Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian differential category being satisfied only "up to an infinitesimal perturbation". In this work, we construct a simply-typed calculus in the spirit of the differential lambda-calculus equipped with syntactic infinitesimals and show how its models correspond to difference lambda-categories, a family of Cartesian difference categories equipped with suitably well-behaved exponentials.

中文翻译：

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差异Lambda演算：差异类别的语言

笛卡尔差分类别是笛卡尔差分类别的最新概括，其引入了满足Kock-Lawvere公理的类似物的“无穷小”箭头的概念，而笛卡尔微分类别的公理仅“直至无穷微扰动”被满足。在这项工作中，我们将根据配备有语法无穷小量的微分lambda微积分的精神构造一个简单类型的微积分，并展示其模型如何对应于差分lambda类别，这是笛卡尔差分类别的一族，配有适当表现良好的指数。