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arXiv · 2206.10234

The Many-Worlds Calculus

Kostia Chardonnet·Marc de Visme·Benoît Valiron·Renaud Vilmart
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Abstract

In this paper, we explore the interaction between two monoidal structures: a multiplicative one, for the encoding of pairing, and an additive one, for the encoding of choice. We propose a colored PROP to model computation in this framework, where the choice is parameterized by an algebraic side effect: the model can support regular tests, probabilistic and non-deterministic branching, as well as quantum branching, i.e. superposition. The graphical language comes equipped with a denotational semantics based on linear applications, and an equational theory. We prove the language to be universal, and the equational theory to be complete with respect to this semantics.

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Kostia Chardonnet, Marc de Visme, Benoît Valiron, Renaud Vilmart. 2022-06-21. The Many-Worlds Calculus. https://doi.org/10.46298/lmcs-21(2%3A13)2025

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