Logic Programming in Tabular Allegories

We develop a compilation scheme and categorical abstract machine for execution of logic programs based on allegories, the categorical version of the calculus of relations. Operational and denotational semantics are developed using the same formalism, and query execution is performed using algebraic reasoning. Our work serves two purposes: achieving a formal model of a logic programming compiler and efficient runtime; building the base for incorporating features typical of functional programming in a declarative way, while maintaining 100% compatibility with existing Prolog programs