A Contextual Logical Framework

Abstract

A new logical framework with explicit linear contexts and names is presented with the purpose of enabling direct and flexible manipulation of contexts, both for representing systems and meta-properties. The framework is a conservative extension of the logical framework LF, and builds on linear logic and contextual modal type theory. We prove that the framework admits canonical forms, and that it possesses all desirable meta-theoretic properties, in particular hereditary substitutions.

As proof of concept, we give an encoding of the one-sided sequent calculus for classical linear logic and the corresponding cut-admissibility proof, as well as an encoding of parallel reduction of lambda terms with the corresponding value-soundness proof.