Jon sterling type theory

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August undefined, 2024

Nettet19. jan. 2024 · This expository chapter introduces cubical type theory as an extension to Martin-Löf’s type theory by an interval \II with two distinct endpoints 0, 1 : \II.The interval is a basic “figure” that defines a notion of path or identification \TpPath{A}{u}{v} between two elements of any type; for instance, to identify u,v:A is the same as to construct a … Nettet6. des. 2015 · Type Theory and its Meaning Explanations Jonathan Sterling At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning …

Revisiting the categorical interpretation of dependent type theory

Nettet14. 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" 3:00-3:30pm : Open Discussion / Break ; 3:30-4:30pm : Loïc Pujet "Merging Martin Löf's identity type and setoid equality" Detailed Progam Favonia "An Order-Theoretic … Nettet16. feb. 2024 · Canonicity in cubical type theory. In contrast to Martin-Löf type theory, there exist cubical type theories, such as XTT, in which UIP is not just an axiom but a theorem.Similarily, there exist cubical type theories in which univalence is not just an axiom but a theorem.As a result, in those cubical type theories, canonicity still holds. … kyle nolan community care

cubical type theory in nLab

NettetI 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 … 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 … 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 … kyle noonan south glens falls ny

[2210.05420] Controlling unfolding in type theory

[1902.08848] Algebraic Type Theory and Universe Hierarchies

Nettet19. jan. 2024 · To state and prove theorems like canonicity and decidability for a type theory, we must have a mathematical definition of the syntax of type theory. Conventionally, the syntax of type theory has been studied in several layers: one starts with a definition of “raw” syntax as trees labeled by the names of the generating … Nettet155 10K views 7 years ago At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations … kyle noyes falmouthNettet23. feb. 2024 · Authors:Jonathan Sterling Download PDF Abstract:It is commonly believed that algebraic notions of type theory support only universes à la Tarski, and … kyle o connor abh

"NettetAnswer (1 of 3): John Sterling is an entertainer. He entertains with his voice. He uses it to create visceral excitement for the listener. As such, I would not call him biased. He is … " - Jon sterling type theory

Jon sterling type theory

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 … Nettet22. 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 …

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Nettet4 DANIEL GRATZER AND MICHAEL SHULMAN AND JONATHAN STERLING In the context of Martin-L of type theory, it is common to study classes of maps that may not satisfy all the axioms above; for instance, type theory is often used in settings that do not have a single well-behaved notion of proposition, so (U2) loses some signi cance. NettetIn 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.

NettetAt one extreme, dependent type theory is a language for mathematically-inspired functional programming that is sufficiently expressive to serve ... , doi = {10.48550/ARXIV.2210.05420}, author = {Gratzer, Daniel and Sterling, Jonathan and Angiuli, Carlo and Coquand, Thierry and Birkedal, Lars}, title = {Controlling unfolding 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.

NettetAt 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 ...

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 …

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 programming: while it has never been controversial that a computer program is a form of mathematical construction, the running hypothesis of the type theoretic community has been the … kyle newspaper texasNettet11. okt. 2024 · Daniel Gratzer, Jonathan Sterling, Carlo Angiuli, Thierry Coquand, Lars Birkedal. We present a novel mechanism for controlling the unfolding of definitions in dependent type theory. Traditionally, proof assistants let users specify whether each definition can or cannot be unfolded in the remainder of a development; unfolding … kyle nowadnick thriventNettet21. apr. 2024 · Request PDF A Review of Algebraic-Style Reasoning for Type Theory ... Jonathan Sterling and Bas Spitters. 2024. Normalization by gluing for free {\lambda} ... kyle nussdorfer corvallis oregonNettetAt the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as d... kyle nueharth dciNettet19. jan. 2024 · For more than four decades, dependent type theory has been positioned as the “common language” that can finally unify mathematics and computer … kyle noyes armed servicesNettet27. jan. 2024 · Jonathan Sterling, Carlo Angiuli. We prove normalization for (univalent, Cartesian) cubical type theory, closing the last major open problem in the syntactic … program to find maximum and minimum in pythonNettet14. 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" … program to find max and min in an array in c#