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Communication Dans Un Congrès Année : 2020

Cones as a model of intuitionistic linear logic

Résumé

For encompassing the limitations of probabilistic coherence spaces which do not seem to provide natural interpretations of continuous data types such as the real line, Ehrhard and al. introduced a model of probabilistic higher order computation based on (positive) cones, and a class of totally monotone functions that they called "stable". Then Crubillé proved that this model is a conservative extension of the earlier probabilistic coherence space model. We continue these investigations by showing that the category of cones and linear and Scott-continuous functions is a model of intuitionistic linear logic. To define the tensor product, we use the special adjoint functor theorem, and we prove that this operation is and extension of the standard tensor product of probabilistic coherence spaces. We also show that these latter are dense in cones, thus allowing to lift the main properties of the tensor product of probabilistic coherence spaces to general cones. Last we define in the same way an exponential of cones and extend measurability to these new operations.
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Dates et versions

hal-02436161 , version 1 (12-01-2020)
hal-02436161 , version 2 (14-12-2020)
hal-02436161 , version 3 (17-10-2021)

Identifiants

Citer

Thomas Ehrhard. Cones as a model of intuitionistic linear logic. LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science, Jul 2020, Saarbrücken Germany, Germany. pp.370-383, ⟨10.1145/3373718.3394758⟩. ⟨hal-02436161v3⟩
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