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.
Keywords
Context Variable Type Family Elimination Form Linear Logic Syntactic CategoryNotes
Acknowledgments
We would like to thank Daniel Gustafsson for invaluable feedback. This work is funded by the DemTech grant 10-092309 of the Danish Council for Strategic Research on Democratic Technologies.
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