A Curry-Howard Correspondence for Linear, Reversible Computation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912496861839360 |
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| author | Chardonnet, Kostia Saurin, Alexis Valiron, Benoît |
| author_facet | Chardonnet, Kostia Saurin, Alexis Valiron, Benoît |
| contents | In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic $μ$MALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy $μ$MALL validity criterion and how the language simulates the cut-elimination procedure of $μ$MALL. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11887 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Curry-Howard Correspondence for Linear, Reversible Computation Chardonnet, Kostia Saurin, Alexis Valiron, Benoît Logic in Computer Science In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic $μ$MALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy $μ$MALL validity criterion and how the language simulates the cut-elimination procedure of $μ$MALL. |
| title | A Curry-Howard Correspondence for Linear, Reversible Computation |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2302.11887 |