Principal Types as Partial Involutions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909570344943616 |
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| author | Honsell, Furio Lenisa, Marina Scagnetto, Ivan |
| author_facet | Honsell, Furio Lenisa, Marina Scagnetto, Ivan |
| contents | We show that the principal types of the closed terms of the affine fragment of $λ$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry of Interaction model à la Abramsky. This permits to explain in elementary terms the somewhat awkward notion of linear application arising in Geometry of Interaction, simply as the resolution between principal types using an alternate unification algorithm. As a consequence, we provide an answer, for the purely affine fragment, to the open problem raised by Abramsky of characterising those partial involutions which are denotations of combinatory terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Principal Types as Partial Involutions Honsell, Furio Lenisa, Marina Scagnetto, Ivan Logic in Computer Science 68Q60 F.3.1 We show that the principal types of the closed terms of the affine fragment of $λ$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry of Interaction model à la Abramsky. This permits to explain in elementary terms the somewhat awkward notion of linear application arising in Geometry of Interaction, simply as the resolution between principal types using an alternate unification algorithm. As a consequence, we provide an answer, for the purely affine fragment, to the open problem raised by Abramsky of characterising those partial involutions which are denotations of combinatory terms. |
| title | Principal Types as Partial Involutions |
| topic | Logic in Computer Science 68Q60 F.3.1 |
| url | https://arxiv.org/abs/2402.07230 |