论文标题
许多世界的微积分
The Many-Worlds Calculus
论文作者
论文摘要
在本文中，我们探讨了两个单体结构之间的相互作用：用于配对的编码和添加剂的乘法结构之间的相互作用。我们提出了一个彩色支柱，以模拟该框架中的计算，其中选择是通过代数副作用参数化的：该模型可以支持常规测试，概率和非确定性分支以及量子分支，即叠加。 该图形语言配备了基于线性应用和方程式理论的典型语义。我们证明了语言是普遍的，并且相对于这种语义而言，方程式理论是完整的。
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.
