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Programs, domains, and logic

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 Achim Jung
Le mardi 09 avril 2013 à 11:00
Salle de Conférence (Pavillon des Jardins)
Achim Jung (University of Birmingham)

In this talk I will give an overview of some research questions that over the years have inspired me and to which I have contributed. While somewhat tutorial in nature, I will also try to explain some of the more technical difficulties which we have encountered along the way, and which have made me change direction a few times.

We will begin with Scott's work of the late 1960's, when he began to lay the foundations for a "mathematical theory of computation", and the correspondence between programs and semantic models initiated by Plotkin in 1977. I will explain the notion of a Scott domain and its associated concepts of "finite element" and "approximation". We'll then see how the desire to deal with real numbers and probabilities led to an interest in continuous domains. Again we'll see its successes but also some of the problems that appeared. For reasons of the latter, the focus for me shifted towards topological spaces. Domain-style approximation being no longer available, this move entailed a closer study of Stone dualities, where instead of spaces one considers "propositions" about elements of a space. Although this may appear as a technical necessity, it does actually emphasise the link between semantics and program logics, something that Samson Abramsky advocated more than 20 years ago in his "Domain theory in logical form".

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mar. 19 février

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