Abstract

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.

Abstract

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.