It is well known in the Constraint Programming community that any non-binary constraint satisfaction problem (with finite domains) can be transformed into an equivalent binary one. One of the most well-known translations is the Hidden Variable Encoding. In this paper we formalize this encoding in the proof assistant Coq and prove that any solution of the binary constraint satisfaction problem makes it possible to build a solution of the original problem and vice-versa. This formal development is used to complete the formally verified constraint solver developed in Coq by Carlier, Dubois and Gotlieb in 2012, making it a tool able to solve any n-ary constraint satisfaction problem, The key of success of the connection between the translator and the Coq binary solver is the genericity of the latter.

中文翻译：

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非二元约束转化为二元约束的形式化验证

在约束编程社区中众所周知，任何非二元约束满足问题（具有有限域）都可以转换为等效的二元约束问题。最著名的翻译之一是隐藏变量编码。在本文中，我们在证明助手 Coq 中将这种编码形式化，并证明二元约束满足问题的任何解决方案都可以构建原始问题的解决方案，反之亦然。这种形式化的开发用于完成 Carlier、Dubois 和 Gotlieb 于 2012 年在 Coq 中开发的形式化验证的约束求解器，使其成为能够解决任何 n 元约束满足问题的工具，翻译器和Coq 二元求解器是后者的通用性。