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1. insertSetMax :: a -> Set a -> NESet a

   nonempty-containers	Data.Set.NonEmpty

   O(log n) Convert a Set into an NESet by adding a value where the value is strictly less than all values in the input set The values in the original map must all be strictly greater than the new value. The precondition is not checked. While this has the same asymptotics as insertSet, it saves a constant factor for key comparison (so may be helpful if comparison is expensive) and also does not require an Ord instance for the key type.

   insertSetMin 7 (Data.Set.fromList [5, 3]) == fromList (3 :| [5, 7])
   valid (insertSetMin 7 (Data.Set.fromList [5, 3])) == True
   valid (insertSetMin 2 (Data.Set.fromList [5, 3])) == False
   valid (insertSetMin 5 (Data.Set.fromList [5, 3])) == False
   

2. insertSetMin :: a -> Set a -> NESet a

   nonempty-containers	Data.Set.NonEmpty

   O(1) Convert a Set into an NESet by adding a value where the value is strictly less than all values in the input set The values in the original map must all be strictly greater than the new value. The precondition is not checked.

   insertSetMin 2 (Data.Set.fromList [5, 3]) == fromList (2 :| [3, 5])
   valid (insertSetMin 2 (Data.Set.fromList [5, 3])) == True
   valid (insertSetMin 7 (Data.Set.fromList [5, 3])) == False
   valid (insertSetMin 3 (Data.Set.fromList [5, 3])) == False
   

3. isProperSubsetOf :: Ord a => NESet a -> NESet a -> Bool

   nonempty-containers	Data.Set.NonEmpty

   O(n+m). Is this a proper subset? (ie. a subset but not equal).

4. isSubsetOf :: Ord a => NESet a -> NESet a -> Bool

   nonempty-containers	Data.Set.NonEmpty

   O(n+m). Is this a subset? (s1 `isSubsetOf` s2) tells whether s1 is a subset of s2.

5. nonEmptySet :: Set a -> Maybe (NESet a)

   nonempty-containers	Data.Set.NonEmpty

   O(log n). Smart constructor for an NESet from a Set. Returns Nothing if the Set was originally actually empty, and Just n with an NESet, if the Set was not empty. nonEmptySet and maybe empty toSet form an isomorphism: they are perfect structure-preserving inverses of eachother. See IsNonEmpty for a pattern synonym that lets you "match on" the possiblity of a Set being an NESet.

   nonEmptySet (Data.Set.fromList [3,5]) == Just (fromList (3:|[5]))
   

6. powerSet :: NESet a -> NESet (NESet a)

   nonempty-containers	Data.Set.NonEmpty

   Calculate the power set of a non-empty: the set of all its (non-empty) subsets.

   t `member` powerSet s == t `isSubsetOf` s
   

   Example:

   powerSet (fromList (1 :| [2,3])) =
   fromList (singleton 1 :| [ singleton 2
   , singleton 3
   , fromList (1 :| [2])
   , fromList (1 :| [3])
   , fromList (2 :| [3])
   , fromList (1 :| [2,3])
   ]
   )
   

   We know that the result is non-empty because the result will always at least contain the original set.

7. toSet :: NESet a -> Set a

   nonempty-containers	Data.Set.NonEmpty

   O(log n). Convert a non-empty set back into a normal possibly-empty map, for usage with functions that expect Set. Can be thought of as "obscuring" the non-emptiness of the set in its type. See the IsNotEmpty pattern. nonEmptySet and maybe empty toSet form an isomorphism: they are perfect structure-preserving inverses of eachother.

   toSet (fromList ((3,"a") :| [(5,"b")])) == Data.Set.fromList [(3,"a"), (5,"b")]
   

8. unsafeFromSet :: Set a -> NESet a

   nonempty-containers	Data.Set.NonEmpty

   O(log n). Unsafe version of nonEmptySet. Coerces a Set into an NESet, but is undefined (throws a runtime exception when evaluation is attempted) for an empty Set.

9. newtype MergeNESet a

   nonempty-containers	Data.Set.NonEmpty.Internal

   Used for cartesianProduct

10. MergeNESet :: NESet a -> MergeNESet a

    nonempty-containers	Data.Set.NonEmpty.Internal

    No documentation available.

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