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The previous VPT 2020 workshop was organized in honour of Professor Alberto Pettorossi on the occasion of his academic retirement from Universit\`a di Roma Tor Vergata. Due to the pandemic the VPT 2020 meeting was cancelled but its proceeding have already appeared in the EPTCS 320 volume. The joint VPT-20-21 event has subsumed the original programme of VPT 2020 and provided an opportunity to meet and celebrate the achievements of Professor Alberto Pettorossi; its programme was further expanded with the newly submitted presentations for VPT 2021. The aim of the VPT workshop series is to provide a forum where people from the areas of program transformation and program verification can fruitfully exchange ideas and gain a deeper understanding of the interactions between those two fields.

We have proved that for any pattern p the tail recursive program model of naive pattern matching may be automatically specialized w.r.t. the pattern p to a specialized version of the so-called KMP-algorithm, using the Higman-Kruskal relation that controls the unfolding/folding. Given an input string, the corresponding residual program finds the first occurrence of p in the string in linear time on the string length. The current state of the automated program specialization art based on unfolding/folding is too weak in order to be able to reproduce the proof, done by hands, of the uniform property above, while it known before that program specialization is sometimes able to produce the KMP-algorithm for a few concrete static patterns., Comment: Pre-proceedings paper presented at the 31st International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2021), Tallinn, Estonia, and Virtual, September 7-8, 2021 (arXiv:2107.10160)

This volume contains a final and revised selection of papers presented at the Seventh International Workshop on Verification and Program Transformation (VPT 2019), which took place in Genova, Italy, on April 2nd, 2019, affiliated with Programming 2019.

We explore an approach to verification of programs via program transformation applied to an interpreter of a programming language. A specialization technique known as Turchin's supercompilation is used to specialize some interpreters with respect to the program models. We show that several safety properties of functional programs modeling a class of cache coherence protocols can be proved by a supercompiler and compare the results with our earlier work on direct verification via supercompilation not using intermediate interpretation. Our approach was in part inspired by an earlier work by E. De Angelis et al. (2014-2015) where verification via program transformation and intermediate interpretation was studied in the context of specialization of constraint logic programs., Comment: In Proceedings VPT 2017, arXiv:1708.06887. The author's extended version is arXiv:1705.06738

This volume contains the proceedings of the Fifth International Workshop on Verification and Program Transformation (VPT 2017). The workshop took place in Uppsala, Sweden, on April 29th, 2017, affiliated with the European Joint Conferences on Theory and Practice of Software (ETAPS). The aim of the VPT workshop series is to provide a forum where people from the areas of program transformation and program verification can fruitfully exchange ideas and gain a deeper understanding of the interactions between those two fields. Seven papers were presented at the workshop. Additionally, three invited talks were given by Javier Esparza (Technische Universit\"at M\"unchen, Germany), Manuel Hermenegildo (IMDEA Software Institute, Madrid, Spain), and Alexey Khoroshilov (Linux Verification Center, ISPRAS, Moscow, Russia).

We explore an approach to verification of programs via program transformation applied to an interpreter of a programming language. A specialization technique known as Turchin's supercompilation is used to specialize some interpreters with respect to the program models. We show that several safety properties of functional programs modeling a class of cache coherence protocols can be proved by a supercompiler and compare the results with our earlier work on direct verification via supercompilation not using intermediate interpretation. Our approach was in part inspired by an earlier work by De E. Angelis et al. (2014-2015) where verification via program transformation and intermediate interpretation was studied in the context of specialization of constraint logic programs., Comment: Fifth International Workshop on Verification and Program Transformation (VPT-2017), April 29th, 2017, Uppsala, Sweden, 37 pages

This volume contains the revised versions of papers presented at the Fourth International Workshop on Verification and Program Transformation (VPT 2016) on April 2, 2016 in Eindhoven, The Netherlands. The workshop is an event of the European Joint Conferences on Theory and Practice of Software (ETAPS 2016). The aim of the VPT workshops is to provide a forum where people from the area of program transformation and the area of program verification can fruitfully exchange ideas and gain a deeper understanding of the interactions between those two fields. The research papers which have been recently published in those fields, show that the interactions are very beneficial and, indeed, go both ways. In one direction, methods and tools developed in the field of program transformation, such as partial deduction, partial evaluation, fold/unfold transformations, and supercompilation, have all been applied with success for the verification of systems, and in particular, the verification of infinite state and parameterized systems. In the other direction, methods developed in program verification, such as model checking, abstract interpretation, SAT and SMT solving, and automated theorem proving, have been used to enhance program transformation techniques, thereby making these techniques more powerful and useful in practice.

Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation) for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems., Comment: In Proceedings VPT 2015, arXiv:1512.02215

This volume contains the papers selected among those which were presented at the 3rd International Workshop on Verification and Program Transformation (VPT 2015) held in London, UK, on April 11th, 2015. Previous editions of the Workshop were held at Saint-Petersburg (Russia) in 2013, and Vienna (Austria) in 2014. Those papers show that methods and tools developed in the field of program transformation such as partial evaluation and fold/unfold transformations, and supercompilation, can be applied in the verification of software systems. They also show how some program verification methods, such as model checking techniques, abstract interpretation, SAT and SMT solving, and automated theorem proving, can be used to enhance program transformation techniques, thereby making these techniques more powerful and useful in practice.

The paper presents two examples of non-traditional using of program specialization by Turchin's supercompilation method. In both cases we are interested in syntactical properties of residual programs produced by supercompilation. In the first example we apply supercompilation to a program encoding a word equation and as a result we obtain a program representing a graph describing the solution set of the word equation. The idea of the second example belongs to Alexandr V. Korlyukov. He considered an interpreter simulating the dynamic of the well known missionaries-cannibals puzzle. Supercompilation of the interpreter allows us to solve the puzzle. The interpreter may also be seen as an encoding of a non-deterministic protocol.