The algebraic lambda-calculus

Lionel Vaux (1)

1 LAMA - Laboratoire de Mathématiques

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.

Mots clés: lambda-calculus; rewriting; confluence; strong normalization; rewriting modulo

Domaines: Logique en informatique [cs.LO]

Lionel Vaux. The algebraic lambda-calculus. Mathematical Structures in Computer Science, 2009, accepted for publication. ⟨hal-00379750⟩