Abstract

This paper uses logical relations for the first time to study the decidability of typechecking and subtyping. The result is proved for F ! , a language with higher-order subtyping and bounded operator abstraction not previously known to be decidable. The proof is via an intermediate system called a typed operational semantics, leading to a powerful and uniform technique for showing metatheoretic results of type systems with subtyping, such as strong normalization, subject reduction and decidability of subtyping. 1 Introduction During the last decade, object-oriented programming languages such as Smalltalk, C++, Modula 3, and Java have become popular because they encourage and facilitate software reuse and abstract design. One attempt to give a theoretical understanding of these object-oriented programming languages has been to introduce type systems with features to model constructs from object-oriented programming languages [5, 7], for example bounded quantification [15] and recur...

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