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Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 2
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While developing a method for reasoning about programs, Pitts defined the ⊤⊤-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts's operational concept of ⊤⊤-closure in a semantic framework. It investigates the non-trivial connection between ⊤⊤-closure and admissibility, showing that ⊤⊤-closure is strictly stronger than admissibility and that every ⊤⊤-closed relation corresponds to an admissible preorder.