On synthetic undecidability in Coq, with an application to the Entscheidungsproblem
We formalise the computational undecidability of validity, satisfiability, and provability of first-
order formulas following a synthetic approach based on the computation native to Coq's …
order formulas following a synthetic approach based on the computation native to Coq's …
The MetaCoq Project
M Sozeau, A Anand, S Boulier, C Cohen… - Journal of automated …, 2020 - Springer
The MetaCoq project aims to provide a certified meta-programming environment in Coq. It
builds on Template-Coq, a plugin for Coq originally implemented by Malecha (Extensible …
builds on Template-Coq, a plugin for Coq originally implemented by Malecha (Extensible …
Computability in constructive type theory
Y Forster - 2021 - publikationen.sulb.uni-saarland.de
We give a formalised and machine-checked account of computability theory in the Calculus
of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof …
of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof …
Hilbert's Tenth Problem in Coq (Extended Version)
D Larchey-Wendling, Y Forster - Logical Methods in Computer …, 2022 - lmcs.episciences.org
We formalise the undecidability of solvability of Diophantine equations, ie polynomial
equations over natural numbers, in Coq's constructive type theory. To do so, we give the first …
equations over natural numbers, in Coq's constructive type theory. To do so, we give the first …
A Coq library of undecidable problems
Y Forster, D Larchey-Wendling… - CoqPL 2020 The Sixth …, 2020 - hal.science
A Coq Library of Undecidable Problems Page 1 HAL Id: hal-02944217 https://hal.science/hal-02944217
Submitted on 21 Sep 2020 HAL is a multi-disciplinary open access archive for the deposit and …
Submitted on 21 Sep 2020 HAL is a multi-disciplinary open access archive for the deposit and …
Completeness theorems for first-order logic analysed in constructive type theory: Extended version
We study various formulations of the completeness of first-order logic phrased in
constructive type theory and mechanised in the Coq proof assistant. Specifically, we …
constructive type theory and mechanised in the Coq proof assistant. Specifically, we …
A certifying extraction with time bounds from Coq to call-by-value -calculus
Y Forster, F Kunze - arXiv preprint arXiv:1904.11818, 2019 - arxiv.org
We provide a plugin extracting Coq functions of simple polymorphic types to the (untyped)
call-by-value $\lambda $-calculus L. The plugin is implemented in the MetaCoq framework …
call-by-value $\lambda $-calculus L. The plugin is implemented in the MetaCoq framework …
Parametric Church's Thesis: Synthetic computability without choice
Y Forster - International Symposium on Logical Foundations of …, 2021 - Springer
In synthetic computability, pioneered by Richman, Bridges, and Bauer, one develops
computability theory without an explicit model of computation. This is enabled by assuming …
computability theory without an explicit model of computation. This is enabled by assuming …
Church's thesis and related axioms in Coq's type theory
Y Forster - arXiv preprint arXiv:2009.00416, 2020 - arxiv.org
" Church's thesis"($\mathsf {CT} $) as an axiom in constructive logic states that every total
function of type $\mathbb {N}\to\mathbb {N} $ is computable, ie definable in a model of …
function of type $\mathbb {N}\to\mathbb {N} $ is computable, ie definable in a model of …
Certified undecidability of intuitionistic linear logic via binary stack machines and Minsky machines
Y Forster, D Larchey-Wendling - Proceedings of the 8th ACM SIGPLAN …, 2019 - dl.acm.org
We formally prove the undecidability of entailment in intuitionistic linear logic in Coq. We
reduce the Post correspondence problem (PCP) via binary stack machines and Minsky …
reduce the Post correspondence problem (PCP) via binary stack machines and Minsky …