Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-14T04:04:33.515Z Has data issue: false hasContentIssue false

Strong normalisation for the linear term calculus

Published online by Cambridge University Press:  07 November 2008

P. N. Benton
Affiliation:
Computer Laboratory, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3QG, UK (e-mail: Nick.Benton@cl.cam.ac.uk)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove a strong normalisation result for the linear term calculus of Benton, Bierman, Hyland and de Paiva. Rather than prove the result from first principles, we give a translation of linear terms into terms in the second-order polymorphic lambda calculus (λ2) which allows the result to be proved by appealing to the well-known strong normalisation property of λ2. An interesting feature of the translation is that it makes use of the λ2 coding of a coinductive datatype as the translation of the !-types (exponentials) of the linear calculus.

Type
Articles
Copyright
Copyright © Cambridge University Press 1995

References

Benton, P. N., Bierman, G. M., Hyland, J. M. E. and de Paiva, V. C. V. (1992) Term Assignment for Intuitionistic Linear Logic (Preliminary Report). Technical Report 262, Computer Laboratory, University of Cambridge.Google Scholar
Benton, P. N., Bierman, G. M., Hyland, J. M. E. and de Paiva, V. C. V. (1992) Linear lambda calculus and categorical models revisited. In Börger, E. et al. (eds.), Selected Papers from Computer Science Logic 1992. LNCS 702, Springer-Verlag, pp. 6184.Google Scholar
Benton, P. N., Bierman, G. M., Hyland, J. M. E. and de Paiva, V. C. V. (1993) A term calculus for intuitionistic linear logic. In M., Bezem and Groote, J. F. (eds.), Proc. Int. Conf. Typed Lambda Calculi and Applications, Utrecht, The Netherlands. LNCS 664, Springer-Verlag, pp. 7590.CrossRefGoogle Scholar
Bierman, G. M. (1993) On Intuitionistic Linear Logic. PhD thesis, Computer Laboratory, University of Cambridge.Google Scholar
Chirimar, J., Gunter, C. A. and Riecke, J. G. (1995) Reference Counting as a Computational Interpretation of Linear Logic. Journal of Functional Programming, to appear.Google Scholar
Gallier, J. H. (1990) On Girard's “candidats de reducibilité”. In Odifreddi, P. (ed.), Logic and Computer Science. Academic Press, pp.123203.Google Scholar
Girard, J.-Y. (1972) Interprétation fonctionnelle et élimination des coupures de l'arithmétique d'ordre supérieur. Thèse de Doctorat d'Etat, Université de Paris VII.Google Scholar
Girard, J.-Y., Lafont, Y. and Taylor, P. (1989) Proofs and Types. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press.Google Scholar
Hofmann, M. and Pierce, B. C. (1992) An Abstract View of Objects and Subtyping (Preliminary Report). Technical Report ECS-LFCS-92-226, Department of Computer Science, University of Edinburgh.Google Scholar
Howard, W. A. (1980) The formulæ-as-types notion of construction. In Hindley, J. R. and Seldin, J. P. (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press.Google Scholar
Mitchell, J. C. and Plotkin, G. D. (1988) Abstract types have existential type. ACM Trans. on Programming Languages and Systems, 10(3): 470502.Google Scholar
Plotkin, G. D. and Abadi, M. (1993) A logic for parametric polymorphism. In Bezem, M. and Groote, J. F. (eds.), Proc. Int. Conf. Typed Lambda Calculi and Applications, Utrecht, The Netherlands. LNCS 664, Springer-Verlag, pp. 361375.CrossRefGoogle Scholar
Reynolds, J. C. (1974) Towards a theory of type structure. Proc. Paris Colloquium on Programming. LNCS 19. Springer-Verlag.Google Scholar
Tait, W. W. (1967) Intensional interpretations of functionals of finite type I. Journal of Symbolic Logic, 32.CrossRefGoogle Scholar
Submit a response

Discussions

No Discussions have been published for this article.