We demonstrate how the Hyland-Tan double glueing construction produces a fully complete model of the unit-free multiplicative fragment of Linear Logic when applied to any of a large family of degenerative ones. This process explains as special cases a number of such models which appear in the literature. In order to achieve this result, we make use of a tensor calculus for compact closed categories with finite biproducts. We show how the combinatorial properties required for a fully complete model are obtained by the construction adding to those already available from the original category.

We present a new category of games on graphs and derive from it a model for Intuitionistic Linear Logic. Our category has the computational flavour of concrete data structures but embeds fully and faithfully in an abstract games model. It differs markedly from the usual Intuitionistic Linear Logic setting for sequential algorithms. However, we show that with a natural exponential we obtain a model for PCF essentially equivalent to the sequential algorithms model. We briefly consider a more extensional setting and the prospects for a better understanding of the Longley Conjecture.