Formal Definitions in tuple relational calculas
- A tuple relational calculus expression is of the form
where is a formula.
Several tuple variables may appear in a formula.
- 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.
- 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 .
- 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.
- Note some equivalences: