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.

@article{paperbot3418,
  title = {The Many-Worlds Calculus},
  author = {Kostia Chardonnet and Marc de Visme and Benoît Valiron and Renaud Vilmart},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 21, Issue 2},
  year = {2025},
  doi = {10.46298/lmcs-21(2:13)2025}
}