Abstract Traits have been proposed as a more flexible mechanism than class inheritance for structuring code in object-oriented programming, to achieve fine-grained code reuse. A trait originally developed for one purpose can be adapted and reused in a completely different context. Formalizations of traits have been extensively studied, and implementations of traits have started to appear in programming languages. So far, work on formally establishing properties of trait-based programs has mostly concentrated on type systems. This paper presents the first deductive proof system for a trait-based object-oriented language. If a specification of a trait can be given a priori, covering all actual usage of that trait, our proof system is modular as each trait is analyzed only once. However, imposing such a restriction may in many cases unnecessarily limit traits as a mechanism for flexible code reuse. In order to reflect the flexible reuse potential of traits, our proof system additionally allows new specifications to be added to a trait in anincrementalway which does not violate established proofs. We formalize and show the soundness of the proof system.

Delta-oriented programming is a modular, yet flexible technique to implement software product lines. To efficiently verify the specifications of all possible product variants of a product line, it is usually infeasible to generate all product variants and to verify them individually. To counter this problem, we propose a transformational proof system in which the specifications in a delta module describe changes to previous specifications. Our approach allows each delta module to be verified in isolation, based on symbolic assumptions for calls to methods which may be in other delta modules. When product variants are generated from delta modules, these assumptions are instantiated by the actual guarantees of the methods in the considered product variant and used to derive the specifications of this product variant.

Traits have been proposed as a more flexible mechanism for code structuring in object-oriented programming than class inheritance, for achieving fine-grained code reuse. A trait originally developed for one purpose can be modified and reused in a completely different context. Formalizations of traits have been extensively studied, and implementations of traits have started to appear in programming languages. However, work on formally establishing properties of trait-based programs has so far mostly concentrated on type systems. This paper proposes the first deductive proof system for a trait-based object-oriented language. If a specification for a trait can be given a priori, covering all actual usage of that trait, our proof system is modular as each trait is analyzed only once. In order to reflect the flexible reuse potential of traits, our proof system additionally allows new specifications to be added to a trait in an incremental way which does not violate established proofs. We formalize and show the soundness of the proof system.