Skip to main content
×
×
Home

On Banach spaces of sequences and free linear logic exponential modality

  • SERGEY SLAVNOV (a1)
Abstract

We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are rigged sequence spaces, Banach spaces of sequences, with norms defined from pairing with finite sequences, and morphisms are bounded linear maps, continuous in a suitable topology. The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.

Copyright
References
Hide All
Blute, R., Ehrhard, T. and Tasson, C. (2012). A convenient differential category. Cahiers de Topologie et Geometrie Differentielle 53 (3) 211232.
Blute, R., Panangaden, P. and Seely, R. (1993). Old foundations for linear logic. In: Proceedings of the 9th Symposium on Mathematical Foundations of Programming Semantics, Lecture Notes in Computer Science, vol. 802, Springer-Verlag, 474–512.
Crubillé, R., Ehrhard, T., Pagani, M. and Tasson, C. (2017). The free exponential modality of probabilistic coherence spaces. In: Esparza, J. and Murawski, A. (eds.) Foundations of Software Science and Computation Structures. FoSSaCS 2017, Lecture Notes in Computer Science, vol. 10203, Springer, Berlin, Heidelberg, 2035.
Danos, V. and Ehrhard, T. (2011). Probabilistic coherence spaces as a model of higher-order probabilistic computation. Information and Computation 209 (6) 966991.
Ehrhard, T. (2002). On Koethe sequence spaces and linear logic. Mathematical Structures in Computer Science 12 579623.
Ehrhard, T. and Regnier, L. (2003). The differential lambda-calculus. Theoretical Computer Science 309 141.
Ehrhard, T. and Regnier, L. (2006). Differential interaction nets. Theoretical Computer Science 364 166195.
Gelfand, I. and Vilenkin, N. (1964). Generalized Functions, vol. 4: Some Applications of Harmonic Analysis. Rigged Hilbert Spaces, Academic Press.
Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science 50 1102.
Girard, J.-Y. (1995). Linear logic: Its syntax and semantics. In: Girard, J.-Y., Lafont, Y. and Regnier, L. (eds.) Advances in Linear Logic, London Mathematical Society Lecture Note Series, vol. 222, Cambridge University Press, 142.
Girard, J.-Y. (1999). Coherent Banach spaces: A continuous denotational semantics. Theoretical Computer Science 227 275297.
Girard, J.-Y. (2004). Between logic and quantic: A tract. In: Ehrhard, Th., Girard, J.-Y., Ruet, P. and Scott, Ph. (eds.) Linear Logic in Computer Science, London Mathematical Society Lecture Note Series, vol. 316, Cambridge University Press, pp. 346381.
Lafont, Y. (1988). Logique, catégories et machines. Thèse de doctorat, Université de Paris 7, Denis Diderot.
Melliés, P.-A. (2009). Categorical semantics of linear logic. In: Curien, P.-L., Herbelin, H., Krivine, J.-L. and Melliés, P.-A. (eds.) Interactive Models of Computation and Program Behaviour, Panoramas et Synthèses, vol. 27, Société Mathématique de France, 1196.
Melliés, P.-A., Tabareau, N. and Tasson, C. (2009). An explicit formula for the free exponential modality of linear logic. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S. and Thomas, W. (eds.) Automata, Languages and Programming. ICALP 2009, Lecture Notes in Computer Science, vol. 5556, 247260.
Rudin, W. (1991). Functional analysis. In: International Series in Pure and Applied Mathematics, McGraw-Hill Science/Engineering/Math.
Seely, R.A.G. (1989). Linear logic, *-autonomous categories and cofree coalgebras. In: Gray, J. and Scedrov, A. (eds.) Categories in Computer Science and Logic, Contemporary Mathematics, vol. 92, American Mathematical Society, 371382.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed