The Abella Interactive Theorem Prover (System Description)

  • Authors:

  • Andrew Gacek

  • Affiliations:

  • Department of Computer Science and Engineering, University of Minnesota, Minneapolis, USA MN 55455

  • Venue:
  • IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
  • Year:
  • 2008

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Abstract

Abella [3] is an interactive system for reasoning about aspects of object languages that have been formally presented through recursive rules based on syntactic structure. Abella utilizes a two-level logic approach to specification and reasoning. One level is defined by a specification logic which supports a transparent encoding of structural semantics rules and also enables their execution. The second level, called the reasoning logic, embeds the specification logic and allows the development of proofs of properties about specifications. An important characteristic of both logics is that they exploit the 茂戮驴-tree syntax approach to treating binding in object languages. Amongst other things, Abella has been used to prove normalizability properties of the 茂戮驴-calculus, cut admissibility for a sequent calculus and type uniqueness and subject reduction properties. This paper discusses the logical foundations of Abella, outlines the style of theorem proving that it supports and finally describes some of its recent applications.