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Title: Game semantics based equivalence checking of higher-order programs
Author: Hopkins, David G. B.
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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This thesis examines the use of game semantics for the automatic equivalence checking of higher-order programs. Game semantics has proved to be a powerful method for constructing fully abstract models of logics and programming languages. Furthermore, the concrete nature of the semantics lends itself to algorithmic analysis. The game-semantic model can be used to identify fragments of languages which have a decidable observational equivalence problem. We investigate decidability results for different languages as well as the efficiency of these algorithms in practice. First we consider the call-by-value higher-order language with state, RML. This can be viewed as a canonical restriction of Standard ML to ground-type references. The O-strict fragment of RML is the largest set of type sequents for which, in the game-semantic denotation, justification pointers from O-moves are always uniquely reconstructible from the underlying move sequence. The O-strict fragment is surprisingly expressive, including higher-order types and difficult examples from the literature. By representing strategies as Visibly Pushdown Automata (VPA) we show that observational equivalence of O-strict terms is decidable (and in fact is ExpTime-complete). We then consider extensions of the O-strict fragment. Adding general recursion or using most non-O-strict types leads to undecidability. However, a limited form of recursion can be added while still preserving decidability (although the full power of DPDA is required). Next we examine languages with non-local control. This involves adding call/cc to our language and is known to correspond to dropping the game-semantic bracketing condition. In the call-by-name game-semantic model of Idealized Algol (IA), in which answers cannot justify questions, the visibility condition still implies a form of weak bracketing. By making bracketing violations explicit we show that we can still model the entire third-order fragment using VPA. We have also implemented tools based on these algorithms. Our model checkers Homer and Hector perform equivalence checking for third-order IA and O-strict RML respectively. Homer uses a naive explicit state method whereas Hector takes advantage of on-the-fly model checking. Our tools perform well on small yet challenging examples. On negative instances, the on-the-fly approach allows Hector to outperform Homer. To improve their performance, we also consider using ideas from symbolic execution. We propose a representation for finite automata using transitions labelled with formulas and guards which aims to take advantage of the symmetries of the game-semantic model so that strategies can be represented compactly. We refer to this representation as Symbolically Executed Automata (SEA). Using SEA allows much larger data types to be handled but is not as effective on larger examples with small data types.
Supervisor: Ong, C.-H. Luke; Murawski, Andrzej S. Sponsor: Microsoft Research
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Theory and automated verification ; Game semantics ; Higher-order programs ; verification ; equivalence checking