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The study of different notions of equivalence is one of the cornerstones of current research in answer-set programming. This is mainly motivated by the needs of program simplification and modular programming, for which ordinary equivalence is insufficient. A recently introduced equivalence notion in this context is hyperequivalence, which includes as special cases strong, uniform, and ordinary equivalence. The people study in this paper the question of replacing programs by syntactically simpler ones preserving hyperequivalence (the authors refer to such a replacement as a casting). In particular, they provide necessary and sufficient semantic conditions under which the elimination of disjunction, negation, or both, in programs is possible, preserving hyperequivalence.
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