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 …

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 …

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 …

Trakhtenbrot's theorem in Coq: a constructive approach to finite model theory

D Kirst, D Larchey-Wendling - … , IJCAR 2020, Paris, France, July 1–4, 2020 …, 2020 - Springer
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type
theory. Employing synthetic accounts of enumerability and decidability, we give a full …

[PDF][PDF] Formal Verification of Bit-Vector Invertibility Conditions in Coq

B Ekici, A Viswanathan, Y Zohar, C Tinelli… - … on Frontiers of …, 2023 - library.oapen.org
We prove the correctness of invertibility conditions for the theory of fixed-width bit-vectors—
used to solve quantified bit-vector formulas in the Satisfiability Modulo Theories (SMT) solver …

Mechanised metamathematics: An investigation of first-order logic and set theory in constructive type theory

D Kirst - 2022 - publikationen.sulb.uni-saarland.de
In this thesis, we investigate several key results in the canon of metamathematics, applying
the contemporary perspective of formalisation in constructive type theory and mechanisation …

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

D Kirst, D Larchey-Wendling - Logical Methods in Computer …, 2022 - lmcs.episciences.org
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type
theory. Employing synthetic accounts of enumerability and decidability, we give a full …

Mechanising syntax with binders in Coq

K Stark - 2019 - publikationen.sulb.uni-saarland.de
Mechanising binders in general-purpose proof assistants such as Coq is cumbersome and
difficult. Yet binders, substitutions, and instantiation of terms with substitutions are a critical …

[PDF][PDF] Certified decision procedures for two-counter machines

A Dudenhefner - … on Formal Structures for Computation and …, 2022 - drops.dagstuhl.de
Two-counter machines, pioneered by Minsky in the 1960s, constitute a particularly simple,
universal model of computation. Universality of reversible two-counter machines (having a …

Formalization of the computational theory of a turing complete functional language model

TMF Ramos, AA Almeida, M Ayala-Rincón - Journal of Automated …, 2022 - Springer
This work presents a formalization in PVS of the computational theory for a computational
model given as a class of partial recursive functions called PVS0. The model is built over …