In a former work we described the system and language R-SQL that overcomes some limitations of recursion of the relational database language SQL. Such limitations are non-linearity, mutual recursion, and some combinations of negation with recursion. In addition, R-SQL improved termination properties of recursive definitions. Next, this language was extended to include a restricted form of hypothetical relations and queries using assumptions, obtaining the language HR-SQL, and a preliminary implementation was developed for it. Here, we develop a new system HR-SQL from scratch and enhance the former system in several areas. First, hypothetical reasoning is fully integrated with recursive definitions. Second, the Python script generated by the system for computing the extension (materialization) of a database is now targeted to several state-of-the-art relational database systems. Third, the system has been interfaced to the integrated development environment ACIDE, allowing both a more friendly user interaction and a graphical view of the dependency graph that shows dependencies between relations. Fourth, being developed in Prolog, we have targeted it to both SICStus Prolog and SWI-Prolog, also providing standalone executables. Finally, the system has been extended with a bundle of commands, highly improving its capabilities with respect to the former system.