论文标题
更改动作：从增量计算到离散导数
Change actions: from incremental computation to discrete derivatives
论文作者
论文摘要
本文的目的是三重：首先，为有关增量计算的推理提供一般的语义设置。其次，在分析意义上建立和阐明衍生物之间的衍生物之间的联系，也就是说，提供了对衍生物的共同定义，而前两个是特定的实例。第三，为此一般设置提供理论上声音的演算。为此，我们定义并探讨了变更动作和变化动作之间的差异图的概念，并通过对数据核心查询的半分数评估的具体示例来说明这些概念如何与增量计算相关。我们还介绍了变更动作模型的概念，作为高阶分化的设置，并展示了一些有趣的例子。最后，我们展示了笛卡尔差异类别是一个特别举止变化行动模型的家族，概括了笛卡尔差异类别，并以Ehrhard和Regnier的差异lambda-alculus的精神产生了微积分。
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in the analytic sense, that is to say, to provide a common definition of derivative of which the previous two are particular instances. Third, to give a theoretically sound calculus for this general setting. To this end we define and explore the notions of change actions and differential maps between change actions and show how these notions relate to incremental computation through the concrete example of the semi-naive evaluation of Datalog queries. We also introduce the notion of a change action model as a setting for higher-order differentiation, and exhibit some interesting examples. Finally, we show how Cartesian difference categories, a family of particularly well-behaved change action models, generalise Cartesian differential categories and give rise to a calculus in the spirit of Ehrhard and Regnier's differential lambda-calculus.
