Frex: Dependently Typed Algebraic Simplification
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| Názov: | Frex: Dependently Typed Algebraic Simplification |
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| Autori: | Allais, Guillaume, Brady, Edwin, Corbyn, Nathan, Kammar, Ohad, Yallop, Jeremy |
| Prispievatelia: | DSpace at Cambridge pro (8.1), University of St Andrews.School of Computer Science, University of St Andrews.Centre for Interdisciplinary Research in Computational Algebra |
| Zdroj: | Proceedings of the ACM on Programming Languages. 9:30-65 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Association for Computing Machinery (ACM), 2025. |
| Rok vydania: | 2025 |
| Predmety: | MCC, FOS: Computer and information sciences, Logic in Computer Science, T-NDAS, Algebraic simplification, Universal algebra, Symbolic Computation (cs.SC), Dependent types, Logic in Computer Science (cs.LO), Homomorphism, Universal property, Free extension, Programming Languages, Symbolic Computation, Frex, Mathematically structured programming, Programming Languages (cs.PL) |
| Popis: | We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's dependently typed interface guarantees that both built-in and user-defined simplification modules are terminating, sound, and complete with respect to a well-specified class of equations. We have implemented the design in the Idris 2 and Agda dependently typed programming languages and shown that it supports modular extension to new theories, proof extraction and certification, goal extraction via reflection, and interactive development. |
| Druh dokumentu: | Article |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 2475-1421 |
| DOI: | 10.1145/3747506 |
| DOI: | 10.48550/arxiv.2306.15375 |
| DOI: | 10.17863/cam.120461 |
| Prístupová URL adresa: | http://arxiv.org/abs/2306.15375 https://hdl.handle.net/10023/32661 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....47eb514af58f34e6bbe49e8ca77dd4ea |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's dependently typed interface guarantees that both built-in and user-defined simplification modules are terminating, sound, and complete with respect to a well-specified class of equations. We have implemented the design in the Idris 2 and Agda dependently typed programming languages and shown that it supports modular extension to new theories, proof extraction and certification, goal extraction via reflection, and interactive development. |
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| ISSN: | 24751421 |
| DOI: | 10.1145/3747506 |