Top-top-closed Relations and Admissibility

While developing a method for reasoning about programs, Pitts defined the tt-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts's operational concept of tt-closure in a semantic framework. It investigates the non-trivial connection between tt-closure and admissibility, showing that tt-closure is strictly stronger than admissibility and that every tt-closed relation corresponds to an admissible preorder.

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