A Semantic Formulation of ⊤ ⊤-Lifting and Logical Predicates for Computational Metalanguage

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Abstract

A semantic formulation of Lindley and Stark’s ⊤ ⊤-lifting is given. We first illustrate our semantic formulation of the ⊤ ⊤-lifting in Set with several examples, and apply it to the logical predicates for Moggi’s computational metalanguage. We then abstract the semantic ⊤ ⊤-lifting as the lifting of strong monads across bifibrations with lifted symmetric monoidal closed structures.