Abstract
Soft Linear Logic (SLL) is a subsystem of second-order linear logic with restricted rules for exponentials, which is correct and complete for PTIME. We design a type assignment system for the λ-calculus (STA), which assigns to λ-terms as types (a proper subset of) SLL formulas, in such a way that typable terms inherit the good complexity properties of the logical system. Namely STA enjoys subject reduction and normalization, and it is correct and complete for PTIME and FPTIME.
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
Preview
Unable to display preview. Download preview PDF.
References
Girard, J.Y.: Light Linear Logic. Information and Computation 143(2), 175–204 (1998)
Lafont, Y.: Soft linear logic and polynomial time. Theoretical Computer Science 318(1-2), 163–180 (2004)
Baillot, P., Mogbil, V.: Soft lambda-calculus: a language for polynomial time computation. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 27–41. Springer, Heidelberg (2004)
Baillot, P., Terui, K.: Light types for polynomial time computation in lambda-calculus. In: Proceedings of LICS 2004, pp. 266–275. IEEE Computer Society Press, Los Alamitos (2004)
Asperti, A.: Light Affine Logic. In: Proceedings of LICS 1998, pp. 300–308. IEEE Computer Society Press, Los Alamitos (1998)
Asperti, A., Roversi, L.: Intuitionistic Light Affine Logic. ACM Transactions on Computational Logic 3(1), 137–175 (2002)
Mairson, H.G., Terui, K.: On the Computational Complexity of Cut-Elimination in Linear Logic. In: Blundo, C., Laneve, C. (eds.) ICTCS 2003. LNCS, vol. 2841, pp. 23–36. Springer, Heidelberg (2003)
Ronchi Della Rocca, S., Roversi, L.: Lambda calculus and Intuitionistic Linear Logic. Studia Logica 59(3) (1997)
Coppola, P., Dal Lago, U., Ronchi Della Rocca, S.: Elementary Affine Logic and the Call by Value Lambda Calculus. In: Urzyczyn, P. (ed.) TLCA 2005. LNCS, vol. 3461, pp. 131–145. Springer, Heidelberg (2005)
Terui, K.: Light Affine Lambda Calculus and Polytime Strong Normalization. In: Proceedings of LICS 2001, pp. 209–220. IEEE Computer Society Press, Los Alamitos (2001)
Barendregt, H.P.: The Lambda Calculus: Its Syntax and Semantics. Elsevier/North-Holland, Amsterdam, London, New York (1984)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gaboardi, M., Ronchi Della Rocca, S. (2007). A Soft Type Assignment System for λ-Calculus. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-74915-8_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
eBook Packages: Computer ScienceComputer Science (R0)