. 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, finite or infinite, 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. 1 Introduction Long ago, Curry and Feys [CuFe58] proved that repeated contraction of leftmostoutermost redexes in any normalizable -term eventually yields its normal form, even if the term possesses infinite reductions as well. The reaso...

We introduce a notion of observation of a computational process on the basis of the observation of (the meaningful information couched by) the syntactic objects involved in the computation. This is formalized by means of observation mappings. We use them to give a semantic description of computational processes, an observable semantics, which is given on a purely syntactic basis; the observation mapping provides for a suitable abstraction level which permits the definition of different kinds of semantic values (which are still syntactic objects) with precise computational interpretations. We show how to use these formal constructions to provide a semantic basis for dynamic analysis. Keywords: computational processes, program analysis, semantics. Work partially supported by grant 252541L of the ' Ecole Polytechnique (France), 1999 Research Support Program of the Universidad Polit'ecnica de Valencia, and Spanish CICYT grant TIC 98-0445-C03-01. 1 Contents 1