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.

Convex set, Domain, Kegelspitze, Probabilistic computation, Recursive type
Logical Methods in Computer Science
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Rennela, M. (2020). Convexity and order in probabilistic call-by-name FPC. Logical Methods in Computer Science, 16(4), 10:1–10:25. doi:10.23638/LMCS-16(4:10)2020