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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Veröffentlicht in:	Logical methods in computer science Jg. 21, Issue 2; H. 2
Hauptverfasser:	Chardonnet, Kostia, de Visme, Marc, Valiron, Benoît, Vilmart, Renaud
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Logical Methods in Computer Science Association 01.05.2025 Logical Methods in Computer Science e.V
Schlagworte:	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-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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