Decidability of Higher-Order Subtyping via Logical Relations

This paper uses logical relations for the rst time to study the decidability of type-checking and subtyping. The result is proved for F ! , a language with higher-order sub-typing 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.

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