Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
FSCD
in Paris,
July 2020
Concurrent Kleene Algebra is an elegant tool for equational reasoning about concurrent programs. An important feature of concurrent programs that is missing from CKA is the ability to restrict legal interleavings. To remedy this we extend the standard model of CKA, namely pomsets, with a new feature, called boxes, which can specify that part of the system is protect from outside interference. We study the algebraic properties of this new model. Another drawback of CKA is that the language used for expressing properties of programs is the same as that which is used to express programs themselves. This is often too restrictive for practical purposes. We provide a logic, `pomset logic', that is an assertion language for specifying such properties, and which is interpreted on pomsets with boxes. We develop the basic metatheory for the relationship between pomset logic and CKA, including frame rules to support local reasoning, and illustrate this relationship with simple examples.
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Related papers | ||
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Equivalence checking for weak bi-Kleene algebra
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Partially Observable Concurrent Kleene Algebra
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with Jana Wagemaker, Simon Docherty, Jurriaan Rot, Tobias Kappé and Alexandra Silva. |
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Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
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with Tobias Kappé, Alexandra Silva, Fabio Zanasi and Jana Wagemaker. |
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Pomsets with Boxes: Protection, Separation, and Locality in Concurrent Kleene Algebra
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with David Pym. |
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On Series-Parallel Pomset Languages: Rationality, Context-Freeness and Automata
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Kleene Algebra with Observations
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Concurrent Kleene Algebra: Free Model and Completeness
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On Decidability of Concurrent Kleene Algebra
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with Damien Pous and Georg Struth. |
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