# A Verified Decision Procedure for Orders in Isabelle/HOL

@inproceedings{Stevens2021AVD, title={A Verified Decision Procedure for Orders in Isabelle/HOL}, author={Lukas Stevens and Tobias Nipkow}, booktitle={ATVA}, year={2021} }

We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders. We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using Isabelle’s code generator. The procedure is already part of the development version of Isabelle as a sub-procedure of the simplifier.

## References

SHOWING 1-10 OF 17 REFERENCES

Isabelle/HOL: A Proof Assistant for Higher-Order Logic

- Computer Science
- 2002

This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.

Isabelle's Metalogic: Formalization and Proof Checker

- Computer Science, PhilosophyArch. Formal Proofs
- 2021

This work formalizes this metalogic and the language of proof terms in Isabelle/HOL, defines an executable (but inefficient) proof term checker and proves the correctness of all the proofs in those theories.

Consistency, Choice, and Rationality

- Economics
- 2010

In Consistency, Choice, and Rationality, economic theorists Walter Bossert and Kotaro Suzumura present a thorough mathematical treatment of Suzumura consistency, an alternative to established…

Linear Quantifier Elimination

- Computer ScienceIJCAR
- 2008

This paper presents verified quantifier elimination procedures for dense linear orders, for real and for integer linear arithmetic, which are defined and verified in the theorem prover Isabelle/HOL, and can be applied to HOL formulae themselves (by reflection).

Proof-theoretical analysis of order relations

- MathematicsArch. Math. Log.
- 2004

Results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one.

Isabelle/HOL

- Education, MedicineLecture Notes in Computer Science
- 2002

This isabelle hol a proof assistant for higher order logic, it will really give you the good idea to be successful.

Data Refinement in Isabelle/HOL

- Computer ScienceITP
- 2013

The paper shows how the code generator of Isabelle/HOL supports data refinement, i.e., providing efficient code for operations on abstract types, e.g., sets or numbers, which allows all tools that employ code generation to compute with these abstract types.