Some Consistent Power Constructions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912265650831360 |
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| author | Zhou, Chengyu Li, Qingguo |
| author_facet | Zhou, Chengyu Li, Qingguo |
| contents | Consistent Hoare, Smyth and Plotkin power domains are introduced and discussed by Yuan and Kou. The consistent algebraic operation $+$ defined by them is a binary partial Scott continuous operation satisfying the requirement: $a+b$ exists whenever there exists a $c$ which is greater than $a$ and $b$. We extend the consistency to be a categorical concept and obtain an approach to generating consistent monads from monads on dcpos whose images equipped with some algebraic operations. Then we provide two new power constructions over domains: the consistent Plotkin index power domain and the consistent probabilistic power domain. Moreover, we verify these power constructions are free. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Consistent Power Constructions Zhou, Chengyu Li, Qingguo Logic in Computer Science 06B35, 54A35, 54D05 Consistent Hoare, Smyth and Plotkin power domains are introduced and discussed by Yuan and Kou. The consistent algebraic operation $+$ defined by them is a binary partial Scott continuous operation satisfying the requirement: $a+b$ exists whenever there exists a $c$ which is greater than $a$ and $b$. We extend the consistency to be a categorical concept and obtain an approach to generating consistent monads from monads on dcpos whose images equipped with some algebraic operations. Then we provide two new power constructions over domains: the consistent Plotkin index power domain and the consistent probabilistic power domain. Moreover, we verify these power constructions are free. |
| title | Some Consistent Power Constructions |
| topic | Logic in Computer Science 06B35, 54A35, 54D05 |
| url | https://arxiv.org/abs/2503.06036 |