Datalog is a deductive query language for relational databases. We introduce LogiQL, a language based on Datalog and show how it can be used to specify mixedinteger linear optimization models and solve them. Unlike pure algebraic modeling languages, LogiQL allows the user to both specify models, and manipulate and transform the inputs and outputs of the models. This is an advantage over conventional optimization modeling languages that rely on reading data via plug-in tools or importing data from external sources via files. In this chapter, we give a brief overview of LogiQL and describe two mixed integer programming case studies: a production-transportation model and a formulation of the traveling salesman problem.

The standard process of data science tasks is to prepare features inside a database, export them as a denormalized data frame and then apply machine learning algorithms. This process is not optimal for two reasons. First, it requires denormalization of the database that can convert a small data problem into a big data problem. The second shortcoming is that it assumes that the machine learning algorithm is disentangled from the relational model of the problem. That seems to be a serious limitation since the relational model contains very valuable domain expertise. In this paper we explore the use of convex optimization and specifically linear programming, for modelling machine learning algorithms on relational data in an integrated way with data processing operators. We are using SolverBlox, a framework that accepts as an input Datalog code and feeds it into a linear programming solver. We demonstrate the expression of common machine learning algorithms and present use case scenarios where combining data processing with modelling of optimization problems inside a database offers significant advantages.

We report our experience with exploring a new point in the design space for formal reasoning systems: the development of the programming language @Wmega. @Wmega is intended as both a practical programming language and a logic. The main goal of @Wmega is to allow programmers to describe and reason about semantic properties of programs from within the programming language itself, mainly by using a powerful type system. We illustrate the main features of @Wmega by developing an interesting meta-programming example. First, we show how to encode a set of well-typed simply typed @l-calculus terms as an @Wmega data-type. Then, we show how to implement a substitution operation on these terms that is guaranteed by the @Wmega type system to preserve their well-typedness.