Tait computability
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 … 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 …
Tait computability
Did you know?
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 … 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 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
WebCompact computability families. Computability `a la Tait is concerned with structures (or properties) that lie over syntactical entities from some type theory; the canonical … Web3 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 …
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 $\infty$ … 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 Sterling and Harper to reconstruct the theory of program modules and their phase separated parametricity, synthetic Tait
Web27 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.
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 ... teaching reading to adultsWeb3 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 south mimms junction m25Web2 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 … south mimms coachesWeb1.1 Synthetic Tait computability This work is closely related to Sterling’s synthetic Tait computability [44, 42]. It is a technique of constructing logical relations using an internal language for the Artin gluing. A logos obtained by the Artin gluing is always equipped with a distinguished proposition in its internal language. The two lex ... teaching reading to adhd studentsWeb19 Jan 2024 · This dissertation has focused almost solely on the development and applications of synthetic Tait computability in the context of pure type theory, but the author originally invented synthetic Tait computability to solve problems in core programming languages, as part of Sterling and Harper’s re-analysis of the phase distinction in ML-style … south mimms msaWebTait computability (STC) from working internally to a single gluing category to applying to a collection of gluing categories interconnected by functors and natu-ral transformations. In particular ... teaching reading to childrenNote 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 computability. This suggests that synthetic Tait computability is one technique in a larger field of synthetic mathematics internal to a glued topos. See more Synthetic Tait computability is an approach to constructing logical relations (also known as Tait’s method of computability) using the internal language of toposes … See more teaching reading to 1st graders