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.Monus.Monus (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.Monus.OverlappingGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.LCM.DistributiveLCMMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.DistributiveGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.LCM.LCMMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.GCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.Cancellative (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.Reductive (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.RightDistributiveGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.RightGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.RightCancellative (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.RightReductive (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.LeftDistributiveGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.GCD.LeftGCDMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.LeftCancellative (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Cancellative.LeftReductive (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.Null.PositiveMonoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Monoid.Null.MonoidNull (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => GHC.Base.Monoid (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => Data.Semigroup.Commutative.Commutative (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Ord a => GHC.Base.Semigroup (Examples.MultiSet.MultiSet a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Examples.MultiSet.MultiSet a)
instance (GHC.Classes.Ord a, GHC.Read.Read a) => GHC.Read.Read (Examples.MultiSet.MultiSet a)
instance GHC.Show.Show a => GHC.Show.Show (Examples.MultiSet.MultiSet a)


-- | A nested map with compound keys, implemented in terms of
--   <a>MonoidMap</a>.
module Examples.NestedMonoidMap
data NestedMonoidMap k1 k2 v
fromFlatList :: (Ord k1, Ord k2, MonoidNull v) => [((k1, k2), v)] -> NestedMonoidMap k1 k2 v
fromFlatMap :: (Ord k1, Ord k2, MonoidNull v) => Map (k1, k2) v -> NestedMonoidMap k1 k2 v
fromNestedList :: (Ord k1, Ord k2, MonoidNull v) => [(k1, [(k2, v)])] -> NestedMonoidMap k1 k2 v
fromNestedMap :: (Ord k2, MonoidNull v) => Map k1 (Map k2 v) -> NestedMonoidMap k1 k2 v
toFlatList :: (Ord k1, Ord k2, MonoidNull v) => NestedMonoidMap k1 k2 v -> [((k1, k2), v)]
toFlatMap :: (Ord k1, Ord k2, MonoidNull v) => NestedMonoidMap k1 k2 v -> Map (k1, k2) v
toNestedList :: (Ord k1, Ord k2, MonoidNull v) => NestedMonoidMap k1 k2 v -> [(k1, [(k2, v)])]
toNestedMap :: NestedMonoidMap k1 k2 v -> Map k1 (Map k2 v)
get :: (Ord k1, Ord k2, MonoidNull v) => k1 -> k2 -> NestedMonoidMap k1 k2 v -> v
set :: (Ord k1, Ord k2, MonoidNull v) => k1 -> k2 -> v -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
adjust :: (Ord k1, Ord k2, MonoidNull v) => (v -> v) -> k1 -> k2 -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
nullify :: (Ord k1, Ord k2, MonoidNull v) => k1 -> k2 -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
nonNullCount :: NestedMonoidMap k1 k2 v -> Int
nonNullKey :: (Ord k1, Ord k2, MonoidNull v) => k1 -> k2 -> NestedMonoidMap k1 k2 v -> Bool
nonNullKeys :: (Ord k1, Ord k2, MonoidNull v) => NestedMonoidMap k1 k2 v -> Set (k1, k2)
intersection :: (Ord k1, Ord k2, MonoidNull v, GCDMonoid v) => NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
intersectionWith :: (Ord k1, Ord k2, MonoidNull v) => (v -> v -> v) -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
union :: (Ord k1, Ord k2, MonoidNull v, LCMMonoid v) => NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
unionWith :: (Ord k1, Ord k2, MonoidNull v) => (v -> v -> v) -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v
isSubmapOf :: (Ord k1, Ord k2, MonoidNull v, Reductive v) => NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> Bool
isSubmapOfBy :: (Ord k1, Ord k2, MonoidNull v, Reductive v) => (v -> v -> Bool) -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> Bool
disjoint :: (Ord k1, Ord k2, MonoidNull v, GCDMonoid v) => NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> Bool
disjointBy :: (Ord k1, Ord k2, MonoidNull v, GCDMonoid v) => (v -> v -> Bool) -> NestedMonoidMap k1 k2 v -> NestedMonoidMap k1 k2 v -> Bool
instance (GHC.Show.Show k1, GHC.Show.Show k2, GHC.Show.Show v) => GHC.Show.Show (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v) => GHC.Base.Semigroup (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.RightReductive v) => Data.Semigroup.Cancellative.RightReductive (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.GCD.RightGCDMonoid v) => Data.Monoid.GCD.RightGCDMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.RightReductive v) => Data.Semigroup.Cancellative.RightCancellative (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.Reductive v) => Data.Semigroup.Cancellative.Reductive (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v) => Data.Monoid.Null.PositiveMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.Monus.OverlappingGCDMonoid v) => Data.Monoid.Monus.OverlappingGCDMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.Monus.Monus v) => Data.Monoid.Monus.Monus (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v) => Data.Monoid.Null.MonoidNull (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v) => GHC.Base.Monoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.LeftReductive v) => Data.Semigroup.Cancellative.LeftReductive (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.GCD.LeftGCDMonoid v) => Data.Monoid.GCD.LeftGCDMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.LeftReductive v) => Data.Semigroup.Cancellative.LeftCancellative (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.LCM.LCMMonoid v) => Data.Monoid.LCM.LCMMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Monoid.GCD.GCDMonoid v) => Data.Monoid.GCD.GCDMonoid (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v) => Data.Semigroup.Commutative.Commutative (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Ord k1, GHC.Classes.Ord k2, Data.Monoid.Null.MonoidNull v, Data.Semigroup.Cancellative.Reductive v) => Data.Semigroup.Cancellative.Cancellative (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)
instance (GHC.Classes.Eq k1, GHC.Classes.Eq k2, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.NestedMonoidMap.NestedMonoidMap k1 k2 v)


-- | An ordinary left-biased map similar to <a>Map</a>, implemented in
--   terms of <a>MonoidMap</a>.
module Examples.RecoveredMap
data Map k v
empty :: Map k v
singleton :: Ord k => k -> v -> Map k v
fromList :: Ord k => [(k, v)] -> Map k v
toList :: Map k v -> [(k, v)]
delete :: Ord k => k -> Map k v -> Map k v
insert :: Ord k => k -> v -> Map k v -> Map k v
keysSet :: Map k v -> Set k
lookup :: Ord k => k -> Map k v -> Maybe v
member :: Ord k => k -> Map k v -> Bool
map :: (v1 -> v2) -> Map k v1 -> Map k v2
mapAccumL :: (s -> v1 -> (s, v2)) -> s -> Map k v1 -> (s, Map k v2)
mapAccumLWithKey :: (s -> k -> v1 -> (s, v2)) -> s -> Map k v1 -> (s, Map k v2)
mapAccumR :: (s -> v1 -> (s, v2)) -> s -> Map k v1 -> (s, Map k v2)
mapAccumRWithKey :: (s -> k -> v1 -> (s, v2)) -> s -> Map k v1 -> (s, Map k v2)
instance GHC.Classes.Ord k => GHC.Base.Monoid (Examples.RecoveredMap.Map k v)
instance (Control.DeepSeq.NFData k, Control.DeepSeq.NFData v) => Control.DeepSeq.NFData (Examples.RecoveredMap.Map k v)
instance (GHC.Classes.Eq k, GHC.Classes.Eq v) => GHC.Classes.Eq (Examples.RecoveredMap.Map k v)
instance GHC.Classes.Ord k => GHC.Base.Semigroup (Examples.RecoveredMap.Map k v)
instance (GHC.Show.Show k, GHC.Show.Show v) => GHC.Show.Show (Examples.RecoveredMap.Map k v)
instance GHC.Base.Functor (Examples.RecoveredMap.Map k)