Reasoning with Higher-Order Abstract Syntax and Contexts: A Comparison

  • Amy Felty
  • Brigitte Pientka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

Abstract

A variety of logical frameworks support the use of higher-order abstract syntax (HOAS) in representing formal systems given via axioms and inference rules and reasoning about them. In such frameworks, object-level binding is encoded directly using meta-level binding. Although these systems seem superficially the same, they differ in a variety of ways; for example, in how they handle a context of assumptions and in what theorems about a given formal system can be expressed and proven. In this paper, we present several case studies which highlight a variety of different aspects of reasoning using HOAS, with the intention of providing a basis for qualitative comparison of different systems. We then carry out such a comparison among three systems: Twelf, Beluga, and Hybrid. We also develop a general set of criteria for comparing such systems. We hope that others will implement these challenge problems, apply these criteria, and further our understanding of the trade-offs involved in choosing one system over another for this kind of reasoning.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Amy Felty
    • 1
  • Brigitte Pientka
    • 2
  1. 1.SITEUniversity of OttawaOttawaCanada
  2. 2.School of Computer ScienceMcGill UniversityMontrealCanada

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