References

  1. E.S. Bainbridge, Peter J. Freyd, Andre Scedrov & Philip J. Scott (1990): Functorial polymorphism. Theoretical Computer Science 70, pp. 35–64, doi:10.1016/0304-3975(90)90151-7.
  2. Michael Barr (1979): ^*-Autonomous Categories. Lecture Notes in Mathematics 752. Springer-Verlag, Berlin, Heidelberg, doi:10.1007/BFb0064582.
  3. R. F. Blute & P. J. Scott (1996): Linear Läuchli semantics. Ann. Pure Appl. Logic 77(2), pp. 101–142, doi:10.1016/0168-0072(95)00017-8.
  4. Richard Blute (1991): Proof nets and coherence theorems. In: P.L. Curien, S. Abramsky, A.M. Pitts, A. Poigné & D.E. Rydeheard: Category Theory and Computer Science. CTCS 1991, Lecture Notes in Computer Science 530. Springer, Berlin, Heidelberg, pp. 121–137, doi:10.1007/BFb0013461.
  5. Richard Blute (1993): Linear Logic, coherence and dinaturality. Theoretical Computer Science 115(1), pp. 3–41, doi:10.1016/0304-3975(93)90053-V.
  6. Richard Blute, Robin Cockett, R.A.G. Seely & T.H. Trimble (1996): Natural deduction and coherence for weakly distributive categories. Journal of Pure and Applied Algebra 113(229), pp. 296, doi:10.1016/0022-4049(95)00159-X.
  7. Daniel de Carvalho & Lorenzo Tortora de Falco (2012): The relational model is injective for multiplicative exponential linear logic (without weakenings). Annals of Pure and Applied Logic 163(9), pp. 1210–1236, doi:10.1016/j.apal.2012.01.004.
  8. Lorenzo Tortora de Falco (2000): Réseaux, cohérence et expériences obsessionnelles. Université Paris 7.
  9. Fernando Ferreira & Gilda Ferreira (2009): Commuting conversions vs. the standard conversions of the "good" connectives. Studia Logica 92(1), pp. 63–84, doi:10.1007/s11225-009-9186-1.
  10. Fernando Ferreira & Gilda Ferreira (2013): Atomic polymorphism. Journal of Symbolic Logic 78(1), pp. 260–274, doi:10.1007/s10992-005-9001-z.
  11. M.P. Fiore, A. Jung, E. Moggi, P. O'Hearn, J. Riecke, G. Rosolini & I. Stark (1996): Domains and denotational semantics: history, accomplishments and open problems. Bulletin EATCS 59, pp. 227–256.
  12. Jürgen Fuchs, Christoph Schweigert & Carl Stigner (2012): Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms. Journal of Algebra 363, pp. 29–72, doi:10.1016/j.jalgebra.2012.04.008.
  13. Jean-Yves Girard (1987): Linear logic. Theoretical Computer Science 50(1), pp. 1–102, doi:10.1016/0304-3975(87)90045-4.
  14. Jean-Yves Girard (1988): Quantifiers in Linear Logic. In: Atti del congresso "Temi e Prospettive della Logica e della Filosofia della Scienza", Cesena, 7-10 Gennaio 1987. CLUEB, Bologna.
  15. Jean-Yves Girard (1991): Quantifiers in Linear Logic II. In: Atti del congresso "Nuovi Problemi della Logica e della Filosofia della Scienza", Viareggio, 8-13 Gennatio 1990. CLUEB, Bologna.
  16. Jean-Yves Girard, Andre Scedrov & Philip J. Scott (1992): Normal forms and cut-free proofs as natural transformations. In: Y. Moschovakis: Logic from Computer Science 21. Springer-Verlag, pp. 217–241, doi:10.1007/978-1-4612-2822-6_8.
  17. Rye Hasegawa (2009): Categorical data types in parametric polymorphism. Mathematical Structures in Computer Science 4(1), pp. 71–109, doi:10.1016/S0049-237X(08)70843-7.
  18. Willem Heijltjes & Robin Houston (2014): No proof nets for MLL with units: proof equivalence in MLL is PSPACE-complete. In: CSL-LICS 2014, doi:10.1145/2603088.2603126.
  19. Willem Heijltjes & Luz Straßburger (2016): Proof nets and semi-star-autonomous categories. Mathematical Structures in Computer Science 26(5), pp. 789–828, doi:10.1016/0001-8708(91)90003-P.
  20. Robin Houston, Dominic Hughes & Andrea Schalk (2017): Modeling Linear Logic without Units (Preliminary Results). https://arxiv.org/pdf/math/0504037.pdf.
  21. Dominic J.D. Hughes: Unification nets: canonical proof net quantifiers. https://arxiv.org/abs/1802.03224.
  22. Dominic J.D. Hughes (2012): Simple free star-autonomous categories and full coherence. Journal of Pure and Applied Algebra 216(11), pp. 2386–2410, doi:10.1016/j.jpaa.2012.03.020.
  23. Thomas Kerler & Volodymyr V. Lyubashenko (2001): Coends and construction of Hopf algebras. In: Non-Semisimple Topological Quantum Field Theoreis for 3-Manifols with Corners, chapter 5, Lecture Notes in Mathematics 1765. Springer, Berlin, Heidelberg, doi:10.1007/3-540-44625-7_6.
  24. François Lamarche & Luz Straßburger (2004): On proof nets for multiplicative linear logic with units. In: CSL 2004, Lecture Notes in Computer Science 3210, pp. 145–159, doi:10.1007/978-3-540-30124-0_14.
  25. François Lamarche & Luz Straßburger (2006): From Proof Nets to the Free ^*-Autonomous Category. Logical Methods in Computer Science 2(4), doi:10.2168/LMCS-2(4:3)2006.
  26. Joachim de Lataillade (2009): Dinatural terms in System F. In: Proceedings of the Twenty-Fourth Annual IEEE Symposium on Logic in Computer Science (LICS 2009). IEEE Computer Society Press, Los Angeles, California, USA, pp. 267–276, doi:10.1109/LICS.2009.30.
  27. Fosco Loregian (2015): This is the (co)end, my only (co)friend. https://arxiv.org/abs/1501.02503.
  28. Saunders MacLane (1978): Categories for the working mathematicians. Graduate Texts in Mathematics 5. Springer-Verlag, New York, doi:10.1007/978-1-4757-4721-8.
  29. Richard McKinley (2013): Proof nets for Herbrand's theorem. ACM Transactions on Computational Logic 14(1), doi:10.1145/2422085.2422090.
  30. Paul-André Melliès (2012): Game semantics in string diagrams. In: LICS '12, New Orleans, Louisiana, pp. 481–490, doi:10.1109/LICS.2012.58.
  31. Paul-André Melliès & Noam Zeilberger (2016): A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine. In: LICS '16, New York, pp. 555–564, doi:10.1145/2933575.2934525.
  32. Paolo Pistone (2018): Proof nets and the instantiation overflow property. https://arxiv.org/abs/1803.09297.
  33. Gordon Plotkin & Martin Abadi (1993): A logic for parametric polymorphism. In: TLCA '93, International Conference on Typed Lambda Calculi and Applications, Lecture Notes in Computer Science 664. Springer Berlin Heidelberg, pp. 361–375, doi:10.1007/BFb0037118.
  34. R.A.G. Seely (1990): Polymorphic linear logic and topos models. Comptes Rendus Mathématiques de l'Académie des Sciences Canada 12(1).
  35. Luz Straßburger (2009): Some Observations on the Proof Theory of Second Order Propositional Multiplicative Linear Logic. In: P.L. Curien: TLCA 2009, Lecture Notes in Computer Science 5608, pp. 309–324, doi:10.1007/BF01622878.
  36. Luca Tranchini, Paolo Pistone & Mattia Petrolo (2017): The naturality of natural deduction. Studia Logica, doi:10.1007/s11225-017-9772-6.
  37. Todd Trimble (1994): Linear logic, bimodules, and full coherence for autonomous categories. Rutgers University.
  38. Tarmo Uustalu & Varmo Vene (2011): The Recursion Scheme from the Cofree Recursive Comonad. Electronic Notes in Theoretical Computer Science 229(5), pp. 135–157, doi:10.1016/j.entcs.2011.02.020.

Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org