一句话:证明 Kegelspitzen 构成概率 call-by-name FPC/pPCF 的指称模型,并讨论概率递归类型解释。
本文研究 Kegelspitzen(Keimel 与 Plotkin 提出、同时刻画凸集与 dcpo 的结构)究竟为何种语言提供模型。作者从范畴论视角出发,证明 Kegelspitzen 可将随机矩阵建模到域范畴上,从而构成 pPCF(一种面向概率计算的抽象函数式语言)的指称模型。文末进一步讨论概率递归类型——如列表与树等可能包含同类型实体的类型——的解释。该工作为概率函数式语言提供了基于凸性与序结构的语义基础,并沟通了概率计算与域理论。
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.