The -calculus (Reflective Higher-Order Calculus) of Meredith and Radestock is a -calculus-like language with unusual features, notably, structured names, runtime generation of free names, and the lack of a scoping operator. These features pose interesting difficulties for proofs of encodability, type system soundness and separation results. We describe two errors in a previous attempt to encode the -calculus in the -calculus by Meredith and Radestock. Then we give a new encoding and prove its correctness, using a set of encodability criteria close to those of Gorla, and discuss the adaptations necessary to work with a calculus with runtime generation of structured names. We create a simple type system for the -calculus to show that the encoding is well-typed, and discuss the limitations that must be imposed when working with structured names. Lastly we prove a separation result, showing that the -calculus cannot be encoded in the -calculus.

中文翻译：

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反射高阶微积分：可编码性、可打字性和分离

Meredith 和 Radestock 的 -calculus（反射高阶微积分）是一种类似 -calculus 的语言，具有不寻常的功能，特别是结构化名称、运行时生成自由名称以及缺少作用域运算符。这些特征给可编码性、类型系统健全性和分离结果的证明带来了有趣的困难。我们描述了 Meredith 和 Radestock 之前尝试将 β 微积分编码到 β 微积分中的两个错误。然后，我们使用一组接近 Gorla 的可编码性标准，给出一种新的编码并证明其正确性，并讨论使用具有运行时生成结构化名称的微积分所需的调整。我们为 演算创建一个简单的类型系统，以表明编码类型良好，并讨论使用结构化名称时必须施加的限制。最后我们证明了分离结果，表明-演算不能被编码在-演算中。