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In the example code below, data item VERS-NUM is defined as a 2-byte binary integer containing a version number. A second data item VERS-BYTES is defined as a two-character alphanumeric variable. Since the second item is redefined over the first item, the two items share the same address in memory, and therefore share the same underlying data ...
In this case, a helpful alternative may be folded, computed or encoded tags, where the tag value is dynamically computed from the contents of the union field. Common examples are the use of reserved values, where, for example, a function returning a positive number may return -1 to indicate failure, and sentinel values, most often used in ...
After some operations of Union, some sets are grouped together. The operation Union(x, y) replaces the set containing x and the set containing y with their union. Union first uses Find to determine the roots of the trees containing x and y. If the roots are the same, there is nothing more to do. Otherwise, the two trees must be merged.
The union is the join/supremum of and with respect to because: L ⊆ L ∪ R {\displaystyle L\subseteq L\cup R} and R ⊆ L ∪ R , {\displaystyle R\subseteq L\cup R,} and if Z {\displaystyle Z} is a set such that L ⊆ Z {\displaystyle L\subseteq Z} and R ⊆ Z {\displaystyle R\subseteq Z} then L ∪ R ⊆ Z . {\displaystyle L\cup R\subseteq Z.}
One of the most common examples of an algebraic data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element x with a list xs to create a new list. Here is an example of how a singly linked list would be declared in Haskell:
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For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...
A disjoint union may mean one of two things. Most simply, it may mean the union of sets that are disjoint. [11] But if two or more sets are not already disjoint, their disjoint union may be formed by modifying the sets to make them disjoint before forming the union of the modified sets. [12]