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

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          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.

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          Most cited references 7

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          Interacting Quantum Observables

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            A mixed linear and non-linear logic: Proofs, terms and models

             P. Benton (1995)
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              QWIRE a core language for quantum circuits

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                Author and article information

                Journal
                25 April 2018
                Article
                1804.09822

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                To appear in LICS 2018
                cs.LO cs.PL math.CT quant-ph

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