Collection analysis for Horn clause programs

TL;DR

This paper introduces a method for analyzing Horn clause programs by approximating data structures with collections, enabling partial correctness proofs through a linear logic-based scheme that can be automated.

Contribution

It presents a novel collection analysis framework for Horn clauses using linear logic to facilitate automatic partial correctness verification.

Findings

Allows static analysis of data structure properties in logic programs

Uses linear logic to underpin the analysis scheme

Enables automation of correctness proofs for list and set operations

Abstract

We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to provide partial correctness properties of logic programs. For example, one might wish to specify than whenever the atom $sort(t,s)$ is proved then the two lists $t$ and $s$ contain the same multiset of items (that is, $s$ is a permutation of $t$). If sorting removes duplicates, then one would like to infer that the sets of items underlying $t$ and $s$ are the same. Such results could be useful to have if they can be determined statically and automatically. We present a scheme by which such collection analysis can be structured and automated. Central to this scheme is the use of linear logic as a omputational logic underlying the logic of Horn clauses.