Mechanizing metatheory in a logical framework

The LF logical framework codifies a methodology for representing deductive systems, such as programming languages and logics, within a dependently typed λ-calculus. In this methodology, the syntactic and deductive apparatus of a system is encoded as the canonical forms of associated LF types; an encoding is correct (adequate) if and only if it defines a compositional bijection between the apparatus of the deductive system and the associated canonical forms. Given an adequate encoding, one may establish metatheoretic properties of a deductive system by reasoning about the associated LF representation. The Twelf implementation of the LF logical framework is a convenient and powerful tool for putting this methodology into practice. Twelf supports both the representation of a deductive system and the mechanical verification of proofs of metatheorems about it. The purpose of this paper is to provide an up-to-date overview of the LF λ-calculus, the LF methodology for adequate represent...

• Type: Journal
• Year: 2007
• Where: JFP
• Authors: Robert Harper, Daniel R. Licata
• Keywords: Canonical Forms, Deductive System, JFP 2007, LF Logical Framework