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 non-determinism and indeed these languages are essentially non-deterministic. In a previous paper we introduced 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 develop a syntax of a deterministic version of the differential lambda-calculus. One nice feature of this new approach to differentiation is that it is compatible with general fixpoints of terms, so our language is actually a differential extension of PCF for which we provide a fully deterministic operational semantics.
翻译：由于Leibniz 规则要求将两个表达式相加,因此,区分羊肉-计算法的绝对模型是加分类别。这意味着,就区别羊肉-计算法和不同的线性逻辑而言,这些模型具有有限的非确定性,这些语言实际上基本上不具有确定性。在前一份文件中,我们提出了一个明确的区分框架,它不要求相加性,并且与确定性模型相容,例如一致性空间和概率模型,例如概率一致性空间。基于这一语义学,我们发展了区别羊羊肉-计算法的确定性组合。这种新的区分方法的一个很好的特点就是它与术语的一般固定点相容,因此我们的语言实际上是PCF的差别扩展,我们为此提供了一种完全确定性的操作性语义学。
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