Subtyping dependent types

Subtyping dependent types

The need for subtyping in type-systems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system λP, which is an abstract version of the type system of the Edinburgh Logicalversion of the type system of the Edinburgh Logical ...

Subtyping Parametric and Dependent Types

A theory of dependent record types with structural subtyping

Type theory stemmed from the philosophical discussion on foundation of logic and set theory, and aroused interest from researchers in logic and formalism who gave it a clear format based on the λ-calculi. With the growth of the discipline of computing, various forms of type theory have brought in a common interest in developing computer-aided proof assistants. From this multi-disciplinary natur...

Dependent Types with Subtyping and Late-Bound Overloading

We present a calculus with dependent types, subtyping and late-bound overloading. Besides its theoretical interest this work is motivated by several practical needs that range from the definition of logic encodings, to proof specialization and reuse, and to object-oriented extension of the SML module system. The theoretical study of this calculus is not straightforward. While confluence is rela...

Subtyping with Power Types

This paper introduces a typed λ-calculus called λPower , a predicative reformulation of part of Cardelli’s power type system. Power types integrate subtyping into the typing judgement, allowing bounded abstraction and bounded quantification over both types and terms. This gives a powerful and concise system of dependent types, but leads to difficulty in the meta-theory and semantics which has i...