Modularity of Strong Normalization and Confluence in the algebraic-lambda-cube

In this paper we present the algebraic--cube, an extension of Barendregt's -cube with first- and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraic--cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada. This result is proven for the algebraic extension of the Calculus of Constructions, which contains all the systems of the algebraic--cube. We also prove that local confluence is a modular property of all the systems in the algebraic--cube, provided that the higher-order rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence. 1 Introduction Many different computational models have been developed and studied by theoretical computer scientists. One of the main motivations for the development This research was partially supported by ESPRIT Basic Research Act..