I give a 'totality space' model for linear logic [4] derived by taking an abstract view of computations on a datatype. The model has similarities with both the coherence space model and game-theoretic models, but is based upon a notion of total object. Using this model, I prove a full completeness result. 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.
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