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<p>In this paper we introduce the concept of <i>multicombinators</i> as an alternative Turing-complete model of computation, modally extending the formalism of Combinatory Logic. We present a diagrammatic representation of multicombinators as presheaves defined over a category of <i>generic figures</i>. By adopting Sergeyev’s <i>grossone</i> numeral system, we obtain a sharper characterization of non-halting multicombinators. As a result of our analysis, we show how results for “infinite” combinators using the grossone formalism involving the notion of <i>observability</i> may be extended to the setting of multicombinators. These results formalize the general concept of tractable properties of multicombinators involving sequences of length less than or equal to grossone.</p>

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Multicombinators as observable presheaves

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Rocco Gangle,
  • Fernando Tohmé,
  • Gianluca Caterina

摘要

In this paper we introduce the concept of multicombinators as an alternative Turing-complete model of computation, modally extending the formalism of Combinatory Logic. We present a diagrammatic representation of multicombinators as presheaves defined over a category of generic figures. By adopting Sergeyev’s grossone numeral system, we obtain a sharper characterization of non-halting multicombinators. As a result of our analysis, we show how results for “infinite” combinators using the grossone formalism involving the notion of observability may be extended to the setting of multicombinators. These results formalize the general concept of tractable properties of multicombinators involving sequences of length less than or equal to grossone.