Formal Definitions   Next: Safety of Expressions Up: The Tuple Relational Previous: Example Queries

Formal Definitions

1. A tuple relational calculus expression is of the form where is a formula.

Several tuple variables may appear in a formula.

2. A tuple variable is said to be a free variable unless it is quantified by a or a . Then it is said to be a bound variable.

3. A formula is built of atoms. An atom is one of the following forms:
• , where is a tuple variable, and r is a relation ( is not allowed).
• , where and are tuple variables, and and are attributes, and is a comparison operator ( ).

• , where is a constant in the domain of attribute .
4. Formulae are built up from atoms using the following rules:
• An atom is a formula.
• If is a formula, then so are and .
• If and are formulae, then so are , and .
• If is a formula containing a free tuple variable , then are formulae also.

5. Note some equivalences:
• • • Page created and maintained by Osmar R. Zaï ane
Last Update: Wed Sep 20 15:45:57 PDT 1995