Theoretical models used in database research often have subtle differences with those occurring in practice. One particular mismatch that is usually neglected concerns the use of marked nulls to represent missing values in theoretical models of incompleteness, while in an SQL database these are all denoted by the same syntactic NULL object. It is commonly argued that results obtained in the model with marked nulls carry over to SQL, because SQL nulls can be interpreted as Codd nulls, which are simply marked nulls that do not repeat. This argument, however, does not take into account that even simple queries may produce answers where distinct occurrences of NULL do in fact denote the same unknown value. For such queries, interpreting SQL nulls as Codd nulls would incorrectly change the semantics of query answers.

To use results about Codd nulls for real-life SQL queries, we need to understand which queries preserve the Codd interpretation of SQL nulls. We show, however, that this is an undecidable problem for relational algebra. Nonetheless, by exploiting the information provided by NOT NULL constraints on the database schema, we devise mild syntactic restrictions on queries that guarantee this preservation. Moreover, these restrictions do not limit the full expressiveness of queries on databases without nulls and can be checked efficiently.