Kegelspitzen are mathematical structures coined by Keimel and Plotkin, in order to encompass the structure of a convex set and the structure of a dcpo. In this paper, we ask ourselves what are Kegelspitzen the model of. We adopt a categorical viewpoint and show that Kegelspitzen model stochastic matrices onto a category of domains. Consequently, Kegelspitzen form a denotational model of pPCF, an abstract functional programming language for probabilistic computing. We conclude the present work with a discussion of the interpretation of (probabilistic) recursive types, which are types for entities which might contain other entities of the same type, such as lists and trees.

@article{Rennela16,
  title = {Convexity and Order in Probabilistic Call-by-Name FPC},
  author = {Mathys Rennela},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 16, Issue 4},
  year = {2020},
  doi = {10.23638/lmcs-16(4:10)2020}
}