Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-17T00:32:52.169Z Has data issue: false hasContentIssue false

Light logics and higher-order processes

Published online by Cambridge University Press:  17 November 2014

UGO DAL LAGO
Affiliation:
Università di Bologna and INRIA, Sophia Antipolis, France Email: dallago@cs.unibo.it, martini@cs.unibo.it and davide.sangiorgi@cs.unibo.it
SIMONE MARTINI
Affiliation:
Università di Bologna and INRIA, Sophia Antipolis, France Email: dallago@cs.unibo.it, martini@cs.unibo.it and davide.sangiorgi@cs.unibo.it
DAVIDE SANGIORGI
Affiliation:
Università di Bologna and INRIA, Sophia Antipolis, France Email: dallago@cs.unibo.it, martini@cs.unibo.it and davide.sangiorgi@cs.unibo.it

Abstract

We show that the techniques for resource control that have been developed by the so-called light logics can be fruitfully applied also to process algebras. In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.

Type
Paper
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Amadio, R. M. and Dabrowski, F. (2007) Feasible reactivity in a synchronous π-calculus. In: Proceedings of the ACM on Principles and Practice of Declarative Programming (PPDP) ACM Press 221230.Google Scholar
Asperti, A. and Roversi, L. (2002) Intuitionistic light affine logic. Transactions on Computational Logic 3 (1) 139.Google Scholar
Baillot, P. and Mogbil, V. (2004) Soft lambda-calculus: A language for polynomial time computation. In: Proceedings of the 7th International Conference Foundations of Software Science and Computation Structures (FOSSACS). Lecture Notes in Computer Science 2987 2741.Google Scholar
Dal Lago, U. et al. (2009) Taming modal impredicativity: Superlazy reduction. In: Proceedings of Logical Foundations of Computer Science (LFCS). Lecture Notes in Computer Science 5407 137151.Google Scholar
Demangeon, R. et al. (2010a) Termination in higher-order concurrent calculi. In: Proceedings of the 3rd International Conference on Fundamentals of Software Engineering (FSEN). Lecture Notes in Computer Science 5961 8196.CrossRefGoogle Scholar
Demangeon, R. et al. (2010b) Termination in impure concurrent languages. In: Proceedings of the 21th International Conference on Concurrency Theory (CONCUR). Lecture Notes in Computer Science 6269 328342.Google Scholar
Ehrhard, T. and Laurent, O. (2010) Acyclic solos and differential interaction nets. Logical Methods in Computer Science 6 (3) 134.Google Scholar
Ehrhard, T. and Regnier, L. (2006) Differential interaction nets. Theoretical Computer Science 364 (2) 166195.Google Scholar
Gaboardi, M. and Ronchi Della Rocca, S. (2007) A soft type assignment system for λ-calculus. In: Proceedings of Computer Science Logic (CSL). Lecture Notes in Computer Science 4646 253267.Google Scholar
Girard, J.-Y. (1987) Linear logic. Theoretical Computer Science 50 1102.CrossRefGoogle Scholar
Girard, J.-Y. (1998) Light linear logic. Information and Computation 143 (2) 175204.Google Scholar
Kobayashi, N. and Sangiorgi, D. (2008) A hybrid type system for lock-freedom of mobile processes. In: Proceedings of the 20th International Conference on Computer Aided Verification (CAV). Lecture Notes in Computer Science 5123 8093.Google Scholar
Lafont, Y. (2004) Soft linear logic and polynomial time. Theoretical Computer Science 318 (1–2) 163180.Google Scholar
Plotkin, G. D. (1975) Call-by-name, call-by-value and the lambda-calculus. Theoretical Computer Science 1 (2) 125159.Google Scholar
Sangiorgi, D. (1996) Bisimulation for higher-order process calculi. Information and Computation 131 (2) 141178.Google Scholar
Sangiorgi, D. and Walker, D. (2001) The π-Calculus: A Theory of Mobile Processes, Cambridge University Press.Google Scholar
Wadler, P. (1994) A syntax for linear logic. In: Proceedings of the Mathematical Foundations of Programming Semantics (MFPS'93). Lecture Notes in Computer Science 802 513529.Google Scholar
Yoshida, N., Berger, M. and Honda, K. (2001) Strong normalisation in the pi-calculus. In: 16th Annual IEEE Symposium on Logic in Computer Science, Proceedings 311–322.Google Scholar