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We present a new model of computation, described in terms of monoidalcategories. It conforms the Church-Turing Thesis, and captures the samecomputable functions as the standard models. It provides a succinct categoricalinterface to most of them, free of their diverse implementation details, usingthe ideas and structures that in the meantime emerged from research insemantics of computation and programming. The salient feature of the languageof monoidal categories is that it is supported by a sound and completegraphical formalism, string diagrams, which provide a concrete and intuitiveinterface for abstract reasoning about computation. The original motivation andthe ultimate goal of this effort is to provide a convenient high levelprogramming language for a theory of computational resources, such as one-wayfunctions, and trapdoor functions, by adopting the methods for hiding the lowlevel implementation details that emerged from practice. In the present paper,we make a first step towards this ambitious goal, and sketch a path to reachit. This path is pursued in three sequel papers, that are in preparation.

Monoidal computer I: Basic computability by string diagrams