The hash value of the value, which allows the value to be an element of a hash-based set or key of a hash-based map. Implementations must respect the constraint that:

• if x==y then x.hash==y.hash.

Therefore, a class which refines equals must also refine hash.

In general, hash values vary between platforms and between executions of the same program.

Note that when executing on a Java Virtual Machine, the 64-bit Integer value returned by an implementation of hash is truncated to a 32-bit integer value by taking the exclusive disjunction of the 32 lowest-order bits with the 32 highest-order bits, before returning the value to the caller.

The number of elements returned by the iterator of this stream, if the iterator terminates. In the case of an infinite stream, this operation never terminates.

A shallow copy of this collection, that is, a collection with identical elements which does not change if this collection changes. If this collection is immutable, it is acceptable to return a reference to this collection. If this collection is mutable, a newly instantiated collection must be returned.

Returns a new Set containing all the elements in this set that are not contained in the given Set.

For example:

set { "hello", "world" } ~ set { 1, 2, "hello" }

Produces the set { "world" } of type Set<String>.

Returns true if the given value belongs to this Category, that is, if it is an element of this Category, or false otherwise.

For any instance c of Category, c.contains(element) may be written using the in operator:

element in c

For most Categorys, the following relationship is satisfied by every pair of elements x and y:

• if x==y, then x in category == y in category

However, it is possible to form a useful Category consistent with some other equivalence relation, for example ===. Therefore implementations of contains() which do not satisfy this relationship are tolerated.

Determine if two values are equal.

For any two non-null objects x and y, x.equals(y) may be written as:

x == y 

Implementations should respect the constraints that:

• if x===y then x==y (reflexivity),
• if x==y then y==x (symmetry),
• if x==y and y==z then x==z (transitivity).

Furthermore it is recommended that implementations ensure that if x==y then x and y have the same concrete class.

A class which explicitly refines equals() is said to support value equality, and the equality operator == is considered much more meaningful for such classes than for a class which simply inherits the default implementation of identity equality from Identifiable.

Note that an implementation of equals() that always returns false does satisfy the constraints given above, as long as the class does not inherit Identifiable. Therefore, in very rare cases where there is no reasonable definition of value equality for a class, for example, function references (Callable), it is acceptable for equals() to be defined to return false for every argument.

Returns a new Set containing only the elements contained in either this set or the given Set, but no element contained in both sets.

Returns a new Set containing only the elements that are present in both this set and the given Set and that are instances of the intersection Element&Other of the element types of the two sets.

For example:

set { "hello", "world" } & set { 1, 2, "hello" }

Produces the set { "hello" } of type Set<String>.

Note that, according to this definition, and even though 1==1.0 evaluates to true (Integer.equals), the expression

set { 1 } & set { 1.0 }

produces the empty set {}.

An iterator for the elements belonging to this stream.

If this is a nonempty stream with type {Element+}, the iterator must produce at least one element.

Returns a new Set containing all the elements of this set and all the elements of the given Set.

For example:

set { "hello", "world" } | set { 1, 2, "hello" }

Produces the set { "hello", "world", 1, 2 } of type Set<String|Integer>.

Note that it is possible for two sets of disjoint element type to be considered to have elements in common. For example, since 1==1.0 evaluates to true (Integer.equals), the expression

set { 1 } | set { 1.0 }

produces the set { 1 }.