Types and Higher-Order Recursion Schemes for Verification of Higher-Order Programs

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Types and Higher-Order Recursion Schemes for Verification of Higher-Order Programs (2009)

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by Naoki Kobayashi

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63 - 14 self

BibTeX

@MISC{Kobayashi09typesand,
    author = {Naoki Kobayashi},
    title = {Types and Higher-Order Recursion Schemes for Verification of Higher-Order Programs },
    year = {2009}
}

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Abstract

We propose a new verification method for temporal properties of higher-order functional programs, which takes advantage of Ong’s recent result on the decidability of the model-checking problem for higher-order recursion schemes (HORS’s). A program is transformed to an HORS that generates a tree representing all the possible event sequences of the program, and then the HORS is modelchecked. Unlike most of the previous methods for verification of higher-order programs, our verification method is sound and complete. Moreover, this new verification framework allows a smooth integration of abstract model checking techniques into verification of higher-order programs. We also present a type-based verification algorithm for HORS’s. The algorithm can deal with only a fragment of the properties expressed by modal μ-calculus, but the algorithm and its correctness proof are (arguably) much simpler than those of Ong’s game-semantics-based algorithm. Moreover, while the HORS model checking problem is n-EXPTIME in general, our algorithm is linear in the size of HORS, under the assumption that the sizes of types and specifications are bounded by a constant.

Keyphrases

higher-order program higher-order recursion scheme new verification method model-checking problem new verification framework hors model temporal property recent result ong game-semantics-based algorithm verification method smooth integration modal calculus type-based verification algorithm abstract model correctness proof previous method higher-order functional program possible event sequence

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