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arXiv · 1003.5518

On Linear Information Systems

A. Bucciarelli·A. Carraro·T. Ehrhard·A. Salibra
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Abstract

Scott's information systems provide a categorically equivalent, intensional description of Scott domains and continuous functions. Following a well established pattern in denotational semantics, we define a linear version of information systems, providing a model of intuitionistic linear logic (a new-Seely category), with a "set-theoretic" interpretation of exponentials that recovers Scott continuous functions via the co-Kleisli construction. From a domain theoretic point of view, linear information systems are equivalent to prime algebraic Scott domains, which in turn generalize prime algebraic lattices, already known to provide a model of classical linear logic.

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A. Bucciarelli, A. Carraro, T. Ehrhard, A. Salibra. 2010-03-29. On Linear Information Systems. https://doi.org/10.4204/eptcs.22.4

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