Abstract
Logical frameworks like LF are used for formal representations of logics in order to make them amenable to formal machine-assisted meta-reasoning. While the focus has originally been on logics with a proof theoretic semantics, we have recently shown how to define model theoretic logics in LF as well. We have used this to define new institutions in the Heterogeneous Tool Set in a purely declarative way.
It is desirable to extend this model theoretic representation of logics to the level of structured specifications. Here a particular challenge among structured specification building operations is hiding, which restricts a specification to some export interface. Specification languages like ASL and CASL support hiding, using an institution-independent model theoretic semantics abstracting from the details of the underlying logical system.
Logical frameworks like LF have also been equipped with structuring languages. However, their proof theoretic nature leads them to a theory-level semantics without support for hiding. In the present work, we show how to resolve this difficulty.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Autexier, S., Hutter, D., Mantel, H., Schairer, A.: Towards an Evolutionary Formal Software-Development Using CASL. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT 1999. LNCS, vol. 1827, pp. 73–88. Springer, Heidelberg (2000)
Astesiano, E., Kreowski, H.-J., Krieg-Brückner, B.: Algebraic Foundations of Systems Specification. Springer, Heidelberg (1999)
Barendregt, H.: Lambda calculi with types. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science, vol. 2, Oxford University Press (1992)
Burstall, R., Goguen, J.: The semantics of Clear, a specification language. In: Bjorner, D. (ed.) Abstract Software Specifications. LNCS, vol. 86, pp. 292–332. Springer, Heidelberg (1980)
Bergstra, J.A., Heering, J., Klint, P.: Module algebra. J. ACM 37(2), 335–372 (1990)
Borzyszkowski, T.: Logical systems for structured specifications. Theor. Comput. Sci. 286(2), 197–245 (2002)
Codescu, M., Horozal, F., Kohlhase, M., Mossakowski, T., Rabe, F., Sojakova, K.: Towards Logical Frameworks in the Heterogeneous Tool Set Hets. In: Workshop on Abstract Development Techniques (2010)
Goguen, J., Burstall, R.: Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39(1), 95–146 (1992)
Goguen, J., Rosu, G.: Composing Hidden Information Modules over Inclusive Institutions. In: Owe, O., Krogdahl, S., Lyche, T. (eds.) From Object-Orientation to Formal Methods. LNCS, vol. 2635, pp. 96–123. Springer, Heidelberg (2004)
Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the Association for Computing Machinery 40(1), 143–184 (1993)
Horozal, F., Rabe, F.: Representing Model Theory in a Type-Theoretical Logical Framework. Theoretical Computer Science (to appear, 2011), http://kwarc.info/frabe/Research/HR_folsound_10.pdf
Harper, R., Sannella, D., Tarlecki, A.: Structured presentations and logic representations. Annals of Pure and Applied Logic 67, 113–160 (1994)
Iancu, M., Rabe, F.: Formalizing Foundations of Mathematics. Mathematical Structures in Computer Science (to appear, 2011), http://kwarc.info/frabe/Research/IR_foundations_10.pdf
Kohlhase, M., Mossakowski, T., Rabe, F.: The LATIN Project (2009), https://trac.omdoc.org/LATIN/
Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents (version 1.2). LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)
Kahrs, S., Sannella, D., Tarlecki, A.: The definition of extended ML: A gentle introduction. Theoretical Computer Science 173(2), 445–484 (1997)
Mossakowski, T., Autexier, S., Hutter, D.: Development graphs - Proof management for structured specifications. J. Log. Algebr. Program. 67(1-2), 114–145 (2006)
Martin-Löf, P.: An Intuitionistic Theory of Types: Predicative Part. In: Proceedings of the 1973 Logic Colloquium, pp. 73–118. North-Holland (1974)
Mossakowski, T., Maeder, C., Lüttich, K.: The Heterogeneous Tool Set, Hets. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 519–522. Springer, Heidelberg (2007)
Mosses, P.D. (ed.): Casl Reference Manual. LNCS, vol. 2960. Springer, Heidelberg (2004)
Mossakowski, T., Tarlecki, A.: Heterogeneous Logical Environments for Distributed Specifications. In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 266–289. Springer, Heidelberg (2009)
Paulson, L.C.: Isabelle: A Generic Theorem Prover. LNCS, vol. 828. Springer, Heidelberg (1994)
Rabe, F.: A Logical Framework Combining Model and Proof Theory. Submitted to Mathematical Structures in Computer Science (2010), http://kwarc.info/frabe/Research/rabe_combining_09.pdf
Rabe, F., Kohlhase, M.: A Scalable Module System (2010), http://kwarc.info/frabe/Research/mmt.pdf
Rabe, F., Schürmann, C.: A Practical Module System for LF. In: Cheney, J., Felty, A. (eds.) Proceedings of the Workshop on Logical Frameworks: Meta-Theory and Practice (LFMTP), pp. 40–48. ACM Press (2009)
Sannella, D., Tarlecki, A.: Specifications in an arbitrary institution. Information and Computation 76, 165–210 (1988)
Sannella, D., Tarlecki, A.: Foundations of Algebraic Specification and Formal Program Development. Springer, Heidelberg (2011)
Sannella, D., Wirsing, M.: A kernel language for algebraic specification and implementation. In: ADT (1983)
Wirsing, M.: Structured algebraic specifications: A kernel language. Theor. Comput. Sci. 42, 123–249 (1986)
Zholudev, V., Kohlhase, M.: TNTBase: a Versioned Storage for XML. In: Proceedings of Balisage: The Markup Conference 2009. Balisage Series on Markup Technologies, vol. 3. Mulberry Technologies, Inc. (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 IFIP International Federation for Information Processing
About this paper
Cite this paper
Codescu, M., Horozal, F., Kohlhase, M., Mossakowski, T., Rabe, F. (2012). A Proof Theoretic Interpretation of Model Theoretic Hiding. In: Mossakowski, T., Kreowski, HJ. (eds) Recent Trends in Algebraic Development Techniques. WADT 2010. Lecture Notes in Computer Science, vol 7137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28412-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-28412-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28411-3
Online ISBN: 978-3-642-28412-0
eBook Packages: Computer ScienceComputer Science (R0)