We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive forward and backward chaining in a sequent calculus style. It is made possible by automated machinery that take care of the necessary structural reasoning and term matching automatically. Our framework can also handle type theoretic correspondences of proofs, effectively allowing the type checking and construction of computational processes via proof. We demonstrate our implementation using a simple propositional logic and its Curry-Howard correspondence to the lambda-calculus, and argue its use with linear logic and its various correspondences to session types.

中文翻译：

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使用HOL Light编码的逻辑进行对象级推理

我们提出了一个通用的框架，该框架使用HOL Light的高阶逻辑定理证明环境中编码的逻辑来促进对象级推理。这涉及以顺序演算方式使用直观的前向和后向链接以任何逻辑证明语句。自动化机器使自动处理必要的结构推理和术语匹配成为可能。我们的框架还可以处理证明的类型理论对应关系，从而有效地允许通过证明进行类型检查和计算过程的构造。我们使用简单的命题逻辑及其与lambda微积分的Curry-Howard对应关系演示了实现，并论证了其与线性逻辑的使用以及与会话类型的各种对应关系。