Relating Church-Style and Curry-Style Subtyping
Adriana Compagnoni, Healfdene Goguen
2011
Electronic Proceedings in Theoretical Computer Science
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
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... al 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.
doi:10.4204/eptcs.45.1
fatcat:e75aonjtu5fi5gkfbioujqglbi