Semigroupoid Interfaces for Relation-Algebraic Programming in Haskell

We present a Haskell interface for manipulating finite binary relations as data in a point-free relation-algebraic programming style that integrates naturally with the current Haskell collection types. This approach enables seamless integration of relation-algebraic formulations to provide elegant solutions of problems that, with different data organisation, are awkward to tackle.Perhaps surprisingly, the mathematical foundations for dealing with finite relations in such a context are not well-established, so we provide an appropriate generalisation of relational categories to semigroupoids to serve as specification for our interface.After having established an appropriate interface for relation-algebraic programming, we also need an efficient implementation; we find this in BDD-based kernel library KURE of recent versions of the Kiel RelView system. We show how this combination enables high-level declarative and efficient relational programming in Haskell.