Year: 2012
Type: article
Abstract: We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms resulting from the reduction of programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We show that the resulting typed lambda-calculus is strongly normalizing and features a weak subject-reduction.
DOI: 10.4204/eptcs.88.1
Institutions: École Normale Supérieure de Lyon, Laboratoire d'Informatique de Grenoble, Laboratoire de l'Informatique du Parallélisme, Pôle de recherche et d'enseignement supérieur Université de Grenoble, Université Sorbonne Paris Nord, Sorbonne Paris Cité, Laboratoire d'Informatique de Paris-Nord, University of Pennsylvania
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2062004415