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Specification Refinement with System F, The HigherOrder Case
, 2000
"... . A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setti ..."
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. A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder 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 higherorder case, we find it necessary firstly to develop an alternative simulation relation and secondly to extend the parametric PERmodel interpretation, both in such a way as to observe data type abstraction barriers more closely. 1 Introduction One framework in algebraic specification that has particular appeal and applicability is that of stepwise specification refi...