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1 LAMA - Laboratoire de Mathématiques

Abstract : We introduce an extension of the pure lambda-calculus by endowing the set of terms with a structure of vector space, or more generally of module, over a fixed set of scalars. Terms are moreover subject to identities similar to usual point-wise 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 normalization results for a simple type system.

Keywords : lambda-calculus rewriting confluence strong normalization rewriting modulo





Author: Lionel Vaux -

Source: https://hal.archives-ouvertes.fr/



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