Axiomatizing Fully Complete Models for ML Polymorphic Types

@inproceedings{Abramsky2000AxiomatizingFC,
  title={Axiomatizing Fully Complete Models for ML Polymorphic Types},
  author={Samson Abramsky and Marina Lenisa},
  booktitle={MFCS},
  year={2000}
}
We present axioms on models of system F, which are sufficient to show full completeness for ML-polymorphic types. These axioms are given for hyperdoctrine models, which arise as adjoint models, i.e. co-Kleisli categories of linear categories. Our axiomatization consists of two crucial steps. First, we axiomatize the fact that every relevant morphism in the model generates, under decomposition, a possibly infinite typed Bohm tree. Then, we introduce an axiom which rules out infinite trees from… 

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