Multisets and Distributions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909126218481664 |
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| author | Kozen, Dexter Silva, Alexandra |
| author_facet | Kozen, Dexter Silva, Alexandra |
| contents | We give a lightweight alternative construction of Jacobs's distributive law for multisets and distributions that does not involve any combinatorics. We first give a distributive law for lists and distributions, then apply a general theorem on 2-categories that allows properties of lists to be transferred automatically to multisets. The theorem states that equations between 2-cells are preserved by epic 2-natural transformations. In our application, the appropriate epic 2-natural transformation is defined in terms of the Parikh map, familiar from formal language theory, that takes a list to its multiset of elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_10812 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multisets and Distributions Kozen, Dexter Silva, Alexandra Logic in Computer Science Programming Languages D.3.1; F.3.2 We give a lightweight alternative construction of Jacobs's distributive law for multisets and distributions that does not involve any combinatorics. We first give a distributive law for lists and distributions, then apply a general theorem on 2-categories that allows properties of lists to be transferred automatically to multisets. The theorem states that equations between 2-cells are preserved by epic 2-natural transformations. In our application, the appropriate epic 2-natural transformation is defined in terms of the Parikh map, familiar from formal language theory, that takes a list to its multiset of elements. |
| title | Multisets and Distributions |
| topic | Logic in Computer Science Programming Languages D.3.1; F.3.2 |
| url | https://arxiv.org/abs/2301.10812 |