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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.03561 |
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| _version_ | 1866909336424415232 |
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| author | Bonchi, Filippo Di Giorgio, Alessandro Di Lavore, Elena |
| author_facet | Bonchi, Filippo Di Giorgio, Alessandro Di Lavore, Elena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Diagrammatic Algebra for Program Logics Bonchi, Filippo Di Giorgio, Alessandro Di Lavore, Elena Logic in Computer Science 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. |
| title | A Diagrammatic Algebra for Program Logics |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2410.03561 |