Abstract

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 [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. 1 Introduction We shall give a model of linear logic by formalising a particular view of what an abstract datatype is. Consider a datatype A. There are objects s of type A, and programs t that accept an argument of type A. Taking any such s and t, we may execute the program on the data, and obtain a particular computation---the trace of the execution of the program. We shall consider only this facet of datatypes. For a given data (or pro...

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