Tarski's least fixed point theorem: A predicative type theoretic formulation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929248512507904 |
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| author | Ray, Ian |
| author_facet | Ray, Ian |
| contents | We provide a type theoretic treatment of the paper "On Tarski's fixed point theorem" by Giovanni Curi. There are benefits to having a type theoretic formulation apart from routine implementation in a proof assistant. By taking advantage of (higher) inductive types, we can avoid complicated set theoretic constructions. Arguably, this results in a presentation that is conceptually clearer. Additionally, due the predicative admissibility of (higher) inductive types we take a step towards the "system independent" derivation that Curi calls for in his conclusion. Finally, we explore a condition on monotone maps that guarantees they are `generated' and give an alternative statement of the least fixed point theorem in terms of this condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00841 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tarski's least fixed point theorem: A predicative type theoretic formulation Ray, Ian Logic We provide a type theoretic treatment of the paper "On Tarski's fixed point theorem" by Giovanni Curi. There are benefits to having a type theoretic formulation apart from routine implementation in a proof assistant. By taking advantage of (higher) inductive types, we can avoid complicated set theoretic constructions. Arguably, this results in a presentation that is conceptually clearer. Additionally, due the predicative admissibility of (higher) inductive types we take a step towards the "system independent" derivation that Curi calls for in his conclusion. Finally, we explore a condition on monotone maps that guarantees they are `generated' and give an alternative statement of the least fixed point theorem in terms of this condition. |
| title | Tarski's least fixed point theorem: A predicative type theoretic formulation |
| topic | Logic |
| url | https://arxiv.org/abs/2401.00841 |