Foundations for SCALA : semantics and proof of virtual types

SCALA is an attractive programming language because it is both very expressive and statically strongly typed. This marriage against nature comes at the price of a certain complexity in the language constructs and the static analysis. This complexity makes type safety unclear. The goal of this thesis is to initiate a rigorous and formal process of validation of the SCALA type system. The correctness of a type system can only be established in relation to a formal description of a program execution. The first contribution of this thesis is the definition of a formal semantics for SCALA, by translation in a minimal class-based calculus. SCALA offers two means for expressing type abstraction: type parameters and type members, also called virtual types. Virtual types seem more primitive since they allow to encode type parameters whereas the existence of a reverse encoding is not clear. The soundness of virtual types has been the object of a long debate in the community; they are now commonly believed to be safe, but at this time, there exists no formal argument that would confirm this belief. The second contribution of this thesis is to provide a formal proof of type safety for virtual types.