Abstract
We present QBAL, an extension of Girard, Scedrov and Scott’s bounded linear logic. The main novelty of the system is the possibility of quantifying over resource variables. This generalization makes bounded linear logic considerably more flexible, while preserving soundness and completeness for polynomial time. In particular, we provide compositional embeddings of Leivant’s RRW and Hofmann’s LFPL into QBAL.
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References
Asperti, A., Roversi, L.: Intuitionistic light affine logic. ACM Transactions on Computational Logic 3(1), 137–175 (2002)
Barendregt, H.: The Lambda Calculus: Its Syntax and Semantics. In: Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam (1984)
Bellantoni, S., Cook, S.: A new recursion-theoretic characterization of the polytime functions. Computational Complexity 2, 97–110 (1992)
Dal Lago, U., Hofmann, M.: Bounded linear logic, revisited. Extended Version (2009), http://arxiv.org/abs/0904.2675
Danos, V., Joinet, J.-B.: Linear logic and elementary time. Information and Computation 183(1), 123–137 (2003)
Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)
Girard, J.-Y.: Light linear logic. Information and Computation 143(2), 175–204 (1998)
Girard, J.-Y., Scedrov, A., Scott, P.: Bounded linear logic: A modular approach to polynomial-time computability. Theoretical Computer Science 97(1), 1–66 (1992)
Hofmann, M.: Programming languages capturing complexity classes. SIGACT News Logic Column 9, 12 (2000)
Hofmann, M.: Linear types and non-size-increasing polynomial time computation. Information and Computation 183(1), 57–85 (2003)
Hofmann, M., Scott, P.: Realizability models for BLL-like languages. Theoretical Computer Science 318(1-2), 121–137 (2004)
Lafont, Y.: Soft linear logic and polynomial time. Theoretical Computer Science 318(1-2), 163–180 (2004)
Leivant, D.: A foundational delineation of computational feasiblity. In: Sixth IEEE Symposium on Logic in Computer Science, Proceedings, pp. 2–11 (1991)
Leivant, D.: Stratified functional programs and computational complexity. In: 20th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Proceedings, pp. 325–333 (1993)
Marion, J.-Y., Moyen, J.-Y.: Efficient first order functional program interpreter with time bound certifications. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS, vol. 1955, pp. 25–42. Springer, Heidelberg (2000)
Murawski, A., Ong, L.: On an interpretation of safe recursion in light affine logic. Theoretical Computer Science 318(1-2), 197–223 (2004)
Schöpp, U.: Stratified bounded affine logic for logarithmic space. In: 22nd IEEE Symposium on Logic in Computer Science, Proceedings, pp. 411–420 (2007)
Troelstra, A., Schwichtenberg, H.: Basic proof theory. Cambridge University Press, Cambridge (1996)
Wadsworth, C.: Some unusual λ-calculus numeral systems. In: Seldin, J.P., Hindley, J.R. (eds.) To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, London (1980)
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Dal Lago, U., Hofmann, M. (2009). Bounded Linear Logic, Revisited. In: Curien, PL. (eds) Typed Lambda Calculi and Applications. TLCA 2009. Lecture Notes in Computer Science, vol 5608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02273-9_8
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DOI: https://doi.org/10.1007/978-3-642-02273-9_8
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