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Trakhtenbrot's Theorem in Coq, A Constructive Approach to Finite Model Theory [article]

Dominik Kirst, Dominique Larchey-Wendling
2020 arXiv   pre-print
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.  ...  All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.  ...  Again, both of these standard results come with their subtleties when explored in a constructive approach of finite model theory.  ... 
arXiv:2004.07390v1 fatcat:nouz7asrcrb3rh43gmhnilsx6i

Trakhtenbrot's Theorem in Coq [chapter]

Dominik Kirst, Dominique Larchey-Wendling
2020 Lecture Notes in Computer Science  
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.  ...  All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs.  ...  Again, both of these standard results come with their subtleties when explored in a constructive approach of finite model theory.  ... 
doi:10.1007/978-3-030-51054-1_5 fatcat:utx3rwhqr5bcdnwf5bnuzvzdyi

Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens [article]

Dominik Kirst, Dominique Larchey-Wendling
2022 arXiv   pre-print
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.  ...  To showcase an application of Trakhtenbrot's theorem, we continue our reduction chain with a many-one reduction from FSAT to separation logic.  ...  Again, both of these standard results come with their subtleties when explored in a constructive approach to finite model theory.  ... 
arXiv:2104.14445v5 fatcat:6257pz5smjah3cvcbr4aq5jw2m

Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq

Dominik Kirst, Marc Hermes, Liron Cohen, Cezary Kaliszyk
2021
We mechanise the undecidability of various first-order axiom systems in Coq, employing the synthetic approach to computability underlying the growing Coq Library of Undecidability Proofs.  ...  In the synthetic setting based on the computability of all functions definable in a constructive foundation, such as Coq's type theory, it suffices to define these reductions as meta-level functions with  ...  [17] give a Coq mechanisation of Trakhtenbrot's theorem [40] , stating the undecidability of finite satisfiability.  ... 
doi:10.4230/lipics.itp.2021.23 fatcat:hknnxdvmlrazzbbjaqfpiitbcq