Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Anders Mörtberg"'
Publikováno v:
Logical Methods in Computer Science, Vol Volume 12, Issue 2 (2016)
This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support essential opera
Externí odkaz:
https://doaj.org/article/60543518a2184fdcb29151d11f14b164
Autor:
Anders Mörtberg
Publikováno v:
Mathematical Structures in Computer Science. 31:1147-1184
Cubical methods have played an important role in the development of Homotopy Type Theory and Univalent Foundations (HoTT/UF) in recent years. The original motivation behind these developments was to give constructive meaning to Voevodsky’s univalen
In Homotopy Type Theory, cohomology theories are studied synthetically using higher inductive types and univalence. This paper extends previous developments by providing the first fully mechanized definition of cohomology rings. These rings may be de
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6afa414e5222ce846cf5b1819b5ac83c
http://arxiv.org/abs/2212.04182
http://arxiv.org/abs/2212.04182
Publikováno v:
Proceedings of the ACM on Programming Languages. 5:1-30
In their usual form, representation independence metatheorems provide an external guarantee that two implementations of an abstract interface are interchangeable when they are related by an operation-preserving correspondence. If our programming lang
Publikováno v:
CPP 2022: Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs
CPP 2022
(à paraître) Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP ’22)
11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2022)
11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2022), Jan 2022, Philadelphia, PA, United States. ⟨10.1145/3497775.3503678⟩
CPP 2022
(à paraître) Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP ’22)
11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2022)
11th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP 2022), Jan 2022, Philadelphia, PA, United States. ⟨10.1145/3497775.3503678⟩
Accepted to CPP 2022; International audience; In previous work (“From signatures to monads in UniMath”), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8fca1362af037f15d322ea13ad149b4a
http://arxiv.org/abs/2112.06984
http://arxiv.org/abs/2112.06984
Publikováno v:
Journal of Functional Programming. 31
Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such
Autor:
Anders Mörtberg, Loïc Pujet
Publikováno v:
CPP 2020-9th ACM SIGPLAN International Conference on Certified Programs and Proofs
CPP 2020-9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Jan 2020, New Orleans, United States. pp.1-14, ⟨10.1145/3372885.3373825⟩
CPP
CPP 2020-9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Jan 2020, New Orleans, United States. pp.1-14, ⟨10.1145/3372885.3373825⟩
CPP
International audience; Homotopy type theory is an extension of type theory that enables synthetic reasoning about spaces and homotopy theory. This has led to elegant computer formalizations of multiple classical results from homotopy theory. However
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d1dd6c3bd38c3425dd418a599625ab5c
https://hal.archives-ouvertes.fr/hal-02394145/file/main.pdf
https://hal.archives-ouvertes.fr/hal-02394145/file/main.pdf
Publikováno v:
Mathematical Structures in Computer Science. 31:1-2
This issue of Mathematical Structures in Computer Science is Part I of a Special Issue dedicated to the emerging field of Homotopy Type Theory and Univalent Foundations.
Publikováno v:
Journal of Automated Reasoning
Journal of Automated Reasoning, Springer Verlag, 2019, 63 (2), pp.285-318. ⟨10.1007/s10817-018-9474-4⟩
Journal of Automated Reasoning, 2019, 63 (2), pp.285-318. ⟨10.1007/s10817-018-9474-4⟩
Journal of Automated Reasoning, Springer Verlag, 2019, 63 (2), pp.285-318. ⟨10.1007/s10817-018-9474-4⟩
Journal of Automated Reasoning, 2019, 63 (2), pp.285-318. ⟨10.1007/s10817-018-9474-4⟩
The term UniMath refers both to a formal system for mathematics, as well as a computer-checked library of mathematics formalized in that system. The UniMath system is a core dependent type theory, augmented by the univalence axiom. The system is kept
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::220aa7e233cc7cde3e930c3bf3c004b0
https://hal.inria.fr/hal-01410487
https://hal.inria.fr/hal-01410487
Publikováno v:
LICS
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly provable in