. We define a perpetual one-step reduction strategy which enables one to construct minimal (w.r.t. L'evy's ordering \Theta on reductions) infinite reductions in Conditional Orthogonal Expression Reduction Systems. We use this strategy to derive two characterizations of perpetual redexes, i.e., redexes whose contractions retain the existence of infinite reductions. These characterizations generalize existing related criteria for perpetuality of redexes. We give a number of applications of our results, demonstrating their usefulness. In particular, we prove equivalence of weak and strong normalization (the uniform normalization property) for various restricted -calculi, which cannot be derived from previously known perpetuality criteria. 1 Introduction The objective of this paper is to study sufficient conditions for uniform normalization, UN, of a term in an orthogonal (first or higher-order) rewrite system, and for the UN property of the rewrite system itself. Here a term is UN if ei...

Many Object-Oriented Programming Languages provide reflective features which may be used to control the interpretive mechanism of the language. Often, these features are defined with respect to a golden braid consisting of objects, classes and metaclasses. This paper describes the Smalltalk golden braid and generalize it for multiple inheritance. Multiple inheritance leads to choices between many different inheritance strategies. The reflective features of Smalltalk cannot affect the basic mechanisms of inheritance and so an arbitrary choice must be made for multiple inheritance. A language is described in which the reflective features of Smalltalk are extended so as to allow programmer defined inheritance strategies. 2 Introduction The evaluation of a programming language expression e in a given context c may be described by the evaluation of a program p which takes a representation of e and c as input. e is termed an object-level construct whilst p and the representations of e and ...