Extensions of logic and functional programming are integrated in RELFUN. Its valued clauses comprise Horn clauses (`true'-valued) and clauses with a distinguished `foot' premise (returning arbitrary values). Both the logic and functional components permit LISP-like varying-arity and higher-order operators. The DATAFUN sublanguage of the functional component is shown to be preferable to relational encodings of functions in DATALOG. RELFUN permits non-ground, non-deterministic functions, hence certain functions can be inverted using an `is'-primitive generalizing that of PROLOG. For function nestings a strict call-by-value strategy is employed. The reduction of these extensions to a relational sublanguage is discussed and their WAM compilation is sketched. Three examples (`serialise', `wang', and `eval') demonstrate the relational/functional style in use. The list expressions of RELFUN's LISP implementation are presented in an extended PROLOG-like syntax.