Evaluation of Logic Programs with Built-Ins and Aggregation: A Calculus for Bag Relations

TL;DR

This paper introduces a calculus for translating logic programs with built-in functions and aggregation into algebraic expressions over bag relations, enabling efficient evaluation through term rewriting and supporting lazy strategies.

Contribution

It provides a novel algebraic calculus and operational semantics for logic programs with aggregation and arithmetic, facilitating optimized query evaluation.

Findings

Supports lazy evaluation strategies

Enables algebraic manipulation of logic programs

Provides a formal semantics for query evaluation

Abstract

We present a scheme for translating logic programs, which may use aggregation and arithmetic, into algebraic expressions that denote bag relations over ground terms of the Herbrand universe. To evaluate queries against these relations, we develop an operational semantics based on term rewriting of the algebraic expressions. This approach can exploit arithmetic identities and recovers a range of useful strategies, including lazy strategies that defer work until it becomes possible or necessary.