Abstract
We investigate various fixpoint operators in a semiring-based setting that models a general correctness semantics of programs. They arise as combinations of least/greatest (pre/post)fixpoints with respect to refinement/approximation. In particular, we show isotony of these operators and give representations of fixpoints in terms of other fixpoints. Some results require completeness of the Egli–Milner order, for which we provide conditions. A new perspective is reached by exchanging the semirings with distributive lattices. They can be augmented in a natural way with a second order that is similar to the Egli–Milner order.We extend our discussion of fixpoint operators to this induced order. We show the impact on general correctness by connecting the lattice- and the semiring-based treatments to obtain results about the Egli–Milner order.
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