The work proposes a model of computation expressed through monoidal categories, a mathematical framework for composing processes and their inputs and outputs. Its central claim is that this categorical model captures the same computable functions as standard computational models, so it conforms to the Church-Turing thesis while offering a common language that abstracts away differences in implementation. Rather than relying only on symbolic formulas, it uses string diagrams: graphical representations of processes and their composition. The diagrams provide an intuitive way to reason about computations, supported by formal soundness and completeness results.
The longer-term aim is a high-level language for describing computational resources relevant to security, including one-way and trapdoor functions, while hiding low-level implementation details. This paper lays the groundwork rather than delivering that full language: it introduces basic computability in the monoidal setting and sketches a program for extending the approach in subsequent work. Its appeal is to readers interested in how category theory and graphical reasoning might unify accounts of computation and support a more abstract treatment of resource-sensitive computation. The paper is a foundational proposal, not an empirical evaluation or a presentation of a finished programming system.
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