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Strong normalization of barrecursive terms without using infinite terms

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Abstract

In this paper a new proof of the strong normalization theorem (SN) for barrecursive terms is presented.

The proof is based on a syntactical version of Howard's compactness of functionals of finite type (see [T, 2.8.6]). The proofs of Tait [Ta], Luckhardt [L], and Vogel [V] are all based on continuity. These proofs use “infinite terms”: ifT 0,T 1, ... is an infinite sequence of terms of type σ, then 〈T 0,T 1, ...〉 is an infinite term of type (0)σ. The proof below does not make use of infinite terms.

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References

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  1. Mathematical Institute, State University of Utrecht, Budapestlaan 6, 3584 CD, Utrecht, The Netherlands

    Marc Bezem

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  1. Marc Bezem
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Bezem, M. Strong normalization of barrecursive terms without using infinite terms. Arch math Logik 25, 175–181 (1985). https://doi.org/10.1007/BF02007566

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