Safe tuple relational calculus

Safe tuple relational calculus restricts tuple relational calculus so that output values come from the finite input relations or explicit constants, with suitable restrictions on quantification. This prevents an apparently simple database query from demanding an infinite result over an unrestricted value universe. Database query safety is a semantic requirement; merely writing a familiar-looking formula does not ensure it.^[ref]

For a finite unary relation $R=\{(1),(3)\}$, the database query $\{t:R(t)\wedge t.x>1\}$ safely returns $\{(3)\}$. In contrast, $\{t:\neg R(t)\}$ over all integers requests every other unary database tuple, an infinite collection. Restricting negation to tuples already drawn from another finite relation gives an expressible finite set difference. Under the usual finite relational model, the safe calculus and relational algebra express the same queries.