|Abstract of Paper|
Semantic and Syntactic Approaches to
by Jo Hannay, 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-logical 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.