Tait computability

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August undefined, 2024

Web5 Dec 2024 · This also provides a higher dimensional version of Sterling's synthetic Tait computability -- a type theory for higher dimensional logical relations. To prove the main result, we establish a precise correspondence between the lex, accessible localizations of an $\infty$-logos and the lex, accessible modalities in the internal language of the $\infty$ …

Artin gluing and the method of computability.

WebI am a Marie Skłodowska-Curie Postdoctoral Fellow hosted at Aarhus University in the Logic and Semantics group by L. Birkedal, and will be starting as an Associate Professor at University of Cambridge in Autumn; I earned my PhD from Carnegie Mellon University under R. Harper.I study programming languages and semantics using type theory, category … Web19 Jan 2024 · Chapter 4: Tait’s Method of Computability [jms-0013] It is simple enough to verify negative properties of a formal system, e.g. the non-derivability of a given assertion … top 10 roofing companies in arizona

Homotopy type theory as internal languages of diagrams of ∞ …

Web2 Aug 2024 · Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability which generalizes the framework to accommodate a type theory with … Web19 May 2024 · Synthetic computability theoryis the study of computability theorysyntheticallyaxiomatizedby structurespresent in the effective toposor other toposes of computable structures, rather than by analyticconstruction such as Turing machinesor lambda calculus. Related concepts synthetic Tait computability synthetic mathematics … Web18 Nov 2024 · First employed by Sterling and Harper to reconstruct the theory of program modules and their phase separated parametricity, synthetic Tait computability is … top 10 roofing companies

chapter 8: a plan for PL Jon Sterling

WebIn the context of dependent type theory, I have recently developed a new technique called Synthetic Tait Computability or STC that smoothly combines multiple levels of abstraction into a single language. Web23 Sep 2024 · First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory Jonathan Sterling 135 subscribers Subscribe 757 views 1 year ago … top 10 rome sightsWeb28 Jun 2024 · information flow, noninterference, denotational semantics, phase distinction, Artin gluing, modal type theory, topos theory, synthetic domain theory, synthetic Tait computability : Seminar: 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2024) Issue date: 2024 : Date of publication: 28.06.2024 top 10 romantic shayari

"Web19 Nov 2024 · In this talk, I introduce Synthetic Tait computability — a new system of axioms that transforms these explicit computations into synthetic manipulations; classical Kripke … " - Tait computability

Tait computability

WebTo address this problem, the EU-funded TypeSynth project exploits Synthetic Tait Computability (STC), a new technique that effortlessly combines multiple levels of abstraction into a single language. STC makes feasible the simpler and more abstract manipulation of low-level details, facilitating their mathematical control, while it also … Web19 Jan 2024 · The modal language of synthetic Tait computability promises a new and more abstract account of refinement types and program extraction via a phase distinction …

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WebIn this dissertation, I add synthetic Tait computability to the arsenal of the objective metatheorist. Synthetic Tait computability is a mathematical machine to reduce diﬃcult … Web23 Jun 2024 · First employed by Sterling and Harper to reconstruct the theory of program modules and their phase separated parametricity, synthetic Tait computability is …

Web13 Jan 2024 · Jonathan Sterling, Aarhus University (Thesis: First Steps in Synthetic Tait Computability: The Objective Metatheory of Cubical Type Theory, October 2024) It is hard to describe my first encounters with Bob in 2014—who blazed with enthusiasm for the unity of constructive mathematics and computer programming. This is a man who inspires strong ... Web2 Jun 2024 · Download PDF Abstract: We consider the conversion problem for multimodal type theory (MTT) by characterizing the normal forms of the type theory and proving normalization. Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability which generalizes the framework to accommodate a type theory with …

Web31 Dec 2024 · Our proof adapts and extends Sterling's technique of synthetic Tait computability (STC) [34,31], which has previously been used to establish parametricity for an ML-style module calculus [34] and... WebSynthetic Tait Computability for Simplicial Type Theory Weinberger, Ahrens, Buchholtz, and North With those modi cations, our current progress indicates that the methods by …

Web19 May 2024 · Synthetic computability theory is the study of computability theory synthetically axiomatized by structures present in the effective topos or other toposes of …

Web19 Jan 2024 · The idea of synthetic Tait computability is to treat both object-level notions (e.g. the collection of terms of type \TpBool) and meta-level notions (e.g. a normal form … pickerington north high school baseballWeb2 Aug 2024 · It is a technique of constructing logical relations using an internal language of a category obtained by the Artin gluing. ... ... The logical relation constructed using synthetic Tait... top 10 roof shingle manufacturersWeb3 Simplicial Synthetic Tait Computability Presentation as a bered signature In his recent PhD thesis [15], Sterling develops a logical framework to de ne a variety of type theories. The idea is to present a type theory by a signature, which speci es abstractly the potential judgments to be formed. The actual top 10 roofing companies in marylandWeb19 Jan 2024 · Chapter 4: Tait’s Method of Computability [jms-0013] It is simple enough to verify negative properties of a formal system, e.g. the non-derivability of a given assertion … top 10 rooftop bars in new york cityWebSynthetic Tait Computability for Simplicial Type Theory Jonathan Weinberger1, Benedikt Ahrens2, Ulrik Buchholtz3, and Paige North4 1 Max Planck Institute for Mathematics, Bonn, Germany [email protected] 2 Delft University of Technology, The Netherlands [email protected] 3 University of Nottingham, UK [email protected] top 10 rooftop bars melbourneWebSynthetic Tait computability is a mathematical machine to reduce diﬃcult problems of type theory and programming languages to trivial theorems of topos theory. First employed by Sterling and Harper to reconstruct the theory of program modules and their phase separated parametricity, synthetic Tait top 10 romantic getaways in californiaWeb27 Jan 2024 · This proof uses a generalization of synthetic Tait computability -- an abstract approach to gluing proofs -- to account for modalities. This extension is based on MTT itself, so that this proof also constitutes a significant case study of MTT. pickerington north high school phone number