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Locally Boolean domains

journal contribution
posted on 2023-06-08, 05:38 authored by J Laird
Bistable bidomains have been used to give a simple order-theoretic construction of a cartesian closed category of sequential functions. In this paper, we investigate the intensional properties of a full subcategory, the locally boolean domains, in which the bistable structure is given by an involution operation. We show that every pointed locally boolean domain is the limit of an ?-chain of “prenex normal forms” constructed using only products and lifted sums. We use this result to describe a model of linear logic (incorporating both intuitionistic and polarized classical fragments). We show that affine and bistable functions correspond to unique “strategies” on the associated normal forms, and that function composition corresponds to “parallel composition plus hiding” of these strategies.

History

Publication status

  • Published

Journal

Theoretical Computer Science

ISSN

03043975

Publisher

Elsevier

Issue

1

Volume

342

Page range

132-148

Pages

17.0

Department affiliated with

  • Informatics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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