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arXiv · 2210.14649

Higher-Order MSL Horn Constraints

Jerome Jochems·Eddie Jones·Steven Ramsay
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Abstract

The monadic shallow linear (MSL) class is a decidable fragment of first-order Horn clauses that was discovered and rediscovered around the turn of the century, with applications in static analysis and verification. We propose a new class of higher-order Horn constraints which extend MSL to higher-order logic and develop a resolution-based decision procedure. Higher-order MSL Horn constraints can quite naturally capture the complex patterns of call and return that are possible in higher-order programs, which make them well suited to higher-order program verification. In fact, we show that the higher-order MSL satisfiability problem and the HORS model checking problem are interreducible, so that higher-order MSL can be seen as a constraint-based approach to higher-order model checking. Finally, we describe an implementation of our decision procedure and its application to verified socket programming.

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Jerome Jochems, Eddie Jones, Steven Ramsay. 2022-10-26. Higher-Order MSL Horn Constraints. https://arxiv.org/abs/2210.14649

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