Union and Disjunction

Expr := Expr ";" Expr
      | "{ ; }"

The semicolon is a generalized union operator.

For example:

// read query
 
def P = (1, 2); (3, 4); (5, 6)
def Q = ("a", 41, "A", 61 ); ("b", 42, "B", 62)
def output = P; Q

The empty set is the neutral element of the union operation, just like the number 0 in arithmetic addition. More precisely, if R is a relation, then the expressions {} ; R and R; {} both evaluate to R.

In the simplified form { ; } the missing operands default to the neutral element. So the expression {;} is equivalent to {{}; {}}, that is, {}.

Examples:

• For any relation p, {}; p is equivalent to p.
• 1; 3 is equivalent to x: x = 1 or x = 3.
• If p and q are unary relations, then:
  • p(x); q(x) is equivalent to p(x) or q(x).
  • p; q is equivalent to x: p(x) or q(x).

The semicolon operator is equivalent to or when its arguments are restricted to relations of arity 0. To illustrate this, here is the table of all possible combinations of two relations with arity 0:

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