Abstract
Using game semantics, we investigate the problem of verifying contextual equivalences in Interface Middleweight Java (IMJ), an imperative object calculus in which program phrases are typed using interfaces. Working in the setting where data types are non-recursive and restricted to finite domains, we identify the frontier between decidability and undecidability by reference to the structure of interfaces present in typing judgments. In particular, we show how to determine the decidability status of problem instances (over a fixed type signature) by examining the position of methods inside the term type and the types of its free identifiers. Our results build upon the recent fully abstract game semantics of IMJ. Decidability is proved by translation into visibly pushdown register automata over infinite alphabets with fresh-input recognition.
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Notes
- 1.
Since the space we can devote in this paper to the exposition of the game model is limited, we kindly refer the reader to [11] for a thorough account.
- 2.
The partitioning depends on the type of the move (e.g. only P-calls can be pushes, and only O-returns can be pops) and is made explicit in the automata construction.
- 3.
As we see next, these actions do not necessarily happen in this order (pops happen first).
- 4.
This is a technical convenience of the interpretation: as we see next, we translate each canonical term into a family of automata, one per (symbolic) initial move-with-store (here, the unique initial move is \({\star }^\emptyset \)). Initial states take the initial move as given and are therefore P-states.
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Murawski, A.S., Ramsay, S.J., Tzevelekos, N. (2015). Game Semantic Analysis of Equivalence in IMJ. In: Finkbeiner, B., Pu, G., Zhang, L. (eds) Automated Technology for Verification and Analysis. ATVA 2015. Lecture Notes in Computer Science(), vol 9364. Springer, Cham. https://doi.org/10.1007/978-3-319-24953-7_30
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