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Summer of Science Talks: An Introduction to Discrete Geometry, with application to the Principles of Concurrent Programming

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A discrete geometry consists of a finite set of points, lines, and figures laid out in two dimensions. In our application, the dimensions stand for execution time and space in the memory of the computer. The points stand for actions performed in program execution, vertical lines record the behaviour of objects, horizontal lines represent transactions, and figures are sets of actions occurring in execution of a syntactic component of the program text. The diagram is similar to a Message Sequence Chart, or a litmus test in the study of relaxed memory. From the Geometry, it is possible to deduce the Principles of Concurrent Programming, as expressed in Hoare Logic or expressed in Plotkinโ€™s structured operational semantics, or in the algebraic laws used for program optimisation.

The exposition is introductory, and requires no background other than an acquaintance with high-school geometry, algebra, and logic.

There will be time after the talk for a more in-depth discussion of the techniques presented and their applications.

This talk is part of the Microsoft Research Cambridge, public talks series.

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