# Formal Definitions in tuple relational calculas

Posted By on October 4, 2014

## 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:

#### Posted by Akash Kurup

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