Type Theory Foundations
Discussions center on explaining type theory, comparing it to set theory and category theory, and exploring Homotopy Type Theory as a computable foundation for mathematics.
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What's Type Theory and how's it different from Set Theory and Category Theory?
What's the difference between type theory and category theory? How are they related?
Checkout the work on homotopy type theory and proof assistants like Coq
What is the significance of Homotopy Type Theory?
You should look into "category theory for programmers" by Bartosz Milewski, or look into the dependently typed languages other people mentioned (Idris, Agda...), or how type theory is replacing set theory as the foundation of mathematics because it makes things computable and is not fundamentally broken (there is an interesting "HoTT book" you can look up that might be relevant).
Where can I get a good, intuitive explanation of what Type Theory really is?
It is only me, or type theory is overrated and oversold?
Type theory and Set theory. For example.
A lot of mathematics is based on sets, whereas sets and types are not formally the same thing.Some mathematicians are trying to formulate a basis for mathematics in type theory. For example, there is the Univalent Foundations of mathematics proposed by Vladimir Veovodsky. This reduces logic, set theory, category theory (actually groupoids) and higher abstractions to homotopy theory (well, certain explicit constructions in such anyway) which is then modelled in Martin-Löf type theory.By the
Type theory, maybe; set theory, no.