Abstract

Abstract

Abstract
Experience in teaching functional programming (FP) on a relational basis has led the author to focus on a graphical style of expression and reasoning in which a geometric construct shines: the (semi) commutative square. In the classroom this is termed the magic square (MS), since virtually everything that we do in logic, FP, database modeling, formal semantics and so on fits in some MS geometry. The sides of each magic square are binary relations and the square itself is a comparison of two paths, each involving two sides. MSs compose and have a number of useful properties. Among several examples given in the paper ranging over different application domains, free-theorem MSs are shown to be particularly elegant and productive. Helped by a little bit of Galois connections, a generic, induction-free theory for ${\mathsf{foldr}}$ and $\mathsf{foldl}$ is given, showing in particular that ${\mathsf{foldl} \, {{s}}{}\mathrel{=}\mathsf{foldr}{({flip} \unicode{x005F}{s})}{}}$ holds under conditions milder than usually advocated.

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[No abstract available]

Abstract
Data intensive applications increasingly make use of multiple data stores in the cloud, providing a diversity of data and query models, as well as durability and scale trade-offs. However, this has a severe impact on reliability, as the key fault-tolerance mechanism for database systems, i.e. ACID transactions, is no longer available. Although it is possible to implement transactions without changes to the database servers, this either requires a proxy server, which compromises scale and availability, or a client-side layer that changes the data schema, excludes legacy applications, and adds significant overhead. We address this challenge with a proposal to delegate functionality from a client-side transactional layer to a server-side query engine such that compatibility with legacy applications is restored. We implemented a proof-of-concept and show that it significantly improves performance for analytical applications.

Abstract
Diversity is crucial in systems that tolerate Byzantine faults. Traditionally, system builders have relied on standardized interfaces (e.g., POSIX for operating systems) to obtain off-the-shelf components or on n-version programming for custom functionality. Unfortunately, standardized alternatives are rare, and the independent development of multiple versions of the same software is costly and justified only on the most critical applications. In this paper, we show that a limited and focused use of LLMs for translation opens up the possibility of leveraging the existing diversity in functionally equivalent but non-standardized components. Specifically, we show that LLMs can produce functionally correct database query translations with minimal guidance and adapt to diverse data models and query contexts, enabling the use of radically different database models, both SQL and NoSQL, together in a Byzantine fault-tolerant replicated system. We outline an approach to achieve this in practice and discuss future research directions.