# Statman's Hierarchy Theorem

@article{Westerbaan2017StatmansHT,
title={Statman's Hierarchy Theorem},
author={Bram Westerbaan and Bas Westerbaan and Rutger Kuyper and Carst Tankink and Remy Viehoff and HENK P. Barendregt},
journal={ArXiv},
year={2017},
volume={abs/1711.05497}
}
• Published 15 November 2017
• Mathematics
• ArXiv
In the Simply Typed $\lambda$-calculus Statman investigates the reducibility relation $\leq_{\beta\eta}$ between types: for $A,B \in \mathbb{T}^0$, types freely generated using $\rightarrow$ and a single ground type $0$, define $A \leq_{\beta\eta} B$ if there exists a $\lambda$-definable injection from the closed terms of type $A$ into those of type $B$. Unexpectedly, the induced partial order is the (linear) well-ordering (of order type) $\omega + 4$. In the proof a finer relation $\leq_{h… 4 Citations A sequent calculus for object-oriented actors with futures that integrates a pointer analysis and bridges the gap between behavioral types and deductive verification is presented. • Computer Science ESORICS • 2018 This paper recast trace equivalence as a reachability problem, to which persistent and sleep set techniques can be applied, and shows how to effectively apply these results in the context of symbolic execution. This dissertation includes an extensive introduction to the basic theory of$C^*\$-algebras and von Neumann algebraes and its category of completely positive normal contractive maps.
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