Canonical bidirectional typechecking
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915660998639616 |
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| author | Mihejevs, Zanzi Hedges, Jules |
| author_facet | Mihejevs, Zanzi Hedges, Jules |
| contents | We demonstrate that the checkable/synthesisable split in bidirectional typechecking coincides with existing dualities in polarised System L, also known as polarised $μ\tildeμ$-calculus. Specifically, positive terms and negative coterms are checkable, and negative terms and positive coterms are synthesisable. This combines a standard formulation of bidirectional typechecking with Zeilberger's `cocontextual' variant. We extend this to ordinary `cartesian' System L using Mc Bride's co-de Bruijn formulation of scopes, and show that both can be combined in a linear-nonlinear style, where linear types are positive and cartesian types are negative. This yields a remarkable 3-way coincidence between the shifts of polarised System L, LNL calculi, and bidirectional calculi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical bidirectional typechecking Mihejevs, Zanzi Hedges, Jules Programming Languages Logic in Computer Science We demonstrate that the checkable/synthesisable split in bidirectional typechecking coincides with existing dualities in polarised System L, also known as polarised $μ\tildeμ$-calculus. Specifically, positive terms and negative coterms are checkable, and negative terms and positive coterms are synthesisable. This combines a standard formulation of bidirectional typechecking with Zeilberger's `cocontextual' variant. We extend this to ordinary `cartesian' System L using Mc Bride's co-de Bruijn formulation of scopes, and show that both can be combined in a linear-nonlinear style, where linear types are positive and cartesian types are negative. This yields a remarkable 3-way coincidence between the shifts of polarised System L, LNL calculi, and bidirectional calculi. |
| title | Canonical bidirectional typechecking |
| topic | Programming Languages Logic in Computer Science |
| url | https://arxiv.org/abs/2512.07511 |