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Abstract

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.