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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
This is the same restriction as in traditional CMTT for LF, since it would lead to commuting conversions.
References
Gacek, A.: The abella interactive theorem prover (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 154–161. Springer, Heidelberg (2008)
Girard, J.-Y.: Linear Logic: Its Syntax and Semantics. London Mathematical Society Lecture Note Series, pp. 1–42. Cambridge University Press, New York (1995)
Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. J. ACM (JACM) 40(1), 143–184 (1993)
Nanevski, A., Pfenning, F., Pientka, B.: Contextual modal type theory. ACM Trans. Comput. Logic (TOCL) 9(3), 23 (2008)
Pfenning, F., Cervesato, I.: A linear logical framework. In: Clarke, E. (ed.) 11th Annual Symposium on Logic in Computer Science – LICS 1996, pp. 264–275. IEEE Computer Society Press, New Brunswick, 27–30 July 1996. This work appeared as Preprint 1834 of the Department of Mathematics of Technical University of Darmstadt, Germany
Pfenning, F., Schürmann, C.: System description: twelf - a meta-logical framework for deductive systems. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 202–206. Springer, Heidelberg (1999)
Pientka, B.: A type-theoretic foundation for programming with higher-order abstract syntax and first-class substitutions. In: 35th Annual ACM Symposium on Principles of Programming Languages (POPL 2008), pp. 371–382. ACM (2008)
Pientka, B., Dunfield, J.: Beluga: a framework for programming and reasoning with deductive systems (system description). In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS, vol. 6173, pp. 15–21. Springer, Heidelberg (2010)
Pitts, A.M.: Nominal logic, a first order theory of names and binding. Inf. Comput. 186(2), 165–193 (2003)
Poswolsky, A.: Functional Programming with Logical Frameworks: The Delphin Project. Ph.D. thesis, Yale University (2008)
Reed, J.: A hybrid logical framework. Ph.D. thesis, School of Computer Science, Carnegie Mellon University (2009)
Watkins, K., Cervesato, I., Pfenning, F., Walker, D.: A concurrent logical framework i: Judgments and properties. Technical report CMU-CS-02-101, Department of Computer Science, Carnegie Mellon University (2002)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_28
Download citation
DOI: https://doi.org/10.1007/978-3-662-48899-7_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48898-0
Online ISBN: 978-3-662-48899-7
eBook Packages: Computer ScienceComputer Science (R0)