A Representation of Fω in LF

Schürmann, Carsten; Yu, Dejian; Ni, Zhaozhong

doi:10.1016/s1571-0661(04)00280-4

Cited by 4 publications

(1 citation statement)

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“…Pfenning (1994) gives a proof of cut elimination for intuitionistic logic. Schürmann et al (2001) present some of the metatheory of F ω . Schürmann and Stehr (2005) present a formalization of Howe's embedding of HOL into NuPRL.…”

Section: Applications Of Lf and Twelfmentioning

confidence: 99%

Mechanizing metatheory in a logical framework

Harper¹,

Licata²

2007

J. Funct. Prog.

107

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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 representation, and the Twelf methodology for mechanizing metatheory. We begin by defining a variant of the original LF language, called Canonical LF, in which only canonical forms (long βη-normal forms) are permitted. This variant is parameterized by a subordination relation, which enables modular reasoning about LF representations. We then give an adequate representation of a simply typed λ-calculus in Canonical LF, both to illustrate adequacy and to serve as an object of analysis. Using this representation, we formalize and verify the proofs of some metatheoretic results, including preservation, determinacy, and strengthening. Each example illustrates a significant aspect of using LF and Twelf for formalized metatheory.

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Section: Applications Of Lf and Twelfmentioning

confidence: 99%