Locally Boolean domains

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 ω-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.