Combining Higher-Order and First-Order Computation Using ρ-calculus: Towards a semantics of ELAN

The ρ-calculus permits to express in a uniform and simple way firstorder rewriting, λ-calculus and non-deterministic computations as well as their combination. In this paper, we present the main components of the ρ-calculus and we give a full first-order presentation of this rewriting calculus using an explicit substitution setting, called ρσ, that generalizes the λσ-calculus. The basic properties of the non-explicit and explicit substitution versions are presented. We then detail how to use the ρ-calculus to give an operational semantics to the rewrite rules of the ELAN language.