Residuation is an operational mechanism for the integration of functions into logic programming languages. The residuation principle delays the evaluation of functions during the unification process until the arguments are sufficiently instantiated. This has the advantage that the deterministic nature of functions is preserved, but the disadvantage of incompleteness: if the variables in a delayed function call are not instantiated by the logic program, this function can never be evaluated, and some answers which are logical consequences of the program are lost. In order to detect such situations at compile time, we present an abstract interpretation algorithm for this kind of programs. The algorithm approximates the possible residuations and instantiation states of variables during program execution. If the algorithm computes an empty residuation set for a goal, then it is ensured that the concrete execution of the goal does not end with a nonempty set of residuations which cannot be evaluated due to insufficient instantiation of argument variables.
