Discrete Normalization and Standardization in Deterministic Residual Structures

? Abstract. We prove a version of the Standardization Theorem and the Discrete Normalization (DN) Theorem in stable Deterministic Residual Structures , which are Abstract Reduction Systems with axiomatized residual relation , and model orthogonal rewrite systems. The latter theorem gives a strategy for construction of reductions L evy-equivalent (or permutation-equivalent) to a given, nite or innnite, regular (or semi-linear) reduction, based on the neededness concept of Huet and L evy. This and other results of this paper add to the understanding of L evy-equivalence of reductions, and consequently , L evy's reduction space. We demonstrate how elements of this space can be used to give denotational semantics to known functional languages in an abstract manner.