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arXiv · 2410.03561

A Diagrammatic Algebra for Program Logics

Filippo Bonchi·Alessandro Di Giorgio·Elena Di Lavore
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Abstract

Tape diagrams provide a convenient notation for arrows of rig categories, i.e., categories equipped with two monoidal products, $\oplus$ and $\otimes$, where $\otimes$ distributes over $\oplus $. In this work, we extend tape diagrams with traces over $\oplus$ in order to deal with iteration in imperative programming languages. More precisely, we introduce Kleene-Cartesian bicategories, namely rig categories where the monoidal structure provided by $\otimes$ is a cartesian bicategory, while the one provided by $\oplus$ is what we name a Kleene bicategory. We show that the associated language of tape diagrams is expressive enough to deal with imperative programs and the corresponding laws provide a proof system that is at least as powerful as the one of Hoare logic.

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Filippo Bonchi, Alessandro Di Giorgio, Elena Di Lavore. 2024-10-04. A Diagrammatic Algebra for Program Logics. https://arxiv.org/abs/2410.03561

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