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:
   • 
   • 
   •