Verifying Temporal Properties of Reactive Systems by Transformation

We show how program transformation techniques can be used for the verification of both safety and liveness properties of reactive systems. In particular, we show how the program transformation technique distillation can be used to transform reactive systems specified in a functional language into a simplified form that can subsequently be analysed to verify temporal properties of the systems. Example systems which are intended to model mutual exclusion are analysed using these techniques with respect to both safety (mutual exclusion) and liveness (non-starvation), with the errors they contain being correctly identified.Comment: In Proceedings VPT 2015, arXiv:1512.02215. This work was supported, in part, by Science Foundation Ireland grant 10/CE/I1855 to Lero - the Irish Software Engineering Research Centre (www.lero.ie), and by the School of Computing, Dublin City Universit

Turchin's Relation for Call-by-Name Computations: A Formal Approach

Supercompilation is a program transformation technique that was first described by V. F. Turchin in the 1970s. In supercompilation, Turchin's relation as a similarity relation on call-stack configurations is used both for call-by-value and call-by-name semantics to terminate unfolding of the program being transformed. In this paper, we give a formal grammar model of call-by-name stack behaviour. We classify the model in terms of the Chomsky hierarchy and then formally prove that Turchin's relation can terminate all computations generated by the model.Comment: In Proceedings VPT 2016, arXiv:1607.0183

Distilling Programs to Prove Termination

The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for deciding whether a program terminates dates back to Turing himself and involves finding a ranking function that maps a program state to a well-order, and then proving that the result of this function decreases for every possible program transition. More recent approaches to proving termination have involved moving away from the search for a single ranking function and toward a search for a set of ranking functions; this set is a choice of ranking functions and a disjunctive termination argument is used. In this paper, we describe a new technique for determining whether programs terminate. Our technique is applied to the output of the distillation program transformation that converts programs into a simplified form called distilled form. Programs in distilled form are converted into a corresponding labelled transition system and termination can be demonstrated by showing that all possible infinite traces through this labelled transition system would result in an infinite descent of well-founded data values. We demonstrate our technique on a number of examples, and compare it to previous work.Comment: In Proceedings VPT/HCVS 2020, arXiv:2008.02483. This work owes a lot to the input of Neil Jones, who provided many useful insights and ideas on the subject matter presented her

The next 700 program transformers

In this paper, we describe a hierarchy of program transformers, capable of performing fusion to eliminate intermediate data structures, in which the transformer at each level of the hierarchy builds on top of those at lower levels. The program transformer at level 1 of the hierarchy corresponds to positive supercompilation, and that at level 2 corresponds to distillation. We give a number of examples of the application of our transformers at different levels in the hierarchy and look at the speedups that are obtained. We determine the maximum speedups that can be obtained at each level, and prove that the transformers at each level terminate

Distillation with labelled transition systems

In this paper, we provide an improved basis for the “distillation” program transformation. It is known that superlinear speedups can be obtained using distillation, but cannot be obtained by other earlier automatic program transformation techniques such as deforestation, positive supercompilation and partial evaluation. We give distillation an improved semantic basis, and explain how superlinear speedups can occur