Species, Profunctors and Taylor Expansion Weighted by SMCC
Species, Profunctors and Taylor Expansion Weighted by SMCC
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SMCC 加权的物种、函子和泰勒展开式
DOI：
10.1145/3209108.3209157
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
C.-H. Luke Ong
中科院分区：
文献类型：
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作者：
Takeshi Tsukada;Kazuyuki Asada;C.-H. Luke Ong
出于Joyal的组合物种和线性逻辑的定量模型之间的紧密联系，本文介绍了加权广义物种（或加权profunctors），其中权重是一个给定的对称monoidal闭范畴（SMCC）的态射。对于每个SMCC W，我们证明了W-加权profunctors的范畴是一个Lafont范畴，线性逻辑的范畴模型与指数。作为一个模型的程序设计语言，本文的建设给出了一个统一的框架，诱导适当的模型的非确定性，概率，代数和量子程序设计语言的权重SMCC的适当选择。
Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show that the category of W-weighted profunctors is a Lafont category, a categorical model of linear logic with exponential. As a model of programming languages, the construction of this paper gives a unified framework that induces adequate models of nondeterministic, probabilistic, algebraic and quantum programming languages by an appropriate choice of the weight SMCC.