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Interesting algorithms in the formalization of the Feit-Thompson theorem?

It looks like George Gonthier and his collaborators have finished formalizing the Odd Order Theorem. In his earlier work on the Four Color Theorem, Gonthier invented a bunch of new algorithms (mostly...

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What is the role of predicativity in inductive definitions in type theory?

We often want to define an object $A in U$ according to some inference rules. Those rules denote a generating function $F$ which, when it is monotonic, yields a least fixed point $mu F$. We take $A :=...

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Proof assistant formalizations of Finite Model Theory

I’m wondering if anyone knows of a formalization (even limited) of any part of finite model theory in any of the major proof assistants. (I’m most familiar with Coq, but Isabelle, Agda, etc. would...

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Coq definition with unusual syntax (Definition … Defined.)

While examining the package Library ZFC.Sets, I found the following definition: Definition Paire : forall E E' : Ens, Ens. intros. apply (sup bool). simple induction 1. exact E. exact E'. Defined. I...

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Certified program development vs. model checking

Sorry if my question is elementary but I want to know more about model checking and certified program development. What is the difference between model checking and certified program development? As I...

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looking for notable applications of ASP (Answer Set Programming) in TCS

a recent difficult question of interest to the group[1] by GB has possibly led to verification of a new graph property by dspyz, by use of Answer Set Programming/ASP. via sophisticated logic...

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Formalizing Homotopy Type theory in Idris

Looking at the homotopy type theory blog one can easily find a lot of library formalizing most of Homotopy Type Theory in Agda and Coq. Is there anyone aware if there is any similar attempt to...

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Curious about computer-assisted NP-completeness proofs

In the paper “THE COMPLEXITY OF SATISFIABILITY PROBLEMS” by Thomas J. Schaefer, the author has mentioned that This raises the intriguing possibility of computer-assisted NP-completeness proofs. Once...

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Formalized priority argument

A priority argument, an important proof technique in recursion theory, was introduced by Friedberg and Muchnik, to solve Post’s Problem, i.e., the existence of two r.e. sets that do not Turing reduce...

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