Structural Logical Relations

Tait’s method (a.k.a. proof by logical relations) is a powerful proof technique frequently used for showing foundational properties of languages based on typed λ-calculi. Historically, these proofs have been extremely difficult to formalize in proof assistants with weak meta-logics, such as Twelf, and yet they are often straightforward in proof assistants with stronger meta-logics. In this paper, we propose structural logical relations as a technique for conducting these proofs in systems with limited meta-logical strength by explicitly representing and reasoning about an auxiliary logic. In support of our claims, we give a Twelf-checked proof of the completeness of an algorithm for checking equality of simply typed λ-terms.

• Type: Conference
• Year: 2008
• Where: LICS
• Authors: Carsten Schürmann, Jeffrey Sarnat
• Keywords: Computer Science, LICS 2008, Logical Relations, Powerful Proof Technique, Proof Assistants