C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e

In this report a comparative semantics is given for a language L p containing probabilistic and non-deterministic choice. The effects of interpreting these operators as local or global are investigated. For three of the possible combinations an operational model and a denotational model are given and compared. First models for local probabilistic choice and local non-deterministic choice are given using a generative approach. By adjusting these models slightly models for global probability and local non-determinism are obtained. Finally models for local probability and global non-determinism are presented using a stratified approach. For use with the denotational models a construction of a complete ultra-metric space of finite multisets is given. 1 Introduction The goal of this paper is to construct comparative semantics for a language combining non-determinism and probabilistic choice. The main interest is the interplay between these two concepts. Since many of the interesting proper...

istic of imperative programs is that they embody the notion of a computation step: a program being a sequence of actions, it forces a sequence of intermediates states. Typically, the intermediate states are observable, meaning that one can observe something about that intermediate state, either by looking up the value of a variable, by witnessing an output operation, etc. When the intermediate states of a computation are observable, it becomes reasonable to talk about infinite (nonterminating) computations. (The classical example of this is of course an operating system, which at least theoretically is an infinite process; the main motivation for the topological approach, as we shall see, is to make sense of such infinite computations.) Contrast this with functional languages, which are often used as motivating examples for the study of semantics. In a pure functional language, all infinite programs are equivalent, and in a traditional denotational semantics based on partial orders (a

I have to admit, I was looking forward to reviewing this book. It answered what was for me a 6-year old question.