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On Continuous Normalization

机译：关于连续规范化

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This work aims at explaining the syntactical properties of continuous normalization, as introduced in proof theory by Mints, and further studied by Ruckert, Buchholz and Schwichtenberg. In an extension of the untyped coinductive λ-calculus by void constructors (so-called repetition rules), a primitive recursive normalization function is defined. Compared with other formulations of continuous normalization, this definition is much simpler and therefore suitable for analysis in a coalgebraic setting. It is shown to be continuous w.r.t. the natural topology on non-wellfounded terms with the identity as modulus of continuity. The number of repetition rules is locally related to the number of β-reductions necessary to reach the normal form (as represented by the Boehm tree) and the number of applications appearing in this normal form.
机译：这项工作旨在解释由Mints在证明理论中引入的并由Ruckert，Buchholz和Schwichtenberg进行进一步研究的连续规范化的句法性质。在通过无效构造函数（所谓的重复规则）对无类型的协导λ演算进行扩展时，将定义原始的递归归一化函数。与连续归一化的其他公式相比，此定义要简单得多，因此适合在煤代环境中进行分析。显示为连续w.r.t.非连续项上的自然拓扑，其身份为连续模数。重复规则的数量与达到正常形式（如Boehm树）所必需的β减少的数量以及以该正常形式出现的应用程序的数量局部相关。

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