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# 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.
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Reports
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https://hal.inria.fr/inria-00073584
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Submitted on : Wednesday, May 24, 2006 - 1:14:51 PM
Last modification on : Thursday, February 3, 2022 - 11:18:27 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:50:54 PM

### Identifiers

• 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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