It is worth noting that our work shares many aspects with the work carried out by Thomas Eiter, Giovambattista Ianni, Roman Schindlauer, and Hans Tompits. They introduce HEX programs, which are nonmonotonic logic programs admitting higher-order atoms as well as external atoms, and extend the answer-set semantics accordingly. A web page with a prototype and some references is available here.
DLV-Complex is a very powerful ASP system, which, besides external predicates, explicitly supports (recursive) functions, sets, and lists, along with libraries for their manipulations. The DLV-EX project is actually moving to DLV-Complex.
DLV is the system into which DLV-EX is implemented.
DLT is an extension to the DLV system providing reusable template predicate definitions. It is maintained by members of the DLV team from Università della Calabria.
DLV-HEX features "second order" external predicates taking relational input an returning relational output, as well as higher order atoms. It allows DLT as a pre-parser.