Abstract
Bounded operator abstraction is a language construct relevant to object oriented programming languages and to ML2000, the successor to Standard ML. In this paper, we introduce F ω ⩽ , a variant of F <: ω with this feature and with Cardelli and Wegner’s kernel Fun rule for quantifiers. We define a typed-operational semantics with subtyping and prove that it is equivalent with F ω ⩽ , using logical relations to prove soundness. The typed-operational semantics provides a powerful and uniform technique to study metatheoretic properties of F ω ⩽ , such as Church–Rosser, subject reduction, the admissibility of structural rules, and the equivalence with the algorithmic presentation of the system that performs weak-head reductions. Furthermore, we can show decidability of subtyping using the typed-operational semantics and its equivalence with the usual presentation. Hence, this paper demonstrates for the first time that logical relations can be used to show decidability of subtyping.
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