References

  1. S. Abramsky & B. Coecke (2004): A categorical semantics of quantum protocols. In: Logic in Computer Science. IEEE. Computer Science Press, pp. 415–425, doi:10.1109/LICS.2004.1319636.
  2. S. Abramsky & B. Coecke (2009): A categorical semantics of quantum protocols. In: K. Engesser, Dov M. Gabbai & D. Lehmann: Handbook of Quantum Logic and Quantum Structures. North Holland, Elsevier. Computer Science Press, pp. 261–323.
  3. E.M. Alfsen (1971): Compact Convex Sets and Boundary Integrals. Ergebnisse der Mathematik und ihrer Grenzgebiete 57. Springer.
  4. L. Asimow & A.J. Ellis (1980): Convexity Theory and its Applications in Functional Analysis. Academic Press, New York.
  5. P. Audebaud & C. Paulin-Mohring (2009): Proofs of randomized algorithms in Coq. Science of Comput. Progr. 74(8), pp. 568––589, doi:10.1016/j.scico.2007.09.002.
  6. J. Baez & M. Stay (2011): Physics, topology, logic and computation: a Rosetta Stone. New structures for physics, pp. 95–172, doi:10.1007/978-3-642-12821-9_2.
  7. H.P. Barendregt (1984): The Lambda Calculus. Its Syntax and Semantics, 2nd rev. edition. North-Holland, Amsterdam.
  8. M. Barr & Ch. Wells (1985): Toposes, Triples and Theories. Springer, Berlin. Revised and corrected version available from URL: www.cwru.edu/artsci/math/wells/pub/ttt.html.
  9. G. Barthe, B. Grégoire & S. Zanella Béguelin (2009): Formal certification of code-based cryptographic proofs. In: Principles of Programming Languages. ACM Press, pp. 90––101, doi:10.1145/1480881.1480894.
  10. F. Borceux (1994): Handbook of Categorical Algebra. Encyclopedia of Mathematics 50, 51 and 52. Cambridge Univ. Press, doi:10.1017/CBO9780511525858.
  11. P. Busch (2003): Quantum states and generalized observables: a simple proof of Gleason's theorem. Phys. Review Letters 91(12):120403, pp. 1–4, doi:10.1103/PhysRevLett.91.120403.
  12. R. Cookea, M. Keanea & W. Morana (1985): Stably continuous frames. Math. Proc. Cambridge Phil. Soc. 98, pp. 117–128.
  13. E. D'Hondt & P. Panangaden (2006): Quantum weakest preconditions. Math. Struct. in Comp. Sci. 16(3), pp. 429–451, doi:10.1017/S0960129506005251.
  14. A. Dvurečenskij (1992): Gleason's Theorem and Its Applications. Mathematics and its Applications 60. Kluwer Acad. Publ., Dordrecht.
  15. A. Dvurečenskij & S. Pulmannová (2000): New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht.
  16. M. Giry (1982): A categorical approach to probability theory. In: B. Banaschewski: Categorical Aspects of Topology and Analysis, Lect. Notes Math. 915. Springer, Berlin, pp. 68–85, doi:10.1007/BFb0092872.
  17. A. Gleason (1957): Measures on the closed subspaces of a Hilbert space. Journ. Math. Mech. 6, pp. 885–893.
  18. S. Gudder (1998): Morphisms, tensor products and σ-effect algebras. Reports on Math. Phys. 42, pp. 321–346, doi:10.1016/S0034-4877(99)80003-2.
  19. B. Jacobs (2010): Convexity, duality, and effects. In: C.S. Calude & V. Sassone: IFIP Theoretical Computer Science 2010, IFIP Adv. in Inf. and Comm. Techn. 82(1). Springer, Boston, pp. 1–19, doi:10.1007/978-3-642-15240-5_1.
  20. B. Jacobs (2011): Probabilities, Distribution Monads, and Convex Categories. Theor. Comp. Sci. 412(28), pp. 3323–3336, doi:10.1016/j.tcs.2011.04.005.
  21. B. Jacobs & J. Mandemaker (2012): Coreflections in Algebraic Quantum Logic. Found. of Physics. From: Quantum Physics and Logic (QPL) 2010.
  22. P.T. Johnstone (1982): Stone Spaces. Cambridge Studies in Advanced Mathematics 3. Cambridge Univ. Press.
  23. C. Jones & G.D. Plotkin (1989): A probabilistic powerdomain of evaluations. In: Logic in Computer Science. IEEE. Computer Science Press, pp. 186–195, doi:10.1109/LICS.1989.39173.
  24. K. Keimel (2009): Abstract ordered compact convex sets and algebras of the (sub)probabilistic power domain monad over ordered compact spaces. Algebra and Logic 48(5), pp. 330–343, doi:10.1007/s10469-009-9065-x.
  25. K. Keimel, A. Rosenbusch & T. Streicher (2011): Relating direct and predicate transformer partial correctness semantics for an imperative probabilistic-nondeterministic language. Theor. Comp. Sci. 412, pp. 2701––2713.
  26. D. Kozen (1981): Semantics of probabilistic programs.. Journ. Comp. Syst. Sci 22(3), pp. 328–350, doi:10.1016/0022-0000(81)90036-2.
  27. E.G. Manes (1969): A triple-theoretic construction of compact algebras. In: B. Eckman: Seminar on Triples and Categorical Homolgy Theory, Lect. Notes Math. 80. Springer, Berlin, pp. 91–118, doi:10.1007/BFb0083083.
  28. E.G. Manes (1974): Algebraic Theories. Springer, Berlin, doi:10.1007/978-1-4612-9860-1.
  29. S. \voidb@x Mac Lane (1971): Categories for the Working Mathematician. Springer, Berlin.
  30. A. McIver & C. Morgan (2004): Abstraction, refinement and proof for probabilistic systems. Monographs in Comp. Sci.. Springer.
  31. P. Panangaden (2009): Labelled Markov Processes. Imperial College Press, doi:10.1142/9781848162891.
  32. S. Pulmannová & S. Gudder (1998): Representation theorem for convex effect algebras. Commentationes Mathematicae Universitatis Carolinae 39(4), pp. 645–659. Available from http://dml.cz/dmlcz/119041.
  33. N. Ramsey & A. Pfeffer (2002): Stochastic lambda calculus and monads of probability distributions. In: Principles of Programming Languages. ACM Press, pp. 154––165, doi:10.1145/503272.503288.
  34. S. Zanella Béguelin (2010): Formal Certification of Game-Based Cryptographic Proofs. École Nationale Supérieure des Mines de Paris.

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