Enriching a Linear/Nonlinear Lambda Calculus: A Programming Language for String Diagrams
Abstract
Linear/nonlinear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda calculus for string diagrams, introduced by Rios and Selinger (with primary application in quantum computing). Our abstract treatment of this language leads to simpler concrete models compared to those presented so far. We also extend the language with general recursion and prove soundness. Finally, we present an adequacy result for the diagramfree fragment of the language which corresponds to a modified version of Benton and Wadler's adjoint calculus with recursion.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.09822
 Bibcode:
 2018arXiv180409822L
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Programming Languages;
 Mathematics  Category Theory;
 Quantum Physics
 EPrint:
 To appear in LICS 2018