Domain Theory for Concurrency
DOI:
https://doi.org/10.7146/brics.v10i43.21815Resumé
A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of comonad yield two expressive metalanguages for higher-order processes, both arising from canonical constructions in the model. Their denotational semantics are fully abstract with respect to contextual equivalence. One language derives from an exponential of linear logic; it supports a straightforward operational semantics with simple proofs of soundness and adequacy. The other choice of comonad yields a model of affine-linear logic, and a process language with a tensor operation to be understood as a parallel composition of independent processes. The domain theory can be generalised to presheaf models, providing a more refined treatment of nondeterministic branching. The article concludes with a discussion of a broader programme of research, towards a fully fledged domain theory for concurrency.Downloads
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2003-12-11
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Nygaard, M., & Winskel, G. (2003). Domain Theory for Concurrency. BRICS Report Series, 10(43). https://doi.org/10.7146/brics.v10i43.21815
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