Attribute Grammars and Categorical Semantics

  • Shin-ya Katsumata
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5126)


We give a new formulation of attribute grammars (AG for short) called monoidal AGs in traced symmetric monoidal categories. Monoidal AGs subsume existing domain-theoretic, graph-theoretic and relational formulations of AGs. Using a 2-categorical aspect of monoidal AGs, we also show that every monoidal AG is equivalent to a synthesised one when the underlying category is closed, and that there is a sound and complete translation from local dependency graphs to relational AGs.


Categorical Semantic Monoidal Category Trace Operator Derivation Tree Computation Unit 
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  1. 1.
    Abramsky, S.: Retracting some paths in process algebra. In: CONCUR 1996. LNCS, vol. 1119, pp. 1–17. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Abramsky, S., Haghverdi, E., Scott, P.J.: Geometry of interaction and linear combinatory algebras. Math. Struct. in Comput. Sci. 12(5), 625–665 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Abramsky, S., Jagadeesan, R.: New foundations for the geometry of interaction. Inf. Comput. 111(1), 53–119 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bainbridge, E.S.: Feedbacks and generalized logic. Inf. Control 31(1), 75–96 (1976)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Bloom, S.L., Ésik, Z.: Iteration theories; the equational logic of iterative processes. Springer, Heidelberg (1993)zbMATHGoogle Scholar
  6. 6.
    Bloom, S.L., Ésik, Z.: Fixed-point operations on ccc’s. part I. Theor. Comput. Sci. 155(1), 1–38 (1996)zbMATHCrossRefGoogle Scholar
  7. 7.
    Boyland, J.: Conditional attribute grammars. ACM Trans. Program. Lang. Syst. 18(1), 73–108 (1996)CrossRefGoogle Scholar
  8. 8.
    Chirica, L.M., Martin, D.F.: An order-algebraic definition of Knuthian semantics. Math. Sys. Theory 13, 1–27 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Courcelle, B., Deransart, P.: Proofs of partial correctness for attribute grammars with applications to recursive procedures and logic programming. Inf. Comput. 78(1), 1–55 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Deransart, P., Jourdan, M., Lorho, B.: Attribute Grammars. LNCS. vol. 323. Springer, Heidelberg (1988)zbMATHGoogle Scholar
  11. 11.
    Fokkinga, M., Jeuring, J., Meertens, L., Meijer, E.: A translation from attribute grammars to catamorphisms. The Squiggolist 2(1), 20–26 (1991)Google Scholar
  12. 12.
    Girard, J.-Y.: Geometry of Interaction I: Interpretation of System F. In: Ferro, R., et al. (eds.) Logic Colloquium 1988. North-Holland, Amsterdam (1989)Google Scholar
  13. 13.
    Hasegawa, M.: On traced monoidal closed categories. Invited talk at Traced Monoidal Categories, Network Algebras, and Applications (2007)Google Scholar
  14. 14.
    Hasegawa, M.: Models of Sharing Graphs: A Categorical Semantics of let and letrec. Springer, Heidelberg (1999)zbMATHGoogle Scholar
  15. 15.
    Jacobs, B., Uustalu, T.: Semantics of grammars and attributes via initiality. In: Reflections on Type Theory, Lambda Calculus, and the Mind. Essays Dedicated to Henk Barendregt on the Occasion of his 60th Birthday, pp. 181–196. Radboud University (2007)Google Scholar
  16. 16.
    Joyal, A., Street, R., Verity, D.: Traced monoidal categories. Mathematical Proceedings of the Cambridge Philosophical Society 119(3), 447–468 (1996)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Kelly, G.M., Laplaza, M.L.: Coherence for compact closed categories. Journal of Pure and Applied Algebra 19, 193–213 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Knuth, D.E.: Semantics of context-free languages. Math. Sys. Theory 2(2), 127–145 (1968); See Math. Sys. Theory, 5(1) 95–96, 1971 for a correctionzbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Leinster, T.: Higher Operads, Higher Categories. London Math. Soc. Lecture Note Series, vol. 298. Cambridge University Press, Cambridge (2004)zbMATHGoogle Scholar
  20. 20.
    MacLane, S.: Categories for the Working Mathematician, 2nd edn. Graduate Texts in Mathematics, vol. 5. Springer, Heidelberg (1998)Google Scholar
  21. 21.
    Selinger, P.: A note on Bainbridge’s power set construction (manuscript, 1998)Google Scholar
  22. 22.
    Swierstra, S.D., Vogt, H.: Higher order attribute grammars. In: Alblas, H., Melichar, B. (eds.) SAGA School 1991. LNCS, vol. 545, pp. 256–296. Springer, Heidelberg (1991)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Shin-ya Katsumata
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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