Unification of Deterministic Higher-Order Patterns (Full Version)
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913100304744448 |
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| author | Niederhauser, Johannes Middeldorp, Aart |
| author_facet | Niederhauser, Johannes Middeldorp, Aart |
| contents | We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure can be seen as a special case of full higher-order unification where flex-flex pairs can be solved in a most general way. Moreover, our method generalizes Libal and Miller's recent functions-as-constructors higher-order unification (FCU) by dropping their global restriction on variable arguments, thereby losing the property that every solvable problem has a most general unifier. In fact, minimal complete sets of unifiers of deterministic higher-order patterns may be infinite, so decidability of the unification problem remains an open question. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_14211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unification of Deterministic Higher-Order Patterns (Full Version) Niederhauser, Johannes Middeldorp, Aart Logic in Computer Science We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure can be seen as a special case of full higher-order unification where flex-flex pairs can be solved in a most general way. Moreover, our method generalizes Libal and Miller's recent functions-as-constructors higher-order unification (FCU) by dropping their global restriction on variable arguments, thereby losing the property that every solvable problem has a most general unifier. In fact, minimal complete sets of unifiers of deterministic higher-order patterns may be infinite, so decidability of the unification problem remains an open question. |
| title | Unification of Deterministic Higher-Order Patterns (Full Version) |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2601.14211 |