近期关于Five ways的讨论持续升温。我们从海量信息中筛选出最具价值的几个要点，供您参考。
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其次，The meaning of Succ is lifting n-ary functions to (n+1)-ary functions. This gives de bruijn shifting a semnantic interpretation. This trick appears in Kiselyov’s SKI semantically https://okmij.org/ftp/tagless-final/ski.pdf , Pavel’s blog post https://pavpanchekha.com/blog/egg-bindings.html , and McBride references Thorsten Altenkirch, Martin Hofmann & Thomas Streicher (1995): Categorical Reconstruction of a Reduction Free Normalization Proof, where there is some neat ML code in the appendix
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第三，Thinnings are kind of taking slotted’s notion of redundancy but tossing out the permutations. https://dl.acm.org/doi/10.1145/3729326 Slotted egraphs. I think I’ve seen Rudi make a diagram representing slots as little lines running though the edges between children. A “thickened” parent child relationship. Thinnings are kind of the same, but they do not allow wire crossing.
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面对Five ways带来的机遇与挑战，业内专家普遍建议采取审慎而积极的应对策略。本文的分析仅供参考，具体决策请结合实际情况进行综合判断。