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The graphical Krivine machine

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Higher-Order and Symbolic Computation

Abstract

We present a natural implementation of the Krivine machine in interaction nets: one rule for each transition and the usual rules for duplication and erasing. There is only one rule devoted to the so-called administration. This way, we obtain a graphical system encoding λ-calculus weak head reduction that can be extended to a λ-calculus normalizer by encoding left reduction.

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References

  1. Asperti, A., Guerrini, S.: The Optimal Implementation of Functional Programming Languages, Cambridge Tracts in Theoretical Computer Science, vol. 45. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  2. Danos, V., Regnier, L.: Reversible, irreversible and optimal λ-machines. Theor. Comput. Sci. 227 (1999)

  3. Girard, J.-Y.: Linear logic. Theor. Comput. Sci. 50(1), 1–102 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gonthier, G., Abadi, M., Lévy, J.-J.: The geometry of optimal lambda reduction. In: Proceedings of the 19th Annnual ACM Symposium on Principles of Programming Languages (POPL’92), pp. 15–26. ACM Press (1992)

  5. Krivine, J.-L.: Un interpréteur pour le λ-calcul. Technical Report, Notes de cours de DEA, Université de Paris 7 (1985)

  6. Krivine, J.-L.: Lambda-Calculus, Types and Models. Ellis Horwood Series in Computers and Their Applications (1993). Transl. from the French by Rene Cori (English)

  7. Lafont, Y.: Interaction nets. In: Proceedings of the 17th Annnual ACM Symposium on Principles of Programming Languages, Orlando, FL, USA, pp. 95–108 (1990)

  8. Lafont, Y.: From proof-nets to interaction nets. In: Advances in Linear Logic. London Mathematical Society Lecture Note Series, vol. 222. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  9. Lafont, Y.: Interaction combinators. Inf. Comput. 137(1), 69–101 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Lamping, J.: An algorithm for optimal lambda-calculus reduction. In: Proceedings of the 17th Annnual ACM Symposium on Principles of Programming Languages, Orlando, FL, USA (1990)

  11. Lang, F.: Modèles de la β-réduction pour les implantations. Ph.D. Thesis, Ecole normale supérieure de Lyon (1998)

  12. Lippi, S.: Encoding left reduction in the lambda-calculus with interaction nets. Math. Struct. Comput. Sci. 12(6) (December 2002)

  13. Lippi, S.: \(\textsf{in}^{2}\) : a graphical interpreter for the interaction nets. In: Proceedings of Rewriting Techniques and Applications (RTA ’02). Springer, New York (2002)

    Google Scholar 

  14. Lippi, S.: Théorie et pratique des réseaux d’interaction. Ph.D. Thesis, Université de la méditerranée (2002)

  15. Mackie, I.: The geometry of implementation. Ph.D. Thesis, Department of Computing, Imperial College of Science, Technology and Medicine (1994)

  16. Mackie, I.: Yale: yet another lambda evaluator based on intetaction nets. In: Proceedings of the 3rd ACM SIGPLAN International Conference on Functional Programming (ICFP’98). ACM Press (1998)

  17. Mackie, I., Sousa Pinto, J.: Encoding linear logic with interaction combinators. Inf. Comput. 176, 153–186 (2002)

    Article  MATH  Google Scholar 

  18. Sousa Pinto, J.: Weak reduction and garbage collection in interaction nets. In: Gramlich, B., Lucas, S. (eds.) Proceedings of the 3rd Int’l Workshop on Reduction Strategies in Rewriting and Programming (2003)

Download references

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy, UMR 6206 du CNRS, 163 avenue de Luminy, case 907, 13288, Marseille Cedex 9, France

    Sylvain Lippi

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  1. Sylvain Lippi
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Correspondence to Sylvain Lippi.

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Lippi, S. The graphical Krivine machine. Higher-Order Symb Comput 20, 295–318 (2007). https://doi.org/10.1007/s10990-007-9011-3

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