Convexity and Order in Probabilistic Call-by-Name FPC

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.