On Continuous Normalization
نویسندگان
چکیده
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 Böhm tree) and the number of applications appearing in this normal form.
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