Variability permeates software development to satisfy ever-changing requirements and mass-customization needs. A prime example is the Linux kernel, which employs the C preprocessor to specify a set of related but distinct kernel variants. To study, analyze, and verify variational software, several formal languages have been proposed. For example, the choice calculus has been successfully applied for type checking and symbolic execution of configurable software, while other formalisms have been used for variational model checking, change impact analysis, among other use cases. Yet, these languages have not been formally compared, hence, little is known about their relationships. Crucially, it is unclear to what extent one language subsumes another, how research results from one language can be applied to other languages, and which language is suitable for which purpose or domain. In this paper, we propose a formal framework to compare the expressive power of languages for static (i.e. compile-time) variability. By establishing a common semantic domain to capture a widely used intuition of explicit variability, we can formulate the basic, yet to date neglected, properties of soundness, completeness, and expressiveness for variability languages. We then prove the (un)soundness and (in)completeness of a range of existing languages, and relate their ability to express the same variational systems. We implement our framework as an extensible open source Agda library in which proofs act as correct compilers between languages or differencing algorithms. We find different levels of expressiveness as well as complete and incomplete languages w.r.t. our unified semantic domain, with the choice calculus being among the most expressive languages.

P4Cub is a new intermediate representation (IR) for the P4 programming language. It has been designed with the goal of facilitating development of certified tools. To achieve this, P4Cub is organized around a small set of core constructs and avoids side effects in expressions, which avoids mutual recursion between the semantics of expressions and statements. Still, it retains the essential domain-specific features of P4 itself. P4Cub has a front-end based on Petr4, and has been fully mechanized in Coq including big-step and small-step semantics and a type system. As case studies, we have engineered several certified tools with P4Cub including proofs of type soundness, a verified compilation pass, and an automated verification tool.

Many problems require working with data that varies in its structure and content. Current approaches, such as schema evolution or data integration tools, are highly tailored to specific kinds of variation in databases. While these approaches work well in their roles, they do not address all kinds of variation and do address the interaction of different kinds of variation in databases. In this paper, we define a framework for capturing variation as a generic and orthogonal con- cern in relational databases. We define variational schemas, variational databases, and variational queries for capturing variation in the structure, content, and information needs of relational databases, respectively. We define a type system that ensures variational queries are consistent with respect to a variational schema. Finally, we design and implement a variational database management system as an abstraction layer over a traditional relational database management system. Using previously developed use cases, we show the feasibility of our framework and demonstrate the performance of different approaches used in our system

Learning novel relations from relational databases is an important problem with many applications. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same database may be represented under different schemas for various reasons, such as data quality, efficiency and usability. The output of current relational learning algorithms tends to vary quite substantially over the choice of schema. This variation complicates their off-the-shelf application. We introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We show that current algorithms are not schema independent. We propose Castor, a relational learning algorithm that achieves schema independence by leveraging data dependencies.

Learning novel relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms leverage the properties of the database schema to find the definition of the target relation in terms of the existing relations in the database. However, the same data set may be represented under different schemas for various reasons, such as efficiency and data quality. Unfortunately, current relational learning algorithms tend to vary quite substantially over the choice of schema, which complicates their off-the-shelf application. We demonstrate Castor , a relational learning system that efficiently learns the same definitions over common schema variations. The results of Castor are more accurate than well-known learning systems over large data.