Transitivity in coercive subtyping

Coercive Subtyping

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory 38] and the type theory UTT 30]. In this approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, the meaning of an object being in a supertype is given by coercive deenition rules for t...

Coercive Subtyping in Type Theory

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory NPS90] and the type theory UTT Luo94]. In this approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, subsumption and coercion are combined in such a way that the meaning of an object ...

Coercive Subtyping and Lexical Semantics

Coercive subtyping: Theory and implementation

Coercive subtyping is a useful and powerful framework of subtyping for type theories. The key idea of coercive subtyping is subtyping as abbreviation. In this paper, we give a new and adequate formulation of T [C], the system that extends a type theory T with coercive subtyping based on a set C of basic subtyping judgements, and show that coercive subtyping is a conservative extension and, in a...

Coercion completion and conservativity in coercive subtyping

Coercive subtyping ooers a general approach to subtyping and inheritance by introducing a simple abbreviational mechanism to constructive type theories. In this paper, we study coercion completion in coercive subtyping and prove that the formal extension with coercive subtyping of a type theory such as Martin-LL of's type theory and UTT is a conservative extension. The importance of coherence c...