
Algebraic Type Theory and Universe Hierarchies
It is commonly believed that algebraic notions of type theory support on...
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Isabelle/Spartan – A Dependent Type Theory Framework for Isabelle
This paper introduces Isabelle/Spartan, an implementation of intensional...
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Dialectica models of type theory
We present two Dialecticalike constructions for models of intensional M...
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An Implementation of Homotopy Type Theory in Isabelle/Pure
In this Masters thesis we present an implementation of a fragment of "bo...
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Denotational semantics for guarded dependent type theory
We present a new model of Guarded Dependent Type Theory (GDTT), a type t...
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Circuit bases for randomisation
After a rich history in medicine, randomisation control trials both simp...
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Formalising perfectoid spaces
Perfectoid spaces are sophisticated objects in arithmetic geometry intro...
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Simple Type Theory is not too Simple: Grothendieck's Schemes without Dependent Types
We report on a formalization of schemes in the proof assistant Isabelle/HOL, and we discuss the design choices made in the process. Schemes are sophisticated mathematical objects in algebraic geometry introduced by Alexander Grothendieck in 1960. This experiment shows that the simple type theory implemented in Isabelle can handle such elaborate constructions despite doubts raised about Isabelle's capability in that direction. We show in the particular case of schemes how the powerful dependent types of Coq or Lean can be traded for a minimalist apparatus called locales.
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