Nontermination inference of logic programs

Abstract

We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized. We give syntactic criteria to statically identify such argument positions from the text of a program. Atomic left looping queries are generated bottom-up from selected subsets of the binary unfoldings of the program of interest. We propose a set of correct algorithms for automating the approach. Then, non-termination inference is tailored to attempt proofs of optimality of left termination conditions computed by a termination inference tool. An experimental evaluation is reported. When termination and non-termination analysis produce complementary results for a logic procedure, then with respect to the leftmost selection rule and the language used to describe sets of atomic queries, each analysis is optimal and together, they induce a characterization of the operational behavior of the logic procedure.

Automated Detection of Non-termination and NullPointerExceptions for Java Bytecode

“…Methods to detect non-termination automatically have for example been studied for term rewriting (e.g., [11,19]) and logic programming (e.g., [18]). We are only aware of two existing tools for automated non-termination analysis of Java: The tool Julia transforms JBC programs into constraint logic programs, which are then analyzed for non-termination [20].…”

A New Approach to Non-termination Analysis of Logic Programs

“…We compared our tool with N T I [10], the only other non-termination analyzer for logic programs. We have shown that our approach improves on the results of N T I and that we are able to prove non-termination of new classes of programs.…”

“…All programs contain between 2 and 15 clauses, except for binary4, which contains 41 clauses. The only other non-termination analyzer, N T I [10], proves non-termination for about 95% of the benchmark programs. Table 1 shows our experimental evaluation on this benchmark using LP-check with pruning, with 4 as a repetition number.…”

“…A termination analysis can be shown to be precise by proving the that the class of queries for which termination could not be proven is actually non-terminating. This has been one of the main goals and achievements of the only non-termination analyzer developed up till now, N T I [10].…”

“…In section 3, we present our conditions implying non-termination and show that we are able to derive classes of non-terminating queries. In Section 4, we present our experimental evaluation and we compare our analyzer with the non-termination inference tool N T I [10]. Finally, Section 5 concludes this paper.…”