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Coherence Spaces

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Coherence spaces are a model of the lambda-calculus which was very influential, eventually leading to the discovery of linear logic. In this talk I will define the category of coherence spaces and stable functions between them, and show how it can be used to interpret e.g. PCF . In the process I will mention how it relates to the usual domain theory. Then I will talk about a special kind of stable functions between coherence spaces, the linear functions. Using these we can refine the category of coherence spaces and stable functions, to get one the first models of linear logic.

If time permits, I’ll talk about a generalisation of coherence spaces to a model of probabilistic computation: these turn out to give a fully abstract model for Probabilistic PCF .

This talk is part of the Logic & Semantics for Dummies series.

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