Computation by infinite descent made explicit
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911672460902400 |
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| author | Enqvist, Sebastian |
| author_facet | Enqvist, Sebastian |
| contents | We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the computational content of this system, in particular we introduce a notion of computability and show that every valid proof is computable. As a consequence, we obtain a normalization result for proofs of what we call finitary formulas. A special case of this result is that every proof of a sequent of the appropriate form represents a unique function on natural numbers. Finally, we derive a categorical model from the proof system and show that least and greatest fixpoint formulas correspond to initial algebras and final coalgebras respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computation by infinite descent made explicit Enqvist, Sebastian Logic in Computer Science We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the computational content of this system, in particular we introduce a notion of computability and show that every valid proof is computable. As a consequence, we obtain a normalization result for proofs of what we call finitary formulas. A special case of this result is that every proof of a sequent of the appropriate form represents a unique function on natural numbers. Finally, we derive a categorical model from the proof system and show that least and greatest fixpoint formulas correspond to initial algebras and final coalgebras respectively. |
| title | Computation by infinite descent made explicit |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2506.22206 |