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...
View ArticleWhat 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 :=...
View ArticleProof 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...
View ArticleCoq 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...
View ArticleCertified 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...
View Articlelooking 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...
View ArticleFormalizing 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...
View ArticleCurious 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...
View ArticleFormalized 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...
View Article