A relation-algebraic approach to the “Hoare logic” of functional dependencies

•This paper expresses functional dependencies using binary relation algebra.•It shows that functional dependency calculus is similar to Hoare logic.•This is based on reasoning about the degree of injectivity of a relation.•Applications are given for query optimization and lexicographic sorting.•The optimizations are obtained by point-free calculations.

Abstract algebra has the power to unify seemingly disparate theories once they are encoded into the same abstract formalism. This paper shows how a relation-algebraic rendering of both database dependency theory and Hoare programming logic purports one such unification, in spite of the latter being an algorithmic theory and the former a data theory.The approach equips relational data with functional types and an associated type system which is useful for database operation type checking and optimization.The prospect of a generic, unified approach to both programming and data theories on top of libraries already available in automated deduction systems is envisaged.