Implicit Coercions in Type Systems

We propose a notion of pure type system with implicit co-ercions. In our framework, judgements are extended with a context of coercions and the application rule is modiied so as to allow coercions to be left implicit. The setting supports multiple inheritance and can be applied to all type theories with-types. One originality of our work is to propose a computational interpretation for implicit coercions. In this paper, we demonstrate how this interpretation allows a strict control on the logical properties of pure type systems with implicit coecions.