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by C. -h. L. Ong
In Proceedings of LICS’02. IEEE
ftp://ftp.comlab.ox.ac.uk/pub/Documents/techpapers/Luke.Ong/lics02.ps.gz
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Abstract:
We prove that observational equivalence of 3rd-order finitary Idealized Algol (IA) is decidable using Game Semantics. By modelling state explicitly in our games, we show that the denotation of a term M of this fragment of IA (built up from finite base types) is a compactly innocent strategy-with-state i.e. the strategy is generated by a finite view function fM. Given any such fM, we construct a real-time deterministic pushdown automata (DPDA) that recognizes the complete plays of the knowing-strategy denotation of M. Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding observational equivalence of 3rdorder finitary IA. This algorithmic representation of program meanings, which is compositional, provides a foundation for model-checking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns 2nd-order IA with recursion: we show that observational equivalence for this fragment is undecidable.
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