Semantic and Syntactic Approaches to Simulation Relations

  title={Semantic and Syntactic Approaches to Simulation Relations},
  author={Jo Erskine Hannay and Shin-ya Katsumata and Donald Sannella},
Simulation relations are tools for establishing the correctness of data refinement steps. In the simply-typed lambda calculus, logical relations are the standard choice for simulation relations, but they suffer from certain shortcomings; these are resolved by use of the weaker notion of pre-logical relations instead. Developed from a syntactic setting, abstraction barrier-observing simulation relations serve the same purpose, and also handle polymorphic operations. Meanwhile, second-order pre… 
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A generalisation of pre-logical predicates and its applications
A generalisation of pre-logical predicates to simply typed formal systems and their categorical models is proposed and two distinguishing properties are shown: equivalence with the basic lemma and closure of binary pre- logical relations under relational composition.


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