Declarative Programming with Intensional Sets in Java Using JSetL.

This article focuses on the integration and exploitation of restricted intensional sets (RISs)—a subclass of intensional sets denoting finite but unbounded sets—within the Java programming language via the JSetL library. RISs, originally defined in a first-order logic language with a complete constraint solver, are extended in JSetL to support declarative programming in an object-oriented setting, enabling programmers to represent sets by properties rather than enumeration and to encode partial functions, recursion, and restricted universal quantification declaratively. The paper details the theoretical framework of RIS, their implementation as Java objects, the extension of JSetL's constraint solver to handle RIS constraints, and demonstrates practical applications including theorem proving and prototyping of classical problems. Empirical evaluations indicate that while JSetL favors expressiveness and flexibility over raw efficiency, it serves as a valuable tool for rapid prototyping, formal specification encoding, and bridging declarative set-based reasoning with conventional Java programming.