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arXiv · 2603.25337

On Representability of Multiple-Valued Functions by Linear Lambda Terms Typed with Second-order Polymorphic Type System

Satoshi Matsuoka
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Abstract

We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching theory. The second is an inductive style, which follows a more traditional mathematical approach. We also discuss several optimizations for these representations. Furthermore, we present a case study that demonstrates the potential applications of our approach across various domains.

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Satoshi Matsuoka. 2026-03-26. On Representability of Multiple-Valued Functions by Linear Lambda Terms Typed with Second-order Polymorphic Type System. https://arxiv.org/abs/2603.25337

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