The Many-Worlds Calculus
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912383163695104 |
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| author | Chardonnet, Kostia de Visme, Marc Valiron, Benoît Vilmart, Renaud |
| author_facet | Chardonnet, Kostia de Visme, Marc Valiron, Benoît Vilmart, Renaud |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10234 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Many-Worlds Calculus Chardonnet, Kostia de Visme, Marc Valiron, Benoît Vilmart, Renaud Logic in Computer Science Quantum Physics 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. |
| title | The Many-Worlds Calculus |
| topic | Logic in Computer Science Quantum Physics |
| url | https://arxiv.org/abs/2206.10234 |