  We study properties of programs with monotone and convex constraints. We
extend to these formalisms concepts and results from normal logic programming.
They include the notions of strong and uniform equivalence with their
characterizations, tight programs and Fages Lemma, program completion and loop
formulas. Our results provide an abstract account of properties of some recent
extensions of logic programming with aggregates, especially the formalism of
lparse programs. They imply a method to compute stable models of lparse
programs by means of off-the-shelf solvers of pseudo-boolean constraints, which
is often much faster than the smodels system.
