Journal of Logic and Computation, Volume 9, Issue 1, pp. 105-130: Abstract.
Department of Computer Science, University of Durham, Durham, UK. E-mail: email@example.com
We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-Löf's type theory and the type theory UTT. In this approach, subtyping with specified 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 definition rules for the definitional equality. This provides a conceptually simple and uniform framework to understand subtyping and inheritance relations in type thoeries with sophisticated type structures such as inductive types and universes. The use of coercive subtyping in formal development and in reasoning about subsets of objects is discussed in the context of computer-assisted formal reasoning.
Key words: Type theory, subypting, coercion, formal reasoning, logical framework.