Enriching a Linear/Non-linear Lambda Calculus: A Programming Language for String Diagrams

## Authors: Bert Lindenhovius, Michael Mislove and Vladimir Zamdzhiev

## Paper Information

Title: | Enriching a Linear/Non-linear Lambda Calculus: A Programming Language for String Diagrams |

Authors: | Bert Lindenhovius, Michael Mislove and Vladimir Zamdzhiev |

Proceedings: | LICS PDF files |

Editors: | Anuj Dawar and Erich GrĂ¤del |

Keywords: | string diagrams, lambda calculi, quantum computing, categorical semantics, programming languages, enriched category theory |

Abstract: | ABSTRACT. Linear/non-linear (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 diagram-free fragment of the language which corresponds to a modified version of Benton and Wadler's adjoint calculus with recursion. |

Pages: | 10 |

Talk: | Jul 09 16:00 (Session 51E) |

Paper: |