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)
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
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 …
Trakhtenbrot's theorem in Coq: a constructive approach to finite model theory
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 …
theory. Employing synthetic accounts of enumerability and decidability, we give a full …
[PDF][PDF] Formal Verification of Bit-Vector Invertibility Conditions in Coq
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 …
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 …
the contemporary perspective of formalisation in constructive type theory and mechanisation …
Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens
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 …
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 …
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 …
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 …
model given as a class of partial recursive functions called PVS0. The model is built over …