Convexity and Order in Probabilistic Call-by-Name FPC

摘要

Kegelspitzen are mathematical structures coined by Keimel and Plotkin, inorder 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 acategorical viewpoint and show that Kegelspitzen model stochastic matrices ontoa category of domains. Consequently, Kegelspitzen form a denotational model ofpPCF, 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 mightcontain other entities of the same type, such as lists and trees.