We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory contains a rich collection of properties of the standard operators on terms, including substitution, swapping and freshness—namely, there are lemmas showing how each of the operators interacts with all the others and with the syntactic constructors. The theory also features induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators.

中文翻译：

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具有绑定的语法的形式化一般理论：扩展版

我们介绍了一种语法理论的形式化，其绑定在过去十年中得到了发展和完善，以支持几项大型形式化工作。术语是为具有不同输入数量的任意数量的构造函数定义的，以 alpha 等价为商并根据绑定签名进行排序。该理论包含了标准运算符在术语方面的丰富属性集合，包括替换、交换和新鲜度——即，有引理显示每个运算符如何与所有其他运算符以及句法构造函数进行交互。该理论还具有归纳和递归原则以及对语义解释的支持，所有这些都是为与绑定和标准运算符的平滑交互而定制的。