Specification Refinement with System F - The Higher-Order Case

A type-theoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higher-order signatures. The type-theoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For first-order signatures, this setting immediately gives a natural notion of specification refinement up to observational equivalence via the notion of simulation relation. Moreover, a proof strategy for proving observational refinements formalised by Bidoit, Hennicker and Wirsing can be soundly imported into the type theory. In lifting these results to the higher-order case, we find it necessary firstly to develop an alternative simulation relation and secondly to extend the parametric PER-model interpretation, both in such a way as to observe data type abstraction barriers more closely.

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