Jon sterling type theory
Nettet13. jun. 2024 · Cubical type theory is an extension of Martin-Löf type theory recently proposed by Cohen, Coquand, Mörtberg, and the author which allows for direct manipulation of n-dimensional cubes and where Voevodsky’s Univalence Axiom is provable. In this paper we prove canonicity for cubical type theory: any natural number … Nettet19. jan. 2024 · For more than four decades, dependent type theory has been positioned as the “common language” that can finally unify mathematics and computer …
Jon sterling type theory
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NettetThe end-of-summer colloquia follow the same schedule on the following dates: August 22: Jon Sterling, How to code your own type theory There is a considerable distance … Nettet22. jul. 2024 · Idea. The initiality conjecture in type theory states that the term model of a type theory should be an initial object in the category of models of that type theory. Initiality guarantees that the relation between type theory and category theory works as expected, hence that formal syntactical proofs in type theory match theorems in …
Nettet27. jan. 2024 · 01/27/21 - We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic metath... DeepAI AI Chat. Log In Sign Up. ⋯. Research; Glossary; APIs; Sign Up; Log In; Normalization for Cubical Type Theory. 01/27/2024 . ∙. by Jonathan Sterling, et al. Nettet18. nov. 2024 · The implementation and semantics of dependent type theories can be studied in a syntax-independent way: the objective metatheory of dependent type theories exploits the universal properties of their syntactic categories to endow them with computational content, mathematical meaning, and practical implementation …
Nettet22. aug. 2024 · HoTTEST Summer School ColloquiumThere is a considerable distance between the formal rules of type theory and the code that you must write in order to animate...
Nettettype theory poorly adapted for categorical manipulation is its strictness: the constructs of type theory are closed under a substitution operation which is coherent in the sense …
Nettet11. okt. 2024 · Daniel Gratzer, Jonathan Sterling, Carlo Angiuli, Thierry Coquand, Lars Birkedal. We present a novel mechanism for controlling the unfolding of definitions in … new jersey condos for saleNettet14. des. 2024 · 11:00am-12:00pm : Paige North "Directed homotopy type theory" 12:00-2pm Lunch Break ; 2:00-3:00pm : Jon Sterling " Controlling unfolding in type theory" … new jersey conference umcNettetAt one extreme, dependent type theory is a language for mathematically-inspired functional programming that is sufficiently expressive to serve ... Daniel Gratzer, and Jonathan Sterling. Unpublished Manuscripts. Oct. 2024: Preprint Controlling unfolding in type theory. D. Gratzer, J. Sterling, C. Angiuli, T. Coquand, and L. Birkedal. Under ... new jersey condominium lawNettet22. aug. 2024 · Jon Sterling, How to code your own type theory 736 views Aug 22, 2024 HoTTEST Summer School Colloquium ...more 1.34K subscribers Very cool! I had a … in the translationNettetI study programming languages and semantics using type theory, category theory, domain theory, and topos theory as a guide. Previously I received a B.A. in Linguistics from U.C. Berkeley. My other interests include category theory, topos theory, … structure of dependent type theory, but I have ultimately come to prefer a classic … January 19, 2024 · Jonathan Sterling Chapter 0: Conspectus on Type Theory … January 19, 2024 · Jonathan Sterling Chapter 6: Cartesian Cubical Type … On the semantic side, type theory needs a number of properties including function … In contrast, type theory is the language of internal mathematics; in type theory one … Cubical type theory is an extension of Martin-Löf type theory recently … new jersey congressional mapNettetIn Type Theory, `a:A`, ... that can be brought over to HoTT to make univalence constructive. One such approach is Synthetic Tait Computability by Jon Sterling in his PhD thesis. new jersey consolidated debarmentsNettetKeywords guarded recursion, clocks, type theory, operational semantics, dependent types ACM Reference Format: Jonathan Sterling and Robert Harper. 2024. Guarded Computational Type Theory. In LICS ’18: LICS ’18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, July 9–12, 2024, Oxford, United Kingdom. ACM, New new jersey conference umc breakthrough