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A Feasible Algorithm for Typing in Elementary Affine Logic

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Book cover Typed Lambda Calculi and Applications (TLCA 2005)

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Abstract

We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type system we consider (denoted EAL*) is a variant where sharing is restricted to variables and without polymorphism. Our algorithm improves over the ones already known in that it offers a better complexity bound: if a simple type derivation for the term t is given our algorithm performs EAL* type inference in polynomial time in the size of the derivation.

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References

  1. Asperti, A., Coppola, P., Martini, S.: (Optimal) duplication is not elementary recursive. In: Proceedings of POPL 2000, pp. 96–107 (2000)

    Google Scholar 

  2. Asperti, A., Roversi, L.: Intuitionistic light affine logic. ACM Transactions on Computational Logic 3(1), 1–39 (2002)

    Article  MathSciNet  Google Scholar 

  3. Asperti, A.: Light affine logic. In: Proceedings of LICS 1998, pp. 300–308 (1998)

    Google Scholar 

  4. Baillot, P.: Checking polynomial time complexity with types. In: Proceedings of IFIP TCS 2002, Montreal, pp. 370–382 (2002)

    Google Scholar 

  5. Baillot, P.: Type inference for light affine logic via constraints on words. Theoretical Computer Science 328(3), 289–323 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  6. Baillot, P., Terui, K.: Light types for polynomial time computation in lambda-calculus. In: Proceedings of LICS 2004, pp. 266–275 (2004), Long version available at http://arxiv.org/abs/cs.LO/0402059

  7. Baillot, P., Terui, K.: A feasible algorithm for typing in elementary affine logic (long version). Technical Report cs.LO/0412028, arXiv (2004), Available from http://arxiv.org/abs/cs.LO/0412028

  8. de Carvalho, D.: Intersection types for light affine lambda calculus. In: Proceedings of 3rd Workshop on Intersection Types and Related Systems, ITRS 2004 (2004) (To appear in ENTCS)

    Google Scholar 

  9. Coppola, P., Martini, S.: Typing lambda-terms in elementary logic with linear constraints. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 76–90. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Coppola, P., Martini, S.: Optimizing optimal reduction. A type inference algorithm for elementary affine logic. ACM Transactions on Computational Logic (2004) (To appear)

    Google Scholar 

  11. Coppola, P., Ronchi della Rocca, S.: Principal typing in Elementary Affine Logic. In: Hofmann, M.O. (ed.) TLCA 2003. LNCS, vol. 2701, pp. 90–104. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Danos, V., Joinet, J.-B.: Linear logic & elementary time. Information and Computation 183(1), 123–137 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Danos, V., Joinet, J.-B., Schellinx, H.: On the linear decoration of intuitionistic derivations. Archive for Mathematical Logic 33(6), 387–412 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Girard, J.-Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Girard, J.-Y.: Light linear logic. Information and Computation 143, 175–204 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Girard, J.-Y., Scedrov, A., Scott, P.: Bounded linear logic: A modular approach to polynomial time computability. Theoretical Computer Science 97, 1–66 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lafont, Y.: Soft linear logic and polynomial time. Theoretical Computer Science 318(1-2), 163–180 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Roversi, L.: A polymorphic language which is typable and poly-step. In: Hsiang, J., Ohori, A. (eds.) ASIAN 1998. LNCS, vol. 1538, pp. 43–60. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  19. Terui, K.: Light affine lambda-calculus and polytime strong normalization. In: Proceedings of LICS 2001, pp. 209–220 (2001), Full version to appear in Archive for Mathematical Logic

    Google Scholar 

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Baillot, P., Terui, K. (2005). A Feasible Algorithm for Typing in Elementary Affine Logic. In: Urzyczyn, P. (eds) Typed Lambda Calculi and Applications. TLCA 2005. Lecture Notes in Computer Science, vol 3461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11417170_6

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  • DOI: https://doi.org/10.1007/11417170_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25593-2

  • Online ISBN: 978-3-540-32014-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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