Logic for Programming, Artificial Intelligence, and Reasoning

Logic for Programming, Artificial Intelligence, and Reasoning pp 402-417

A Contextual Logical Framework

Conference paper

DOI: 10.1007/978-3-662-48899-7_28

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9450)
Cite this paper as:
Bock P.B., Schürmann C. (2015) A Contextual Logical Framework. In: Davis M., Fehnker A., McIver A., Voronkov A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. Lecture Notes in Computer Science, vol 9450. Springer, Berlin, Heidelberg

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.IT University of CopenhagenCopenhagenDenmark

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