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The algebraic lambda calculus

Published online by Cambridge University Press:  24 August 2009

LIONEL VAUX
LIONEL VAUX*
Affiliation:
Laboratoire de Mathématiques de l'Université de Savoie, UFR SFA, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France E-mail: lionel.vaux@univ-savoie.fr
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Abstract

We introduce an extension of the pure lambda calculus by endowing the set of terms with the structure of a vector space, or, more generally, of a module, over a fixed set of scalars. Moreover, terms are subject to identities similar to the usual pointwise definition of linear combinations of functions with values in a vector space. We then study a natural extension of beta reduction in this setting: we prove it is confluent, then discuss consistency and conservativity over the ordinary lambda calculus. We also provide normalisation results for a simple type system.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Issue 5 , October 2009 , pp. 1029 - 1059
Copyright
Copyright © Cambridge University Press 2009

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