Synthetic tait computability
WebThe aim of staged compilation is to enable metaprogramming in a way such that we have guarantees about the well-formedness of code output, and we can also mix together object-level and meta-level code in a concise and convenient manner. In this ... Webtheory as well as synthetic Tait computability, a recent technique to establish syntactic properties of type theories and programming languages. In the context of multiple …
Synthetic tait computability
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WebMay 19, 2024 · Synthetic computability theory is the study of computability theory synthetically axiomatized by structures present in the effective topos or other toposes of … Synthetic Tait computability is an approach to constructing logical relations (also known as Tait’s method of computability) using the internal language of toposes constructed using Artin gluing. See more Note that despite the name, synthetic Tait computability is not a subfield of synthetic computability theory, but rather a synthetic approach to Tait's method of … See more
Web$\begingroup$ I'd say the state of the art in terms of mathematical convenience is NbE + HOAS, like in "synthetic Tait computability". Although that's not feasible to fully machine-check now, because it uses switching between internal and external languages, which is basically not possible in any current proof assistant. $\endgroup$ WebThe conversion problem for multimodal type theory (MTT) is considered by characterizing the normal forms of the type theory and proving normalization, which follows from a novel adaptation of Sterling’s Synthetic Tait Computability. Expand
WebJan 19, 2024 · This dissertation positively resolves the decidability conjecture for cubical type theory, the last remaining open question in its syntactic metatheory. Standard … WebIn the spirit of Halmos’ book Naïve Set Theory, I advocate for a new viewpoint on logical relations based on synthetic Tait computability, the internal language of categories of logical relations. In synthetic Tait computability, logical relations are manipulated as if they were sets, making the essence of many complex logical relations arguments accessible …
WebUniversity of Nottingham - Cited by 212 - homotopy type theory - constructive mathematics - higher topos theory
WebJan 19, 2024 · This chapter develops a more sophisticated application of synthetic Tait computability, the proof of normalization and decidability of Martin-Löf’s type theory with … foot is always coldWebSep 23, 2024 · [Thesis Defense]The implementation and semantics of dependent type theories can be studied in a syntax-independent way: the objective metatheory of … elevation chiropractic calgaryWebJun 28, 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 elevation chiropractic fort collinsWebJan 19, 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 … elevation chiropractic tigardWebwww.cs.cmu.edu foot ischemia symptomsWebJan 13, 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. elevation chocolate shakeWebtheory as well as synthetic Tait computability, a recent technique to establish syntactic properties of type theories and programming languages. In the context of multiple universes, the realignment property also implies a coherent choice of codes for connectives at each universe level, thereby interpreting the cumulativity laws present in popular elevation chocolate mint high protein bar