Types and higher-order recursion schemes for verification of higher-order programs

  • Authors:

  • Naoki Kobayashi

  • Affiliations:

  • Tohoku University, Sendai, Japan

  • Venue:
  • Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • 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 model-checked. 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 mu-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 specification formulas are bounded by a constant.