Higher-order multi-parameter tree transducers and recursion schemes for program verification

  • Authors:

  • Naoki Kobayashi;Naoshi Tabuchi;Hiroshi Unno

  • Affiliations:

  • Tohoku University, Sendai, Japan;Tohoku University, Sendai, Japan;Tohoku University, Sendai, Japan

  • Venue:
  • Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2010

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Abstract

We introduce higher-order, multi-parameter, tree transducers (HMTTs, for short), which are kinds of higher-order tree transducers that take input trees and output a (possibly infinite) tree. We study the problem of checking whether the tree generated by a given HMTT conforms to a given output specification, provided that the input trees conform to input specifications (where both input/output specifications are regular tree languages). HMTTs subsume higher-order recursion schemes and ordinary tree transducers, so that their verification has a number of potential applications to verification of functional programs using recursive data structures, including resource usage verification, string analysis, and exact type-checking of XML-processing programs. We propose a sound but incomplete verification algorithm for the HMTT verification problem: the algorithm reduces the verification problem to a model-checking problem for higher-order recursion schemes extended with finite data domains, and then uses (an extension of)Kobayashi's algorithm for model-checking recursion schemes. While the algorithm is incomplete (indeed, as we show in the paper, the verification problem is undecidable in general), it is sound and complete for a subclass of HMTTs called linear HMTTs . We have applied our HMTT verification algorithm to various program verification problems and obtained promising results.