Work

Linear-algebraic lambda-calculus

Year: 2005

Type: preprint

Abstract: With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite system. The linear-algebraic lambda-calculus hereby constructed is linear in a different (yet related) sense to that, say, of the linear lambda-calculus. These various notions of linearity are discussed in the context of quantum programming languages. KEYWORDS: quantum lambda-calculus, linear lambda-calculus, $λ$-calculus, quantum logics.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.quant-ph/0501150

Authors: Arrighi, Pablo, Dowek, Gilles

Institutions: Laboratoire d'Informatique Gaspard-Monge, Institut national de recherche en sciences et technologies du numérique, École Polytechnique, Laboratoire d'Informatique de l'École Polytechnique

Language: English

Topic: Logic, programming, and type systems

Subfield: Software

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W1541150383

Cites: 27

Cited by: 11

Related to: 10