isSubsetOf -package:intern

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

(s1 `isSubsetOf` s2) indicates whether s1 is a subset of s2.

s1 `isSubsetOf` s2 = all (`member` s2) s1
s1 `isSubsetOf` s2 = null (s1 `difference` s2)
s1 `isSubsetOf` s2 = s1 `union` s2 == s2
s1 `isSubsetOf` s2 = s1 `intersection` s2 == s1

Inclusion of sets.

Examples

>>> fromList [1,3] `isSubsetOf` fromList [1,2,3]
True

>>> fromList [1,2] `isSubsetOf` fromList [1,3]
False

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

O(m*log(n/m + 1)), m <= n. (s1 `isSubsetOf` s2) indicates whether s1 is a subset of s2.

s1 `isSubsetOf` s2 = all (`member` s2) s1
s1 `isSubsetOf` s2 = null (s1 `difference` s2)
s1 `isSubsetOf` s2 = s1 `union` s2 == s2
s1 `isSubsetOf` s2 = s1 `intersection` s2 == s1

Checks if the first range is a subset of the second range.

>>> IPv4.isSubsetOf (IPv4.IPv4Range (IPv4.fromOctets 192 0 2 128) 25) (IPv4.IPv4Range (IPv4.fromOctets 192 0 2 0) 24)
True

>>> IPv4.isSubsetOf (IPv4.IPv4Range (IPv4.fromOctets 192 0 2 0) 30) (IPv4.IPv4Range (IPv4.fromOctets 192 0 2 4) 30)
False

Checks if the first range is a subset of the second range.

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

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

Check whether the first argument is a subset of the second one.

Subset test.

>>> prove $ empty `isSubsetOf` (full :: SSet Integer)
Q.E.D.

>>> prove $ \x (s :: SSet Integer) -> s `isSubsetOf` (x `insert` s)
Q.E.D.

>>> prove $ \x (s :: SSet Integer) -> (x `delete` s) `isSubsetOf` s
Q.E.D.

Is this a subset?

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

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

Is this a subset? (i1 `isSubsetOf` i2) tells whether i1 is a subset of i2.

Is this a subset? (i1 `isSubsetOf` i2) tells whether i1 is a subset of i2.

Is this a subset? (is1 `isSubsetOf` is2) tells whether is1 is a subset of is2.

Flipped version of contains. Check if interval X a subset of interval Y

>>> (25 ... 35 :: Interval Double) `isSubsetOf` (20 ... 40 :: Interval Double)
True

>>> (20 ... 40 :: Interval Double) `isSubsetOf` (15 ... 35 :: Interval Double)
False

O(n+m). Is the first set a subset of the second set? This is always true for equal sets.

O(n log n). Checks that all elements of the first list are elements of the second.

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