What can programming languages say about data exchange?

Data Exchange, defined generally, is the process of taking data structured under one schema and transforming it into data structured under another independent schema. This process is present in enough scenarios both theoretical and practical that it has been addressed in many different ways. Most prominent amongst the solutions to the problem is that proposed by database literature, in which one constructs schema mappings, using (a subset of) first-order predicate calculus, to establish the high-level relationship among the database schemas participating in the exchange. From a schema mapping an executable process is derived to perform the exchange. This line of research has made significant progress and come to impressive findings, but has some theoretical and practical shortcomings as well. For instance, there are theoretical limitations as to how to compose or invert such mappings in a complete and unique way, which is a barrier to making such mappings bidirectional. It is possible to address some of these shortcomings by looking to solutions from a different discipline-a construct from the programming language literature called a lens-that addresses similar problems from a different perspective. By combining solutions from these two disciplines, one ends up with a new direction of research as well as a result that might be greater than the sum of its parts.