subtyping

Our objective is to provide a model in type theory, using identity types, for parametric polymorphism, subtypes and inheritance. The resulting programming language is a monomor-phic language that has the advantages of polymorphic languages. Since the implementation is using only identity types and since identity types are primitive components of type theory, desirables like type safety, uniqueness of types and the soundness of the system are given at no cost. That is, unlike competing approaches, this way of modeling poly-morphism is not through an extension of the type theory; rather we are using a primitive component of the theory hence no extra work is needed to check whether this new functionality of the system has any side effects on its type safety, uniqueness of types and soundness.

The concept of " change of perspective " , where a single object is viewed from different angles, each providing a different image (that is a different formal description) but each lacking nothing of the ipseity of the object nor of its essential qualities, has received no formalization so far. In this paper we formalize this concept using identity types in pure intentional type theory and we briefly give the sketch of two of the applications of this formalization in natural language processing and programming languages.