Stability: An Abstract Domain for the Trend of Variation of Numerical Variables
summary
Defines a per-variable trend lattice that records whether each instruction makes a numeric variable increase strictly, decrease strictly or stay stable relative to the previous state, and composes those trends across sequences and branches by simple table rules. Semantics query an auxiliary numeric domain via an open product (examples: sign returns too imprecise, intervals recover precision for a multiplication case). Prototype integrates into the Lisa static analyzer over IMP, shows use for proving covariant/contravariant balances, hints at loop termination and a sliding tolerance window for floating‑point error, but lacks a soundness proof and full benchmarks.
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