On a Dependently Typed Encoding of Matching Logic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911157753741312 |
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| author | Kurucz, Ádám Bereczky, Péter Horpácsi, Dániel |
| author_facet | Kurucz, Ádám Bereczky, Péter Horpácsi, Dániel |
| contents | Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of matching $μ$-logic, a sorted, polyadic variant of the logic. Metatheoretic reasoning requires the logic to be expressed within a foundational theory; opting for a dependently typed one enables well-sortedness in the object theory to correspond directly to well-typedness in the host theory. In this paper, we present the first dependently typed definition of matching $μ$-logic, ensuring well-sortedness via sorted contexts encoded in type indices. As a result, ill-sorted syntax elements are unrepresentable, and the semantics of well-sorted elements are guaranteed to lie within the domain of their associated sort. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a Dependently Typed Encoding of Matching Logic Kurucz, Ádám Bereczky, Péter Horpácsi, Dániel Logic in Computer Science F.4.1 Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of matching $μ$-logic, a sorted, polyadic variant of the logic. Metatheoretic reasoning requires the logic to be expressed within a foundational theory; opting for a dependently typed one enables well-sortedness in the object theory to correspond directly to well-typedness in the host theory. In this paper, we present the first dependently typed definition of matching $μ$-logic, ensuring well-sortedness via sorted contexts encoded in type indices. As a result, ill-sorted syntax elements are unrepresentable, and the semantics of well-sorted elements are guaranteed to lie within the domain of their associated sort. |
| title | On a Dependently Typed Encoding of Matching Logic |
| topic | Logic in Computer Science F.4.1 |
| url | https://arxiv.org/abs/2509.13018 |