References

  1. S. Abramsky & A. Jung (1995): Domain Theory. In: S. Abramsky, D. M. Gabbay & T. S. E. Maibaum: Semantic Structures, Handbook of Logic in Computer Science 3. Oxford University Press, pp. 1–168. Available at https://www.cs.bham.ac.uk/~axj/pub/papers/handy1.pdf.
  2. Samson Abramsky (1987): Domain Theory and the Logic of Observable Properties. Queen Mary College, University of London.
  3. Andrej Bauer & Iztok Kavkler (2009): A constructive theory of continuous domains suitable for implementation. Annals of Pure and Applied Logic 159(3), pp. 251–267, doi:10.1016/j.apal.2008.09.025.
  4. Nick Benton, Andrew Kennedy & Carsten Varming (2009): Some Domain Theory and Denotational Semantics in Coq. In: Stefan Berghofer, Tobias Nipkow, Christian Urban & Makarius Wenzel: Theorem Proving in Higher Order Logics (TPHOLs 2009), Lecture Notes in Computer Science 5674. Springer, pp. 115–130, doi:10.1007/978-3-642-03359-9_10.
  5. Errett Bishop & Douglas Bridges (1985): Constructive Analysis. Grundlehren der mathematischen Wissenschaften 279. Springer-Verlag, doi:10.1007/978-3-642-61667-9.
  6. Douglas Bridges & Fred Richman (1987): Varieties of Constructive Mathematics. London Mathematical Society Lecture Note Series 97. Cambridge University Press, doi:10.1017/cbo9780511565663.
  7. Douglas S. Bridges & Luminiţa Simona Vîţǎ (2011): Apartness and Uniformity: A Constructive Development. Springer, doi:10.1007/978-3-642-22415-7.
  8. Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini (2003): Inductively generated formal topologies. Annals of Pure and Applied Logic 124(1–3), pp. 71–106, doi:10.1016/s0168-0072(03)00052-6.
  9. Robert Dockins (2014): Formalized, Effective Domain Theory in Coq. In: Gerwin Klein & Ruben Gamboa: Interactive Theorem Proving (ITP 2014), Lecture Notes in Computer Science 8558. Springer, pp. 209–225, doi:10.1007/978-3-319-08970-6_14.
  10. Martin Escardo (2008): Exhaustible sets in higher-type computation. Logical Methods in Computer Science 4(3), doi:10.2168/LMCS-4(3:3)2008.
  11. G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove & D. S. Scott (2003): Continuous Lattices and Domains. Encyclopedia of Mathematics and its Applications 93. Cambridge University Press, doi:10.1017/CBO9780511542725.
  12. Reinhold Heckmann (1998): Domain Environments. Available at https://www.rw.cdl.uni-saarland.de/people/heckmann/private/papers/newdomenv.ps.gz. Unpublished manuscript.
  13. Michael Hedberg (1996): A type-theoretic interpretation of constructive domain theory. Journal of Automated Reasoning 16(3), pp. 369–425, doi:10.1007/BF00252182.
  14. Peter T. Johnstone (1984): Open locales and exponentiation. In: J. W. Gray: Mathematical Applications of Category Theory, Contemporary Mathematics 30. American Mathematical Society, pp. 84–116, doi:10.1090/conm/030/749770.
  15. Tom de Jong & Martín Hötzel Escardó (2021): Domain Theory in Constructive and Predicative Univalent Foundations. In: Christel Baier & Jean Goubault-Larrecq: 29th EACSL Annual Conference on Computer Science Logic (CSL 2021), Leibniz International Proceedings in Informatics (LIPIcs) 183. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, pp. 28:1–28:18, doi:10.4230.LIPIcs.CSL.2021.28.
  16. Tom de Jong & Martín Hötzel Escardó (2021): Predicative Aspects of Order Theory in Univalent Foundations. In: Naoki Kobayashi: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021), Leibniz International Proceedings in Informatics (LIPIcs) 195. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, pp. 8:1–8:18, doi:10.4230/LIPIcs.FSCD.2021.8.
  17. Tatsuji Kawai (2017): Geometric theories of patch and Lawson topologies. ArXiv:1709.06403.
  18. Tatsuji Kawai (2021): Predicative theories of continuous lattices. Logical Methods in Computer Science 17(2), pp. 22:1–22:38, doi:10.23638/LMCS-17(2:22)2021.
  19. Jimmie Lawson (1997): Spaces of maximal points. Mathematical Structures in Computer Science 7(5), pp. 543–555, doi:10.1017/S0960129597002363.
  20. David Lidell (2020): Formalizing domain models of the typed and the untyped lambda calculus in Agda. Chalmers University of Technology and University of Gothenburg. Available at https://hdl.handle.net/2077/67193.
  21. John Longley & Dag Normann (2015): Higher-Order Computability. Springer, doi:10.1007/978-3-662-47992-6.
  22. Maria Emilia Maietti & Silvio Valentini (2004): Exponentiation of Scott Formal Topologies. In: A. Jung M. Escardó: Proceedings of the Workshop on Domains VI 73, pp. 111–131, doi:10.1016/j.entcs.2004.08.005.
  23. Per Martin-Löf (1970): Notes on Constructive Mathematics. Almqvist and Wicksell, Stockholm.
  24. Sara Negri (1998): Continuous lattices in formal topology. In: Eduardo Giménez & Christine Paulin-Mohring: Types for Proofs and Programs (TYPES 1996), Lecture Notes in Computer Science 1512. Springer, pp. 333–353, doi:10.1007/BFb0097800.
  25. Sara Negri (2002): Continuous domains as formal spaces. Mathematical Structures in Computer Science 12(1), pp. 19–52, doi:10.1017/S0960129501003450.
  26. Dirk Pattinson & Mina Mohammadian (2021): Constructive Domains with Classical Witnesses. Logical Methods in Computer Science 17(1), pp. 19:1–19:30, doi:10.23638/LMCS-17(1:19)2021.
  27. Jan von Plato (2001): Positive Lattices. In: Peter Schuster, Ulrich Berger & Horst Osswald: Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum, Synthese Library (Studies in Epistemology, Logic, Methodology, and Philosophy of Science) 306. Springer, pp. 185–197, doi:10.1007/978-94-015-9757-9_16.
  28. G. D. Plotkin (1977): LCF considered as a programming language. Theoretical Computer Science 5(3), pp. 223–255, doi:10.1016/0304-3975(77)90044-5.
  29. Fred Richman Ray Mines & Wim Ruitenburg (1988): A Course in Constructive Algebra. Springer-Verlag, doi:10.1007/978-1-4419-8640-5.
  30. Giovanni Sambin (1987): Intuitionistic formal spaces—a first communication. In: Mathematical logic and its applications. Springer, pp. 187–204, doi:10.1007/978-1-4613-0897-3_12.
  31. Giovanni Sambin, Silvio Valentini & Paolo Virgili (1996): Constructive domain theory as a branch of intuitionistic pointfree topology. Theoretical Computer Science 159(2), pp. 319–341, doi:10.1016/0304-3975(95)00169-7.
  32. Dana S. Scott (1982): Lectures on a Mathematical Theory of Computation. In: Manfred Broy & Gunther Schmidt: Theoretical Foundations of Programming Methodology: Lecture Notes of an International Summer School, directed by F. L. Bauer, E. W. Dijkstra and C. A. R. Hoare, NATO Advanced Study Institutes Series 91. Springer, pp. 145–292, doi:10.1007/978-94-009-7893-5_9.
  33. Dana S. Scott (1993): A type-theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science 121(1), pp. 411–440, doi:10.1016/0304-3975(93)90095-B.
  34. M. B Smyth (1993): Topology. In: S. Abramsky & T. S. E. Maibaum: Background: Mathematical Structures, Handbook of Logic in Computer Science 1. Oxford University Press, pp. 641–761.
  35. Michael B. Smyth (2006): The constructive maximal point space and partial metrizability. Annals of Pure and Applied Logic 137(1–3), pp. 360–379, doi:10.1016/j.apal.2005.05.032.
  36. Bas Spitters (2010): Locatedness and overt sublocales. Annals of Pure and Applied Logic 162(1), pp. 36–54, doi:10.1016/j.apal.2010.07.002.
  37. A.S. Troelstra & D. van Dalen (1988): Constructivism in Mathematics: An Introduction (Volume II). Studies in Logic and the Foundations of Mathematics 123. Elsevier Science Publishers.
  38. Steven Vickers (1989): Topology via Logic. Cambridge University Press.
Comments and questions to: eptcs@eptcs.org
For website issues: webmaster@eptcs.org