Dependent Types and Fibred Computational Effects

We study the interplay between dependent types and general computational effects. We define a language with both value types and terms, and computation types and terms, where types depend only on value terms. We use computational Σ-types to account for typedependency in the sequential composition of computations. Our language design is justified by a natural class of categorical models. We account for both algebraic and non-algebraic effects. We also show how to extend the language with general recursion, using continuous families of cpos.