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Implementation of Operational calculus on programming spaces with Applications

We provide an illustrative implementation of an analytic, infinitely-differentiable virtual machine, implementing infinitely-differentiable programming spaces and operators acting upon them, as constructed in the paper Operational calculus on programming spaces and generalized tensor networks[1]. Implementation closely follows theorems and derivations of the paper, intended as an educational guide. Analytic virtual machines allow nested transformations, with operational calculus opening new doors in program analysis. We outline the process of employing such a machine to several causes, seamlessly inter-weaving operational calculus and algorithmic control flow. Nothing at all takes place in the universe in which some rule of maximum or minimum does not appear.