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Towards this end, the theory of modular stratification, formulates a subset of normal logic programs whose literals can be statically reordered so that the program can be evaluated using a fixed-order computation rule. However, exploration of larger classes of stratified programs that can be evaluated in this manner has been left open in the literature, perhaps due to the lack of implementation methods that can benefit from such results. We address the limits of fixed-order computation by adapting results of Przymusinski to formulate the class of left-to-right dynamically stratified programs. We show that this class properly includes other classes of fixed-order stratified programs. Furthermore, we introduce SLG-strat, a variant of SLG resolution that uses a fixed-order computation rule, and prove that it correctly evaluates ground left-to-right dynamically stratified programs. We outline how SLG-strat can be used as a basis for restricting the space of possible SLG derivations and, finally, outline how these results are used in the abstract machine of XSB, and can be used in other methods such as Ordered Search of CORAL.