Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

Distilling programs for verification

In this paper, we show how our program transformation algorithm called distillation can not only be used for the optimisation of programs, but can also be used to facilitate program verification. Using the distillation algorithm, programs are transformed into a specialised form in which functions are tail recursive, and very few intermediate structures are created. We then show how properties of this specialised form of program can be easily verified by the application of inductive proof rules. We therefore argue that the distillation algorithm is an ideal candidate for inclusion within compilers as it facilitates the two goals of program optimization and verification

Measuring the Propagation of Information in Partial Evaluation

We present the first measurement-based analysis of the information propagated by a partial evaluator. Our analysis is based on measuring implementations of string-matching algorithms, based on the observation that the sequence of character comparisons accurately reflects maintained information. Notably, we can easily prove matchers to be different and we show that they display more variety and finesse than previously believed. As a consequence, we are able to pinpoint differences and inaccuracies in many results previously considered equivalent. Our analysis includes a framework that lets us obtain string matchers - notably the family of Boyer-Moore algorithms - in a systematic formalism-independent way from a few information-propagation primitives. By leveraging the existing research in string matching, we show that the landscape of information propagation is non-trivial in the sense that small changes in information propagation may dramatically change the properties of the resulting string matchers. We thus expect that this work will prove useful as a test and feedback mechanism for information propagation in the development of advanced program transformations, such as GPC or Supercompilation

Generalization Strategies for the Verification of Infinite State Systems

We present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools. To appear in Theory and Practice of Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table