Presented is the design, implementation and evaluation of a system for computing with non-enumerative set representations. The implementation is in the form of a set assembly language (Sal) whose operations correspond to an implementation of the algebra of sets, with minimal added syntactic sugar; a compiler (Salc) for validation and static optimization of Sal definitions; and a virtual machine architecture (Svm) for executing Sal definitions. Sal/Svm has turned out to be a surprisingly versatile framework for a growing number of problems. One such application, as a framework for declaratively specifying computational problems with the same level of precision that traditional machine languages enable the specification of computational algorithms, is presented. Copyright © 2010 ACM.