English

A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus

Logic in Computer Science 2012-08-01 v4

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.

Keywords

Cite

@article{arxiv.1012.4032,
  title  = {A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus},
  author = {Pablo Arrighi and Alejandro Díaz-Caro and Benoît Valiron},
  journal= {arXiv preprint arXiv:1012.4032},
  year   = {2012}
}

Comments

In Proceedings DCM 2011, arXiv:1207.6821

R2 v1 2026-06-21T17:00:51.967Z