Synthetic tait computability
WebSynthetic 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 … 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. $\endgroup$
Synthetic tait computability
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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 ... WebNov 19, 2024 · Synthetic Tait computability has already been employed to positively resolve the normalization and decidability conjectures for cubical type theory, as well as a number of other recent results. This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.
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 … WebJun 29, 2024 · This realignment property has proved essential for the semantics of univalent universes in homotopy type theory [29,42,43,17] as well as Sterling's synthetic Tait computability [49], an ...
WebJun 23, 2024 · Synthetic Tait computability is a mathematical machine to reduce difficult problems of type theory and programming languages to trivial theorems of topos theory. … WebUniversity of Nottingham - Cited by 212 - homotopy type theory - constructive mathematics - higher topos theory
WebJan 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.
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 lds primary baptism songsWebwww.cs.cmu.edu lds primary baptism program templateWebFeb 24, 2024 · Unfortunately, sheafification seems not to preserve an important realignment property enjoyed by the presheaf universes that plays a critical role in models of univalent … lds primary baptismWebMay 19, 2024 · Synthetic computability theory is the study of computability theory synthetically axiomatized by structures present in the effective topos or other toposes of … lds primary baptism towel poemWebJan 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 … lds primary birthday ideasWebtheory 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 lds primary birthday cardsWebThis flexibility is essential for the application of synthetic Tait computability and allows us to avoid tedious calculations. Remark 1. We emphasize, however, this change of … lds primary baptism ideas