Polymorphic type inference for the relational algebra

TL;DR

This paper introduces a formalism for polymorphic type inference in relational algebra, providing an algorithm to compute principal types that specify valid attribute assignments and output types, enhancing understanding of type safety and expressiveness.

Contribution

It presents a novel formalism of type formulas and an algorithm for principal type inference in relational algebra, addressing complexity and expressive power.

Findings

Algorithm computes principal types for relational algebra expressions.

Formalism captures polymorphic type assignments and output types.

Analysis of complexity and expressive power of the type system.

Abstract

We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given expression. The principal type of an expression is a formula that specifies, in a clear and concise manner, all assignments of types (sets of attributes) to relation names, under which a given relational algebra expression is well-typed, as well as the output type that expression will have under each of these assignments. Topics discussed include complexity and polymorphic expressive power.