# The $\lambda \mu^{\wedge \vee}$-calculus

Abstract : The $\lambda \mu^{\wedge \vee}$-calculus is an extension of the $\lambda$-calculus associated to the full classical natural deduction.
The main results of this thesis are:
- A standardization theorem, the confluence theorem, and an extension of J.-L. Krivine machine to the $\lambda \mu^{\wedge \vee}$-calculus.
- A semantical proof of the strong normalization theorem of the cut elimination procedure.
- A semantics of realizability for the $\lambda \mu^{\wedge \vee}$-calculus and characterization of the operational behavior of some closed typed terms.
- A completeness theorem for the simply typed $\lambda \mu$-calculus.
- A confluent call-by-value $\lambda \mu^{\wedge \vee}$-calculus.
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https://tel.archives-ouvertes.fr/tel-00415845
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Submitted on : Friday, September 11, 2009 - 11:26:08 AM
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• HAL Id : tel-00415845, version 1

### Citation

Khelifa Saber. The $\lambda \mu^{\wedge \vee}$-calculus. Mathematics [math]. Université de Savoie, 2007. English. ⟨tel-00415845⟩

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