# Meta-Theoretical Properties of lambda_phi: A Left-Linear Variant of lambda_sigma

Abstract : In this paper we consider explicit substitutions calculi that allow open terms. In particular, we propose a variant of the $\lambda_\sigma$-calculus, that we call $\lambda_\phi$. For this calculus and its simply-typed version, we study its meta-theoretical properties. The $\lambda_\phi$-calculus enjoys the same general characteristics as $\lambda_\sigma$, i.e. a simple and finitary first-order presentation, confluent on terms with meta-variables, with a composition operator and with simultaneous substitutions. However, $\lambda_\phi$ does not have the non-left-linear surjective pairing rule of $\lambda_\sigma$ which raises technical problems in some frameworks.
Type de document :
Rapport
[Research Report] RR-3107, INRIA. 1997
Domaine :

https://hal.inria.fr/inria-00073584
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 13:14:51
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:50:54

### Identifiants

• HAL Id : inria-00073584, version 1

### Citation

César Muñoz. Meta-Theoretical Properties of lambda_phi: A Left-Linear Variant of lambda_sigma. [Research Report] RR-3107, INRIA. 1997. 〈inria-00073584〉

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