Combining Higher-Order & First-Order Computation Using ρ-calculus: Towards a semantics of ELAN Full-version
Résumé
The recently introduced ρ-calculus permits to express in a uniform and simple way first-order rewriting, λ-calculus and non-deterministic computations as well as their combination. In this work, we emphasize the expressiveness of ρ-calculus and we give a full first-order presentation of this rewriting calculus using an explicit substitution setting ρσ that generalizes the λσ-calculus. Its basic properties in the untyped as well as typed cases are presented. We then detail how to use the ρ-calculus to give an operational semantics to the rewrite based language Elan.