Deciding the equivalence of SQL queries is a fundamental problem in data management. As prior work has mainly focused on studying the theoretical limitations of the problem, very few implementations for checking such equivalences exist. In this paper, we present a new formalism and implementation for reasoning about the equivalences of SQL queries. Our formalism, Usemiring, extends SQL's semiring semantics with unbounded summation and duplicate elimination. U-semiring is defined using only very few axioms and can thus be easily implemented using proof assistants such as Coq for automated query reasoning. Yet, they are sufficient enough to enable us reason about sophisticated SQL queries that are evaluated over bags and sets, along with various integrity constraints. To evaluate the effectiveness of U-semiring, we have used it to formally verify 68 equivalent queries and rewrite rules from both classical data management research papers and real-world SQL engines, where many of them have never been proven correct before.

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Computing students often learn to program individually or in variously-sized groups whilst studying in computing laboratories and face-to-face classes. Previous research indicates that learning via pair programming can lead to students improving the quality of their programming, enhancing their programming skills and increasing their self-confidence when programming. Pair programming also is well established as a mechanism that supports peer learning and self-assessment for novice and more experienced students of programming. Observed benefits include increased self-efficacy, sharing of expertise, improved communication and teamworking-all enhancing employability. A considerable amount of existing work has examined pair programming benefits as they relate to campus-based students pairing face-to-face in a laboratory class-but how can distance learning students experience such benefits? This paper describes the preliminary results from a pilot study to investigate the benefits to distance learning students of engaging in Remote Pair Programming in their learning. Our investigation goes beyond academic learning to explore community, social and employability benefits, all of which are relevant to national measures of student satisfaction.

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