论文标题
从停止问题到半统一的建设性多一减少（扩展版）
Constructive Many-one Reduction from the Halting Problem to Semi-unification (Extended Version)
论文作者
论文摘要
半统一是一阶统一和一阶匹配的组合。 1990年代，Kfoury，Tiuryn和Urzyczyn证明了半统一的不可证明性，这是通过图灵机器不朽（存在分歧配置）而减少的。特定的图灵还原是复杂的，使用非计算原则，并涉及各种计算中间模型。目前的工作使从图灵机器停止问题到半统一的建设性降低了。这确立了在多个减少下的半统一的重新组合。 COQ证明助手中的无公理机械化见证了还原函数，参数的建设性以及参数的正确性的可计算性。可以说，这是当前结果的全面，精确和可调查的证据。该机械化已纳入现有的，良好的证明性证明的COQ库中。值得注意的是，Hooper关于Turing Machine不朽的不可证明的论点是机械化的一部分。
Semi-unification is the combination of first-order unification and first-order matching. The undecidability of semi-unification has been proven by Kfoury, Tiuryn, and Urzyczyn in the 1990s by Turing reduction from Turing machine immortality (existence of a diverging configuration). The particular Turing reduction is intricate, uses non-computational principles, and involves various intermediate models of computation. The present work gives a constructive many-one reduction from the Turing machine halting problem to semi-unification. This establishes RE-completeness of semi-unification under many-one reductions. Computability of the reduction function, constructivity of the argument, and correctness of the argument is witnessed by an axiom-free mechanization in the Coq proof assistant. Arguably, this serves as comprehensive, precise, and surveyable evidence for the result at hand. The mechanization is incorporated into the existing, well-maintained Coq library of undecidability proofs. Notably, a variant of Hooper's argument for the undecidability of Turing machine immortality is part of the mechanization.
