Comprehending nulls

TL;DR

This paper explores how to incorporate SQL-style nulls and incomplete information into the Nested Relational Calculus (NRC), proposing explicit and implicit approaches and analyzing their implications for language integration and formal properties.

Contribution

It introduces explicit and implicit methods for handling nulls in NRC, providing translations and discussing their impact on language integration and normalization.

Findings

Explicit and implicit null handling approaches are proposed.

Translations relate the two approaches.

Extensions of normalization and conservativity are sketched.

Abstract

The Nested Relational Calculus (NRC) has been an influential high-level query language, providing power and flexibility while still allowing translation to standard SQL queries. It has also been used as a basis for language-integrated query in programming languages such as F#, Scala, and Links. However, SQL's treatment of incomplete information, using nulls and three-valued logic, is not compatible with `standard' NRC based on two-valued logic. Nulls are widely used in practice for incomplete data, but the question of how to accommodate SQL-style nulls and incomplete information in NRC, or integrate such queries into a typed programming language, appears not to have been studied thoroughly. In this paper we consider two approaches: an explicit approach in which option types are used to represent (possibly) nullable primitive types, and an implicit approach in which types are treated as possibly-null by default. We give translations relating the implicit and explicit approaches, discuss handling nulls in language integration, and sketch extensions of normalization and conservativity results.