# Combining Higher-Order & First-Order Computation Using $\rho$-calculus: Towards a semantics of ELAN Full-version

1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The recently introduced $\rho$-calculus permits to express in a uniform and simple way first-order rewriting, $\lambda$-calculus and non-deterministic computations as well as their combination. In this work, we emphasize the expressiveness of $\rho$-calculus and we give a full first-order presentation of this rewriting calculus using an explicit substitution setting $\rho\sigma$ that generalizes the $\lambda\sigma$-calculus. Its basic properties in the untyped as well as typed cases are presented. We then detail how to use the $\rho$-calculus to give an operational semantics to the rewrite based language Elan.
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https://hal.inria.fr/inria-00098736
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:21:58 AM
Last modification on : Thursday, January 11, 2018 - 6:19:58 AM
Document(s) archivé(s) le : Friday, November 25, 2016 - 11:50:59 AM

### Identifiers

• HAL Id : inria-00098736, version 1

### Citation

Horatiu Cirstea, Claude Kirchner. Combining Higher-Order & First-Order Computation Using $\rho$-calculus: Towards a semantics of ELAN Full-version. [Intern report] 98-R-220 || cirstea98b, 1998. 〈inria-00098736〉

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