Combining Algebraic and Set-Theoretic Specifications (Extended Version)

Specification frameworks such as B and Z provide power sets and cartesianproducts as built-in type constructors, and employ a rich notation fordefining (among other things) abstract data types using formulae of predicatelogic and lambda-notation. In contrast, the so-called algebraic specification frameworks often limit the type structure to sort constants andfirst-order functionalities, and restrict formulae to (conditional) equations.Here, we propose an intermediate framework where algebraic specificationsare enriched with a set-theoretic type structure, but formulae remain in thelogic of equational Horn clauses. This combines an expressive yet modestspecification notation with simple semantics and tractable proof theory