  We present a new model of computation, described in terms of monoidal
categories. It conforms the Church-Turing Thesis, and captures the same
computable functions as the standard models. It provides a succinct categorical
interface to most of them, free of their diverse implementation details, using
the ideas and structures that in the meantime emerged from research in
semantics of computation and programming. The salient feature of the language
of monoidal categories is that it is supported by a sound and complete
graphical formalism, string diagrams, which provide a concrete and intuitive
interface for abstract reasoning about computation. The original motivation and
the ultimate goal of this effort is to provide a convenient high level
programming language for a theory of computational resources, such as one-way
functions, and trapdoor functions, by adopting the methods for hiding the low
level implementation details that emerged from practice. In the present paper,
we make a first step towards this ambitious goal, and sketch a path to reach
it. This path is pursued in three sequel papers, that are in preparation.
