Erik Palmgren: From Type Theory to Setoids and Back
Explore the concept of setoids and their role in formalizing constructive mathematics in this lecture from the Hausdorff Trimester Program on Types, Sets and Constructions. Delve into Errett Bishop's type-theoretic languages and their application in computer formalizations. Examine the challenges of implementing setoid models in Martin-Löf type theory and proof assistants. Gain an introduction to setoids and their use in formalizing Bishop-style mathematics, with the majority of the content accessible without in-depth knowledge of dependent type theories. Learn about the evolution from type theory to setoids and back, covering topics such as Bishop-Bridges' concept of sets, dependent type theory, and the setoid model of Martin-Löf type theory.