Relating Church-Style and Curry-Style Subtyping

Adriana Compagnoni
(Stevens Institute of Technology)
Healfdene Goguen
(Google, Inc.)

Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variable's bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.

Invited Presentation in Elaine Pimentel, Betti Venneri and Joe Wells: Proceedings Fifth Workshop on Intersection Types and Related Systems (ITRS 2010), Edinburgh, U.K., 9th July 2010, Electronic Proceedings in Theoretical Computer Science 45, pp. 1–15.
Published: 21st January 2011.

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