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.

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Logical Methods in Computer Science
Centrum Wiskunde & Informatica, Amsterdam (CWI), 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