Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses
Abstract
Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification. Less is known about its relation to larger classes of higher-order verification problems. Motivated by program equivalence, we introduce a coinductive version of HoCHC that enjoys a greatest model property. We define an encoding of higher-order recursion schemes (HoRS) into HoCHC logic programs. Correctness of this encoding reduces decidability of the open HoRS equivalence problem -- and, thus, the LambdaY-calculus B\"ohm tree equivalence problem -- to semi-decidability of coinductive HoCHC over a complete and decidable theory of trees.
Cite
@article{arxiv.2109.04632,
title = {Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses},
author = {Jerome Jochems},
journal= {arXiv preprint arXiv:2109.04632},
year = {2021}
}
Comments
In Proceedings HCVS 2021, arXiv:2109.03988