The Many-Worlds Calculus

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 effe...

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Bibliographic Details
Published in:Logical methods in computer science Vol. 21, Issue 2; no. 2
Main Authors: Chardonnet, Kostia, de Visme, Marc, Valiron, Benoît, Vilmart, Renaud
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 01.05.2025
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - logic in computer science
Logic in Computer Science
Physics
Quantum Physics
Graphical Languages
Geometry of Interaction
Linear Logic
Quantum Control
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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Summary: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.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-21(2:13)2025