相干微分
Coherent differentiation
摘要：
微分代数的范畴模型是加法范畴，因为莱布尼茨规则要求两个表达式求和。这意味着，就微分微积分和微分线性逻辑而言，这些模型具有有限的非确定性，实际上这些语言本质上是非确定性的。我们引入了一个分类框架分化，不需要添加剂，是兼容的确定性模型，如相干空间和概率模型，如概率相干空间。基于这种语义，我们勾勒出一个确定性的版本的差分dacalculus的语法。
英文摘要：
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential linear logic are concerned, these models feature finite nondeterminism and indeed these languages are essentially non-deterministic. We introduce a categorical framework for differentiation which does not require additivity and is compatible with deterministic models such as coherence spaces and probabilistic models such as probabilistic coherence spaces. Based on this semantics we sketch the syntax of a deterministic version of the differential lambdacalculus.
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