Modularity of strong normalization and confluence in the algebraic-λ-cube

Presents the algebraic-λ-cube, an extension of Barendregt´s (1991) λ-cube with first- and higher-order algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraic-λ-cube, provided that the first-order rewrite rules are non-duplicating and the higher-order rules satisfy the general schema of Jouannaud and Okada (1991). This result is proven for the algebraic extension of the calculus of constructions, which contains all the systems of the algebraic-λ-cube. We also prove that local confluence is a modular property of all the systems in the algebraic-λ-cube, provided that the higher-order rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence