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Abella is an interactive system for reasoning about aspects of objectlanguages that have been formally presented through recursive rules based onsyntactic structure. Abella utilizes a two-level logic approach tospecification and reasoning. One level is defined by a specification logicwhich supports a transparent encoding of structural semantics rules and alsoenables their execution. The second level, called the reasoning logic, embedsthe specification logic and allows the development of proofs of propertiesabout specifications. An important characteristic of both logics is that theyexploit the lambda tree syntax approach to treating binding in objectlanguages. Amongst other things, Abella has been used to prove normalizabilityproperties of the lambda calculus, cut admissibility for a sequent calculus andtype uniqueness and subject reduction properties. This paper discusses thelogical foundations of Abella, outlines the style of theorem proving that itsupports and finally describes some of its recent applications.

The Abella Interactive Theorem Prover (System Description)