Interpreting higher computations as types with totality

Refinement Types as Higher-Order Dependency Pairs

Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher-order rewrite systems is still the subject of active research. We observe that a variant of refinement types allows us to express a form of higher-order dependency pai...

Feasible Computation with Higher Types

We restrict recursion in finite types so as to characterize the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types ρ → σ and terms λx̄r as well as ρ ( σ and λxr. Here we use two sorts of typed variables: complete ones x̄ and incomplete ones x.

Density Theorems for the Domains-with-Totality Semantics of Dependent Types

Categories of domains with totality

We investigate domains with totality where density in general does not hold. We define three categories of domains X with totality X̄ satisfying certain structural properties. We then define the ordered set of evaluation structures. These will induce domains with totality. We show that the set of evaluation structures in a natural way is closed under dependent sums and products and under direct ...

Higher-Order Algebra with Transfinite Types