The Many-Worlds Calculus

• URL: http://arxiv.org/abs/2206.10234v4
• Date: Fri, 25 Oct 2024 16:57:24 GMT
• Title: The Many-Worlds Calculus
• Authors: Kostia Chardonnet, Marc de Visme, Benoît Valiron, Renaud Vilmart,
• Abstract summary: We propose a colored PROP to model computation in this framework. The model can support regular tests, probabilistic and non-deterministic branching, as well as quantum branching. We prove the language to be universal, and the equational theory to be complete with respect to this semantics.
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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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