2024 Jon sterling type theory

Jon sterling type theory

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August undefined, 2024

NettetThese theorems, sometimes called "metatheorems" or "admissibilities", are the means by which we conceive and justify computerized implementations of type theory, including … Nettet1. aug. 2014 · This paper shows how a Curry-Howard interpretation of a formal proof of normalization for monoids almost directly yields a coherence proof for monoidal categories and formalizes this coherenceProof in intensional intuitionistic type theory and shows how it relies on explicit reasoning about proof objects for intensional equality. 31.

cubical type theory in nLab

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 … 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 … mobility scooters wgc

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Nettet21. 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} ... 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. inkscape reload fonts

Normalization for Cubical Type Theory DeepAI

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. 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. … inkscape remove background of photoNettet7. jul. 2024 · Jonathan Sterling; Carlo Angiuli. Normalization for Cubical Type Theory.In: 2024 36th Annual ACM/IEEE Symposium on Logic in Computer Science.Jul 7, 2024. 10.1109/LICS52264.2024.9470719. [sterling-angiuli-2024] inkscape remove color from image

"NettetGLUING MODELS OF TYPE THEORY ALONG FLAT FUNCTORS JONATHAN STERLING AND CARLO ANGIULI Abstract. We extend the theory of Artin gluing to strict dependent type theory: given a …at functor C F E from the category of contexts of a model of Martin-L¨of type theory into a Grothendieck topos E, we may construct the … " - Jon sterling type theory

Jon sterling type theory

LambdaConf 2015 - Type Theory and its Meaning Explanations Jon …

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 … Nettet2 Darryl McAdams, Jonathan Sterling 1Type Theory and its Meaning Explanation Intuitionistic Type Theory is an approach to ﬁrst-order and higher-order logic, …

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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 … 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 …

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 … 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 …

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 … 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 ...

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 …

Nettet30. jun. 2024 · He was born in 1938, a year before World War II began. He lived on the Upper East Side, longing to grow up. “I wanted to be an adult before my time,” Sterling said. He had a nice relationship ... inkscape remove transparencyNettet19. 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 … inkscape remove part of objectNettetThe 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 … inkscape remove background pdfNettet22. 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 … inkscape remove canvasNettetIn 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. mobility scooters which reportNettetKeywords 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 inkscape remove white backgroundNettet13. 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 … inkscape remove border around object