The Abella Interactive Theorem Prover (System Description)

Abstract

Abella 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 lambda tree syntax approach to treating binding in object languages. Amongst other things, Abella has been used to prove normalizability properties of the lambda 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.

7 pages, to appear in IJCAR'08

Cited by in corpus (8)

• A Higher-Order Abstract Syntax Approach to the Verified Compilation of Functional Programs
• An Improved Implementation and Abstract Interface for Hybrid
• Relating Nominal and Higher-order Abstract Syntax Specifications
• Combining Deduction Modulo and Logics of Fixed-Point Definitions
• Syntax and Semantics of Abstract Binding Trees
• Reasoning in Abella about Structural Operational Semantics Specifications
• A two-level logic approach to reasoning about computations
• A Meta-Programming Approach to Realizing Dependently Typed Logic Programming