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**1 - 1**of**1**### Semantic and Syntactic Approaches to Simulation Relations

, 2003

"... 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 su#er from certain shortcomings; these are resolved by use of the weaker notion of pre-logic ..."

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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 su#er 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 prelogical relations directly generalise pre-logical relations to polymorphic lambda calculus (System F). We compile the main refinement-pertinent results of these various notions of simulation relation, and try to raise some issues for aiding their comparison and reconciliation.