Linear types, approximation, and topology

We enrich the *-autonomous category of complete lattices and maps preserving all suprema with the important concept of approximation by specifying a *-autonomous full subcategory LFS of linear FS-lattices. This is the greatest *-autonomous full subcategory of linked bicontinuous lattices. The modalities !() and ?() mediate a duality between the upper and lower powerdomains. The distributive objects in LFS give rise to the compact closed *-autonomous full subcategory CD of completely distributive lattices. We characterise algebraic objects in LFS by forbidden substructures 'a la Plotkin'.<<ETX>>

[1]  K. Hofmann,et al.  A Compendium of Continuous Lattices , 1980 .

[2]  Samson Abramsky,et al.  Interaction Categories , 1993, Theory and Formal Methods.

[3]  Radha Jagadeesan,et al.  New foundations for the geometry of interaction , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[4]  George N. Raney,et al.  Completely distributive complete lattices , 1952 .

[5]  Samson Abramsky,et al.  Domain Theory in Logical Form , 1991, LICS.

[6]  Michael W. Mislove,et al.  Local compactness and continuous lattices , 1981 .

[7]  Robert D. Tennent,et al.  Semantics of programming languages , 1991, Prentice Hall International Series in Computer Science.

[8]  Gordon D. Plotkin,et al.  A Powerdomain Construction , 1976, SIAM J. Comput..

[9]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..