Arrighi, Pablo and Dowek, Gilles - Lineal: A linear-algebraic Lambda-calculus

lmcs:3203 - Logical Methods in Computer Science, March 17, 2017, Volume 13, Issue 1
Lineal: A linear-algebraic Lambda-calculus

Authors: Arrighi, Pablo and Dowek, Gilles

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus with the possibility to make arbitrary linear combinations of terms alpha.t + beta.u. We describe how to "execute" this language in terms of a few rewrite rules, and justify them through the two fundamental requirements that the language be a language of linear operators, and that it be higher-order. We mention the perspectives of this work in the field of quantum computation, whose circuits we show can be easily encoded in the calculus. Finally, we prove the confluence of the entire calculus.


Source : oai:arXiv.org:quant-ph/0612199
DOI : 10.23638/LMCS-13(1:8)2017
Volume: Volume 13, Issue 1
Published on: March 17, 2017
Submitted on: March 17, 2017
Keywords: Quantum Physics,Computer Science - Logic in Computer Science,Computer Science - Programming Languages,03B40, 68N18, 81P68,F.4.1,F.4.2,F.1.1


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