Operations on Fixpoint Equation Systems
arXiv:2304.07162 · doi:10.46298/lmcs-20(3:5)2024
Abstract
We study operations on fixpoint equation systems (FES) over arbitrary complete lattices. We investigate under which conditions these operations, such as substituting variables by their definition, and swapping the ordering of equations, preserve the solution of a FES. We provide rigorous, computer-checked proofs. Along the way, we list a number of known and new identities and inequalities on extremal fixpoints in complete lattices.