Linear Logic, Totality and Full Completeness

I give a ‘totality space ’ model for linear logic [4], de-rived by taking an abstract view of computations on a datatype. The model has similarities with both the co-herence space model and game-theoretic models [1, 5], but is based upon a notion of total object. Using this model, I prove a full completeness result, along the lines of the results for game theoretic models in [1] and [5]. In other words, I show that the mapping of proofs to their interpretations (here collections of total objects uniform for a given functor) in the model is a surjection.