This paper introduces a new approach to type theory called pure subtype systems. Pure subtype systems differ from traditional approaches to type theory (such as pure type systems)...
We propose a new way to reason about general recursive functional programs in the dependently typed programming language Agda, which is based on Martin-L¨of’s intuitionistic ty...
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for...
—There are two usual ways to describe equality in a dependent typing system, one that uses an external notion of computation like beta-reduction, and one that introduces a typed ...
Termination of recursive functions is an important property in proof assistants based on dependent type theories; it implies consistency and decidability of type checking. Type-bas...